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On the degradation of porous stainless steel in low and intermediate temperature solid oxide fuel cell… Rose, Lars 2011

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ON THE DEGRADATION OF POROUS STAINLESS STEEL IN LOW AND INTERMEDIATE TEMPERATURE SOLID OXIDE FUEL CELL SUPPORT MATERIALS  by  Lars Rose  M.Sc., Chalmers University of Technology, Sweden, 2005  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate Studies  (Materials Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2011  © Lars Rose, 2011  Abstract Research on oxidation kinetics of stainless steel traditionally focuses on flat sheet material. Little is known about the oxidation of steel within porous structures or particles of different sizes. In cases where oxidation of porous materials is reported, the data are seldom related to the actual surface area of the material. Instead, the mass change is often reported as a percentage mass gain only. In some literature references, the oxidation mass gain is assumed to increase with increasing porosity, often without information of the surface area of the pores. If an area‐normalized oxidation mass gain is calculated, it is often normalized to the outside dimensions of the investigated specimens, making comparisons between different microstructures difficult. In this work, oxidation of spherical stainless steel powders with different powder particle sizes and of porous sintered stainless steel specimens is analyzed. Oxidation kinetics are correlated to the powder particle size and initial metal surface area of spherical stainless steel powders, addressing this knowledge gap. For oxidation kinetics of spherical steel powders, the dynamic change in metallic surface area over time is taken into account in the model Msph developed in this work. Maximum oxidation mass gain of stainless steel powder based on composition and changes in phase structure, microstructure, and composition of oxides growing under the influence of prolonged exposure to solid oxide fuel cell (SOFC) operating temperatures is analyzed. The oxidation mass gain of sintered porous stainless steel is influenced by microstructure. The oxidation mass gain correlated to the entire surface area of the 3‐D structure of the sintered porous specimens indicates slightly lower oxidation rate kinetics per unit surface area at 1073 K than published kinetics of similar materials in dense form. Additionally, the chromium diffusion through four spinel coatings that have been proposed as protective coatings for stainless steels used in SOFCs is analyzed in this work. Al‐Mg‐type spinels have the lowest Cr‐diffusion rate at the investigated conditions and among the investigated materials.  ii  Preface The research and data analysis was performed by Lars Rose. This thesis was written by L. Rose with revisions, additions, and comments by Dr. Tom Troczynski, University of British Columbia (UBC), Dr. O. Kesler, University of Toronto (UofT), Dr. Yongsong Xie, National Research Council Institute for Fuel Cell Innovation (NRC IFCI), MSc. David Edwards (NRC IFCI), Dr. Heidrun Spohr (UBC), Dr. Daan Maijer (UBC), Dr. Matthias Militzer (UBC), Dr. Peter Barr (UBC), Dr. Elöd Gyenge (UBC), Dr. Radenka Maric (University of Connecticut), and Dr. Eric Croiset (University of Waterloo).  Sections 1‐3: The sections were written entirely by the candidate, L. Rose (100%), including all literature research, implications for the research, justification of project proposal, and experimental design. The section includes revisions by the internal and external thesis examining committee and suggestions by colleagues during the annual thesis progress review meetings. Section 4: The section was written entirely by the candidate, L. Rose (100%). The experiments were instigated, designed, and executed by the candidate. Measurement holders for Archimedes measurements and oxidation experiments were designed and machined by the candidate. Four repeat experiments of mercury porosimetry were performed by Dr. Tetyana Sobolyeva, Simon Fraser University (SFU), for result confirmation. The section includes revisions by the internal and external thesis examining committees and suggestions by colleagues during the annual thesis progress review meetings. Section 5: The section was written entirely by the candidate, L. Rose (100%). The experiments were designed and executed by the candidate; novel gas permeability measurement jigs were designed and machined by the candidate. The fluid dynamics calculations were suggested by Dr. Cyrille Decès‐Petit, NRC IFCI. The section includes revisions by the internal and external thesis examining committees and suggestions by colleagues during the annual thesis progress review meetings. iii  Section 6: The section was written entirely by the candidate, L. Rose (100%). The experiments were suggested by Prof. Radenka Maric, University of Connecticut. The experiments and calculations were designed and executed by the candidate. The experimental section includes revisions by Prof. R. Maric, University of Connecticut, and the internal and external thesis examining committees. The mathematical modelling section was suggested by Prof. Matthias Militzer, UBC, and Prof. Daan Maijer, UBC, and includes revisions suggested by the internal and external thesis examining committees. Section 7: The section was written entirely by the candidate, L. Rose (100%). The experiments were suggested by Dr. Yongsong Xie, NRC IFCI. The experiments were designed and executed by the candidate. Spray pyrolysis was performed together with MSc Baisheng Yao, NRC IFCI. The section includes revisions by the internal and external thesis examining committees, with additional comments by various colleagues during the regular thesis review meetings and the internal NRC IFCI project progress meetings. Section 8: The section was written entirely by the candidate, L. Rose (100%). Section 9: The section was written entirely by the candidate, L. Rose (100%). Appendices: The appendices were written entirely by the candidate, L. Rose (100%). The appendices include revisions by the internal and external thesis examining committees.  A version of section 4 and section 5 was published in: Lars Rose, Olivera Kesler, Cyrille Decès‐Petit, Tom Troczynski, Radenka Maric: Characterization of Porous Stainless Steel 430 for Low‐ and Intermediate‐Temperature Solid Oxide Fuel Cell (SOFC) Substrates, International Journal of Green Energy 6 (2009) 638‐645. This manuscript was written and the research carried out by the candidate, L. Rose (100%), with revisions, corrections, and suggestions by the co‐authors.  iv  Table of Contents Abstract ................................................................................................................................ii Preface ................................................................................................................................ iii Table of Contents ................................................................................................................. v List of Tables ...................................................................................................................... vii List of Figures ...................................................................................................................... ix List of Symbols .................................................................................................................. xix List of Abbreviations ...................................................................................................... xxvii List of Compound Abbreviations .................................................................................... xxix Acknowledgements.......................................................................................................... xxx 1. Introduction ................................................................................................................. 1 1.1. Advantages and disadvantages of fuel cells .................................................. 2 1.2. Principle of fuel cell operation ...................................................................... 3 1.3. The solid oxide fuel cell ................................................................................. 5 1.4. SOFC materials............................................................................................... 7 2. Literature review........................................................................................................ 12 2.1. Oxidation of porous stainless steel ............................................................. 12 2.1.1. Metallic components in SOFCs: Interconnects and cell supports ..... 12 2.1.2. Porous materials ................................................................................ 19 2.1.3. Gas permeability measurements ....................................................... 23 2.1.4. Summary and justification for the presented investigation of porous stainless steel oxidation ......................................................... 24 2.2. Oxidation of spherical stainless steel microspheres ................................... 25 2.3. Protective coatings for stainless steel materials in SOFCs .......................... 29 2.3.1. Cr diffusion through spinels ‐ spinels containing Cr .......................... 30 2.3.2. Spinels containing Mg and Al ............................................................. 31 2.3.3. Other spinels ...................................................................................... 31 3. Objectives .................................................................................................................. 35 4. Influence of porosity, pore size distribution, and pore surface curvature on stainless steel oxidation ........................................................................................ 37 4.1. Material characterization ............................................................................ 37 4.2. Porous metal foam characterization ........................................................... 39 4.2.1. Surface profilometry .......................................................................... 39 4.2.2. Porosity measurements ..................................................................... 45 4.2.3. 3‐D pore morphology ......................................................................... 49 4.3. Oxidation behaviour of porous AISI 430 ..................................................... 57 4.4. Calculation of growth rate constants from mass gain data ........................ 67 4.4.1. Calculation of area normalized mass change from image analysis on polished cross sections .................................................... 67 4.4.2. Oxidation growth rates ...................................................................... 75 4.5. Conclusions – Oxidation of porous stainless steel ...................................... 85 5. Gas permeability of oxidized porous AISI 430 specimens ......................................... 87 5.1. Introduction ................................................................................................. 87 v  5.2.  Gas flow measurements .............................................................................. 88 5.2.1. Permeability measurement, experimental set‐up ............................. 88 5.3. Selection of gas for permeability testing and instrument settings ............. 91 5.4. Results and discussion of gas flow through oxidized porous AISI 430 specimens .................................................................................................... 94 5.5. Conclusions ‐ Permeability of oxidized porous stainless steel .................. 102 6. Oxidation of spherical surfaces and complete oxidation of stainless steel ............ 104 6.1. Introduction ............................................................................................... 104 6.2. Experimental procedure ............................................................................ 105 6.3. Results and discussion of the mass gain experiments .............................. 108 6.4. Model (Msph) describing the oxidation of spherical particles ................... 123 6.5. Conclusions ‐ Oxidation of spherical steel particles .................................. 140 7. Chromium diffusion in protective spinel coatings for intermediate temperature solid oxide fuel cells....................................................................... 144 7.1. Introduction ............................................................................................... 144 7.2. Experimental procedure ............................................................................ 144 7.3. Results and discussion ............................................................................... 149 7.4. Conclusions ‐ Cr diffusion in spinels .......................................................... 167 8. Summary and conclusions of the work presented .................................................. 169 9. Future work.............................................................................................................. 176 Bibliography .................................................................................................................... 178 Appendices ...................................................................................................................... 180 Appendix A Fe‐Cr phase diagram ........................................................................ 180 Appendix B Elemental analysis of the AISI 430 specimens ................................. 181 Appendix C Discussion of common porosity measurements.............................. 183 Appendix D Specimen holder for Archimedes measurement preparation......... 187 Appendix E Specimen holder for oxidation experiments ................................... 188 Appendix F Confidence intervals of porous AISI 430 oxidation EA ..................... 189 Appendix G Oxidation rates of sintered porous AISI 430 .................................... 192 Appendix H Calculations of gas pressure, temperature and density .................. 194 Appendix I Friction and pressure loss in the gas permeability set‐up ............... 200 Appendix J Mechanical design of gas permeability jig V5 .................................. 210 Appendix K Influence of oxidation on permeability............................................ 212 Appendix L Oxidation mass gain model based on elemental composition ........ 242 Appendix M Reproducibility and peak intensity of the XRD measurements ....... 254 Appendix N BET surface area of AISI 440C powder ............................................. 256 Appendix O Confidence intervals of the Msph oxidation activation energy......... 259 Appendix P Literature reference value for diffusion coefficients in spinels ....... 261 Appendix Q Ternary phase diagrams of the spinel‐Cr systems investigated ...... 265 Appendix R Bibliography of appendices .............................................................. 269  vi  List of Tables Table 1.1: Some of the materials typically used in SOFCs [24]. .......................................... 7 Table 1.2: Globally mined elemental production data [26]................................................ 8 Table 2.3: Typical composition of several proposed alloy materials for SOFCs (max. values, in mass%) [57], [72], [74], [82], [83]. ................................................. 17 Table 4.1: Average bulk volume of the sintered AISI 430 discs (Vdisc). ............................. 38 Table 4.2: Heat treatment of sintered porous AISI 430 specimens.................................. 58 Table 4.3: Time ranges with a constant slope in the area normalized mass gain as a function of square root of time graphs used to calculate oxidation rate constants of sintered porous AISI 430 specimens. If no microstructure is indicated, the range applies to all microstructures not specifically mentioned at that oxidation temperature. ................................................... 75 Table 4.4: Comparison between activation energies for different metals and alloys. .... 82 Table 4.5: Activation energies for porous AISI 430 oxidation calculated in this work. .... 83 Table 5.1: Lower limit of permeability at which an NRC‐IFCI test station may shut down as a safety precaution due to an increase in pressure by 34.5 kPa. ......................................................................................................... 99 Table 6.1: Mass fractions of the sieved AISI 440C powders ........................................... 108 Table 6.2: Mean particle diameters and mass specific surface areas of sieved powder fractions, calculated from the particle size distributions shown in Figure 6.1.................................................................................................. 110 Table 6.3: Phases found by XRD analysis of the oxidized metal powders. ..................... 112 Table 6.4: Density, molar mass and molar volume of Fe, Cr (m) and their oxides (ox). .............................................................................................................. 124 Table 6.5: Cr2O3 oxidation growth rate constants (ks,1, in h‐0.5m‐1) for different AISI 440C sieved powder size fractions. ...................................................... 128 Table 6.6: Fe2O3 oxidation growth rate constants (ks,2, in 103 h‐0.5m‐1) for different AISI 440C sieved powder size fractions. ...................................................... 128 Table 6.7: Cr2O3‐Fe2O3 oxidation rate switch time, in hours, for the different sieved powder size fractions constants. ...................................................... 133 Table 6.8: Parameters for the prediction of oxidation behavior of Cr2O3 on spherical steel particles (ks,1) based on curve fitting results performed in this work. .................................................................................................. 135 Table 6.9: Parameters for the prediction of oxidation behavior of Fe2O3 on spherical steel particles (ks,2) based on curve fitting results performed in this work. .................................................................................................. 135 Table 6.10: Parameters for the prediction of the time (in hours) until the surface oxidation of stainless steel spheres changes from ks,1 to ks,2, depending on oxidation temperature (large error). ...................................................... 135 Table 6.11: Parameters for the prediction of the time (in hours) until the surface oxidation of stainless steel spheres changes from ks,1 to ks,2, depending on mean particle diameter Dmp. .................................................................. 135 Table 7.1: Spinel preparation by coprecipitation method.............................................. 145 vii  Table 7.2: Phases found in addition to spinel phases in the Cu‐Mn system, depending on preparation method. Abbreviations used: CoPNa – Coprecipitation with (Na) carbonates, CoPK – Coprecipitation with (K) carbonates, EG – Ethylene glycol, EtOH – Ethanol, EtAcH – Ethoxy acetylacetone, CIT – Citric acid organic complex method, MAL – Malic acid organic complex method, CoPUr – Urea coprecipitation, PEC – Pechini method. ........................................................................................... 151 Table 7.3: Calculated electron interaction depth and width in solids. .......................... 153 Table 7.4: Measured CTE compared with literature values for CTE and electronic conductivity. ................................................................................................. 155 Table 7.5: Activation energy EA of Cr cation diffusion in different spinels. .................... 163 Table 7.6: Recommended minimum thickness, in μm, of spinel coatings based on Cr cation diffusion at 873‐1123 K. ............................................................... 167 Table B.1: Elemental compositions (at%) of the AISI 430 discs, as reported by the manufacturer (Fe=balance). ........................................................................ 181 Table B.2: Elemental compositions (at%) of the AISI 430 discs, analyzed by inductive coupled plasma mass spectrometry (5% measurement error, Fe=balance). ................................................................................................. 182 Table C.1: Summary of various porosity measurement methods. *Cost unknown, **Argonne National Lab (ANL) [369], ***PMI Analytical [370], ****University of Calgary, Dept. Cell Biology. ............................................ 184 Table G.1: Measured oxidation rates (k’’ and k’) calculated in this work (section 4.4.2)............................................................................................... 192 Table G.2: Reference values for oxidation rates (k’’, k’) and for expected oxide scale thicknesses after 40,000 h. Percentage values are given in mass%. .. 193 Table H.1: Density of moist air, ρgas, based on the dew point of the air stream. ........... 195 Table H.2: Calculations of molar composition and relative humidity of the analyzed water/air gas mixture system. ..................................................................... 197 Table H.3: Sutherland constants, and applicability ranges for a number of gases. ....... 198 Table I.4: Average surface roughness of various tube materials.................................... 202 Table L.1: Assumptions made for oxidation model Mel₁ ................................................. 244 Table L.2: Assumptions made for oxidation model Mel₂. ................................................ 245 Table P.1: Diffusion coefficients in spinels, in cm2sec‐1. ................................................. 261 Table P.1, continued: Diffusion coefficients in spinels, in cm2sec‐1................................ 262 Table P.1, continued: Diffusion coefficients in spinels, in cm2sec‐1................................ 263 Table P.1, continued: Diffusion coefficients in spinels, in cm2sec‐1................................ 264  viii  List of Figures Figure 1.1: Principle of operation of a single solid oxide fuel cell. ..................................... 4 Figure 1.2: Materials development in SOFCs. Temperatures reflect the targeted temperatures in fuel cell development at TOFC/Risø [31]. FeCr: Ferritic stainless steel. Reprinted from [31] with permission of Elsevier. ................... 9 Figure 2.3: Select chromium species over the surface of Cr2O3 at various temperatures [48]. Reprinted from [48] with permission of Elsevier. .......... 13 Figure 2.4: Alloys of the Fe‐Cr‐Ni system considered as SOFC materials [38]. Reprinted with permission of ASM International®. All rights reserved......... 15 Figure 2.5: Mass change during heat treatment of different Crofer22 batches in air [71]. Reproduced with permission of Dr. Quadakkers, Forschungszentrum Jülich, and ThyssenKrupp VDM GmbH.......................... 15 Figure 2.6: Comparison of mass gain between four SOFC candidate alloys exposed to air at 1073 K for 500 h (H = Haynes) [72]. Reprinted from [72] with permission of Elsevier. ................................................................................... 16 Figure 2.7: Oxidation mass gain of several SOFC candidate alloys in air at 1073 K [74]. Reprinted with permission of Dr. Quadakkers, Forschungszentrum Jülich, and published under unported non‐ commercial Creative Commons License 3.0. ................................................. 18 Figure 2.8: Contact resistance of different SOFC candidate alloys oxidized in air at 1073 K [74]. Reprinted with permission of Dr. Quadakkers, Forschungszentrum Jülich, and published under unported non‐ commercial Creative Commons License 3.0. ................................................. 18 Figure 2.9: Different grain structures of a Ti‐48Al‐2Cr alloy analyzed for their oxidation behaviour in air at 1073 K by Haanappel et al. [120]. A: γ‐TiAl grain structure, B: Duplex and lamellar structure, C: Lamellar grain structure. No influence of these grain structures on oxidation was observed......................................................................................................... 22 Figure 4.1: Ratio of molar fractions fCr/fFe of the different porous AISI 430 specimens analyzed in this work, compared before and after sintering. ..... 38 Figure 4.2: Surface roughness, Ra, of porous AISI 430 specimens with various microstructures, indicated by media grade. .................................................. 40 Figure 4.3: Surface of an MG0.2 specimen recorded by stylus profilometry. .................. 41 Figure 4.4: SEM micrograph of the surface of an MG0.2 specimen. ................................ 41 Figure 4.5: Surface of an MG0.5 specimen recorded by stylus profilometry. .................. 41 Figure 4.6: SEM micrograph of the surface of an MG0.5 specimen. ................................ 41 Figure 4.7: Surface of an MG1 specimen recorded by stylus profilometry. ..................... 41 Figure 4.8: SEM micrograph of the surface of an MG1 specimen. ................................... 41 Figure 4.9: Surface of an MG2 specimen recorded by stylus profilometry. ..................... 42 Figure 4.10: SEM micrograph of the surface of an MG2 specimen. ................................. 42 Figure 4.11: Surface of an MG5 specimen recorded by stylus profilometry. ................... 42 Figure 4.12: SEM micrograph of the surface of an MG5 specimen. ................................. 42 Figure 4.13: Surface of an MG40 specimen recorded by stylus profilometry. ................. 42 ix  Figure 4.14: SEM micrograph of the surface of an MG40 specimen. ............................... 42 Figure 4.15: Surface of an MG100 specimen recorded by stylus profilometry................ 43 Figure 4.16: SEM micrograph of the surface of an MG100 specimen. ............................. 43 Figure 4.17: Polished cross sections of the various AISI 430 specimens: (A) MG0.2, (B) MG0.5, (C) MG1, (D) MG2, (E) MG5, (F) MG40, and (G) MG100. ............ 44 Figure 4.18: XRD patterns of as‐received porous AISI 430 specimens, showing a typical Fe‐Cr steel pattern (black dots), such as the pattern shown in reference [255]. ............................................................................................. 46 Figure 4.19: Results of the different porosity analyses performed. ................................. 48 Figure 4.20: Pressure at maximum incremental mercury intrusion and pore size diameter as a function of porosity of the analyzed AISI 430 specimens. ...... 50 Figure 4.21: Pore size diameter at maximum incremental mercury intrusion and characteristic length (pore size diameter at point of inflection of cumulative mercury intrusion as a function of pressure) shown as a function of the AISI 430 porosity measured by the XRD/mass method. Error in pore size diameter derives from multiple measurements of the same specimen type; error in porosity is due to the experimental error of the XRD/mass measurements. .................................................................. 52 Figure 4.22: Log differential intrusion of mercury as a function of pore size diameter. Inset numbers indicate media grade. ........................................... 54 Figure 4.23: Cumulative specific pore surface area as a function of porosity. ................ 55 Figure 4.24: Relationship between tortuosity and porosity of the analyzed AISI 430 specimens, measured by mercury porosimetry. ........................................... 56 Figure 4.25: Relative mass gain of AISI 430 substrates at (A) 873 K, (B) 973 K, and (C) 1073 K for different microstructures........................................................ 59 Figure 4.25, continued: Relative mass gain of AISI 430 substrates at (D) 920 K, (E) 1020 K, and (F) 1125 K, for different microstructures. Inset in (F) shows the changes in slope at short times, especially for MG0.2 specimens, as indicated by the arrow. .......................................................... 60 Figure 4.26: Surface microstructure of MG0.2 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 920 K. Only few oxidation products can be seen, even after long oxidation times................................. 62 Figure 4.27: Surface microstructure of MG0.2 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 1020 K. Oxides close the pores by platelet growth. ............................................................................... 63 Figure 4.28: Surface microstructure of MG0.2 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 1125 K. Oxide growths close the pores. ....................................................................................................... 63 Figure 4.29: Surface microstructure of MG40 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 1125 K. After 2000 h, the original microstructures of both metal substrate and Cr2O3 oxide layer were grown over by a different (Fe2O3) metal oxide (D). .............................. 64 Figure 4.30: EDX elemental map of a cross section of AISI 430 MG0.2 specimens after 1000 h at 1073 K.................................................................................... 65 x  Figure 4.31: Grazing incidence XRD pattern of the surface of a MG100 specimen oxidized for 1000 h at 1073 K. The recorded XRD pattern shown here was compared with literature data: Open triangles: Fe‐Cr phase [255], Circles: eskolaite phase [272]. ....................................................................... 65 Figure 4.32: Locked couple XRD pattern of the surface of a MG40 specimen oxidized for 1500 h at 1125 K. The recorded XRD pattern shown here was compared with literature data: Rectangles: Fe2O3 [273]. ..................... 66 Figure 4.33: Magnified image of a recorded cross section of a MG0.2 specimen. (A) Optical image. (B) and (C) pores marked by image analysis, using different grey scale settings. .......................................................................... 67 Figure 4.34: SV of as‐received, cleaned porous metal specimens as a function of media grade, shown for 50x and 100x magnification. .................................. 69 Figure 4.35: Area (As) normalized oxidation mass change of porous AISI 430 specimens at (A) 873 K, (B) 973 K, and (C) 1073 K for different microstructures. As was determined by image analysis. ............................... 71 Figure 4.35, continued: Area (As) normalized oxidation mass change of porous AISI 430 specimens at (D) 920 K, (E) 1020 K, and (F) 1125 K, for different microstructures. As was determined by image analysis. ................ 72 Figure 4.36: Area normalized oxidation mass change of porous AISI 430 specimens at 1125 K, for different microstructures, magnifying the changes in mass gain for the first 1500 h, which are barely visible in Figure 4.35 F. ...... 73 Figure 4.37: Cross section of an AISI430 MG1 specimen after 500 h at 973 K, indicating the geometry assumed for the calculation of the oxide scale thickness......................................................................................................... 76 Figure 4.38: Calculated values of k’’ at different temperatures (873 K – 1125 K), as a function of media grade. ............................................................................. 77 Figure 4.39: Calculated values of k’' at different temperatures, as a function of pore curvature as characterized by mercury porosimetry (Figure 4.21). X‐axis error bars derive from the distribution of pore surface curvatures observed in mercury porosimetry and y‐axis error bars derive from the measurement errors of Sv, Vdisc, and Δmox (Eq. 4.18). ......... 79 Figure 4.40: Calculated oxide scale thickness after 40,000 hours at elevated temperatures, using the oxide growth rates shown in Figure 4.39, as a function of pore curvature. The dashed line indicates the pore size radius (PSR) at maximum volumetric mercury intrusion. Oxides growing thicker than this radius will close off the pores, and all specimens and temperatures in the shaded area are consequently not usable for 40,000 hours. ................................................................................ 80 Figure 4.41: Arrhenius‐type plot of oxidation rate k" for oxidized specimens. Error bars are within the data markers................................................................... 81 Figure 4.42: Activation energy of oxidation of the various porous AISI 430 microstructures examined in this work. ........................................................ 83 Figure 5.1: Gas permeability set‐up with jig V1 as the specimen holder. ........................ 89 xi  Figure 5.2: Opened (horizontally cross sectioned) gas permeability jig V2&V3 with porous AISI 430 disc shown on the right half. The largest o‐ring shown on the left half provides the outer seal between measurement chamber and the environment. ..................................................................... 89 Figure 5.3: Vertical cross section of a V5 gas permeability jig designed in this work. The long vertical arrow indicates the gas flow direction; the x‐marks indicate the position of the porous sintered specimens inserted in the permeability jig. ............................................................................................. 90 Figure 5.4: Difference in gas flow rate of (A) air and (B) helium through various as‐ received porous AISI 430 specimens using measurement jig V3. ................. 92 Figure 5.5: Porosity divided by tortuosity and helium flow at 6.9 kPa as a function of porosity. ..................................................................................................... 93 Figure 5.6: Air flow rate through as‐received porous AISI 430 specimens using the measurement jig V5. ...................................................................................... 94 Figure 5.7: SEM micrograph of a cross section of a pore in a MG5 specimen, heat treated for 10 h at 1273 K. The internal pathways for the reactant gases can be seen to be partially blocked due to oxide growth. ................... 96 Figure 5.8: SEM micrograph of a cross section of multiple pores in a MG0.2 specimen, heat treated for 1000 h at 1073 K. The internal pathways for the reactant gases can be seen to be blocked due to oxide growth. ............ 96 Figure 5.9: Gas permeability of porous AISI 430 specimens with varying microstructure oxidized at (A) 873 K, (B) 973 K, and (C) 1073 K (measured in jig V3). Inset italic numbers in (A) indicate the porous specimen media grade. Dashed lines and dotted lines indicate calculated maximum tolerable reduction in permeability for a 1 kW stack for a high flow rate and low flow rate operation, respectively. The dashed lines are shown only for the materials with the highest porosity for which the measured permeability was reduced below the tolerable limit. .............................................................................................. 100 Figure 5.9, continued: Gas permeability of porous AISI 430 specimens with varying microstructure oxidized at (D) 920 K, (E) 1020 K, and (F) 1125 K, (measured in jig V5). Dashed lines and dotted lines indicate calculated maximum tolerable reduction in permeability for a 1 kW stack for a high flow rate and low flow rate operation, respectively. The dashed lines are shown only for the materials with the highest porosity for which the measured permeability was reduced below the tolerable limit. ............................................................................................................. 101 Figure 6.1: Particle size analysis (PSA) of AISI 440C powder size fractions by dynamic laser light scattering. ..................................................................... 108 Figure 6.2: SEM micrograph of AISI 440C powders before oxidation. ........................... 109 Figure 6.3: XRD pattern of AISI 440C powders after 10 h at 1073 K. 5 sec/step high resolution XRD scan of the 2θ region from 35.1° to 36.6°. Peaks indicated based on these references: Fe2O3: [273], Cr2O3: [307] ............... 111 xii  Figure 6.4: XRD pattern of AISI 440C powder, after 1000 h at 1073 K. The powder appears to be completely oxidized. All peaks fit the Fe2O3 phase described in reference [273]. ....................................................................... 111 Figure 6.5: Scherrer crystallite sizes of oxidized AISI 440C powder, heat treated at different temperatures for 150 h each, after having been exposed to 1073 K for 1000 h (the initial crystallite size after the pre‐exposure is indicated by the value at 1073 K). ............................................................... 113 Figure 6.6: Comparison of mass gain relative to unoxidized mass at 1073 K between the different AISI 440C powder size fractions. ............................. 115 Figure 6.7: Comparison of relative mass gain of the different AISI 440C powder size fractions at 920 K. ........................................................................................ 116 Figure 6.8: Comparison of relative mass gain of the different AISI 440C powder size fractions at 1023 K. ...................................................................................... 117 Figure 6.9: Oxidation mass change of AISI 440C sheet at 1073 K as a reference from published literature. Data reprinted from [174] with permission of Elsevier. .................................................................................................... 118 Figure 6.10: SEM micrograph of unsieved AISI 440C powder after (A) 10 h at 873 K and (B) 100 h at 873 K. Some oxide crystals (bright spots) can be seen on the surface of the particles after 100 h. ................................................. 119 Figure 6.11: SEM micrograph of unsieved AISI 440C powder after (A) 10 h at 973 K and (B) 100 h at 973 K, showing the oxide surface of the particles. ........... 119 Figure 6.12: SEM micrograph of unsieved AISI 440C powder after (A) 10 h at 1073 K and (B) 100 h at 1073 K, showing severe oxidation of a particle. ... 119 Figure 6.13: SEM micrograph of unsieved AISI 440C powder after (A) 100 h at 873 K and (B) 1500 h at 873 K. After 100 h, there is little evidence of oxidation on the surface of the particles. After 1500 h, a thin oxide film has formed on the surfaces. ........................................................................ 121 Figure 6.14: EDX elemental maps of unsieved AISI 440C powder cross sectioned after 100 h at 873 K (Figure 6.13 A). Maps: SE=secondary electron image, O=oxygen, Cr=chromium, Fe=iron. .................................................. 121 Figure 6.15: SEM micrograph of unsieved AISI 440C powder after (A) 100 h at 973 K and (B) 1000 h at 973 K. After 100 h, a surface oxide film is visible on the spheres, after 1000 h, some of the oxide layers have grown together. ........................................................................................... 121 Figure 6.16: EDX elemental maps of unsieved AISI 440C powder cross sectioned after 100 h at 973 K (Figure 6.15 A). Maps: SE=secondary electron image, O=oxygen, Cr=chromium, Fe=iron. .................................................. 121 Figure 6.17: SEM micrograph of unsieved AISI 440C powder after (A) 100 h at 1073 K and (B) 1000 h at 1073 K. Oxidation products are already visible throughout the spheres after 100 h, and after 1000 h, most of the oxides have grown together. ....................................................................... 122 Figure 6.18: EDX elemental maps of unsieved AISI 440C powder cross sectioned after 100 h at 1073 K (Figure 6.17 A at a lower magnification). Maps: SE=secondary electron image, O=oxygen, Cr=chromium, Fe=iron. ............ 122 xiii  Figure 6.19: Oxidizing sphere model schematic, cross section. ..................................... 124 Figure 6.20: Time‐dependent oxide scale thickness over time‐dependent metal surface area as a function of square root of time, indicating the two linear sections from which the oxidation constants ks were extracted, at the example of the ‐25/+20 µm size fraction of AISI 440C powder oxidized at 1023 K. ....................................................................................... 128 Figure 6.21: Arrhenius‐type graph showing the activation energy of ks,1 (Cr2O3) with different size fractions of spherical AISI 440C particles. ..................... 129 Figure 6.22: Influence of the mean particle diameter, Dmp, on the oxidation growth rate constant ks,1 (Cr2O3) at the analyzed temperatures. ............................ 130 Figure 6.23: Arrhenius‐type graph of ks,2 (Fe2O3) with different size fractions of spherical AISI 440C particles. Due to the similar values of ks,2 at higher temperatures (1023 K and 1073 K), the error in the slope is large. ............ 131 Figure 6.24: Influence of the mean particle diameter, Dmp, on the oxidation growth rate constant ks,2 (Fe2O3) at the analyzed temperatures. ............................ 132 Figure 6.25: Arrhenius‐type graph of oxidation duration at which ks,1 switches to ks,2, as determined by the mass gain measurements of AISI 440C powders with different sieved size fractions. .............................................. 133 Figure 6.26: Oxidation time, ts, at which ks,1 switches to ks,2, as determined by the mass gain measurements of AISI 440C powders with different sieved size fractions. ............................................................................................... 134 Figure 6.27: Calculated relative mass gain compared with measured relative mass gain for a spherical oxidation curve fitting model Msph at 920 K. (A) unsieved, (B) ‐20 μm, (C) ‐25/+20 μm, (D) +25 μm powder size fraction of AISI 440C powders. .................................................................................. 137 Figure 6.28: Calculated relative mass gain compared with measured relative mass gain for a spherical oxidation curve fitting model Msph at 1023 K. (A) unsieved, (B) ‐20 μm, (C) ‐25/+20 μm, (D) +25 μm powder size fraction of AISI 440C powders. .................................................................................. 138 Figure 6.29: Calculated relative mass gain compared with measured relative mass gain for a spherical oxidation curve fitting model Msph at 1073 K. (A) unsieved, (B) ‐20 μm, (C) ‐25/+20 μm, (D) +25 μm powder size fraction of AISI 440C powders. .................................................................................. 138 Figure 7.1: Schematic drawing of the spray pyrolysis apparatus. .................................. 147 Figure 7.2: Thermogravimetric analysis of (A) Mg‐Al, and (B) Mn‐Fe powder following drying to 623 K. ............................................................................ 152 Figure 7.3: Sintering shrinkage of the diameter of various sol gel derived pressed ceramic powders. ......................................................................................... 154 Figure 7.4: XRD patterns of MgAl2O4 sintered at 1273‐1723 K. Crystal structures were determined based on these references: Rectangles: MgAl2O4[347], circles: Al2O3[348],[349], diamonds: MgO[350]. The sintering temperature of the material increases upwards in the graph. .... 156 Figure 7.5: XRD patterns of the Mn‐Fe material, sintered at 1273‐1773 K. Crystal structures were determined based on these references: Rectangles: xiv  MnFe2O4 [351], circles (only at 1273 K): (Mn0.37Fe0.63)2O3 [352], diamonds: α‐Fe2O3 [353], x: FeMn2O4 [354], # (at T=1773 K): Al2O3 from refractory [348], circles (at T≥1648 K): Mn2O3 [355]. No information available for peaks 2θ>90° in the reference databases. The sintering temperature of the material increases upwards in the graph. ................... 157 Figure 7.6: XRD patterns of MgFe2O4. The MgFe2O4 phase appears stable at the investigated temperatures. Crystal structures were determined based on these references: XRD peaks of MgO (circles) [350] overlay the MgFe2O4 (rectangles) peaks and cannot be distinguished by this method, diamonds: (Al2O3)1.333 [357]. No evidence of Fe2O3 [353] was found. The sintering temperature of the material increases upwards in the graph. ..................................................................................................... 158 Figure 7.7: XRD patterns of Co1.5Mn1.5O4. Crystal structures were determined based on these references: Rectangles: (Mn,Co)(Mn,Co)2O4, Mn:Co ratio 1:1 [358], [359], diamonds: (Mn,Co)(Mn,Co)2O4, Mn:Co ratio 1:0.5 [358]. No evidence of Mn3O4 [360] was found. The sintering temperature of the material increases upwards in the graph. ................... 159 Figure 7.8: Polished cross section of as‐deposited Cr2O3 layer on spinel substrates. A dense Cr2O3 layer formed at the surface and an up to 25 µm porous layer formed above the dense layer. (A): Mn1.5Co1.5O4, (B): MgAl2O4, (C): MgFe2O4, (D): MnFe2O4. ........................................................................ 160 Figure 7.9: EDX elemental analysis of MgAl2O4 spinel in contact with a spray‐ pyrolized Cr2O3 surface layer. A: Micrograph of a polished cross‐section after 500 h at 1273 K indicating three linescans recorded in this micrograph, B, C, D: EDX linescans corresponding to A. ............................. 161 Figure 7.10: Example of a normalized EDX CrKα₁ linescan data (diamonds) overlaid with the closest normalized fit (rectangles). ............................................... 162 Figure 7.11: Arrhenius‐type graph showing the diffusion constants calculated in this work. ...................................................................................................... 163 Figure 7.12: Diffusion depth profiles after 40,000 h based on the calculated diffusion coefficients for different proposed IT‐SOFC operating temperatures. (A): Mn1.5Co1.5O4, (B): MgAl2O4. The profile changes with temperature are indicated in (A). ................................................................ 165 Figure 7.12, continued: Diffusion depth profiles after 40,000 h based on the calculated diffusion coefficients for different proposed IT‐SO FC operating temperatures. (C): MgFe2O4, (D): MnFe2O4. ............................... 166 Figure A.1: Fe‐Cr phase diagram showing which phases can be expected at equilibrium for different combinations of chromium content and temperature[366]. The shaded area indicates typical compositions of ferritic stainless steels and operating temperatures for metal supported SOFCs. Lower operating temperatures have also been proposed (e.g. [31]). α: Ferrite phase, γ: Austenite phase, σ: Intermetallic Fe‐Cr phase leading to embrittlement. Phase diagram xv  used with permission of Dr. A. Kajinic and Computational Thermodynamics Inc [366]. ......................................................................... 180 Figure D.1: Porous steel specimen holder for Archimedes measurement preparation. ................................................................................................. 187 Figure E.1: Porous steel specimen holder for oxidation experiments............................ 188 Figure F.1: Linear least squares regression analysis of the oxidation activation energy data presented in section 4.4.2. The solid line shows the predicted slope in the Arrhenius‐type graph, the dotted lines show the 95% confidence interval of the data. A: MG0.2, B: MG0.5, C: MG1, D: MG2, E: MG5, F: MG40, G: MG100. ............................................................. 191 Figure H.1: Change of viscosity of single gases with changes in temperature. Graph drawn with data from [434], with permission of Dr. B. Ulrich and NASA. .. 198 Figure H.2: Change of viscosity of air/water mixtures with changes in temperature. Water contents are given in (0‐30) mol%. Graph drawn with data from [438], with permission of Springer Science and Business Media. ............... 199 Figure I.3: Change of flow regimes with change in Reynolds number Reproduced from with permission of Dr. Glenn Elert. .................................................... 200 Figure I.4: Air flow rate through tubes (Di=3.2 mm) of various lengths and connected with one or two 406 μm diameter orifices. Lengths: short = 6 cm, medium = 8 cm, long = 38 cm. ............................................... 204 Figure I.5: Air flow rate as a function of gauge pressure for an empty set‐up (V5) and a set‐up with an MG0.2 specimen inserted. The difference in air flow rate between using two 17 cm long steel tubes (Di=5.6 mm) and two 6 cm long polymer tubes (Di=9.3 mm) were small and were only noticeable at gauge pressures above 5 kPa. ................................................ 206 Figure I.6: Calculated theoretical values of residence time, total power loss and pressure loss in the V5 set‐up using a MFM20. Errors include the errors from the calculation of gas viscosity. Differences in the turbulent range result from using different surface roughness values in the calculations; Circles: 15 µm (typical for the insides of stainless steel tubes (Table I.4), Upwards triangles: 40 µm. ............................................... 206 Figure I.7: Calculated theoretical values of residence time, total power loss and pressure loss of the V3 set‐up using an MFM0.05. ..................................... 207 Figure I.8: Air flow rate as a function of gas gauge pressure applied across an empty jig V5 and two 6 cm length tubes (Di=9.3 mm) (rectangles) compared with the pressure values corrected for the pressure loss due to the entire set‐up. Inset: Magnification of the highest recorded datum. .......................................................................................................... 208 Figure I.9: Air flow rate through a set‐up that includes either one or two 406 μm diameter orifices, corrected for the pressure loss due to the single (or double) orifice using the calculations shown in Figure I.6........................... 209 Figure J.1: Gas permeability measurement jig V5, top part. .......................................... 210 Figure J.2: Gas permeability measurement jig V5, bottom part. ................................... 211 xvi  Figure K.1: Air flow rate through MG0.2 specimens, and the change in gas flow versus gauge pressure slopes resulting from increasing the pressure by 34.5 kPa, which would cause a typical 1 kW stack to shut down. ............... 212 Figure L.1: Relative mass change of dense AISI 430 specimens oxidized at 1273 K and 1473 K in air. ......................................................................................... 242 Figure L.2: SEM micrograph of a fractured cross section of an AISI 430 specimen oxidized for 40 h at 1473 K. The image shows two microstructurally distinct oxide layers. The outer oxide scale (left and right in the image) was comprised of a dense iron‐rich oxide layer and the core oxide was comprised of a porous chromium‐rich oxide............................................... 246 Figure L.3: XRD spectrum of ground core oxide powder of an AISI 430 specimen oxidized for 40 h at 1473 K. The oxides had a Fe2O3 crystal structure (rectangle markers) such as described in this reference: [273], adjusted for the specimen's lattice parameter by multiplying the d‐spacing by 0.9957, likely resulting from a solid solution of Fe2O3, Cr2O3 and the other alloying elements. .............................................................................. 247 Figure L.4: XRD spectrum of ground outer oxide powder of an AISI 430 specimen oxidized for 40 h at 1473 K. The oxides had a Fe2O3 crystal structure (rectangle markers) as described in this reference: [273] ........................... 247 Figure L.5: SEM micrograph of a fractured cross section of an AISI 430 specimen oxidized for 400 h at 1273 K showing two microstructurally distinct porous oxide layers. ..................................................................................... 248 Figure L.6: XRD spectrum of ground oxide of an AISI 430 specimen oxidized for 400 h at 1273 K. The oxides had a Fe2O3 crystal structure (rectangle markers) as described in reference [273], adjusted for the specimen's lattice parameter by multiplying the d‐spacing by 0.9937, likely resulting from a solid solution of Fe2O3, Cr2O3 and the other alloying elements....................................................................................................... 248 Figure L.1: Phase diagram of FeO/Fe2O3 and P2O5. Wus = Wustite (FeO), Q = iron phosphate phase with 10 ± 1.5 at% P. Reprinted with permission of Dr. A. Schommers, copyright 1963 Verlag Stahleisen GmbH, Düsseldorf, Germany. ...................................................................................................... 250 Figure L.2: Phase diagram of Mn2O3 and Cr2O3. Reprinted with permission of John Wiley and Sons, Blackwell, and the American Ceramic Society.[457. ......... 251 Figure L.3: Phase diagram of Fe, SiO2, and Cr2O3............................................................ 251 Figure L.4: Phase diagram of the system Fe2(MoO4)3‐NiMoO4 Reprinted with permission of B.V. Straalen and Springer Science and Business Media. ..... 252 Figure L.5: Phase diagram of the system CuO‐Cu2O‐Fe2O3‐Fe3O4 on the CuO‐Fe2O3‐ T plane at pO₂ = 2.1 x 104 Pa and Ptot = 1 x 105 Pa [460]. .............................. 252 Figure L.6: Phase diagram of FeO and Cr2O3 [461]. ........................................................ 253 Figure M.1: Phase fraction ratio of the main peak of the BCC steel spectrum and the oxide spectrum as a function of time at 1073 K. ................................... 254 Figure N.1: BET surface area isotherms of AISI 440C powder size fractions. ................. 257 xvii  Figure N.2: BET surface analysis of AISI 440C size fractions: BJH pore volume as a function of average pore diameter recorded during the nitrogen desorption cycle. .......................................................................................... 257 Figure O.1: Linear least squares regression analysis of the activation energy data of the duration of oxidation, ts, until the oxidation changes from ks,1 to ks,2, presented in section 6.4. The solid line shows the predicted slope in the Arrhenius‐type graph, the dotted lines show the 95% confidence interval of the data. AISI 440C size fractions: A: Unsieved, B: ‐20 µm, C: ‐25/+20 µm, D: +25 µm. Due to the large deviations observed, a mean particle size dependent analysis may be better used in a predictive model. .......................................................................................................... 259 Figure O.2: Linear least squares regression analysis of the oxidation activation energy data of ks (ks,1, Cr2O3) presented in section 6.4. The solid line shows the predicted slope in the Arrhenius‐type graph, the dotted lines show the 95% confidence interval of the data. AISI440C size fractions: A: Unsieved, B: ‐20 µm, C: ‐25/+20 µm, D: +25 µm..................... 260 Figure O.3: Linear least squares regression analysis of the oxidation activation energy data of ks (ks,2, Fe2O3) presented in section 6.4. The solid line shows the predicted slope in the Arrhenius‐type graph, the dotted lines show the 95% confidence interval of the data. AISI440C size fractions: A: Unsieved, B: ‐20 µm, C: ‐25/+20 µm, D: +25 µm..................... 260 Figure Q.1: Ternary phase diagram of the Al‐Mg‐Cr‐O system, at 1173 K, created with the assistance of Dr. A. Petric, McMaster University ......................... 265 Figure Q.2: Miscibility gap of the system MgAl2O4‐MgCr2O4 [472]. Reproduced from [472] with permission of Springer. ...................................................... 265 Figure Q.3: Phase diagram of the system MgO‐Cr2O3‐Fe2O3 at 1573 K. Reprinted with permission of John Wiley and Sons and Blackwell Publishing[473]. ... 266 Figure Q.4: Phase diagram of the system Co‐Mn‐Cr in air, at 873 K, created by and used with permission of Dr. A. Petric, McMaster University [474]. ........... 266 Figure Q.5: Phase diagram of the system Co‐Mn‐Cr in air, at 1073 K, created by and used with permission of Dr. A. Petric, McMaster University [474]. ............ 267 Figure Q.6: Phase diagram of the system Co‐Mn‐Cr in air, at 1273 K, created by and used with permission of Dr. A. Petric, McMaster University [474]. ............ 267 Figure Q.7: Phase diagram of the system Cr2O3‐Fe3O4‐Mn3O4 at 1673 K in air [475]. Used with permission of Deutsche Bunsen‐Gesellschaft. .......................... 268  xviii  List of Symbols Symbol  Definition  Unit  Value  a ahkl A A*  Number of metal atoms per molecule of metal oxide Unit cell parameter Atomic mass Pre‐exponential factor (oxidation activation energy)  ‐ m g/mol same unit as k  ahkl3  Unit cell volume  m3  Ai  Inner cross sectional area of a tube  m2  Am  Metal surface area (before oxidation)  m2  As,m  Changing metal surface area of a sphere during oxidation m2  aO₂  Oxygen activity  ‐  AS  Surface area  m2  Aseal  Area covered by seals in gas permeability measurement  m2  B b bi by  Full XRD peak width at half peak height Number of oxygen atoms per molecule of metal oxide XRD instrument effect on peak broadening Y‐axis intercept  ° ‐ ° Same a y‐axis  c(x,t)  Concentration of solute at depth x after time t  mol/m3  c0  Wobus formula constant  ‐  6.1078  c1  Wobus formula constant  ‐  7.5  c2  Wobus formula constant  ‐  237.3  cO  Oxygen concentration  mol/m3  cCr  Chromium cation concentration  mol/m3  CTE  Coefficient of thermal expansion  ppm/K  cw,mass  Gravimetric concentration of water in air  g/m3  cw,mol  Molar concentration of water in air  mol/m3  Cτ  Distance between the ends of a curve  m  D  Diffusion coefficient  m2/s  D0  Pre‐exponential factor (diffusion coefficient)  same unit as D  Ddisc  Diameter of a disc‐shaped specimen  m  del  Depth of electron interaction  m  dhkl  Inter‐atomic spacing (between crystal places)  m  Di  Inner diameter of a tube  m  Dj  Average pore diameter  m  Dmp  Mean diameter of pores  m  xix  Symbol  Definition  Unit  Dm  Diameter of individual metal sphere  m  Dmp  Mean particle diameter  m  DO  Outer diameter of a tube  m  Dp  Pore diameter  m  E0  Standard electrode potential  V  EA  Activation energy  J/mol  Eac  Accelerating voltage  keV  Er  Open circuit voltage calculated with Nernst formula  V  F  Faraday constant  C/(mol e‐)  fCr  Molar fraction of chromium in steel  %  fFe  Molar fraction of iron in steel  %  Flam  Darcy‐Weisbach friction factor for laminar flow  ‐  fn  Molar fraction of element in an alloy or compound  %  fm  Mass fraction of element in a compound  %  Ftur  Darcy‐Weisbach friction factor for turbulent flow  ‐  fv  Particle size distribution volume fraction  %  h, k, l  Miller indices  ‐  Ij  Incremental mercury intrusion volume  m3  K  Scherrer form factor  ‐  k’  Porous stainless steel scaling constant  cm2/s  k’’  Oxide growth rate  g2/(cm4s)  kB  Boltzmann constant  J/K m/s0.5  ks  Effective materials dependent parabolic oxide growth rate constant Oxidation rate constant (spherical model)  m‐1 h‐0.5  ks,1  Oxidation rate constant of Cr2O3 (spherical model)  m‐1 h‐0.5  ks,2  Oxidation rate constant of Fe2O3 (spherical model)  m‐1 h‐0.5  Kw  Friction  ‐  Kα₁  X‐ray photon energy (photoelectric effect LIII to K shell)  keV  Kα₂  X‐ray photon energy (photoelectric effect LII to K shell)  keV  Kβ₁  X‐ray photon energy (photoelectric effect M to K shell)  keV  L  Length of a tube  m  Leq  Equivalent length  ‐  kp,eff  Value  96,485  1.38*10‐23  xx  Symbol  Definition  Unit  Value  LS  Total length of line per surface area  1/m  Ltot  Total length of all tube components  m  Lτ  Length of a curve  m  m  Slope of a line in a graph  Dependent on graph  Average atomic mass of a unit cell  g  Mav  Average molar mass  g/mol  MCr₂O₃  Molar mass of chromia  g/mol  mdisc  Mass of a disc‐shaped specimen  g  Mdry  Molar mass of dry air  g/mol  mdry  Mass of dry air  g  MFe₂O₃  Molar mass of iron(III)oxide  g/mol  mgas  Gas mass  g  MH₂O  Molar mass of water  g/mol  mH₂O  Mass of water vapour  g  min  Mass of material prior to oxidation  g  mm  Metal mass  g  mm (t=0)  Initial mass of unoxidized metal powder before oxidation g  mO  Mass of oxygen added during oxidation  g  MO  Molar mass of an oxygen atom  g/mol  mox  Mass of oxidized material  g  Mox  Molar mass of a metal oxide  g/mol  mrel ms,m  Relative oxidation mass gain Metal mass of one sphere  % g  ms,m,ox  Mass of metal cations in oxide on one sphere  g  ms,m,r  Remaining mass of unoxidized metal in one sphere  g  ms,ox  Mass of oxide on one sphere  g  mtot(t)  Mass of the oxidized powder at time t  g  mt n nB nt  Number of non‐straight tube components Number of recorded data points Bragg order Number of straight tube components  ‐ ‐ ‐ ‐  Na  Avogadro's number  1/mol  152 28.96 159.7 18  16  integer 6.022*1023  xxi  Symbol  Definition  Unit  Number of atoms per unit cell  ‐  ndry  Molar quantity of dry air  mol  nH₂O Nm,ox  Molar quantity of water vapour Molar quantity of oxidized metal cations  mol mol  NO  Molar quantity of oxygen atoms  mol  Nox  Molar quantities of metal oxide  mol  ns  Average number of particles in a particle size distribution ‐  P  Power loss in tube system  W Pa Pa  pdry  Standard pressure (at sea level) Saturation pressure of nitrogen at the temperature of the BET measurement Dry air pressure  pgas  Average pressure  Pa  pgas,inst  Average atmospheric pressure measured by the MFM  Pa  pgas,tot  Overall gas pressure  Pa  pHg  Pressure of mercury in mercury porosimeter  Pa  phkl  ‐  pO₂  Number of crystallite planes per crystallite Number of points of phase boundaries per unit length of a line Oxygen partial pressure  Pp  Percent porosity  %  psat  Saturation water vapour pressure  Pa  pvap  Water vapour pressure  Pa  Qgas  Gas discharge, volumetric flow rate  m3/s  R  Universal gas constant  J/(K*mol)  Ra  Surface roughness parameter  m  RA,rel  Relative surface roughness  ‐  Rc  Correlation coefficient (statistics)  ‐  Rdry  Specific gas constant of dry air  J/(K*g)  Re  Reynolds number  ‐  rel  Range of electron interaction  m  Rgas  Specific gas constant  J/(K*g)  RH  Relative humidity  %  0  p  p0  PL  Value  101,325  Pa  1/m Pa  8.314  0.287  xxii  Symbol  Definition  Unit  Value  RH₂O  Specific gas constant of water vapour  J/(K*g)  0.461  RHe  Specific gas constant of helium  J/(K*g) 3  2.077 2  rHF  High flow rate  m /(s*m )  Rinit  Initial metal radius (before oxidation)  m  rLF  Low flow rate  m3/(s*m2)  Rm  Remaining metal core radius (after oxidation)  m  RPB RCG Rtot  Pilling Bedworth Ratio Calculated Geometric Ratio Total radius of an oxidizing sphere  ‐ ‐ m  S  Sutherland constant  K  s  Sample standard deviation  same unit as data  sb  Sample standard deviation (of the y‐axis intercept)  same unit as data  sm  Sample standard deviation (of the slope)  same unit as data  sy  Sample standard deviation (of the regression)  same unit as data  SAm  Mass specific metal surface area  m2/g  SAp  Cumulative specific pore surface area  m2/g  Sv  Surface area per unit volume  1/m  Sxx  Sums of the squares of the devia ons of x from x̅ Sums of the cross product of the devia ons of x from x̅ and y from y̅ Sums of the squares of deviations of y from y̅ Temperature (dry bulb)  ‐  Standard temperature (electrochemistry)  K  t  Diffusion time  s  tα,ν  t‐distribution  ‐  T0  Reference temperature for Sutherland's formula  K  Tc  Gas temperature in °C  °C  tdisc  Thickness of a disc‐shaped specimen  m  TDP  Dew point temperature  K  tf  Time span in which gas flow is measured  s  Tgas  Average gas temperature  K  Tgas,inst  Average temperature measured by the MFM  K  thkl  Scherrer crystallite thickness  m  tox  Oxidation duration  h  Sxy Syy T T  0  ‐ ‐ K (or °C if noted) 273.15  xxiii  Symbol  Definition  Unit  tres  Residence time of gas in tube system  s  ts  h  Vdisc  Oxidation type switch time Sea‐level temperature according to International Standard Atmosphere (ISO 2533:1975) Volume of a disc‐shaped specimen  vgas  Speed of gas in tube system  m/s  Vgas  Gas volume  m3  Vi  Inner volume of a tube  m3  Vm  Metal particle volume  m3  VM,m VM,ox  Molar volume of a metal alloy Molar volume of a metal oxide  m3/mol m3/mol  Vp Vs,init  Pore volume Initial volume of metal in an unoxidized sphere  m3 m3  Vs,m  Changing volume of metal in a sphere during oxidation  m3  Vs,ox  Oxide shell volume on one sphere  m3  Vs,ox,i  Volume of oxide between initial metal volume and remaining metal volume Volume of oxide between initial metal volume and total oxidized sphere volume Length of electron interaction perpendicular to el. beam  m3  m same unit as x, y  xh  Diffusion depth in material Generic average values Diffusion depth in material at which the solute concentration is negligible Specific humidity  xH₂  Molar concentration of hydrogen gas at electrode  mol/m3  xH₂O  Molar concentration of water at electrode  mol/m3  xi  Generic data points  ‐  xi,ox  Oxidation mass change measurement data points  g  xi,Sv  Surface area per volume measurement data points  1/m  xi,vol  Volume measurement data points  m3  xO₂  Molar concentration of oxygen  mol/m3  x̄ox  Average oxidation mass change  g  x̄Sv  Average surface area per volume  1/m  xtot  Generic total value of calculation product  same unit as x  Ts  Vs,ox,o wel x x̄, y̅ x’  K  Value  288.15  m3  m3 m  m ‐  xxiv  Symbol  Definition  Unit  x̄vol  Average volume  m3  ypred Z Zh α β  Predicted y‐values of linear regression Atomic number Surface height (surface roughness measurement) Significance level Theoretical XRD peak broadening  Same unit as y ‐ m % °  γHg  Surface tension of mercury  N/m  Δmox,rel Δmox,s  Relative mass change due to oxidation Area normalized mass gain  ‐ g/m2  δox  Oxide scale thickness  m  δox,40kh  Oxide scale thickness after 40,000 h  m  δox,i  m  δox,t  Metal oxide thickness between initial and remaining metal radius Metal oxide thickness between initial metal radius and total oxidized sphere radius Oxide scale thickness after time t  m  ε Δp  Pore shape exponent Pressure drop in tube system  ‐ Pa  Δpapp  Pressure drop across specimen  Pa  Δy  Distance between ypred and confidence interval  same unit as y  θ  XRD Bragg diffraction angle  °  Mercury‐specimen contact angle  °  Apparent mercury‐specimen contact angle  °  κ  Gas permeability  m2  κs  Surface curvature  1/m  λ  Wavelength of CuKα radiation  m  Λ  Gas permeance  m/(Pa*s)  µ  Population mean  ‐  μ0  Reference viscosity for Sutherland's formula  Pa*s  μdry  Dry air viscosity  Pa*s  μgas  Gas viscosity  Pa*s  μHe  Helium gas viscosity  Pa*s  ν  Degrees of freedom  ‐  π  Pi constant  ‐  δox,o  θc θc  ρ  *  Bulk density  Value  0.485  m  130  1.542 Å  3.1415 3  g/m  xxv  Symbol  Definition  Unit  Value  ρCr₂O₃  Density of chromia  g/m3  5210*103  ρFe₂O₃  Density of iron oxide Fe2O3  g/m3  5250*103  ρgas  Gas density  g/m3  ρgas,mix  Density of moist air  g/m3  ρm  Metal density  g/m3  ρox  Metal oxide density  g/m3  ρt  Theoretical density  g/m3  σ σel  Generic standard deviation Electrical conductivity  same unit as data S/cm  σint  Standard deviation of XRD intensity measurements  ‐  σox  Standard deviation of mass change  g  σSv  Standard deviation of surface area per volume  1/m  σtot  Generic total standard deviation  same unit as data  σvol  Standard deviation of volume  m3  τ  Tortuosity  ‐  φgas  Gas flux (rate of volume flow across a unit area)  m/s  ωr  Surface roughness factor (>1)  ‐  xxvi  List of Abbreviations Acronym ACS AFC AISI ANL ANSI APU ASR a.u. BAL BCC BET BJH CI CIT CoPK CoPNa CoPUr CTE DLS DOE DTA EDX EG EtAcH EtOH FCC FWHM g GE H HRC IT‐SOFC LT‐SOFC MAL Mel₁ Mel₂  Denomination American Chemical Society (Standard) Alkaline Fuel Cells American Iron and Steel Institute Argonne National Laboratory American National Institute of Standards Auxiliary Power Unit Area Specific Resistance Arbitrary Units Elemental Composition Balance Body‐Centered Cubic Brunauer Emmett Teller Method Barnett Joyner Halenda Method Confidence Interval Citric Acid Organic Complex Method Coprecipitation Method with Potassium Carbonates Coprecipitation Method with Sodium Carbonates Urea Coprecipitation Method Coefficient of Thermal Expansion Dynamic Light Scattering Department of Energy, United States of America Differential Thermal Analysis Energy Dispersive X‐Ray Spectroscopy Ethylene Glycol Ethoxy Acetylacetone Ethanol Face‐Centered Cubic Full Width at Half Maximum Gaseous General Electric Haynes (Type of Steel) Rockwell Hardness Test, Scale C Intermediate Temperature Solid Oxide Fuel Cell Low Temperature Solid Oxide Fuel Cell Malic Acid Organic Complex Method Elemental Oxidation Model 1 Elemental Oxidation Model 2 xxvii  Acronym Msph MFM MG MIM NIST OCV PAFC PEC PEMFC PID PM PMI PSA PSD PSR REF rpm SE SIMS SOFC SRM TGA TMA TOFC TPB UNS XPS XRD  Denomination Spherical Oxidation Model Mass Flow Meter Media Grade Metal Injection Moulding National Institute of Standards and Technology Open Circuit Voltage Phosphoric Acid Fuel Cells Pechini Method Proton Exchange Membrane Fuel Cell Proportional‐Integral‐Derivative Powder Metallurgy Porous Materials Incorporated Particle Size Analysis Pore Size Diameter Pore Size Radius Reference Revolutions Per Minute Secondary Electron Image Secondary Ion Mass Spectroscopy Solid Oxide Fuel Cell Standard Reference Material Thermogravimetric Analysis Thermomechanical Analysis Topsoe Fuel Cell A/S Triple Phase Boundary Unified Numbering System for Metals and Alloys X‐Ray Photoelectron Spectroscopy X‐Ray Diffraction  xxviii  List of Compound Abbreviations Acronym  Denomination  Composition  CGO  Gadolinia doped ceria  Ce1‐xGdxO2‐x/2  Cu‐Mn  Manganese‐copper spinel  CuMn2O4  Fa FeCr Hem  Fayalite Ferritic Stainless Steel Hematite  Fe2SiO4 ‐ Fe2O3  LC  Lanthanum chromite  LaCrO3  LSCF  Lanthanum strontium cobalt ferrite  La1‐xSrxCo1‐yFeyO3  LSCo  Lanthanum strontium cobaltite  La1‐xSrxCoO3  LSM  Strontium doped lanthanum manganite  La1‐xSrxMnO3  LST  Lanthanum doped strontium titanate  Sr1‐xLaxTiO3  Mag  Magnetite  Fe3O4  Mg‐Al  Magnesia‐alumina spinel  MgAl2O4  Mg‐Fe  Magnesia‐iron spinel  MgFe2O4  Mn‐Co  Manganese‐cobalt spinel  Mn1.5Co1.5O4  Mn‐Fe Q S  Manganese‐iron spinel Iron phosphate Silica  MnFe2O4 FePO4 SiO2  SSZ Wus YSZ  Scandia stabilized zirconia Wustite Yttria stabilized zirconia  Zr1‐xScxO2‐x/2 FeO Zr1‐xYxO2‐x/2  xxix  Acknowledgements I would like to offer my gratitude to the dedicated staff, faculty, and fellow students at the UBC Department of Materials Engineering who continue to inspire me in research and development. I would like to gratefully acknowledge the help of Dr. Tom Troczynski and Dr. Olivera Kesler, for their inquisitive questions and helpful comments along the way. Special thanks also to the examiners and chairs of the comprehensive exam, and the internal and external defences: Dr. Matthias Militzer, Dr. Daan Maijer, Dr. Elöd Gyenge, Dr. Yongsong Xie, Dr. Dave Ghosh, and Dr. Eric Croiset (U. Waterloo) as examiners, Dr. Steve Cockroft, Dr. Peter Barr, and Dr. Grenfell Patey as examination chairs. Further thanks to Mary Fletcher for her kind introduction to microscopy and spectroscopy methods and Dr. Sina Shahandeh for his comments on image analysis. I am also thankful to all previous members of the former UBC Solid Oxide Fuel Cell group, and to Markus Fengler, Dr. Craig Metcalfe, and Dr. Michael Poon for teaching me how to use a lathe. Special thanks to Materials Engineering staff Michelle Tierney, Nancy Oikawa, Mary Jansepar, Fiona Webster, Glenn Smith, Serge Milaire, and Gary Lockhart. I would also like to acknowledge the support of my colleagues at the National Research Council (NRC) Canada, Institute for Fuel Cell Innovation (IFCI). Special thanks here to Dr. Yongsong Xie, the NRC co‐supervisor of the project, and for the useful comments along the way from the entire High Temperature Fuel Cell group, especially Dr. Radenka Maric for her kind and concise guidance, Dr. Shiquang Hui, MSc. Wei Qu, Dr. Cyrille Decès‐Petit, Dr. Roberto Neagu, Dr. Nima Shaigan, Dr. Xinge Zhang, Dr. Min Kyong‐Bok, Mark Robertson, and Sing Yick, as well as MSc. Dave Edwards for his outstanding comments, Dr. Tetyana Sobolyeva, Dr. Kourosh Malek, Marius Dinu, Cibele Halmenschlager, Kerry Seifried, and librarians Nancy Glass, Tamara McLaughlin, and Aleteia Greenwood, and everybody else who gave me constructive ideas and critiques. Special thanks are owed to my parents, who have supported me through my years of education and research. Very special thanks to my cyber grandmother, Ilse Koch, for her unfaltering, optimistic support via skype. And, of course, special thanks to my own family, Dr. Heidrun Spohr for her moral support. xxx  1. Introduction One of the greatest challenges of mankind today is that the world's energy consumption per capita is increasing continuously. The majority of our power production today comes from the combustion of fossil fuels, including coal, with additional significant contributions from hydroelectric and nuclear energy conversion. All of these energy conversion methods create varying kinds of pollution. Fossil fuels, as the name suggests, are a finite resource of solar energy stored in floral and faunal fossils over many millions of years. The ever increasing demand for a finite and dwindling resource has the potential to significantly increase the cost of these resources [1]. Additionally, an undesirable consequence of the thermo‐chemical conversion of fossil fuels by combustion is environmental contamination. The reaction products from combustion can be harmful to humans on a local scale, and may contribute to global climatic changes [2]. Fossil fuel resources are unevenly distributed over the globe, leading to geopolitical unrest as a result of the competition for resource access. Clearly, the energy demands of our society need to be satisfied in a more appropriate, sustainable, and efficient way. Potentially cleaner devices for energy conversion are fuel cells. Fuel cells are devices that convert the chemical energy released in oxidation of hydrogen, hydrocarbon, or carbon fuels directly into electrical energy. Fuel cells are based on electrochemical reactions rather than thermochemical combustion. They operate more efficiently, produce less pollution, are modular, and are less likely to fail mechanically since they have fewer moving parts than energy conversion based on combustion. Replacing energy conversion based on combustion with highly efficient fuel cell systems is one step in the direction of reducing the environmental impact of energy production, as typical combustion processes produce NOx, SOx, and COx gases and harmful particulates [3]. Fuel cells produce mainly water as their local exhaust if hydrogen is used as a fuel. Fuel cells using hydrocarbons as fuels may also produce smaller amounts of CO2 as exhaust than energy conversion based on combustion using the same type of fuel. 1  1.1.  Advantages and disadvantages of fuel cells  Fuel cells receive the anode and cathode reactants that participate in the energy conversion process in a continuous manner, in contrast to batteries, which store finite amounts of energy chemically. Rechargeable batteries typically require long times for a recharge or change‐out and lose some of their energy storage capacity over time, especially Li‐ion batteries [4]. Devices powered by fuel cells can have comparably little downtime compared to batteries [4]. The idea of fuel cells is not new and different fuel cell types have been researched since the 1970s on a large scale. The original invention of fuel cells is generally credited to the early experiments by Grove [5]. He showed that the gases produced during electrolysis of diluted sulphuric acid could react to form water on the surface of platinum electrodes. Many companies are currently working on the commercialisation of fuel cells and successful applications are becoming more and more common. Among the different types of fuel cells, alkaline fuel cells (AFCs) and phosphoric acid fuel cells (PAFCs) were the main technologies used in applications until the mid‐1990s. Phosphoric acid fuel cells, once the most researched fuel cell technology of large‐scale power conversion systems, can no longer economically compete with the reduction in costs of the other fuel cell types [6]. The focus of research has shifted towards highly efficient solid oxide fuel cells (SOFCs) for stationary power generation and polymer‐based proton exchange membrane fuel cells (PEMFCs) for portable devices [6], [7], [8]. SOFCs can potentially supply heat and power independently of the power distribution grids [9] and due to a combination of high fuel flexibility and efficiency, SOFCs are ideal candidates for cleaner stationary power generation [10]. This is the technology that was investigated in this work. All fuel cell types have their particular advantages and disadvantages. PEMFCs require costly precious metal catalysts, which are highly susceptible to poisoning by fuel impurities such as carbon monoxide and sulphur [11], [12]. In contrast, the high operating temperatures of SOFCs are sufficient to facilitate catalysis by nickel, 2  eliminating the need for noble metals. Addressing material degradation at SOFC operating temperatures up to 1273 K and the high production costs associated with the use of ceramic materials are two of the main goals of materials engineering research in SOFC technologies today. These considerations are also driving fuel cell development toward operating temperatures below 1073 K. At such low operating temperatures, stainless steels become candidate materials for SOFC substrates, interconnects, and Balance of Plant components. The energy required to produce SOFCs depends on the manufacturing method. The following calculations by Karakoussis et al. show the energy input required for the manufacturing of each 1 kW sized SOFC module from a given set of raw materials [13]. These calculations do not take into account the energy required for the production of these materials. The authors calculated that the energy input required to produce co‐sintered planar SOFCs is 26x106 Joules for the production of each 1 kW‐sized SOFC module and 35 MJ/kW for the production of planar SOFCs with individually sintered layers [13]. For tubular SOFCs produced by cathode extrusion and sintering, and by using atmospheric plasma spraying for the deposition of doped lanthanum chromite interconnects, the authors calculated a required energy input of 275 MJ/kW [13].  1.2.  Principle of fuel cell operation  Fuel cells consist of three electrochemically active layers, the porous anode and the porous cathode, physically separated by a dense electrolyte. These parts comprise one single fuel cell. To increase the output power, cells can be combined in series or in parallel into stacks, depending on the design. The cathode is in contact with an oxygen source, typically air. In SOFCs, oxygen molecules in the cathode pores dissociate and combine with free electrons coming from the external circuit, forming O2‐ ions. These ions migrate through the electrolyte of the SOFC, which is a dense, gas‐tight ceramic layer with high mobile vacancy content that facilitates the migration of oxygen ions to the anode. At the anode, which contains the fuel reactants, the oxygen ions combine with hydrogen, carbon monoxide, or 3  hydrocarbon molecules to form water (the only exhaust product if H2 is the fuel) and CO2 (for carbon based fuels). The electrons released in the oxidation reaction pass through an external circuit, creating usable electricity and closing the circuit. Figure 1.1 shows the operating principle of an SOFC, in the case of hydrogen being used as a fuel.  Figure 1.1: Principle of operation of a single solid oxide fuel cell. The principal reactions are as follows. The SOFC cathode half‐cell reaction is: 0.5 O  Eq. 1.1  2e →O  The SOFC anode half cell reaction for hydrogen fuel is: H  O  →H O  Eq. 1.2  2e  When no power is drawn from the cell, one single unit cell generates an open circuit voltage (OCV) of approximately 1 V. The exact voltage depends on the operating conditions such as oxygen partial pressure, reactant and product concentration, and temperature. At standard conditions (T0 = 273.15 K, p0 = 101,325 Pa), the OCV (Er) can be calculated from the Nernst equation (Eq. 1.3) using the standard electrode potential E0, the universal gas constant R (8.314 J/(K*mol)), operating temperature Tgas, operating pressure pgas, Faraday’s constant F (96,485 C/mol), and mole fractions at their respective electrodes of water (xH₂O), hydrogen (xH₂) and oxygen (xO₂) [14], [15]. E p  ,T  E p ,T  RT x ₂ ln 2F x ₂ x  ₂  RT lnp 4F  Eq. 1.3  4  As a consequence of this low voltage, most applications require the fuel cells to be connected in series into a stack. This is done by means of dense interconnects that physically separate the single cells while providing the external electronic pathway. Not all of the fuel and oxygen molecules fed to the cell react. The fuel exhaust stream contains a mixture of the fuel and water; the cathode exhaust stream contains air with reduced oxygen content. The reactants must be transported to the cells via internal or external manifolds. The reactants are typically supplied through flow fields machined in the dense interconnect surfaces, and may spread over the plane of the cell by diffusing through the porous support and electrode structures. When drawing power from the cell, the operating voltage that can be achieved with a fuel cell is lower than the OCV due to irreversible losses or cell polarization. These losses in the cell are due to the ionic ohmic resistance of the electrolyte and the supply gas mass flow restrictions of the electrodes and the porous support materials, and the reaction kinetics. These losses can be reduced by choosing new material sets, some of which are described in section 1.4, novel production methods, and device architectures.  1.3.  The solid oxide fuel cell  All components of an SOFC are completely solid state. This allows for a large variety of geometries that are difficult to realize with other types of fuel cells. Tubular fuel cell design, in particular, is a unique way of profiting from the solid state of the fuel cell components, especially since reaction products occur in gaseous form at the operating temperatures. The electrolyte is comprised of a dense, ionically conductive ceramic membrane that prevents direct combustive reaction of fuel and oxidant gases and does not conduct electrons. In the case of the SOFC, the electrolyte is typically an oxygen ion (O2‐) conductor. Mixed proton / oxygen ion conductors are also under development [16]. The electrodes, by contrast, must be electronically conductive. To achieve high efficiencies, they should also be able to conduct ions, thus enlarging the reaction interface. This interface between reactant, electronically conductive phase, and ionically conductive 5  phase is known as the triple phase boundary (TPB). Dense, gas‐tight, electronically conductive interconnects provide the series connection of several fuel cells to form an SOFC stack. The reason for the high operating temperatures of an SOFC is the thermally activated ionic conductivity in ceramics. The conductivity of oxygen ions, with an average size of 124‐128 pm [17], increases with increasing temperature [18]. Since SOFCs conduct oxygen ions from the air side (cathode) to the fuel side (anode) of the cell, they have a large fuel flexibility compared with other types of fuel cells. SOFCs can use hydrogen, and also hydrocarbons, carbon monoxide, or coal syngas as fuels, either by direct oxidation or via steam reforming. SOFC systems are typically built to recycle waste heat internally, to make the system more efficient. However, waste heat can also be used to power gas or steam turbines. Consequently, SOFCs are highly flexible systems that can generate electrical power at very high efficiencies and with very low pollution. The U.S. Department of Energy (DOE) has set a lifetime target for residential and commercial fuel cells to 40,000 h [19], [20], [21]. More recently, the lifetime target has been lowered to account for the fact that SOFCs provide both heat and power, as opposed to combustion furnaces that only provide heat. The Helmholtz Research Centre Jülich in Germany uses 100,000 h as a reference for the lifetime requirements for large scale power generators [19]. As a target lifetime of 40,000 h has been the standard value for most of the past years, this work will use that target for lifetime projection calculations. During several years at elevated temperatures, the materials in the SOFC stack may degrade. For example, tubular SOFCs have been operated for up to 70,000 h with a voltage decrease of 0.5% per 1000 h [22]. Microstructures may change due to sintering or stress in the material. Stresses can be introduced by thermal cycling as well as by the SOFC production method and may lead to cracking and spallation. Various atomic species may diffuse through the cell and cause reduced conductivities, and some of the components may change their oxidation state, especially if metallic components are 6  used in the cell and stack production, leading to the formation of oxide scales. Stresses may be introduced due to the uneven distribution of heat from the hot inlet gases, and the uneven distribution of electrochemical reaction sites throughout the cell, both of which can result in thermal gradients in the materials, which may lead to mechanical failure of some of the SOFC layers [23].  1.4.  SOFC materials  Table 1.1 shows some of the most commonly used materials for each component of the SOFC and the material acronyms used in this work [24]. Each component is intensively researched worldwide with the aim to optimize its performance, long‐term thermochemical stability, and stack compatibility, to reduce its production and operating cost, and to make the fuel cell stack more reliable [25]. Electronically conductive electrodes may be mixed together with electrolyte material used in the SOFC in order to increase the TPB length, and to reduce differences in thermal expansion coefficients. Information about mixed electrode materials is omitted from Table 1.1 for clarity reasons. Table 1.1: Some of the materials typically used in SOFCs [24]. Component Anode Electrolyte Electrolyte Electrolyte  Material Ni Zr1‐xYxO2‐x/2 Zr1‐xScxO2‐x/2 Ce1‐xGdxO2‐x/2  Electrolyte  Sr1‐xLaxTiO3  Cathode  La1‐xSrxMnO3  Cathode  La1‐xSrxCo1‐yFeyO3  Interconnect  LaCrO3  Interconnect  Fe or Ni based stainless steels  Denomination Nickel Yttria stabilized zirconia Scandia stabilized zirconia Gadolinia doped ceria Lanthanum doped strontium titanate Strontium doped lanthanum manganite Lanthanum strontium cobaltite ferrite Lanthanum chromite Stainless steel (using the designations from the American Iron and Steel Institute)  Acronym Ni YSZ SSZ CGO LST LSM LSCF LC AISI  7  Since some of the materials used in SOFC production are less commonly used than for example iron, manganese, or chromium, the global production data of elements used in both ceramic and metallic SOFC components (as indicated in Table 1.1) are listed for the years 2004 and 2008 in Table 1.2 [26]. Table 1.2 shows that the main elements used in SOFC production are produced at sufficiently high levels. However, materials that are used as dopants in SOFC components, such as Sc in electrolytes or Nb in some stainless steels, may be rare and only available from high priced monopolists, a fact that has already been noted by some European SOFC alloy manufacturers [27], [28]. Table 1.2: Globally mined elemental production data [26]. Element Co Cr Cu Fe Mn Mo Nb Ni Sc Rare earth minerals (Ce, La, Pr, Nd, Th, Y) Sr Ti V Zr  Year 2004 [103 tonnes] 52 18,000 14,600 1,373,000 28,400 161 2 1,390 0.002 [29, 30]  Year 2008 [103 tonnes] 65 23,300 15,500 2,188,000 41,800 223 1 1,530 0.002  100  126  890 10,700 65 1,280  880 12,900 67 1,410  Figure 1.2 shows how different SOFC material sets relate to different operating temperatures using the example of the material sets under development in 2006 at Topsoe Fuel Cell A/S (TOFC) and Risø National Research Labs, Roskilde, Denmark (Risø) [31], [32].  8  Figure 1.2: Materials development in SOFCs. Temperatures reflect the targeted temperatures in fuel cell development at TOFC/Risø [31]. FeCr: Ferritic stainless steel. Reprinted from [31] with permission of Elsevier. YSZ is a material that exhibits thermally activated oxygen ion conductivity and has consequently been used as the traditional electrolyte material in SOFCs. Early SOFCs used the electrolyte as the mechanical support (Figure 1.2, 1273 K). The high internal resistance of these electrolyte supported cells led to the development of SOFCs that derive their structural integrity from an electrode support (Figure 1.2, 1123‐973 K). A well‐established technique of producing these mostly anode supported fuel cells is tape casting of the anode support with subsequent reactive or colloidal spraying or screen printing of the porous Ni‐YSZ cermet anode and dense YSZ electrolyte to produce half‐ cells [33]. After high temperature sintering above 1573 K, a porous LSM‐YSZ cathode is applied to the electrolyte, and the fuel cell is sintered at approximately 1273 K. The conductivity of LSM is low at operating temperatures below 1023 K [34], at which temperature cathode materials such as LNF and LSCF are used together with ceria‐ based electrolytes. The use of doped ceria electrolytes also prevents the formation of low‐conductivity phases between cathode materials and zirconia. Functionally grading LSM with LSCF and CGO can reduce the polarization resistance of the graded electrode compared to ungraded mixed electrodes [35]. Furthermore, mixing electrolyte material with the electrode material both increases the TPB length and helps match the coefficient of thermal expansion (CTE) between the components of the fuel cell, reducing stress in the system. Interconnects connect single fuel cells in series. They act as a physical separation barrier between the two electrode gases and as a current collector. Some fuel cell designs use a porous current collector to allow gas diffusion to the electrodes adjacent 9  to the dense interconnects. Interconnects should be gas tight and have zero porosity to separate anode and cathode gases from two cells, have good stability (physical, chemical, microstructural, electrical) in both oxidizing and reducing atmospheres and with respect to contact with electrodes and/or electrode contact layers. Both the unoxidized material and the developing oxide scales should have high electrical conductivity, good adhesion of oxide scales to initial material, and CTEs that are sufficiently matched to those of the other materials in the stack. Of further advantage are good machinability for the creation of flow channels for gas delivery, good electrical contact with the fuel cells, and good thermal cycling capability. The traditionally used interconnect material for high temperature (1273 K) SOFC operation is doped lanthanum chromite (LC). Doping with certain elements such as Ca, Mg, or Sr (A‐site doping), or Ni or Ti (B‐site doping) [36] can both increase the electrical conductivity and adjust the CTE to more closely match that of the other materials in the stack [37]. LC is a ceramic material that can easily withstand the traditional 1273 K operating temperature in both cathodic and anodic conditions. However, raw material and fabrication costs are high. It is difficult to obtain high density chromite parts at reasonable sintering temperatures and chromite interconnects tend to partially reduce at the fuel gas‐interconnect interface, causing them to warp [38]. This warping is due to the introduction of oxygen vacancies, leading to material expansion [39]. Furthermore, the introduction of oxygen vacancies under reducing conditions leads to ionic conductivity in the interconnect and reduced fuel efficiencies due to internal ion short circuiting between two adjacent cells [39]. The recent trends in developing lower temperature, more cost‐effective cells with ever thinner micron‐scale electrolytes and novel electrolyte materials with improved conductivity make it feasible for lanthanum chromite to be replaced by metallic alloys as interconnect materials. Metallic interconnects are generally more gastight and can be machined more easily than ceramic interconnects. Compared to doped LC, metallic alloys offer significantly lower raw material and fabrication costs [40], [41]. However, during long exposures to the SOFC operating conditions, high 10  temperatures, humidity, and oxidizing and reducing atmospheres, metals form surface oxide layers over time. Consequently, the most likely application of metallic alloys in SOFCs will be at temperatures below 1073 K [42], [43].  11  2. Literature review 2.1.  Oxidation of porous stainless steel  2.1.1. Metallic components in SOFCs: Interconnects and cell supports Metal supported cells are expected to have lower electrical resistance than ceramic supported cells, with the additional advantage of reduced production costs. The electrodes and electrolyte are produced at thicknesses below 60 µm directly on a porous metallic support. This can be done within minutes when using modern deposition techniques such as plasma spraying [44]. The cell support structure has to be porous to facilitate gas flow to and from the SOFC, driving the electrochemical reaction. The porous metallic support structure is in contact with the dense metallic interconnects that connect and seal the cells, collect the current, and provide gas flow channels to allow the gases to permeate the stack structure. Porous metal supported cells (Figure 1.2, 823 K) are targeted as the future of SOFCs, but still have to be developed to produce a satisfactory power output along with reasonable degradation rates. Metal components in the SOFC are advantageous as they are cheaper, are more easily machined than ceramic components, are reasonably stable in reducing environments, and possess a high electronic conductivity [45], [46], [47]. Even the typically used stainless steels are susceptible to corrosion and can leak Cr into the cell [48] (Figure 2.3), where Cr ions poison the cathode by suppressing the reduction of oxygen and by degrading cathodic perovskites into (Cr,Mn) spinels [49] or SrCrO4 [50].  12  Figure 2.3: Select chromium species over the surface of Cr2O3 at various temperatures [48]. Reprinted from [48] with permission of Elsevier. Producing the entire SOFC on porous metal substrates allows the production of thinner electrode and electrolyte layers, resulting in lower internal resistances, increasing the performance and lowering the production cost, compared with ceramic supported cells. If the cell is designed and prepared properly, the stainless steel can also be used as an internal reformer [51], [52], or as a heat exchanger [53]. Different alloys based on Fe (stainless steels) with varying levels of elements such as Mn, Ti, Al, Ni, Si, Cr, and Mo have been proposed and tested for their applicability in SOFC environments [54]. Oxide formers like Al or Si can significantly reduce corrosion of the metal [55], but their oxides are insufficiently conductive and thus interconnect and porous substrate alloys typically contain these elements in as small quantities as possible [41], [56]. Bender found that AISI 441 alloys with <0.4 mass% Si had low increases of area specific resistance (ASR) with time, but also had reduced resistance to oxidation [57]. The following points summarize the driving force behind low and intermediate temperature SOFC alloy research (for both dense interconnects and porous cell supports), giving an overview of standard alloying elements [58], [59]. 13    Any alloy used should form a protective surface oxide scale during operation. This usually requires a minimum Cr content of 12 mass% [60] to 17 mass% [58].    Cr can diffuse into electrode contact materials such as (La,Sr)MnO3, LaCoO3, or (La,Sr)CoO3 via solid‐state diffusion, or as volatile chromium oxides and hydroxides (Figure 2.3), which may result in a local enrichment of La2O3 that can cause mechanical degradation due to its hygroscopic properties [61].    If Cr migrates into the cell, it is depleted in the metallic components (interconnect or cell substrate). In order to compensate for high migration rates over long operating times, some authors recommend that SOFC alloys should contain >22 mass% Cr [58], although high Cr and Mo additions may lead to detrimental intermetallic phases [62], [63], [64]. Also, protective coatings may be applied to reduce the Cr leakage into the SOFC (see section 7).    High Cr contents lead to coefficients of thermal expansion (CTEs) that are lower than those of standard Ni‐YSZ anodes. To counterbalance this effect, alloying elements such as Nb, Mo, W, Ta, and Ni can be added [58], [65].    High Cr content may lead to low mechanical strength of the alloy [66], [67].    Decreased oxide growth rates and improved oxide scale adherence can be achieved by alloying with Y, Ce, La, Zr, and Hf [58], [59].    Reduction of Cr evaporation can be achieved by applying diffusion barrier coatings or by alloys forming spinel type oxide layers. These can be formed directly on the alloy or on top of a surface chromia layer. Additions of Ti and Mn can help in the formation of these spinels [58], [59].    Increased electrical conductivity of chromia and spinels can be achieved by doping with elements, for example Co, that form conductive phases such as CoCr2O4 spinel with a conductivity of 7.4 Scm‐1 at 1073 K [68].    Contents of oxide formers with good oxidation resistance, but low electrical conductivity (Al, Si), should be kept to a minimum [58], [59].    Additions of Nb, Ta, Ti, Nb may lead to precipitations in the presence of C, which can be avoided by correct heat treatments of the alloy [65].  14  Figure 2.4 shows some of the alloys generally considered for SOFC metallic components.  Figure 2.4: Alloys of the Fe‐Cr‐Ni system considered as SOFC materials [38]. Reprinted with permission of ASM International®. All rights reserved. An alloy engineered specifically for SOFC operation is Crofer22 (designation "JS‐3"), with 20‐24 mass% Cr and only low additions (<0.5 mass%) of Si and Al for corrosion resistance [69]. This alloy was specifically developed by Thyssen Krupp and Research Centre Jülich, Germany, to be used in SOFC interconnects in auxiliary power units (APUs). However, the batches produced to date vary in terms of oxide mass gain (Figure 2.5) [70], [71].  Figure 2.5: Mass change during heat treatment of different Crofer22 batches in air [71]. Reproduced with permission of Dr. Quadakkers, Forschungszentrum Jülich, and ThyssenKrupp VDM GmbH. 15  One significant advantage of Crofer22 is its ability to form a dense (Mn,Cr)3O4 spinel above the Cr2O3 scale [58], [72]. This spinel layer reduces Cr evaporation from the metallic  substrate  and  subsequent  deposition  in  the  electrode [73],  while  simultaneously maintaining an electronic conductivity higher than that of Cr2O3 [58]. It has been shown that these layers can have a contact resistance which is three orders of magnitude lower than alumina‐rich scales formed by most ferritic stainless steels [74]. In combination with suitable perovskite‐type contact layers, steel components may react at operating temperatures to form mixed‐oxide layers with low electronic resistance and good Cr evaporation suppression [74], [75]. Another Fe‐based alloy targeted for SOFC components is E‐brite, with 26 mass% Cr and 1 mass% Mo. Other candidates for SOFC interconnects are based on Ni, such as Haynes alloys H230 and H242 [76]. They form NiO scales on top of the Cr2O3 scale, effectively reducing the Cr evaporation into the cell. However, NiO scales formed on the surface of Haynes 230 do not grow into a continuous layer and thus do not prevent Cr evaporation. E‐brite contains only little Ni (content of (Ni + Cu) <0.5 mass%) [77] and thus the chromia is directly exposed to the electrode atmosphere. E‐brite and Haynes 230 have low oxidation mass gain in air at 1073 K, as shown in Figure 2.6. However, more Cr volatilizes from these alloys compared with Crofer 22 [69].  Figure 2.6: Comparison of mass gain between four SOFC candidate alloys exposed to air at 1073 K for 500 h (H = Haynes) [72]. Reprinted from [72] with permission of Elsevier. 16  Haynes 242 forms NiO scales that grow together to a continuous film upon long exposure to high temperatures [72]. Haynes 242 also forms Ni3Mo layers under the Cr2O3 layer. If oxide spallation occurs in thermal cycling, a NiO layer forms readily on the exposed metal surface, due to the high Ni content in the Ni3Mo layer. Haynes 242 stabilizes a Ni‐Cr‐Mo phase after 500 h at 1073 K in air [78], [79], [80]. Thermo‐ mechanical tests for this phase are unavailable to date, and the CTE of this phase has not yet been determined [72]. Thus it remains unknown whether it has any significant detrimental properties for SOFC operation. Quadakkers et al. investigated several other commercially available steels (see Table 2.3 for their composition, or refer to [81] for other SOFC alloy compositions and oxide growth kinetics), but found that the oxide scales generally tended to spall easily during long‐term oxidation [74]. The mass change during cyclic oxidation for the alloys tested by Quadakkers [74] can be seen in Figure 2.7.  Table 2.3: Typical composition of several proposed alloy materials for SOFCs (max. values, in mass%) [57], [72], [74], [82], [83]. 82  Alloy  Fe  C  AISI 430  Bal  0.12  Bal  0.9‐ 1.2  AISI 440C AISI 441HP  Bal 0.015  Cr  Si  S  Mn  16‐18  <1.00  0.03  1.00  16‐18  <1.00  0.03  1.00 0.75  17.7  Al  0.04  AISI 446  Bal  25  1.4509  Bal  18  1.4015‐3C  Bal  16  1.4742  Bal  17  1.04  ZMG 232  Bal  22  E‐brite  Bal  26  Crofer22  Bal  Haynes 242  0.03  Haynes 230 Inconel 600  6‐ 10  Ni625  1.9  0.38  Mo  0.3  Ni  P  0.75  0.04  Ti  0.3  0.2  0.5  0.70  0.38  0.12  0.41  0.3  0.26  0.93  0.31  0.18  0.01  0.19  0.35  0.45  0.24  0.02  >18  0.03  0.70  0.38  0.12  0.12  8  0.5  0.80  0.80  0.10  22  0.3  0.40  0.10  14‐ 17  0.50  19.4  0.37  0.50 0.015  Co  Cu  W  B  0.04  0.29 0.03  La/Nb  0.1  0.05 0.12  1 25 2  Bal Bal  1.00  Bal  0.16 11.2  Bal  2.5 0.02 (La)  5  0.5  0.006 14  0.015  2.1 (Nb)  17  Figure 2.7: Oxidation mass gain of several SOFC candidate alloys in air at 1073 K [74]. Reprinted with permission of Dr. Quadakkers, Forschungszentrum Jülich, and published under unported non‐commercial Creative Commons License 3.0. Quadakkers et al. proposed several alloys developed at Research Centre Jülich, Germany, (JS‐1‐3) with specific (undisclosed) Mn, Ti and La concentrations as viable metallic SOFC materials with little spallation and low electrical resistances (Figure 2.8).  Figure 2.8: Contact resistance of different SOFC candidate alloys oxidized in air at 1073 K [74]. Reprinted with permission of Dr. Quadakkers, Forschungszentrum Jülich, and published under unported non‐commercial Creative Commons License 3.0. Another Fe‐based, internationally standardized material that is more easily available than the above mentioned alloys is stainless steel AISI 430 (for typical elemental compositions see Table 2.3, for a Fe‐Cr phase diagram see Appendix A) [83]. 18  With a CTE of 11.4‐12.5 ppm K‐1 [83], [84], this material is relatively closely matched with standard 8 mol% YSZ electrolytes (10.5 ppm K‐1) [85] and Ni‐YSZ anode cermets (12‐13.5 ppm K‐1, depending on the composition used) [54]. This makes AISI 430 a material that can be used in SOFC interconnects. With properly designed seals made from mica and glasses, alloys such as Inconel 600 with higher mechanical strength and better oxidation resistance, but a higher CTE (19 ppm K‐1), can be used with a calculated fuel leakage rate of 0.9% for a 60 cell stack [84]. However, Chou et al. found that the leakage rates during thermal cycling were at least twice as high for the tested Inconel 600 compared to a better CTE‐matched AISI 430 [84]. Stroosnijder et al. found that additions of Y to AISI 430 can have a positive influence on the oxidation resistance of these alloys [86]. Employing dip coating techniques in sol gel solutions, Qu et al. found that Co oxide layers converted discontinuous Cr2MnO4 films on AISI 430 surfaces into a continuous, adherent layer of similar thickness to the chromia layer formed adjacent to the metal substrate during oxidation [87], [88], [89]. The authors furthermore found up to 50% reductions in oxide mass gain when using Y and Y‐Co oxide layers to protect the AISI 430 surface, accompanied by a reduction in electronic resistance by a factor of four. Hou et al. found that additions of reactive elements such as Y, Ce, La, and Zr can reduce the oxidation rate, and that additions of NiO can increase the oxide scale conductivity [90]. Kofstad attributed this result to the change of diffusional transport from predominant outward Cr diffusion for alloys without reactive elements to inward oxygen diffusion for alloys with reactive elements [39], [91]. Hou et al. further found that the oxide scales grown in reducing conditions possess a lower conductivity than the same oxide grown in an oxidizing atmosphere. They did not, however, give any reason for this phenomenon; further work is necessary to evaluate it [90].  2.1.2. Porous materials Porous metal structures are increasingly used in industrial applications, not just in SOFCs [92]. Applications of porous metals can include stainless steel filters [93], [94], 19  biomedical applications [95], [96], and clean energy technologies such as low temperature solid oxide fuel cells (LT‐SOFCs) [97]. Porous metals can be produced as foams [98], meshes [99], weaves [100], cloths [101], by laser machining [102], continuous zone melting [103], or by powder metallurgy (PM) [104]. Consolidation of powders can be performed by methods such as dry isostatic pressing or by tape casting and sintering under reducing atmosphere [105], [106], [107]. Since porous stainless steels are often used in corrosive environments, it is crucial to be able to determine the influence of microstructure on oxidation. This analysis was performed in section 4. In order for the gases supplied through the flow channels on the surfaces of the SOFC interconnects to reach the fuel cell, they have to diffuse through the porous cell support. For low temperature operation, this support can be produced from stainless steel. While some commercial vendors use powder metallurgy to produce porous stainless steel materials without additional layers, other methods include producing metal SOFC substrates as a tape using binders and cosintering them together with some of the fuel cell layers [108]. While corrosion studies of dense Fe‐Cr bulk alloys, especially in oxidizing atmospheres, are available in abundance [41], [42], [54], [109], [110], [111] [112], the influence of the microstructure of such alloys on oxidation has received far less attention. Also, production of porous metals typically occurs at higher cost than dense sheet production of similar alloys. Furthermore, some studies indicate that metals subjected to dual atmospheres (cathode gases on one side, anode gases on the other side) experience differences in oxide growth rate, microstructure, and oxide species formed when compared with metals subjected to a single atmosphere on all sides. Yang et al., for example, found (Mn,Fe,Cr)3O4 spinel formation on top of the usually observed oxide scale on the air side of a dense Crofer22 alloy and Haynes alloy when subjecting the alloys to dual atmospheres [113], [114]. The authors attributed these changes to hydrogen transport through the bulk metal. Ilavsky et al. found that a thermal spray deposited mixture of 50% metal particles with 50% ceramic particles oxidized faster than dense materials [115]. The 20  authors credited this effect to the increase in specific surface area of the metal component per unit volume of cermet, but the surface area of the metal was not measured. Similarly, Mukherjee et al. found that powder compacted Al2O3 / ferritic stainless steel mixtures corroded faster with increasing porosity [116]. However, the authors also found that the addition of 6 vol% of Al2O3 to ferritic stainless steel powders reduced the mass gain both during sintering in hydrogen at 1623 K and oxidation in oxygen at 823 K by at least one order of magnitude compared with pure steel powders [117]. The oxidation mass gain in these studies was correlated only with the outer geometrical surface of the sintered specimens. Song et al. found that the corrosion resistance of diecast AZ91D alloy (Al=8.4 mass%, Zn=0.73 mass%, Mg=Balance) was significantly lowered in porous regions of the analyzed specimens [118]. The authors found that micro‐porosity leads to a higher (unspecified) surface area and the formation of auto‐catalytic corrosion cells, however, the amount of porosity or the effect of different pore sizes was not studied. Lopez et al. found that different heat treatments of carbon steels resulted in different microstructures, which influenced the corrosion behaviour of the materials [119]. They also found that the effect was small compared to the changes in corrosion behaviour resulting from adding corrosion inhibitors to the corrosion solutions. The porosity resulting from the pre‐treatment of the specimens was not analyzed. Haanappel et al. found no relation between grain microstructure and the cyclic or isothermal oxidation of Ti‐48Al‐2Cr alloy at 1073 K in air [120]. The growth rates of the oxide scales and the composition, structure, and morphology of the oxides were unaffected by the grain microstructures (Figure 2.9). However, as the materials contained no porosity, only the influence of grain microstructure on oxidation was investigated.  21  Figure 2.9: Different grain structures of a Ti‐48Al‐2Cr alloy analyzed for their oxidation behaviour in air at 1073 K by Haanappel et al. [120]. A: γ‐TiAl grain structure, B: Duplex and lamellar structure, C: Lamellar grain structure. No influence of these grain structures on oxidation was observed. Kawakita et al. found that AISI 316L coatings with 4% porosity corroded faster in sea water than coatings with 1% porosity, but the surface area of the pores was not calculated [121]. Bocchini found that the steam oxidation of sintered iron powders formed Fe3O4 scales on the iron surfaces and proposed to use this oxidation as a method to densify porous components produced by powder metallurgy [122]. Alitavoli et al. similarly found that sintered porous stainless steel and copper powders densified at oxidation temperatures as low as 773 K within less than one hour of oxidation [123]. While the oxidation mass gain of porous AISI 430L [124], porous Fe30Cr [125], and porous 316L [104] specimens has been tested, the findings all calculated the mass gain as a function of the outer surface area of the specimens. Antepara et al. found that specimens with (unspecified) porosity had significantly higher oxidation rate constants than dense specimens of similar composition [125], but the oxidation behaviour was not correlated to the actual surface area of the materials. Hubbard et al. found that porous ferritic stainless steel was less susceptible to cyclic oxidation mass gain than porous austenitic stainless steels, but did not calculate the surface area or the porosity of the materials [126], [127], [128]. Bautista et al. found that the oxidation mass gain (normalized to the outer surface area of the specimens) at 1073 K was very similar for porous AISI 430L, Fe22Cr, and Ni625 (see Table 2.3 for composition), and found that Ni20Cr alloys had an oxidation mass gain within the first 50 hours that was at least one order of magnitude higher than for the other three materials [129]. Bautista et al. also studied porous mixed austenitic (316L) and ferritic (434L) steels oxidized at 22  1173 K [130]. The authors analyzed the average pore size of the specimens by image analysis and calculated a surface area of the specimens from this average pore size. While this calculation approximates the surface area, it may still not properly reflect the actual surface area prior to oxidation, as it uses only an estimate of average pore size (with unknown geometry). The authors found a higher increase in mass during the initial 20 h long thermal cycle for porous AISI 316L compared to porous AISI 434L, but the oxidation growth rates of porous AISI 316L, AISI 434L, and mixtures of the two steels were very similar thereafter [130].  2.1.3. Gas permeability measurements In a fuel cell, the reactant gases react within the electrodes at interfaces between ionic conductor, electronic conductor, and gas phase, known as Triple Phase Boundaries (TPB), that are completely connected to the source of each reacting species [131]. Traditionally, reactant gases are supplied to planar cells by means of flow channels machined into both sides of each interconnect [132]. From these channels, the reactant gases must diffuse through the fuel cell support and the fuel cell electrodes towards the TPB to react, and the reaction product and unreacted gases diffuse outwards through the electrodes and the cell support to the flow channels to leave the cell. In this work, the gas permeability through the specimens was measured due to the use of a simple experimental setup. In order to calculate the gas permeability through the analyzed specimens, the flux of helium or air molecules through the various oxidized porous AISI 430 substrates was measured at room temperature, and the results are presented in section 5. Permeability of gases and liquids through porous solids can be measured in many different ways. Vacuum systems can be used to calculate the permeability of materials [133], [134], [135], [136]. For example, Bodosci et al. measured gas permeability through concrete by recording the pressure drop created by a specimen as a function of the different applied pressures to the other side of the specimen [137]. Often, however, these experiments take a long time, depending on the permeability of 23  the specimens. Other methods used to measure permeability include the use of variable volumes on each side of the specimen [138]. However, Todd et al. found that the accuracy of measurements using variable volume was often influenced by small temperature and atmospheric pressure changes [138]. Stern et al. found 15‐30% differences between measurements of gas permeability compared between variable volume and variable pressure methods, and attributed this effect to long gas residence times and a long time to steady‐state in case of the methods relying on variable pressure [139]. Zelengur et al. measured the changes in air velocity through porous media at room temperature to calculate permeability [140]. Davis et al. developed a method by which two chemically different gas streams separated by the porous specimens flow past the specimens, and the impurity content of the respective other gas is measured in each exhaust stream [141]. In this work (section 5), a permanent pressure was applied to one side of the specimen, and the resulting volumetric gas flow was measured. This measurement was performed for specimens oxidized at various temperatures for different durations, to characterize the influence of oxidation on permeability.  2.1.4. Summary and justification for the presented investigation of porous stainless steel oxidation Since the oxidation growth rate data of porous metals are usually simply related to the outside dimensions of the investigated specimens and only rarely related to the actual surface area of the system, comparisons between different microstructures are difficult. Furthermore, previous studies indicate that the higher the porosity, the faster will be the oxidation mass gain, but the porosity was often low (4%), and is sometimes only estimated or not measured [117], [124], [130]. The analyses typically disregard the pore size distributions and microstructures of the materials. Also, previous studies often focus on one single oxidation temperature. For devices, such as SOFCs, which may be operated at different temperatures, it is crucial to know the behaviour of oxidation as a function of temperature. Consequently, there is a need to analyze the oxidation 24  behaviour of porous stainless steels parametrically as a function of microstructure, porosity, and temperature, and to measure the oxidation of porous materials while taking into account the actual surface area of the porous structure, thus allowing oxidation results to be directly compared between measurements on materials with different microstructures. Furthermore, gas permeability reduction due to oxide scale formation in porous media impacts on the performance of the SOFC. Measurements of the changes of gas permeability due to oxide formation consequently constitute essential information that complements mass gain analysis. This work correlates the effects of temperature, specimen porosity, and microstructure on oxidation kinetics, and combines the findings with the observed changes in gas permeability.  2.2.  Oxidation of spherical stainless steel microspheres  The material investigated in section 6 was stainless steel AISI 440C (UNS S44004) powder [142], [143], [144], [145], [146], a material that has been demonstrated as a thin film porous sintered stainless steel support for SOFCs that could provide flexibility under mechanical load without breaking the SOFC [147]. The application of AISI 440C powders in metal injection moulding (MIM) processes has been studied extensively, making  it  a  good  material  of  choice  for  the  manufacturing  of  SOFCs [148], [149], [150], [151]. However, Wohlfromm et al. have reported that sintering of AISI 440C (16.7‐17.2 mass% Cr) steel powders has to be performed in a very narrow temperature window to avoid the formation of undesired microstructures [151]. They also found that nitrogen and carbon present in the alloys reacted with Cr and so depleted Cr from the Fe‐Cr solid solution near the surface, reducing the oxidation resistance of the alloy [151]. In oxidizing environments, Fe and Cr oxides are typically the major oxidation products on the surface of ferritic stainless steels. Onto these surface films, oxygen adsorbs and diffuses into the underlying bulk structure. During oxidation of chromia forming alloys (for example AISI 430 (Fe‐16Cr) [152], alloys with approximately 25 mass% chromium and 20‐35 mass% nickel [153], alloys with 10‐30 mass% 25  chromium [154], or pure chromium [155]), some oxygen ions diffuse through surface oxides to form oxide at the surface oxide layer / bulk metal interface. However, the majority of the oxide growth is dominated by metal ion diffusion to the oxide / air interface [152], [153], [154], [155],  with  preferential  diffusion  through  grain  boundaries [153], leaving behind porosity at the metal / oxide interface [154]. The overall diffusivity of metal and oxygen ions determines the oxide growth rate in the case of a dense oxide layer. Inert marker layers of, for example, gold can be applied at the diffusion interface to find out exactly which diffusion mechanism is dominant in a diffusion couple [156]. Differences in molar volumes and thermal expansion coefficients between the oxide and the substrate can lead to stresses and cracking at the oxide layer / bulk metal interface [157], [158], [159]. If such cracking leads to spallation of the oxide scale, the oxide layer is no longer protective and rapid oxidation will occur on the metal surface underneath the spalled oxide. The initial formation of nano‐scale oxide layers on such as‐formed metallic surfaces is well studied [160]. These initial oxide layers are part of the material surfaces that are characterized by BET surface analysis, which can give information about the pore structure (up to 150 nm diameter pores) and surface morphology of the spherical particles prior to high temperature treatment. The composition and microstructure of this initial layer determines the growth mechanism of further oxidation [160]. Saeki et al. found that during the initial 15 seconds at 1273 K, dense AISI 430 sheet produced a thin (<1 nm) Fe2O3 layer, which was grown over by Cr2O3 until the end of their experiments (after 180 seconds) [161]. Jin et al. found that an effective oxidation barrier is formed once a dense chromium oxide layer has formed on the surface [160]. The authors furthermore found that Fe and Cr oxides are the major oxidation products on a wide variety of stainless steels (0‐80 mass% Cr, 0‐25 mass% Ni, 0‐4 mass% Mo) investigated under various atmospheric conditions. Jin et al. also observed that the oxide film thickness decreases with increasing Cr concentration in the stainless steel, and that the Cr concentration in the oxide layer is typically higher than the Fe concentration [160]. Oxidation rates of Fe‐25.6Cr and Fe‐26.8Cr‐6.5Mo were reported 26  to be between the rates of pure Fe and pure Cr [162]. Jin et al. [160], Olefjord et al. [163], Covino et al. [164], and Bjornkvist et al. [165] found that after exposure to pure oxygen at a pressure of 20.3 kPa at room temperature for one hour, the oxide films on pure iron were approximately five times thicker than on pure Cr (1 nm) [166]. Oxide scale compositions of Cr2‐xFexO3 [167], Cr2O3 [168], and mixtures of Fe and Cr oxides [168] on stainless steel surfaces were also observed. An x‐ray photoelectron spectroscopy (XPS) study by Castle et al. on an as‐cast polished Fe16.8Cr alloy surface found that the initial Fe:Cr atomic ratio decreased when exposed even to a low oxygen pressure (10 µPa) at 673 K [169]. Didziulis et al. found that as‐polished and solvent‐ cleaned AISI 440C steel was covered by a 2.5 nm thick iron oxide layer on top of a 1.5 nm thick chromium oxide layer, with metal carbides present at the interface between the chromia and the bulk steel [170]. These layers possess similar thicknesses as the major pores on the surface of AISI 440C spheres found by BET analysis in this work. This indicates that the nano pores on the surface of the metal are likely formed by oxide growths with irregularities that are on the same order of magnitude as that of the oxide film thickness. XPS studies by Didziulis et al. showed that the ratio of the molar fraction of Fe and Cr (fFe/fCr) of AISI 440C surfaces decreased from 2.5 as‐prepared to 1.8 after oxidation at 623 K and to 1.17 after oxidation at 723 K [171]. Kotenev et al. noticed that Fe18.1Cr steel exhibits changes in oxidation kinetics, notably a significant acceleration of oxidation exclusively in the temperature range of 833 K to 843 K [172], [173]. The authors attributed these findings to the temperature boundary of the Fe3O4/FeO phase transformation between 833 K and 843 K. The authors found that certain oxidation mechanisms are temperature dependent and that phase and microstructural changes in the metal can enable or facilitate different oxide growth mechanisms. Liang et al. observed changes in metal microstructure and density for AISI 440C powders heat treated up to 1583 K in an Ar atmosphere [148]. A density increase of the final material from 6.8 gcm‐3 to 7.2 gcm‐3 and a volume change of 5‐14% were observed as a result of the different heat treatments at 1483 K – 1563 K. These are  27  macroscopically observable indicators of the microstructural changes that occur during heat treatment which could influence oxidation behaviour. Many different alloys, for example AISI 304 [174], 316L [104], 430L [175], and Fe30Cr [176] have been prepared by powder metallurgy. Molin et al. found that porous AISI 316L specimens produced by sintering metal powders formed (Fe,Cr)2O3 in air at 673 K and 1073 K, and Cr2O3 in humidified hydrogen at the same temperatures [104], but no correlation between the material microstructure and the oxidation behaviour was presented by the authors [104], [124]. Antepara et al. found that the mass gain of sintered porous Fe30Cr alloys during oxidation in air at 1073K increased with increasing porosity [176]. However, the results were not correlated to total surface area. Paldey et al. found that the oxide scales formed on dense, flat AISI 440C sheets spalled when exposed to temperatures between 1173 K and 1273 K, even for short time spans of under ten hours, and that coating an AISI 440C flat sheet with Fe‐Al layers prevented spallation for fifty hours at 1173 K with an accompanying mass gain of 3.3 mgcm‐2, compared with 0.75 mgcm‐2 for an AISI 304 dense flat sheet. On the other hand, oxidation mass gain for a dense AISI 440C sheet was a factor of approximately three lower than for a dense AISI 304 sheet at 1073 K [174]. The changes in crystal structure, microstructure and surface oxides after prolonged exposure to high temperatures (above 873 K) were not investigated by the authors [174]. Many shrinking models describing chemical reactions on particles with a shrinking diameter exist [177], [178], [179]. In most of these cases, however, the reaction rate of diffusion constant of the materials is known. This work takes a different approach. By measuring the mass gain of the material, a corresponding mass gain rate constant was calculated. The mass transfer coefficients and diffusion properties of oxygen on the surface of the spherical AISI 440C particles were not measured. Future extensions to this model will incorporate such assumptions.  28  2.3.  Protective coatings for stainless steel materials in SOFCs  SOFCs can use a wide variety of fuels that include hydrocarbons and carbon monoxide, giving SOFCs high operational flexibility [180], [181], [182]. Furthermore, operating temperatures below 1123 K enables the use of stainless steel as a material for SOFC components, such as cell substrates, interconnects, and balance of plant [42]. Metals typically have higher mechanical toughness and lower cost than traditionally used cermet or ceramic support layers. However, metallic substrates introduce new challenges to SOFC operation. Metals are more susceptible to degradation in the operating  conditions  of  either  highly  oxidizing  or  reducing  moist  atmospheres [106], [183], [184]. Such conditions are experienced on either side of the interconnects that connect single fuel cells in series. In order to decrease the rate of oxidation, protective surface coatings can be applied on the steels used in SOFCs [185], [186], [187]. Spinel coatings such as MnCo2O4 have been shown to lower the oxidation rate of stainless steel by two orders of magnitude (see Table G.2 in Appendix G) [401]. Oxygen diffusion through spinel coatings has been studied for many metals and ceramics [188], [189] and chromium diffusion in steels has been studied for several alloy compositions [190], [191], [192], [193], [194], [195]. Knowledge of the diffusion behaviour in metals is important, since chromium depletion in alloys can lead to phase changes if the Cr content falls below 7.5 mass%, as reported by Amadou et al. [196]. Furthermore, regions with reduced chromium content in steel following thermal treatment or oxidation can be replenished with Cr by prolonged heat treatment and chromium diffusion [197]. Self‐diffusion coefficients of radioactive tracers have been extensively studied for single‐cation oxides such as NiO [198], MgO [199], [200], or CoO [201], [202], [203], [204]. The chemical diffusion coefficient, measured by conductivity relaxation experiments where the material response to abrupt changes in gas composition at constant elevated temperatures is measured, has also been studied extensively for single‐cation oxides such as CoO [204], [205], [206], [207], [208], [209], [210], [211]. The surface reactivity and diffusivity of CoO was investigated by Morin et al., who found 29  slow  surface  reaction  kinetics  in  various  atmospheres,  including  pure  oxygen [212], [213]. The authors explain that this phenomenon is not readily observed, and mention that it is often missed in other studies, and that it has only been reported for thin (<17 µm) specimens of Cu2O and NiO [192], [214]. Spinels have been found to be stable in SOFC operating conditions, and their conductivities and thermal expansion behaviour allow many different spinels to be used in SOFCs [215]. However, studies of diffusion in spinels are less common and have mostly focused on iron‐containing devices [216], where such diffusion processes are of interest to the engineering of joints between spinels. Furthermore, studies involving diffusion in spinels typically focus on self‐diffusion and do not include the diffusion of other cations such as chromium in the spinel, unless the spinel itself contains chromium.  2.3.1. Cr diffusion through spinels ‐ spinels containing Cr The diffusion coefficient of chromium through ceramics has been studied for some materials such as chromia [189], chromium‐containing spinels of type MCr2O4 (M=Fe [217], [218], Mn [217], [219], Ni [220], Mg [221], Co [222]), and other select spinels such as NiAlCrO4 [220]. Gilewicz‐Wolter et al. found that in an SO2 atmosphere with <0.01% oxygen at 105 Pa and 1173 K, radioactive manganese tracers diffused by bulk volume diffusion, and chromium and iron diffused through high‐diffusivity paths such as along free surfaces of cracks and grain boundaries [219]. Chulkalkin et al. found that 1 MeV neutron radiation can distort the lattice periods and symmetries in spinels, which can change the diffusion properties [223]. Toepfer et al. found that for (CrxFe1‐x)3O4 spinels at 1473 K, the diffusion of iron, cobalt and manganese tracers was approximately four orders of magnitude faster than chromium tracer diffusion [218]. Sakai et al. observed an enrichment of iron on the surface of spark plasma sintered MnCrFeO4 spinels, a simultaneous depletion of chromium at the surface of more than one order of magnitude, and a less pronounced reduction in manganese [236]. They found that the diffusion of  18  O was at least four orders of magnitude higher for  MnCrFeO4 compared with MnCr2O4. 30  2.3.2. Spinels containing Mg and Al Martinez‐Gallegos et al. showed that chromium diffuses through MgAl2O4 (created as a reaction product from hydrated Mg1‐xAlx(OH)2) to form MgAl2‐xCrxO4 at 1273 ‐ 1473 K, but the value of the diffusion coefficient was not determined [224]. Sarkar et al. found that excess Cr2O3 can completely dissolve in MgAl2O4 spinel above 1923 K through the substitution of aluminum ions with chromium ions [225]. At temperatures above 1823 K, the oxidation state of chromium changes to higher values, causing a defective spinel structure, increasing cation diffusion in the spinel and the solid solubility of chromia in the MgAl2O4 spinel structure [226], [227]. Sarkar and co‐workers further found that Cr2O3 forms a solid solution with MgAl2O4 rather than forming a separate phase in both spinel grains and grain boundaries, although some MgAl2O4‐MgCr2O4 formed by the reaction of MgAl2O4 with MgO and Cr2O3 [225]. Dieckmann  and  co‐workers  measured  the  diffusivity  of  iron  tracers  in  (Al0.005Mg0.995)0.9975O at 1473 K and found it to decrease with a reduction in pO₂ (see Table P.1, page 261) [228]. The authors also found that iron tracer diffusion increased with increasing pO₂ for MgAl2O4, and attributed this fact to the presence of two cation sublattices, in which iron ions can change their coordination after oxidation from octahedral to tetrahedral coordination, allowing fast movement of Fe3+ on different sublattices [228], [229].  2.3.3. Other spinels The interactions between MgFe2O4, MgAl2O4, MgCr2O4 and Fe3‐xSixO4 slag were investigated by Donald et al. at 1473 K in a CO/CO2 gas mixture containing 0.1 mPa oxygen [230]. They found that MgCr2O4 and Fe3‐xSixO4 formed FeCr2O4, but diffusion kinetics were not studied. The authors also observed that in spinel mixtures containing the following elements, the respective oxides could be found in varying levels; Mg: 2‐5 mass% MgO, Al: 3‐11 mass% Al2O3, Cr: <1 mass% Cr2O3, showing that the chromium‐containing spinels investigated were the most likely to develop spinel‐type 31  phases at elevated temperatures. Smith et al. found that during precipitation of MgFe2O4 in glass slag, Fe2+ and Mg2+ diffuse to the free surface [231]. Chromium was found to influence the kinetics of the ordering process in Mg(Al2‐xCrx)O4 spinels [232]. The activation energy for Mg‐Al ordering was found to decrease with an increase in Cr content. However, no diffusion coefficients of chromium were measured in Mg‐Al spinels in these studies. Hermeling measured tracer diffusion in (FexMg1‐x)2SiO4 olivine spinels, but did not report the diffusion properties of chromium in the material [233]. Kang et al. measured the electronic conductivity of (MgxFe1‐x)3‐dO4 and found that as the Mg content increases, the ferrite spinel becomes more prone to the formation of interstitial ions, reducing its capacity for oxidation [234]. The self‐diffusion coefficients of iron and titanium in (FexTi1‐x)3‐dO4 were studied by Aggrawal et al., who found that iron diffuses at least one order of magnitude faster than titanium [235]. Hermeling et al. found that due to high bulk diffusion, the contributions of grain boundaries and dislocations to tracer diffusion in (FexMg1‐x)2SiO4 spinels were negligibly small at the measured temperature (1403 K) [233]. The diffusion of radioactive tracers in MnM2‐xFexO4 (M=Zn, Cr) spinels was investigated, for example, by Sakai et al. [236], Lu et al. [237], and Lee et al. [238]. Some of the results are limited to the calculation of the total cation transference number [239], while others list the diffusion coefficients of each individual cation under specific  measurement  conditions  (summarized  in  Table P.1  in  Appendix P)  [236], [237], [238]. However, the studies did not include an investigation of the diffusion of Cr. Dieckmann and co‐workers systematically studied the defect structure and related transport properties of spinel solid solutions (Co,Fe,Mn)3O4 [240], [241], [242] and found that at constant cationic composition, cation tracer diffusion coefficients exhibit distinct minimums indicating changes in diffusion mechanism from interstitial cation to cation vacancy diffusion. The authors also found that the mean cation mobility remained constant, independent of cobalt composition. Chromium ion tracer diffusion, however, was not measured. 32  Diffusion coefficients in cobalt‐iron spinels have not been studied since Co3O4 is not stable at atmospheric pressure at 1473 K [243], and Co‐Fe spinel is thermodynamically stable only at low oxygen partial pressures [244]. Mn‐Co spinel was found to be thermodynamically stable only at a cobalt content smaller than 0.5 [245], [246], and CoFeMnO4 spinel was found to be stable only with a Co content smaller than 0.33 [247]. While the diffusion of elements has been studied for some spinel compositions, the aim was often to determine diffusion of, for example, iron atoms in ferrite spinel materials during bonding at elevated temperatures. Spinels play a major role in surface oxidation of steels [185] as well as in fabrication of devices such as those for ferrite spinel energy storage [216]. For example, in the bonding of two ferrite components, cation diffusion determines the electronic properties of the bonded material [239]. This phenomenon has only recently become more important as SOFC technology migrates towards stainless steel supports and interconnects at lower operating temperatures. This could result in increased levels of chromium in the cell, leading to decreased performance. Protective spinel coatings can prevent the Cr from migrating into the SOFC. Therefore, further basic understanding of the defect structure and transport properties of foreign elements in spinels is essential. With respect to SOFC operation, it is important to minimize the inter‐reaction of chromium with the electrochemically active parts of the cell, and consequently, the diffusion of chromium in both the spinels that grow naturally on steels and in protective layers that are applied to steel surfaces has to be fundamentally understood. In order to determine if a protective coating is capable of preventing Cr ions from reaching the surface of an interconnect and from there to migrate into the electrode, further research into the diffusion properties of Cr in ceramics is necessary. This work analyzes several coating materials that may be candidates for SOFC protective coatings [248]: MgAl2O4, Mn1.5Co1.5O4, MnFe2O4, and MgFe2O4. In order to avoid changes in the diffusion coefficient due to the presence of other elements in any particular metal alloy, Cr2O3 was selected as the source material for Cr ion diffusion. 33  Different interconnect alloys have different chromium contents, and various other alloying contents, and the surface of the steel can become Cr depleted. In fact, Gilewicz‐ Wolter et al. found that a steel plate mounted to a spinel/tracer diffusion couple could change the radioactive iron tracer diffusion by two orders of magnitude, and also influence the Cr and Mn diffusion to a lesser extent [217], [219]. This work investigates the Cr diffusion in spinels using Cr2O3 as the chromium source under accelerated test conditions at temperatures above typical SOFC operating temperatures. The goal of the work presented in section 7 is to calculate a minimum thickness for protective spinel coatings that will prevent chromium migration to their surfaces over the projected lifetime of an SOFC, assuming that the oxide scale does not spall or degrade during that time.  34  3. Objectives As outlined in section 2.1.2, porous metal oxidation is currently not completely understood. Previous investigations often relate oxide mass gain to the outer geometric surface area, which makes comparisons between different metallic microstructures difficult. This work investigates the oxidation behaviour of porous stainless steel, and correlates it with the actual metallic surface area and the radius of curvature of the pores. Consequently, the principal objective of this work was to analyze sintered porous AISI 430 stainless steel specimens with different porosities and metal particle sizes, and to correlate the findings in mass gain normalized to the actual surface area of the material with the pore curvature and porosity (section 4). Porous AISI 430 specimens are currently used in the UBC SOFC group as substrates for plasma sprayed SOFCs, so there is a need to identify a good substrate microstructure for SOFC production, and to characterize the oxidation behaviour over longer times at targeted operating temperatures. Sufficient gas flow through SOFCs is essential to facilitate the electrochemical reactions, and therefore another objective of this work was to characterize the gas permeability of the sintered porous AISI 430 specimens exposed to elevated temperatures (section 5). The results of the permeability measurements can be used as another indicator besides oxidation mass gain for choosing a good SOFC substrate microstructure. Since sintered materials exhibit very complex geometry, the oxidation of spherical stainless steel powders without the influence of sintering necks was also analyzed (section 6). The powders chosen for this work are the powders used at NRC IFCI for metal supported SOFCs, AISI 440C, with similar composition to AISI 430 (Table 2.3). The objective of this part of the research (section 6) was to correlate potential differences in oxidation mass gain to the surface curvature of several sieved steel powder size fractions. The results of the oxidation analysis can be used as a guide 35  to avoid microstructural feature sizes with detrimental oxidation behaviour in porous steels for high temperature applications. Another objective of the spherical steel oxidation measurements was to determine how the mass gain behaviour observed for the different powder size fractions relates to the geometry of the particles. To that end, a model describing the spherical geometry of AISI 440C steel particles was created and explored to explain the oxidation behaviour observed. Besides metal oxidation and the reduction in gas permeability, metallic components in SOFCs may also degrade the electrochemical performance due to the volatilization of Cr. Spinel coatings have been found to be stable in SOFC operating environments, to have reasonable electrical conductivity at operating temperatures, and to reduce the Cr volatilization in SOFCs. Consequently, the last objective of the work was to investigate the diffusion of Cr from a model pure source (Cr2O3) through various spinel materials that have been proposed as protective coatings for stainless steel components in SOFCs, and to project the Cr diffusion behaviour to SOFC operating temperatures of 873 K to 1123 K (section 7).  36  4. Influence of porosity, pore size distribution, and pore surface curvature on stainless steel oxidation Section 4, Tab: 0, Fig: 0, Eq.: 0  4.1.  Material characterization  A literature review of the oxidation of porous stainless steels is presented in section 2.1.2. In this work, porous ferritic AISI 430 stainless steel substrates (Mott Corporation, Farmington, CT, U.S.A.), identified by media grade (MG) and powder metallurgically produced and sintered as disc shapes in reducing atmosphere, were analyzed. The media grade of a specimen expresses the minimum particle size (in μm) of particles in a suspension that can be blocked by the porous stainless steel filter medium in aqueous environments. AISI 430 was selected for the oxidation experiments of sintered stainless steel presented in this work since it has a good CTE match with the other components of the cell, is easily available and not covered by intellectual property restrictions as some of the newer alloys are, and generally has lower cost than alloys with higher alloying content (such as Cr, Mo) [27], [249]. The compositional analyses of the materials before and after sintering are shown in detail in Appendix B (page 181). The Cr content was lower after sintering compared with the initial steel powders. The ratio of the molar fractions of chromium atoms to iron atoms fCr/fFe (Figure 4.1) changed from the production of the alloy (Table B.1, page 181) to the sintered product used in the oxidation experiments (Table B.2, page 182). Specifically, the sintered alloys contained less Cr, which may result in not completely protective chromia scales that form on the surface during oxidation. The company selling the sintered products was unable to provide further details of the sintering process.  37  Figure 4.1: Ratio of molar fractions fCr/fFe of the different porous AISI 430 specimens analyzed in this work, compared before and after sintering. The substrate geometry chosen for the production of SOFCs at the UBC and UofT SOFC groups has a disc shape. The average diameter, Ddisc, thickness, tdisc, and volume, Vdisc, of the analyzed disc shaped specimens are shown in Table 4.1. The dimensions of the specimens were measured on four different specimens of each kind, recording four measurements of thickness and four measurements of diameter per disc. Table 4.1: Average bulk volume of the sintered AISI 430 discs (Vdisc). MG 0.2 0.5 1 2 5 40 100  Average diameter Ddisc (10‐3 m) 25.7±0.01 25.2±0.04 25.4±0.05 25.4±0.03 25.4±0.02 25.2±0.04 25.7±0.13  Average thickness tdisc (10‐3 m) 1.52±0.01 1.63±0.04 1.50±0.02 1.67±0.03 1.60±0.01 2.11±0.02 2.37±0.05  Average volume Vdisc (10‐7 m3) 7.85±0.03 8.11±0.21 7.61±0.12 8.47±0.16 8.08±0.03 10.5±0.07 12.3±0.19  38  4.2.  Porous metal foam characterization  4.2.1. Surface profilometry Surface profilometry (Pneumo Form TalySurf Series 2 Stylus Profilometer, Ametek Ultra Precision Technologies, Paoli, PA, U.S.A.) was performed using a stylus with a 5 µm diameter spherical diamond tip to analyze the surface of the metallic substrates [250]. Large, deep gaps between solid metallic protrusions increase the difficulty of continuous fuel cell layer production on the surface and consequently a low surface roughness is preferable. Since thermally sprayed layers may spall from flat, dense surfaces, some surface roughness is advantageous for SOFC production [251]. The specimens were fixed on a 2‐D (y/z) table (Accudex, Pittsburgh, PA, U.S.A.) at a set height (z), while the stylus was pulled over the surface by a mechanical arm in the x‐direction. The profilometer was calibrated on the surface of a 2.55 cm diameter traceable reference sphere. For two dimensional surface profiles and roughness measurements, a 2 cm long line was measured at a speed of 0.5 mm/sec. For the three dimensional measurements a 2.5 x 2.45 mm area was scanned in 100 lines with 100 data points collected along each line. At the end of each recorded line, the table moved one increment in the y‐direction, and the stylus was pushed back to its original starting position. The data were collected by the software Taylor Hobson Ultra (K510/1038‐02, Issue 6), and the surfaces analyzed by Talymap Universal software. To obtain the surface roughness, Ra, recorded surface profiles were normalized so that the overall mean of the recorded surface height (Zh) values was set to zero. This normalized line was laid on a Cartesian coordinate system wherein the mean line was in the x‐direction, and the surface height was plotted in the z‐direction. Ra was the resulting arithmetic mean value of all n recorded values of surface height Zh (Eq. 4.1). R  1 n  Z  Eq. 4.1  The values of Ra recorded for each specimen type can be seen in Figure 4.2. Both the surface roughness and the measurement deviation (of the measurements of the 39  front and backsides of three specimens of each type) increased significantly for the larger media grade specimens (especially MG40 and MG100 specimens).  Figure 4.2: Surface roughness, Ra, of porous AISI 430 specimens with various microstructures, indicated by media grade. Low surface roughness may be beneficial in minimizing defects during fuel cell production, depending on the utilized production method. However, such a microstructure can be restrictive for gas permeability. The influence of oxidation of porous metallic specimens on gas permeability through these specimens is described in section 5.4. To confirm the stylus surface profilometry results, optical surface profilometry analysis was attempted, but scanning the metallic substrates resulted in unreliable data due to the shiny metal surfaces with deep grooves. Figure 4.3 to Figure 4.16 show the surface reconstructions of the porous AISI 430 discs recorded by the mechanical stylus profilometer and SEM surface images of the analyzed specimens. The figures show that the porosity and surface roughness increase with increasing media grade.  40  Figure 4.3: Surface of an MG0.2 specimen recorded by stylus profilometry.  Figure 4.4: SEM micrograph of the surface of an MG0.2 specimen.  Figure 4.5: Surface of an MG0.5 specimen recorded by stylus profilometry.  Figure 4.6: SEM micrograph of the surface of an MG0.5 specimen.  Figure 4.7: Surface of an MG1 specimen recorded by stylus profilometry.  Figure 4.8: SEM micrograph of the surface of an MG1 specimen.  41  Figure 4.9: Surface of an MG2 specimen recorded by stylus profilometry.  Figure 4.10: SEM micrograph of the surface of an MG2 specimen.  Figure 4.11: Surface of an MG5 specimen recorded by stylus profilometry.  Figure 4.12: SEM micrograph of the surface of an MG5 specimen.  Figure 4.13: Surface of an MG40 specimen recorded by stylus profilometry.  Figure 4.14: SEM micrograph of the surface of an MG40 specimen.  42  Figure 4.15: Surface of an MG100 specimen recorded by stylus profilometry.  Figure 4.16: SEM micrograph of the surface of an MG100 specimen.  Figure 4.17 shows some typical cross sections of the different AISI 430 specimens. The images were taken with an optical microscope (Clemex microscope, 100x magnification) using polished cross sections of the porous AISI 430 specimens. Image analysis (Clemex Vision, Clemex Technologies, Guimond, QC, Canada) was performed to measure the surface area of the metal. The images in Figure 4.17 show the change in microstructure from many very fine pores (MG0.2 specimens) to fewer, larger pores in the MG100 specimens.  43  A  B  C  D  E  F  G  Figure 4.17: Polished cross sections of the various AISI 430 specimens: (A) MG0.2, (B) MG0.5, (C) MG1, (D) MG2, (E) MG5, (F) MG40, and (G) MG100. 44  4.2.2. Porosity measurements Various methods to measure porosity exist, and for each method many different experimental procedures have been developed. While there is no one individual measurement that could be identified to have the best characteristics of all measurements, each measurement has its own set of advantages and drawbacks, including cost, availability of instruments, or porosity type analyzed (open or closed). The differences between the porosity measurement methods are identified in Appendix C, outlining the advantages and disadvantages of using the different methods. It was shown that porosity measurements need to be quoted with respect to the measurement method used in order to be comparable between different analyses. In this work, four methods of porosity measurement were compared. The porosity of the materials was analyzed by the Archimedes method [385], using a balance with a specimen dish that allowed weight measurement in air and under water (PG‐203‐S, Mettler Toledo, Mississauga, ON, Canada). To prepare the disc‐shaped sintered porous AISI 430 specimens for the measurement, the pores had to be filled with water. This was done by inserting the specimens in an alumina holder specifically designed for this method (shown in Appendix D). In this holder, the specimens can stand upright in a beaker filled with distilled water without touching the heating plate installed below the beaker, thus reducing the risk of entrapment of gas inside the pores. The glass beaker in which specimens and holder were immersed in held at least 23 cm of distilled water above the specimens. Evaporating water was allowed to cool and condense on a heat exchanger. The specimens were boiled in water in order to allow water to penetrate the pores over a period of 15 hours, followed by soaking for an additional 24 hours. Image analysis (Clemex Vision, Clemex Technologies, Guimond, QC, Canada) on optical micrographs (Clemex microscope, 100x magnification) was performed on polished (1 µm diamond surface finish) cross sections [252]. Mercury porosimetry (Autopore IV 9500, Micromeritics, Norcross, GA, U.S.A.) was performed in order to identify the pore structure by the intrusion of liquid mercury at different pressures 45  ranging from 9.5 kPa to 0.2 GPa, which corresponds to pore size diameters of 131 µm to 5 nm [253]. The porosity measurements by image analysis, Archimedes method, and mercury porosimetry were compared with measurements of physical substrate mass and dimension combined with calculations of theoretical density from XRD (D8 Advance, Bruker AXS, Karlsruhe, Germany) determinations of unit cell volume (XRD / mass). The theoretical density in this work was calculated from unit cell analysis with information obtained by x‐ray diffraction (XRD). Figure 4.18 shows the XRD spectra of the as‐ received porous AISI 430 specimens. The recorded XRD patterns were compared with the database shown in reference [254].  Figure 4.18: XRD patterns of as‐received porous AISI 430 specimens, showing a typical Fe‐Cr steel pattern (black dots), such as the pattern shown in reference [255]. 255  If stresses remain within the material structure due to sintering, they are smaller than can be resolved with the presented method. The BCC ferritic stainless steel XRD peaks of the reference [255] align with the measured XRD peaks. The inter‐atomic spacing dhkl of the diffraction planes of the materials was calculated from the data in Figure 4.18 using the Bragg equation (Eq. 4.2), and assuming that only negligible stresses exist in the materials [256]. 46  n λ Eq. 4.2 2sinθ In Eq. 4.2, nB is an integer determined by the Bragg order, λ is the wavelength of d  the CuKα radiation (0.154 nm), and θ is the angle between the incident ray and the scattering planes. Using the diffraction angle θ from the XRD data shown in Figure 4.18, the unit cell parameter ahkl of the body‐centered cubic (BCC) phase was determined using Eq. 4.3 and the Miller indices h, k, and l [257], [258]. h  d  a  k  The average unit cell volume,  a3hkl ,  l  Eq. 4.3  of each specimen type was determined from  the unit cell lengths calculated for each of the crystallographic (111), (200), (211), (220), and (310) planes found by XRD (Figure 4.18). The theoretical density ρt of the materials was calculated by dividing the average atomic mass ma3 of the unit cell of each hkl  specimen (based on composition) by the unit cell volume [259] (Eq. 4.4). m  ρ  Eq. 4.4  a  The average atomic mass ma3 of the unit cell of each specimen was calculated hkl  by dividing the average molar mass Mav of the specimen (based on atomic composition) by Avogadro's number Na (6.022 x 1023 mol‐1) and multiplying it by the number of atoms na3 present in each unit cell (two, in the case of a BCC lattice) (Eq. 4.5). hkl  M  n  m  Eq. 4.5  N  The bulk density ρ of the porous specimens, the ratio of the mass of the solid material present in the specimens to the volume of the solid in each specimen and the voids within the solid, was calculated by dividing the mass of a specimen mdisc by its geometric volume Vdisc (calculated by measuring the outer dimensions of the porous specimens such as thickness tdisc and diameter Ddisc) [395], [260]. The resulting density value ρ (Eq. 4.6) was averaged for four measured specimens per media grade. ρ  m πt  m V  Eq. 4.6  The percent porosity Pp was determined using Eq. 4.7 [261]. 47  ρ Eq. 4.7 ρ The porosity values obtained by the different methods are shown in Figure 4.19. The P  100 1  measurement deviations derive from the analysis of multiple specimens of each type for each individual measurement method.  Figure 4.19: Results of the different porosity analyses performed. The resulting values of porosity vary between the methods used. Mercury porosimetry results in lower porosity values than the other three methods. The porosity of MG100 could not be determined by mercury porosimetry as its open pore structure did not allow the instrument to determine the outer geometric volume (the volume measured when using a calliper on the outside of the specimens) of the material. Some mercury intrudes into the largest pores without applying any pressure. The other three methods, Archimedes method, image analysis, and XRD / mass analysis are in good agreement with each other, varying by an amount ranging from ±1% porosity for MG0.2 specimens to ±2% porosity for MG100 specimens, which is in good agreement with differences of ±2% porosity found between various porosity measurement methods by Bruckschen et al. [367]. Including mercury porosimetry analysis, values differ up to ±4% in porosity. Both image analysis and XRD / mass analysis determine the total (open and closed) porosity, and could consequently be expected (and were found) to yield the 48  highest porosity values. Porosity values determined by image analysis had the largest measurement deviations, especially for the large pore structures of MG40 and MG100 specimens. Image analysis was consequently found to be more useful for porosity analysis on specimens with a microstructure that is more similar to MG0.2‐MG5 (with average pore sizes of less than 14 µm). BET surface area analysis (SA3100, Beckman Coulter, Fullerton, CA, USA) was also attempted on the specimens. However, it was determined that the surface area of the specimens was lower than the minimum limit that the instrument could analyze. Consequently, the surface area was determined by image analysis on polished cross sections and the porosity was analyzed by the methods presented here.  4.2.3. 3‐D pore morphology Mercury porosimetry was used to provide insight into the internal structure of the pores. Figure 4.20 shows the pressure at maximum incremental mercury intrusion, the pressure at which the highest incremental volume of mercury penetrates a porous specimen, as a function of porosity for the different porous AISI 430 specimens that were investigated. Smaller pore sizes require a higher pressure to intrude mercury into the pore. Depending on the specimen pore size distribution, different volumes of mercury may be intruded at different pressures. The pressure at which the highest volume is intruded indicates the pore size diameter which occurs most prevalently in the specimen. For the specimens studied, the pore size diameters and total porosity both increased with increasing media grade (Figure 4.20).  49  Figure 4.20: Pressure at maximum incremental mercury intrusion and pore size diameter as a function of porosity of the analyzed AISI 430 specimens. As shown in Figure 4.20, there was a significant increase of pressure at maximum incremental mercury intrusion between MG0.5 specimens (with 19% porosity) and MG0.2 specimens (with 17% porosity), and between MG2 specimens (with 28% porosity) and MG1 specimens (with 23% porosity). Consequently, the pore sizes of MG0.5 specimens and MG1 specimens, as well as MG2 specimens and MG5 specimens, respectively, are similar. As will be shown in section 5.4, the gas permeability for MG2 and MG5 was significantly higher than for the lower media grade specimens. These two specimens are consequently good candidates for SOFC substrates. This observation will be discussed in further detail in sections 4.5 and 5.5 in combination with the oxidation kinetics and gas permeability studies. The relation between applied mercury pressure, pHg, and pore diameter, Dp, is described by Eq. 4.8, assuming cylindrical pores [262], [263].  D  4γ cos θ p  Eq. 4.8 50  Here, γHg is the surface tension of liquid mercury (0.485 N/m), and θc is the contact angle of mercury on the specimens (130°) [264]. Ellison et al. found that the contact angle of mercury on polished stainless steel is in the range of θc=123°‐146° at 298 K [265]. In this work, the instrument standard contact angle for stainless steel surfaces (130°) was used [264]. Strictly, Eq. 4.8 is only valid for smooth surfaces. Better descriptions of the wetting of rough surfaces are the models developed by Wenzel [266], [267], [268] (Eq. 4.9) and Cassie‐Baxter [269].  cos θ∗  ω cos θ  Eq. 4.9  In Eq. 4.9, θc* is the apparent contact angle that corresponds to the minimum free energy state of the system, and ωr is the roughness factor which is a measure of how the roughness affects the wetting of a homogeneous surface. The surface roughness factor was not used in this work, further research is necessary to investigate its exact value. As a result, the pore size diameter determined in this work will be slightly underestimated. Figure 4.21 shows the graph resulting from converting mercury pressure into pore size diameter and correlating it with porosity, using the data shown in Figure 4.20. The pore size diameter of the porous AISI 430 discs increases with porosity. Figure 4.21 correlates both the pore size diameter that corresponds to the maximum incremental mercury intrusion (from Figure 4.20), and the pore size diameter that corresponds to the point of inflection of a cumulative volumetric mercury intrusion versus pressure curve, also referred to as "characteristic length", to specimen porosity.  51  Figure 4.21: Pore size diameter at maximum incremental mercury intrusion and characteristic length (pore size diameter at point of inflection of cumulative mercury intrusion as a function of pressure) shown as a function of the AISI 430 porosity measured by the XRD/mass method. Error in pore size diameter derives from multiple measurements of the same specimen type; error in porosity is due to the experimental error of the XRD/mass measurements. For specimens that have a narrow pore size distribution, the pore size diameter corresponding to the maximum incremental mercury intrusion and the diameter that corresponds to the characteristic length are very similar. This can be seen in Figure 4.21 for specimens MG0.2 (17% porosity) to MG5 (31% porosity). MG40 (50% porosity) and MG100 (60% porosity) specimens have broader pore size distributions, and consequently, the values of characteristic length and pore size diameter at maximum incremental intrusion differ significantly more for MG40 and MG100 specimens than for the other specimens. It was observed that the pore size diameter at maximum incremental intrusion increased by 2.5 μm from 3.2 μm for MG0.2 specimens (17% porosity) to 5.7 μm for MG0.5 specimens (19% porosity). However, the increase of pore diameter at maximum incremental mercury intrusion from 5.7 μm for MG0.5 specimens (19% porosity) to 7.2 μm for MG1 specimens (23% porosity) was only 1.5 μm, despite an 52  increase in porosity of 4%. Structural effects such as pore size distribution and tortuosity are present that influence the pressure necessary to intrude mercury into the specimens. For example, the pressure needed to intrude mercury into MG0.2 (17% porosity) specimens was almost twice as high as the pressure needed to intrude mercury into MG0.5 (19% porosity) specimens, despite an only two percent difference in porosity. For the specimens with a porosity value below 19% (MG0.2), the changes of the pore size diameter with porosity were found to differ from those in the 19‐50% porosity region. For high porosity values (for example MG100 specimens with 60% porosity), the increase in pore size diameter with an increase in porosity appeared to be lower than in the 19‐50% porosity region. For an increase in porosity from MG40 specimens (50% porosity) to MG100 specimens (60% porosity), the pore diameter at maximum incremental intrusion increased by the same factor, 1.3, that it increased between the MG0.5 specimens (19% porosity) and MG1 specimens (23% porosity). This indicates that in porous structures with large, open pores, such as found in MG100 specimens (60% porosity), mercury intrusion of the porous structure may occur at low pressures, and material flow through the porous structure encounters little resistance. Consequently, MG100 specimens have large scatter in the value of the pore diameter. The volume of mercury forced into a porous specimen, normalized by the mass of the specimen, shows which pore size is the most prevalent in a given microstructure. The measured specimens with up to 31% porosity all had a well‐defined maximum incremental mercury intrusion at a particular pressure (Figure 4.22). MG40 specimens (50% porosity), and even more so MG100 specimens (60% porosity), exhibited a broader distribution of pore size diameters than found in specimens with finer microstructures (Figure 4.22). With large pores as found for MG100 specimens by mercury porosimetry, the mercury encounters little opposing force in the substrate structure, and measuring such large pore sizes as in the case of MG100 specimens becomes challenging. Such specimens may exhibit small, poorly defined peaks in the pressure‐related intrusion of mercury into the pores, but will also exhibit a broader distribution of pore size diameters at which mercury intrusion occurs. As a result of a 53  broad distribution with no defined peak in the incremental mercury intrusion at any pore size diameter, as in the case of MG100 specimens (60% porosity), the measured porosity value becomes unreliable.  Figure 4.22: Log differential intrusion of mercury as a function of pore size diameter. Inset numbers indicate media grade. Cumulative specific pore surface area SAp can be calculated from the mercury volume intrusion data, assuming that the pores into which the mercury intrudes are cylindrical (Eq. 4.10) [264]. SA  SA  4V D  m  Eq. 4.10  Here, n is the number of pore size diameters measured, Dmp is the mean diameter of the pores, mm is the metal mass of the specimens, and Vin is the incremental intrusion volume at each Dmp. Each discrete pressure at which mercury intrudes into pores corresponds to a defined minimum pore size diameter, and a defined volume of mercury intruded into 54  pores of this size. The volumes were summed for all analyzed pressures, resulting in the cumulative pore volume, from which the cumulative pore surface area was calculated. The cumulative pore surface area in contact with mercury decreased with increasing porosity (Figure 4.23). Figure 4.23 also shows that the pore surface area is low (<0.04 m2/g for all specimens analyzed), which indicates that BET analysis is not a good method to measure the specific surface area these porous AISI 430 specimens.  Figure 4.23: Cumulative specific pore surface area as a function of porosity. Mercury porosimetry was also used to determine the tortuosity of the analyzed specimens. The tortuosity of a porous structure indicates its twistedness. For a curve in 2D, tortuosity (τ) is defined as the length of a curve Lτ divided by the distance Cτ between the ends of the curve (Eq. 4.11) [270]. L Eq. 4.11 C Using mercury porosimetry, the value of τ is determined from Eq. 4.12 using VP τ  as pore volume, ρ as the bulk density of the material, ΔIj as the difference in mercury intrusion volume, Ij, for two adjacent applied pressures (j and j+1), Dj as the average 55  pore diameter for the interval between the two adjacent recorded data points, SAp as the surface area of all n pores, and 1+ε is a pore shape exponent that has been assigned a value of 1 by Carniglia for cylindrical pores [264], [271]. The assumption here is that the material is isotropic. The relation between tortuosity and porosity of the analyzed porous AISI 430 specimens is shown in Figure 4.24.  τ  2.23  1.13V ρ  0.92  4 SA  ∆I D  Eq. 4.12  Figure 4.24: Relationship between tortuosity and porosity of the analyzed AISI 430 specimens, measured by mercury porosimetry. Specimens with low porosities, such as MG0.2 specimens (17% porosity) and MG0.5 specimens (19% porosity) were found to have a high tortuosity (>8) compared with the other specimens analyzed. This means that material flowing through such a specimen has to travel significantly longer distances than it would if it were to travel in a straight line, and, consequently, mass flow through these specimens may be restricted. This will be shown in further detail in the permeability experiments in section 5.4. 56  The tortuosity decreased significantly from approximately 8 for MG0.5 specimens (19% porosity) to approximately 4 for MG1 specimens (23% porosity) and to approximately 2.5 for MG2 specimens (28% porosity). This reduction in tortuosity indicates that the pathways through the specimens with low porosity (below 23%) are more convoluted than the pathways through the specimens with high porosity. Porous structures with 31% porosity (MG5 specimens) had a tortuosity value of 2.2±0.1. This means that the path of a substance permeating these specimens is approximately twice as long as a straight path would be. The specimens with the highest porosity (MG100 specimens, 60% porosity) had a tortuosity value close to unity. The average tortuosity of MG100 specimens was found to be 1.4±0.3, meaning that their structures are so open that permeating matter can almost follow a straight path through the porous structure. Metal oxidation may decrease the pore size of these structures over time at SOFC operating temperatures. It is consequently necessary to not only know the pore structures of the specimens, but also the oxidation and gas permeability behaviour of these materials at operating conditions, which will be analyzed in the later sections of this work.  4.3.  Oxidation behaviour of porous AISI 430  The sintered porous AISI 430 specimens were cleaned by sonication for 15 minutes each in ethanol, acetone, and ethanol again, and then dried with a stream of filtered air followed by drying in air overnight in a drying oven at 353 K prior to recording the initial mass. AISI 430 stainless steel discs were oxidized at 873 K, 920 K, 973 K, 1020 K, 1073 K, or 1125 K in still air (Thermolyne 48000, Thermo Fisher Scientific, Waltham, MA, U.S.A.). The furnaces had a specimen cavity (dimensions: 18x13x26 cm) that was electrically heated through the insulating walls, and they were equipped with a 2.5 cm inner diameter ceramic chute in the top part that was open to the atmosphere. Special ceramic specimen holders were designed that allowed the steel discs to stand upright during thermal treatment, in order to allow the atmosphere to have access to 57  the specimens from all sides of the discs (see Appendix E for the design). The heat treatment of the porous sintered stainless steel specimens is shown in Table 4.2.  Table 4.2: Heat treatment of sintered porous AISI 430 specimens. Temperature (K) 873 1073 973 920 1020 1125  Heating cycles, overall time (h) 10, 25, 50, 100, 500 10, 25, 50, 100, 500 10, 25, 50, 100, 500, 1000 10 h intervals to 100 h, 150 h interval to 250 h, 250 h intervals to 3000 h  }  Number of specimens of each type 4 (2 removed after 100 h) 4 (2 removed after 100 h) 6 (2 removed after 100 h, 2 removed after 500 h) 5 5 5  The temperatures of the furnaces used for the 920 K, 1020 K, and 1125 K experiments were confirmed by National Institute of Standards and Technology (NIST) calibrated thermocouples, and the atmospheric conditions (pressure, humidity, and temperature) in the room in which the furnaces stood were recorded. The humidity of the atmosphere in which the oxidation furnaces were operated at 920 K, 1020 K, and 1125 K was measured once daily. From the average data it was calculated that the atmosphere to which the furnaces were exposed to contained approximately 0.8 mol% water. For the oxidation experiments at 873 K, 973 K, and 1073 K, this calibrated equipment was not yet available. The relative mass change due to oxidation (Δmox,rel) was calculated following Eq. 4.13, where mox is the mass of the oxidized material, and mm is the initial mass of the metallic specimen prior to oxidation. Δm  m ,  m m  x100%  Eq. 4.13  The resulting mass gain graphs are shown in Figure 4.25. The graphs are shown as a function of the square root of time, as it is assumed that the oxidation rate is limited by the diffusion of cation vacancies and oxygen ions through a dense oxide layer. 58  A  B  C  Figure 4.25: Relative mass gain of AISI 430 substrates at (A) 873 K, (B) 973 K, and (C) 1073 K for different microstructures. 59  D  E  F  Figure 4.25, continued: Relative mass gain of AISI 430 substrates at (D) 920 K, (E) 1020 K, and (F) 1125 K, for different microstructures. Inset in (F) shows the changes in slope at short times, especially for MG0.2 specimens, as indicated by the arrow. 60  The microstructures of the specimens were analyzed by SEM over the course of the oxidation experiments. In the case of MG0.2 and MG0.5 specimens, an almost complete disappearance of the initial porous features can be observed at 1125 K (Figure 4.28), which explains the significant reduction in the slope of the oxidation mass gain of the specimens with lower porosities (for example MG0.2, MG0.5, or MG1 specimens, with the onset of the reduction in slope indicated by the arrow in Figure 4.25F), and the reduction in gas permeability over time (as shown in section 5.4). The changes in microstructure during oxidation are shown for MG0.2 specimens at 920 K (Figure 4.26), 1020 K (Figure 4.27), and 1125 K (Figure 4.28). The pores become progressively more filled with oxide as time and temperature increase. Figure 4.28 shows that after 100 h at 1125 K, most of the initial pores become filled with oxide growth. This correlates well with the abrupt change to almost no additional mass gain after 250 h observed for these specimens, as the pore surface area can no longer be easily reached by oxygen molecules. At 920 K, oxidation occurs by small crystallite growth at isolated locations on the surface with little changes in microstructure. At 1020 K, oxidation occurs as a continuous layer over the entire surface. In the case of the MG0.2 specimens, oxide platelets appear after 500 h, and grow in diameter over time. The oxide layer may significantly reduce the access of oxygen molecules to the entire metal surface area, which may be the reason for the significantly reduced oxidation mass gain in the case of the MG0.2 specimens after more than 1000 h at 1020 K, similar to oxygen access limitations for MG0.2 specimens observed after 250 h at 1125 K. At 1125 K, plate‐like growth of oxides can be observed. For some of the low porosity specimens (MG0.2, MG0.5), these plates grow into a dense layer covering the entire surface. For the other microstructures, large (up to 25 µm diameter, with less than 2 µm thickness) plates are distributed over the surface. On all specimens investigated, some small (<1 µm) crystals form after 100 h (not shown here). After more than 1250 h at 1125 K, the microstructure of parts of or of the entire surface of all different porous AISI 430 specimens changes. This is most evident in the case of MG40 specimens. The entire microstructure of both the initial porous metal structure and the oxide layer that 61  formed during the first 1000 h is grown over by a different type of oxide (Figure 4.29) that had a gray sheen and was identified by XRD to be Fe2O3. Mass gain of these MG40 specimens approached the maximum mass gain to be expected for these alloys (Figure 4.25 F, as calculated in Appendix L), and the specimens warped. Similar fast oxidation was observed after more than 2000 h at 1125 K for all microstructures except MG0.2 and MG0.5 specimens, which were covered in a dense Cr2O3 layer even after short oxidation times. This oxide growth limits oxygen access to the metal surfaces and thereby also significantly reduces permeability, as discussed in section 5.4. SOFC operating temperatures at which either effect (closing of pores due to oxidation and appearance of Fe2O3) occurs should be avoided.  A  B  C  D  Figure 4.26: Surface microstructure of MG0.2 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 920 K. Only few oxidation products can be seen, even after long oxidation times.  62  A  B  C  D  Figure 4.27: Surface microstructure of MG0.2 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 1020 K. Oxides close the pores by platelet growth.  A  B  C  D  Figure 4.28: Surface microstructure of MG0.2 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 1125 K. Oxide growths close the pores. 63  A  B  C  D  Figure 4.29: Surface microstructure of MG40 specimens after: (A) 100 h, (B) 500 h, (C) 1000 h, and (D) 2000 h of oxidation at 1125 K. After 2000 h, the original microstructures of both metal substrate and Cr2O3 oxide layer were grown over by a different (Fe2O3) metal oxide (D). The phase of the surface oxides was analyzed by XRD and the composition by EDX (energy dispersive x‐ray spectroscopy). It was found that the oxide scales contained the element chromium (Figure 4.30) with a corundum‐type crystal structure of eskolaite (Cr2O3, Figure 4.31). No other oxides were found within the detection threshold of the methods used for all temperatures and microstructures except at 1125 K, where spots of Fe2O3 oxides appeared after more than 1000 h heat treatment (Figure 4.32).  64  Figure 4.30: EDX elemental map of a cross section of AISI 430 MG0.2 specimens after 1000 h at 1073 K. XRD analysis can be performed by the locked couple method, where the x‐ray emitter and the detector are rotated around the specimen simultaneously, or by a grazing incidence method, whereby the x‐ray emitter is set at a fixed low angle, and only the detector is rotated around the specimen. Since locked couple XRD investigation of the surface oxide showed too much influence of the underlying metallic structure, grazing incidence XRD scans with the x‐ray emission source fixed at an incident angle of 2θ=1° were used for MG100 specimens oxidized for 1000 h at 1073 K (Figure 4.31), magnifying the relative x‐ray diffraction intensity of the surface oxide crystals compared to the underlying metallic phase.  Figure 4.31: Grazing incidence XRD pattern of the surface of a MG100 specimen oxidized for 1000 h at 1073 K. The recorded XRD pattern shown here was compared with literature data: Open triangles: Fe‐Cr phase [255], Circles: eskolaite phase [272].  272  65  The presence of only Cr2O3 on the surface indicates that a protective oxide coating seems to have formed. Only at 1125 K after over 1000 h does Fe2O3 form on the surface, and complete oxidation of the metals in the porous AISI 430 specimens occurs. Chromia is typically a protective oxide, and no spallation was observed in SEM analysis from the surface of the porous specimens, showing that these materials can be considered for SOFC applications. Fe2O3 appeared on the entire surface of MG40 specimens after 1250 h at 1125 K. Additional mass gain was significantly reduced after 1750 h at 1125 K, indicating that almost complete oxidation of the specimens had occurred. The XRD patterns of the crystal phases found on the surface of MG40 specimens after 1500 h at 1125 K are shown in Figure 4.32 and indicate the presence of Fe2O3.  Figure 4.32: Locked couple XRD pattern of the surface of a MG40 specimen oxidized for 1500 h at 1125 K. The recorded XRD pattern shown here was compared with literature data: Rectangles: Fe2O3 [273]. 273  In order to determine the oxide scale thickness after long operating times, the growth rate constants of the specimens were calculated (section 4.4).  66  4.4.  Calculation of growth rate constants from mass gain data  4.4.1. Calculation of area normalized mass change from image analysis on polished cross sections Traditionally, oxide growth rate constants of porous metallic structures are often calculated by relating the observed mass gain to the outer bulk surface area of the analyzed specimens [104], [117], [124]. In this work, the actual metal surface area of the 3‐D structure of the porous specimens was evaluated by image analysis on polished cross sections and used for the area‐normalized oxidation mass change calculations. In preparation, the porous AISI 430 stainless steel discs were impregnated with epoxy and cross sectioned. These cross sections were then analyzed by image analysis in an optical microscope to determine overall (open and closed) porosity and average pore size. Similar information was also obtained by mercury porosimetry. The pore size diameter derived from the peak in the log volumetric mercury intrusion versus pore size diameter graph shown in Figure 4.21 was used to determine the radius of curvature used in this section. Figure 4.33 shows a magnified sample image of a recorded polished cross section of an MG0.2 specimen and the selection of the pores by the software, using two different grey scale settings to estimate the position of the interface. Porosity and SV values were averaged from the values calculated using each of the two grey scale settings.  Figure 4.33: Magnified image of a recorded cross section of a MG0.2 specimen. (A) Optical image. (B) and (C) pores marked by image analysis, using different grey scale settings. Also obtained from the image analysis was the line length of the interface between metal and air as a function of overall cross sectional area, LS. The lengths of all 67  lines with a one pixel thickness on the surface of all the marked pores of each image (Figure 4.33) were summed up in order to calculate the overall line length. If a random distribution of features exists in the specimens, then: S  L  P  Eq. 4.14  In Eq. 4.14, SV is the total surface area per unit volume, and PL is the number of points of phase boundaries per unit length of a line. In the case of the images analyzed, the length of the surface of the metal in contact with the epoxy was obtained and related to the total area shown in the image for which this length was obtained, which is equal to the surface area of the metal per unit volume, if the following assumptions are true: The material is isotropic and the pores are distributed equally throughout the specimens. At higher magnifications, more details may be observed, and consequently slightly higher values of SV were found. A second effect observed was that surface defects such as dirt, scratches, oxidation, polishing residues, and discolorations due to polishing agents (for example, dark particles from diamond polish, and bright smears from acidic alumina suspension) become more pronounced at higher magnifications. Furthermore, the optical components at higher magnifications have larger optical aberration. Another problem encountered was sub‐surface metal shining through the epoxy, especially at higher magnifications, making the analysis more challenging. Images taken at 200x and 500x magnification had large error margins and noticeable light reflections from metal inside pores underneath the surface and did not represent the polished cross‐sectional area well. They were consequently not used for further analysis. Figure 4.34 shows the different calculated SV values for two different magnifications, 50x and 100x. In order to be consistent throughout the dataset, the 100x magnification was chosen for the image analysis of all specimens. A 50x magnification is typically too small, as details are not very clear.  68  Figure 4.34: SV of as‐received, cleaned porous metal specimens as a function of media grade, shown for 50x and 100x magnification. The results from Figure 4.34 were combined with the results from Table 4.1 to obtain an average surface area per specimen (Eq. 4.15). A  S ∗V  Eq. 4.15  Here, AS is the average total surface area of one specimen before oxidation and Vdisc the average volume per specimen before oxidation. The error analysis was done as follows. It was assumed that the standard deviations of volumetric measurement (σvol), mass change (σox), and SV measurements (σSv) were all independent. Each individual standard deviation σ is given by Eq. 4.16, where n is the number of data points collected: 1 n  σ  x  x  Eq. 4.16  The arithmetic mean ̅ of the values xi is given by Eq. 4.17: x  1 n  x  Eq. 4.17  Here, x̄ and xi are the average values and data points of the respective measurements (i.e. volumetric measurement xv̄ ol and xi,vol, oxidation mass change xō x and xi,ox, and 69  surface area per volume xS̄ v and xi,Sv). Since the results of all three measurements are multiplied with each other, the resulting total standard deviation σtot is calculated as in Eq. 4.18 [274]. σ x  σ x  σ x  σ x  Eq. 4.18  Here, xtot is the resulting value of the product of the calculations, for example oxidation rate constant (defined later). The mass gain data (Figure 4.25) were converted into surface area (AS) normalized mass gain Δmox,s (Eq. 4.19) by subtracting the initial metal mass mm, from the oxidized oxide and metal mass, mox, and dividing the resulting oxide mass by the surface area AS. Δm  m  m ,  A  Eq. 4.19  The resulting graphs of area normalized mass gain versus the square root of time are shown in Figure 4.35. A precipitous mass increase can be observed from the start of the experiment to the first measured mass value, although less noticeably so at higher temperatures due to the larger scale of the area normalized mass gain. Bautista et al. attributed this phenomenon to the formation of a continuous oxide layer on the surface of the material. Such a layer may reduce the direct air ingress to the entire surface that was available prior to oxidation [129]. Additionally, small pores may close throughout each specimen. They also suggested that subsequent oxidation of surfaces closed off from direct access to air then may rely on solid‐state diffusion or micro‐channel transportation of oxygen through the formed oxide layer. Since the mass changes during the initial 1500 h are barely distinguishable in Figure 4.35 F, the data up to 1500 h are shown in Figure 4.36, emphasizing the mass changes of the specimens before the onset of the rapid mass increase due to Fe2O3 formation. The data for MG40 specimens were also excluded from the graph in Figure 4.36 as the onset of the rapid Fe2O3 formation occurred earlier than 1500 h from the start of the experiment. The reduction in area‐ normalized mass gain of the MG0.2 specimens after 250 h and MG0.5 specimens after 500 h resulting from the closing of the pores due to oxidation can be seen in Figure 4.36. 70  A  B  C  Figure 4.35: Area (As) normalized oxidation mass change of porous AISI 430 specimens at (A) 873 K, (B) 973 K, and (C) 1073 K for different microstructures. As was determined by image analysis. 71  D  E  F  Figure 4.35, continued: Area (As) normalized oxidation mass change of porous AISI 430 specimens at (D) 920 K, (E) 1020 K, and (F) 1125 K, for different microstructures. As was determined by image analysis. 72  Figure 4.36: Area normalized oxidation mass change of porous AISI 430 specimens at 1125 K, for different microstructures, magnifying the changes in mass gain for the first 1500 h, which are barely visible in Figure 4.35 F. As will be shown in section 5.4, the measurable gas permeability through the specimens becomes restricted due to oxide growth. The influence of oxidation growth on the ability of oxygen molecules to reach the surfaces of all pores throughout the specimens was more noticeable for finer microstructures and at higher temperatures. At 1020 K, MG0.5 specimens appeared unaffected by the surface‐area reducing effect of oxide growth at elevated temperatures observed for MG0.5 specimens at 1125 K. At 1020 K, MG0.2 specimens showed deviations from parabolic behaviour above 1250 h (as shown in Figure 4.35 E). Consequently, oxide growth constants were calculated by using the slope of area normalized mass gain as a function of square root of time only up to 1250 h. Similarly, the slope of the mass gain of MG0.2 specimens at 1073 K in Figure 4.35 C was calculated up to 100 h. At 1125K, shallower slopes due to oxygen access restrictions resulting from oxide growths in the pores (as indicated by oxide microstructures in SEM analysis, for example in Figure 4.28) occurred for the different 73  microstructures, and were more pronounced for the finer microstructures (Figure 4.35 F). Slopes used in the oxide growth rate constant calculations were selected to be as independent of these changes as possible. At 1125 K, the effect of oxide growth is so strong that the surface area available for oxidation is significantly reduced. As a result, the mass gain effectively stops at 0.4 mg/cm2 area specific (4.2% relative) mass gain for MG0.2 specimens. Similarly, reduced mass gain can be observed for MG0.5, MG1, MG2, and MG5 after 500 h oxidation at 1125 K, as a result of Cr2O3 oxidation. However, the oxidation rate reductions were most pronounced for MG0.2 and MG0.5 specimens. As a consequence, the slopes of the graphs that relate oxidation mass gain to the square root of time at 1125 K were determined only when the parabolic rate law was observed (Figure 4.35 F). At 1125 K, oxide growth rates increased significantly for MG40 specimens after 1250 h of oxidation, and started to increase after longer oxidation times (1750 h to 3000 h) for all other microstructures except MG0.2 and MG0.5 specimens. For MG0.2 and MG0.5 specimens, the access limitations of oxygen molecules to the pore surfaces due to oxidation may have delayed the onset of the second, rapid oxidation rate. MG40 specimens experience an early occurrence of Fe2O3 formation and, as a consequence, completely oxidize within 2000 h. The second rapid oxidation is related to the Fe2O3 growths, as XRD analysis indicates the appearance of Fe2O3 in the specimens after 2000 h of oxidation (Figure 4.32). For all specimens, the initial, linear portion of the area normalized mass gain as a function of square root of time was used to calculate the oxidation growth rate constants. The oxidation rate constants of the specimens at the temperatures not discussed here were calculated using the entire recorded time scale. This analysis disregards effects of closing pores and rapid oxidation for the projection of oxide scale thicknesses. Temperatures at which fast Fe2O3 oxidation or a complete closing of pores due to oxide formation occurs (for example 1125 K) are too high to be of technological interest for metal supported SOFCs. Table 4.3 shows an overview of the selected time ranges for which linearity was observed.  74  Table 4.3: Time ranges with a constant slope in the area normalized mass gain as a function of square root of time graphs used to calculate oxidation rate constants of sintered porous AISI 430 specimens. If no microstructure is indicated, the range applies to all microstructures not specifically mentioned at that oxidation temperature. Temperature (K) 873 920 973 1020  Time range (h) 10‐1000 5‐3000 10‐1000 5‐3000 5‐1250 (MG0.2) 10‐1000 10‐100 (MG0.2)  1073  Temperature (K) 1125  Time range (h) 5‐100 (MG0.2) 5‐500 (MG0.5) 5‐750 (MG1) 5‐2250 (MG2) 5‐2000 (MG5) 5‐1000 (MG40) 5‐1750 (MG100)  4.4.2. Oxidation growth rates The slopes, m, of the graphs shown in Figure 4.35 (excluding the non‐linear behaviour due to pore closing and fast Fe2O3 oxidation) were used to calculate the oxide growth rate (k’’, the square of the ratio between unit mass change and square root of time), as shown in Eq. 4.20 [275], [276]. These calculations follow the calculations proposed by Molin et al. [124] and Mukherjee et al. [117] for sintered porous ferritic stainless steel. The oxygen concentration in the atmosphere was assumed to be constant throughout the specimens, and at tox=0 h there was assumed to be no oxidation. k  Δm  ,  Eq. 4.20  t  In Eq. 4.20, tox is the oxidation duration, and Δmox,s is the metal surface area normalized mass gain of the material. Assuming that all mass change is due entirely to MaOb oxide formation of the type Cr2O3 (as indicated by XRD results), an effective (materials dependent) parabolic oxide growth rate constant (kp,eff) was calculated according to Eq. 4.21. k  ,  M bM ρ  k′′  Eq. 4.21 75  In Eq. 4.21, MCr₂O₃ and MO are the molar masses of chromia and oxygen, respectively, b is the number of oxygen atoms per mol of oxide, and ρCr₂O₃ is the density of chromia (5.21 g/cm3 [17]). A porous stainless steel scaling constant k’ relating the oxidation growth to oxide layer thickness δox was defined as shown in Eq. 4.22, with 0<δox<δox,t with δox,t as the thickness of the oxide at time t, and 0<t<tox as the time interval analyzed. k , k′ dδ Eq. 4.22 δ dt δ The geometry of the system is shown in Figure 4.37 overlaid on a cross‐section micrograph of an MG1 specimen oxidized for 500 h at 973 K (with cO indicating the concentration of oxygen).  Figure 4.37: Cross section of an AISI430 MG1 specimen after 500 h at 973 K, indicating the geometry assumed for the calculation of the oxide scale thickness. From Eq. 4.22, the oxide scale thickness after a certain time δox,t (for example 40,000 h, δox,40kh, which for a long time was the targeted lifetime of SOFCs as defined by the U.S. Department of Energy [277]), can be calculated. The oxidation growth rates k" calculated from the slopes in Figure 4.35 were related to media grade in Figure 4.38.  76  Figure 4.38: Calculated values of k’’ at different temperatures (873 K – 1125 K), as a function of media grade. The oscillations in the data shown in Figure 4.38 are larger than the error calculated. One potential reason for the changes in oxidation rate is the influence of small differences in composition (Appendix B). The resulting trends in Figure 4.38 show that even when normalized by surface area, MG0.2 specimens had higher oxidation rates than specimens with a different microstructure at all temperatures except 1125 K. At 1125 K, access to the total surface area of MG0.2 specimens in the pores was restricted so quickly that the resulting oxidation growth rate, even using data only to 100 h, appeared to be slower than for specimens with a MG40 microstructure (as shown in the top data series in Figure 4.38). For all microstructures, some of the pores may be blocked by oxide growth, and the resulting surface area available to oxygen may change with time as seen at 1125 K (Figure 4.35). Oxygen ions may diffuse through oxide layers to reach these closed‐off pores, but this becomes more difficult when thick, dense oxide layers are present and the pores become closed due to oxidation to such an extent that the pores are no longer visible on the surface of the specimens by 77  microscopy. While MG0.2 and MG0.5 specimens differed in overall porosity only by 2%, the differences in oxidation growth rates were significant. MG0.2 specimens had a pore structure with many small pores and small (<20 µm) metallic features, whereas MG0.5 specimens had fewer pores of a larger diameter. This difference in pore structure may account for some of the differences in oxidation growth rates observed. When correlated with the chromium content of the porous AISI 430 specimens after sintering (Figure 4.1), the oxidation rate constants (Figure 4.38) do not appear to be directly correlated with Cr content of the base composition after sintering (Figure 4.1), which implies that microstructure influences the oxidation behaviour. While a slightly higher Cr content in the MG0.5 specimens compared with the MG0.2 and MG1 specimens could have some influence on the observed differences in oxidation rate constants, the MG2 specimens have a lower Cr content than the MG1 specimens, while the oxidation rate constants are lower for MG2 specimens. On the other hand, MG40 specimens appear to have the lowest relative Cr content of all the specimens, and at high temperatures (1125 K), the second (Fe2O3) oxidation rate constant does appear earliest for the MG40 specimens, so the appearance of the second, fast oxidation rate could be a result of lower Cr content in the MG40 alloy than in the other alloys. In Figure 4.39, the oxide growth rates shown in Figure 4.38 are related to average surface curvature, κs, which is defined as the reciprocal of the average pore radius. The average pore radius was determined as half the pore diameter derived from the peak in the log volumetric mercury intrusion versus pore diameter graph shown in Figure 4.21. MG0.2 specimens with the smallest pores (and the largest curvature) had a faster oxidation growth rate compared with the oxidation growth rates of the other specimens, except at 1125 K, at which temperature mass flow limitations may have influenced the oxidation growth rate (Figure 4.39). This may indicate that specimens with a fine microstructure similar to MG0.2 specimens should be avoided in high temperature applications.  78  Figure 4.39: Calculated values of k’' at different temperatures, as a function of pore curvature as characterized by mercury porosimetry (Figure 4.21). X‐axis error bars derive from the distribution of pore surface curvatures observed in mercury porosimetry and y‐axis error bars derive from the measurement errors of Sv, Vdisc, and Δmox (Eq. 4.18). The calculated average oxide thickness of the various specimens after 40,000 hours is shown in Figure 4.40 in relation to the average pore size diameter obtained from mercury porosimetry. Not only do oxide layers close off pores and consequently limit access of reactant gases to the fuel cells, they also introduce additional electrical resistance to the system, and may, for example due to the volumetric changes and resulting changes in the mass flow of the hot reactant gasses, introduce stresses in the fuel cell support structure that may lead to spallation of the oxide layer [23]. Based on Figure 4.40, a selection can be made of what substrate microstructures may be favourable within a predefined maximum of oxidation layer thickness. Specimens that grow an oxide layer with a thickness above the pore size radius (PSR, shaded area above the dashed line in Figure 4.40) are not suitable as SOFC substrates for 40,000 h of operation. The calculations were made assuming continuous oxide growth based on the sections from Figure 4.35 that exhibit parabolic oxidation growth rate. The changes in k" due to the closing of pores and due to the formation of Fe2O3 were disregarded in this calculation. However, these effects were observed mainly at 1125 K, a temperature at 79  which, even using the initial parabolic growth rate, the substrates were already not usable for 40,000 hours (see shaded area in Figure 4.40).  Figure 4.40: Calculated oxide scale thickness after 40,000 hours at elevated temperatures, using the oxide growth rates shown in Figure 4.39, as a function of pore curvature. The dashed line indicates the pore size radius (PSR) at maximum volumetric mercury intrusion. Oxides growing thicker than this radius will close off the pores, and all specimens and temperatures in the shaded area are consequently not usable for 40,000 hours. The variation of the oxidation rate growth constants k (i.e. k", k', or kp,eff) is temperature dependent on the activation energy for diffusion of the rate limiting species (metal cations or oxygen anions), and follows an Arrhenius‐type relation, shown in Eq. 4.23. k  A∗ e  Eq. 4.23  Here, A* is the pre‐exponential factor, EA is the activation energy for oxidation, R is the universal gas constant (8.314 JK‐1mol‐1), and T the absolute temperature. To evaluate the activation energy of the analyzed porous AISI 430 specimens, an Arrhenius‐type plot of the oxidation growth rate constants k'' is shown in Figure 4.41. It shows that most of the specimens have similar oxidation activation energies. One 80  notable exception is MG0.2, which up to 1020 K appears to have a higher oxidation activation energy, which may further indicate that the pores of these specimens closed at elevated temperature (≥1073 K), thus changing the available surface area, and reducing the oxidation rate. A linear least squares regression analysis of the activation energy data shown in Figure 4.41 is discussed in Appendix F.  Figure 4.41: Arrhenius‐type plot of oxidation rate k" for oxidized specimens. Error bars are within the data markers. Kubaschewski et al. found that below 843 K, just 30 K lower than the lowest temperature analyzed in this work, FeO is not stable and will not form, while it may be found on the surface of steels at higher temperatures [278]. Suwattananont et al. used this information to claim that for the low carbon steel analyzed in their work, oxidation above 843 K is mainly controlled by the formation of FeO [279]. The authors also found that the activation energy seemed to change to lower values at lower temperatures; however, only one average activation energy (147 kJ/mol) was reported. While the EDX and XRD analysis of the surface oxides found in this work indicates mainly Cr2O3 in the oxide scale (except at 1125 K after long oxidation times), some iron oxide may exist beneath the interaction volume of electrons or x‐rays with the surface oxide layer, and could account for changes in activation energy. 81  The activation energy for the porous media studied in this work is high (270‐322 kJ/mol) compared with literature values found, for example 123 kJ/mol for uncoated bulk AISI 430 exposed to 1373 K, 1423 K, and 1473 K, and analyzed for a maximum of 30 minutes [280]. This may indicate that having a porous structure as opposed to a flat, dense material could have an impact on the temperature dependence of oxidation, although the differences between the activation energies of the analyzed porous AISI 430 specimens was found to be small (Figure 4.41). Cr2O3 forms a protective film on the surface of the steel. Table 4.4 shows literature values of activation energies for comparison with the activation energies found in this work (shown in Table 4.5), and includes the oxidation activation energies of Fe and Cr, and for comparison, Ti, Ni, and Cu alloys [281]. Table 4.4: Comparison between activation energies for different metals and alloys. (ASR*) – Activation energy calculated from area specific resistance. It includes both the activation energy of oxidation and of the conductivity of the oxide scale [282]. Ref Material Temperature range EA (kJ/mol) investigated (K) AISI 430 1373‐1473 (for 30 min.) 123 [280] AISI 304 1373‐1473 (for 30 min.) 226 [280] * Crofer22 (CuMn1.8O4 coated) n/a 75 (ASR ) [283] * Crofer22 n/a 81 (ASR ) [283] * 26%Cr, 1%Mo, bal: Fe 823‐1173 87 (ASR ) [284] * AISI 430 (blank, and coated 673‐1223 87‐106 (ASR ) [285] with Inconel, LSCo, or LSCr) Crofer22 873‐1173 100 (ASR*) [282] * Haynes 230 873‐1173 96‐100 (ASR ) [282] Ti50Ni50 973‐1273 180 [281] Ti50Ni40Cu10 973‐1273 226 [286] Various steels, described as n/a 193 [287] "former standard value" Cold worked iron 673‐723 243 [288] Cold worked iron 723‐853 96 [288] Cold worked iron 853‐973 172 [288] FeO formation on steel 823, 843, 873 96, 134, 251 [288]  82  Table 4.5: Activation energies for porous AISI 430 oxidation calculated in this work. Specimen MG0.2 MG0.5 MG1 MG2 MG5 MG40 MG100  Temperature range investigated (K) 873‐1125 873‐1125 873‐1125 873‐1125 873‐1125 873‐1125 873‐1125  EA (kJ/mol) 270 ± 13 283 ± 19 277 ± 11 294 ± 12 288 ± 12 315 ± 15 322 ± 19  Using the activation energy data of all microstructures studied, it appears that there is a trend towards higher activation energies for the specimens with higher porosity (Figure 4.42, error bars include the 95% confidence interval described in Appendix F). Smaller porosities may offer some impediment for the oxygen atoms from the atmosphere to arrive at all the surfaces in the porous structure. If small pores close, the access of oxygen atoms to the surface will change. At higher temperatures, the small microstructures are more likely to close off due to oxide growth.  Figure 4.42: Activation energy of oxidation of the various porous AISI 430 microstructures examined in this work. The composition of the different media grade specimens differs between media grades (Table B.1 in Appendix B) and specimen batches [289], which may account for some of the differences observed. Also, as‐received specimen preparation may have 83  involved different sintering temperatures prior to testing. Some impurities may not be removed by the cleaning method used, although EDX and XRD analysis found no elements or separate phases within the detection thresholds of the instruments. The oxidation rate constants found in this work are shown graphically in Figure 4.39 and in tabulated form in Table G.1 (Appendix G) and are compared with some literature values of observed oxide growth rates listed in Table G.2 (Appendix G). The oxidation rate constants observed for all investigated specimens in this work are slightly smaller than the observed values for flat sheets. Jonghe et al. published recommended maximum oxidation rate constants of metallic SOFC materials of k"=10‐15‐10‐14 g2cm‐4sec‐1 in 2004 [290]. The k" values for MG0.2‐MG100 specimens range from 0.9‐3.2*10‐13 g2cm‐4sec‐1 at 1125 K, compared with 13*10‐13 g2cm‐4sec‐1 at 1123 K for AISI 430 sheet [401], 2.3*10‐13 g2cm‐4sec‐1 for E‐brite sheet (24%Cr, 1%Mo) at 1123 K [284], and 8.7*10‐13 g2cm‐4sec‐1 for E‐brite sheet coated with LSCo at 1123 K [284], and are of the same order of magnitude as the approximate k" value published for porous AISI 434L and AISI 316L materials of 10‐13 g2cm‐4sec‐1 [129]. The wide ranges in the oxidation rate constants may contribute to the uncertainty observed in the oxidation activation energy. The range of the oxidation rate constants found in this work are lower than the ones published for dense flat sheets of the same AISI 430 composition. In fact, the oxidation rate constants of porous AISI 430 specimens analyzed in this work seem to be in the same range as higher (24%) chromium content flat steel, and lower than the 24% chromium steel when it is coated with LSCo. This may be due to oxides completely closing off some pores, and shows that oxidation of porous structures differs from flat sheet oxidation. Even when compared with flat sheets of higher chromium content (24%Cr, 1%Mo) [284] at a lower temperature (1073 K), the oxidation rate constants in this work range from 2.1‐5.9*10‐14 g2cm‐4sec‐1 and are lower than the k"=8.8*10‐14 g2cm‐4sec‐1 found for the 24%Cr steel, yet of a similar range as AISI 444 coated with LaCrO3, with an oxidation rate of k"=5.8*10‐14 g2cm‐4sec‐1 [402]. However, spinel coatings such as MnCo2O4 were found to lower the oxidation rate of AISI 430 steels by at least two orders of magnitude at 1123 K [401]. Since they may also lower Cr 84  migration from metallic components to the SOFC, spinels will be analyzed in further detail in section 7.  4.5.  Conclusions – Oxidation of porous stainless steel  Porous AISI 430 specimens with various microstructures were proposed as a substrate material for intermediate temperature solid oxide fuel cells. The oxidation behaviour of specimens with various porosities and microstructures was investigated in air at 873 K – 1125 K. Oxidation rate constants were calculated and compared with literature values of flat sheet material. It was found that the oxidation rate constants of the porous AISI 430 materials analyzed in this work appear to be lower than those of dense, flat materials, and similar to those of flat, dense steel with 24% Cr. The oxidation rate constants measured at 1125 K were found to be k"=0.9‐3.2*10‐13 g2cm‐4sec‐1 for the seven microstructures analyzed, compared with k"=13*10‐13 g2cm‐4sec‐1 at 1123 K for AISI 430 sheet [401], and 2.3*10‐13 g2cm‐4sec‐1 for E‐brite sheet (24%Cr, 1%Mo) [284]. The surface roughness of the specimens was investigated in order to judge their applicability in fuel cell production. For MG0.2 specimens (17% porosity) and MG0.5 specimens (19% porosity), the surface roughnesses were lowest (Ra=1.6‐2.4 µm), MG1 specimens (23% porosity), MG2 specimens (28% porosity), and MG5 specimens (30% porosity) had slightly higher surface roughnesses (Ra=4.2‐6.5 µm). All of these specimens are good candidate materials as SOFC substrates at the temperatures indicated in Figure 4.40 (typically below 1020 K). MG40 specimens (50% porosity), and MG100 specimens (60% porosity) had higher surface roughness (Ra=23‐41 µm), and may consequently not be usable as SOFC substrates, at least not without first filling the surface pores before SOFC production. However, they serve as sample microstructures with higher porosities for this work. Additionally, spinel coatings applied to the surfaces of these porous microstructures may reduce the oxidation rate of steels by several orders of magnitude [401]. Consequently, such large, open microstructures could in the future be coated with suitable protective coatings. Dip coating, for example, could be employed to cover the entire porous medium with a protective coating that could 85  reduce oxidation rates and Cr volatilization [402]. Such a coating would also reduce the porosity and pore sizes of the specimens. The porosity of the specimens was investigated by various methods. Mercury porosimetry was found to be a good method to analyze the pore size distributions of the specimens, and was used for calculations of the radius of curvature of the pores. Additionally, the tortuosity of the specimens was analyzed. It was found that MG100 (60% porosity) specimens have an average tortuosity of 1.4±0.3, indicative of their large, open pore structure. The pore structures with 17% and 19% porosity had higher tortuosity values than the other specimens (a tortuosity value of 9.2 and 8.2, respectively), and consequently may offer significant resistance to mass transport (see section 5.4). Of the four porosity measurement methods used, the Archimedes method, the XRD / mass measurements, and the image analysis measurements produced porosity results that differed by up to ±2% porosity when comparing the averaged porosity values of these three methods. When including mercury porosimetry in the comparisons, the porosity differed by up to ±4% porosity between all methods of investigation. Impregnation methods such as mercury porosimetry and Archimedes measurements analyze only open porosity, while image analysis and XRD / mass analysis measure total porosity. Image analysis was found to have large measurement errors, especially for specimens with more than 50% porosity. Consequently, porosity values analyzed by only one method do not provide a complete representation of the porosity of any given specimen. It is recommended that all porosity measurements follow strict standard measurement techniques, and that quoted porosity values are always referred to their measurement method, in order to be able to compare the values between different investigations. BET analysis could not be performed on the specimens because the specific surface area was too low for the measurement resolution of the instrument. The gas permeability through the analyzed specimens and the influence of oxidation on permeability are presented in section 5. 86  5. Gas permeability of oxidized porous AISI 430 specimens Section5, Tab:0, Fig: 0, Eq.: 0  5.1.  Introduction  Using modern pressure transducers, set‐ups that use variable pressure are easier to design than set‐ups that depend on variable volume and were consequently used in this work. The design of the gas permeability jigs used in this work was changed over time. Initially, an open design was used to detect gas leaks in dense, flat electrolytes. This system leaked gas into the environment and several improved designs for electrolyte, electrode, and fuel cell substrate permeability testing were subsequently analyzed. Since the size of the mass flow meter (MFM) was found to influence the measurement results, the appropriate range of MFM was selected. The set‐up with the least impact on measurements, the highest gas flow rate, and the best differentiation between the different specimens that was designed and developed during this work consisted of two separate parts with a straight gas flow channel with an inner diameter of 9.3 mm (shown in Appendix J). The gas inlet flow channel was inserted into the permeability chamber and sealed against the specimens using an o‐ring with a large 22.2 mm inner diameter (thereby reducing the measurement error resulting from local variations of specimen microstructure when using smaller o‐rings), sealing against the specimen, the permeability testing chamber, and two faces of the inlet flow channel. This design allows specimens up to a thickness of 13 mm to be tested. The insides of the gas channels became larger towards the analyzed specimens to allow good distribution of the gases over the specimens. The jig was machined from 6061‐T6 grade aluminum for longevity and good surface finish. Differences in gas permeability measurement results were found due to different inner diameters of tubing and o‐ring sealing configurations used. In order to quantify the influence of gas supply tube diameters and lengths, the gas viscosity and theoretical pressure loss within the different measurement set‐ups were calculated. This was done so that the influence of the measurement set‐up could be deconvoluted from the measured data. 87  5.2.  Gas flow measurements  The gas permeability was measured by sealing the specimens inside a permeability chamber and applying a constant pressure to one side, then measuring the downstream mass flow at each applied pressure differential. The gases used in this work were helium and air. Helium is typically used for small flow rate measurements of leaks through dense membranes such as SOFC electrolytes, as it is a small, non‐polar molecule. Air was used as this is the actual gas that is used in the SOFCs on the cathode side. In order to calculate the gas permeability, the gas density and viscosity should be known. For helium, these values were taken from the literature (Appendix H). For experiments with compressed air, the influence of the water content on density and viscosity of the air/water mixture was calculated (Appendix H) and was found to be negligible. Before using a gas flow system, the influences of the design and scale of the individual components and the entire set‐up on gas flow behaviour should be known. This can determine how much the measurements are influenced by the set‐up. The pressure losses due to the gas permeability set‐up (including those from the connections between the pressure controller and the permeability jig, inside the jig, and tubes from the jig to the mass flow meter) were calculated using fluid mechanics calculations described in Appendix I. While the early jig designs had restrictive influences on the measurement, leading to gas molecule residence times of hundreds of seconds at flow rates of several millilitres per minute from one end of the set‐up to the other, the set‐ups created during this work were designed to have a negligible influence on the measurements (Appendix I).  5.2.1. Permeability measurement, experimental set‐up This section includes a description of the evolution of the gas permeability measurement set‐ups. They differ mainly in the inner diameter and length of the tubes, and the sealing method. Gas was supplied via tubes, typically at a pressure of 689.5 kPa, and regulated by a pressure controller (Alicat Scientific, Tucson, Arizona, U.S.A., Model 88  PCD‐5PSIG‐D, 2 pneumatic valves) to a set pressure at the inlet to the measurement chamber. After pressure stabilization, the flow of gas through the specimens was measured at the outlet of the set‐up by a mass flow meter (Alicat Scientific, Model M‐20SLPM‐D_H2), and recorded by the software FlowVision (Alicat Scientific, Tucson, V2.3) in real time. The initial measurements were performed using a permeability jig that was open to the environment (jig version V1, Figure 5.1).  Figure 5.1: Gas permeability set‐up with jig V1 as the specimen holder. Since gas could freely escape through the sides of the open design of jig V1, a second version was made, sealed to the porous AISI 430 specimens with 2 o‐rings, and against the outside atmosphere via a third, large rubber o‐ring (jig V2, Figure 5.2).  2.55 cm  Figure 5.2: Opened (horizontally cross sectioned) gas permeability jig V2&V3 with porous AISI 430 disc shown on the right half. The largest o‐ring shown on the left half provides the outer seal between measurement chamber and the environment. 89  A third permeability jig version was produced to address changes in specimen thickness (V3). All three jigs had gas flow tubing that was smaller than 2 mm in diameter. A fourth version was made to allow approximately 4 mm diameter tubes to be used (V4). Polymer tubes of that diameter were found to be too restrictive to gas flow. Also, parts of this set‐up were machined using an 1100 grade aluminum alloy for the body of the jig, which proved to be too soft for repeated sealing with steel screws. Additionally, the gas flow channels machined into the jig included two 90° bends, influencing the gas flow. A final version was designed and machined to address all of these issues (V5, shown in Figure 5.3). It had no bends in the gas flow channels, had a minimal inner diameter of all components of 9.3 mm, and had a new sealing method with an o‐ring with a large diameter (22.2 mm) that sealed the specimens from the surrounding atmosphere, reducing the measurement error resulting from local variations of specimen microstructure when using smaller o‐rings. The design allowed for the measurement of specimens with large variations in thickness without compromising sealing, and was machined from 6061‐T6 grade aluminum for longevity and better surface finish. See Appendix J for the mechanical design of jig V5.  2.55 cm  Figure 5.3: Vertical cross section of a V5 gas permeability jig designed in this work. The long vertical arrow indicates the gas flow direction; the x‐marks indicate the position of the porous sintered specimens inserted in the permeability jig. 90  5.3.  Selection of gas for permeability testing and instrument settings  As described in section 5.2, gas flow restrictions through the gas supply tubes influence gas flow measurements at high flow rates, effectively changing the total gas flow at high applied pressures. Proportional‐integral‐derivative (PID) settings of p=100, d=60,000 were found to result in stable mass flow readings on the high flow rate mass flow meter (MFM20) at a flow rate above 1.5 dm3min‐1. The flow rate of helium and air through as‐received porous AISI 430 specimens was measured using the whole pressure range of the pressure controller, up to 34.5 kPa. The resulting gas flow rates as a function of gauge pressure are shown in Figure 5.4. At the same applied pressures, the flow rate of helium was higher compared with air. This compares well with results by Geus et al. [291] and Bakker et al. [292], who analyzed the permeability of zeolite membranes supported on porous AISI 316 substrates using various gases (neon, n‐butane, isobutane, and methane). The authors found that the flow rates at the same applied pressures were similar (within a factor of five) for neon, n‐butane, and methane which resulted in the highest permeability, while the flow rates for isobutane were more than two orders of magnitude lower, and took longer to stabilize.  91  A  B  Figure 5.4: Difference in gas flow rate of (A) air and (B) helium through various as‐ received porous AISI 430 specimens using measurement jig V3. In Figure 5.5, the results of the helium gas permeability measurements through porous AISI 430 specimens were correlated with the porosity/tortuosity values of the porous 3‐D microstructure of the porous AISI 430 specimens obtained by mercury porosimetry (Figure 4.24). Figure 5.5 shows that the increase in the porosity/tortuosity value is largest from MG5 (31% porosity) specimens to MG40 (50% porosity) specimens. From MG40 (50% porosity) specimens to MG100 (60% porosity) specimens, the helium flow rate increases only little. This indicates that the specimens tested with 50% or higher porosity have internal structures that do not hinder gas flow much. 92  Figure 5.5: Porosity divided by tortuosity and helium flow at 6.9 kPa as a function of porosity. It was found that the gas flow rates differed between different gases used. Gas flow rates of helium were approximately twice as high as gas flow rates of air for the same pressure drops in a V3 jig set‐up. The porous AISI 430 specimens oxidized at 873 K, 973 K, and 1073 K were measured using the V3 jig, as the newer permeability jig version had not been designed at the time. The permeability of the specimens oxidized at 920 K, 1020 K, and 1125 K was measured using the V5 jig. Since air is the gas that is transported in the SOFC cathode, the permeability was measured using air as the permeating gas. The gas permeability (calculated in section 5.4) through as‐received and oxidized specimens was measured using the set‐up described in Appendix J, which was designed to have the least influence on the measurements. Figure 5.6 shows that the gas permeability of the MG2 specimens (with 28% porosity) was almost as high as that of the MG5 specimens (with 31% porosity), while MG1 specimens with just 5% less porosity than MG2 specimens had significantly lower gas permeability. Consequently, due to a combination of good gas permeability and ease of SOFC production resulting 93  from a low surface roughness, MG2 specimens appear to be a good candidate for fuel cell production, at suitable operating temperatures according to the mass gain measurements shown in section 4.4.2 (Figure 4.40, p. 80). The air flow rates measured in the jig V5 set‐up were significantly higher than in the jig V3 set‐up (Figure 5.4), indicating an improved design. In typical SOFC test designs, reactant gas flow rates are in the range of 18‐160 cm3/min per square centimeter of SOFC surface area [293], [294]. For the configuration used in these experiments, this means the specimens would have to permit approximately 70‐620 cm3/min of gas. Such a throughput can be realized with the present testing design.  Figure 5.6: Air flow rate through as‐received porous AISI 430 specimens using the measurement jig V5.  5.4.  Results and discussion of gas flow through oxidized porous AISI 430 specimens  The gas permeability through oxidized porous AISI 430 specimens was recorded for all oxidation times and temperatures analyzed in this work. Using the area covered  94  by the o‐ring seals, Aseal, the gas flux, φgas, can be calculated following Darcy’s Law (Eq. 5.1). Φ  V tA  Q A  κΔp μ t  Eq. 5.1  Here, Vgas is the volume of gas passing through the specimen, tf is the time span within which the gas flow is measured, Qgas is the volumetric flow rate or discharge, tdisc is the specimen thickness, κ is the permeability, μgas is the dynamic viscosity of the gas at the temperature of the experiment, and Δpapp is the pressure drop across the specimen. The pressure normalized permeance, Λ, can be derived by dividing the gas flux by the pressure drop (Eq. 5.2). Λ  Φ  Eq. 5.2  Δp  This value can now be multiplied by the specimen thickness, yielding permeability κ Eq. 5.3 . κ  Λt  μ  Eq. 5.3  The dynamic viscosity of gases is dependent on temperature, and was calculated using  an  average  gas  temperature  of  Tgas=294.4±0.9 K  and  pressure  pgas=101.35 ± 0.80 kPa (see Appendix H for details), yielding a helium gas viscosity μHe of 20.07 ± 0.40*10‐6 Pa•s and a dry air viscosity μdry of (18.44 ± 0.37)*10‐6 Pa•s. The effect of oxidation on specimen mass and surface microstructure was shown in section 4. The micrographs in Figure 5.7 and Figure 5.8 show examples of the oxide growth inside pores of specimens heat treated for 10 h at 1273 K (Figure 5.7), and for 1000 h at 1073 K (Figure 5.8). The resulting reduced open pore volume (dark areas) due to oxide growth can be seen in the images. This reduction in pore volume reduced the gas permeability of the specimens compared to non‐oxidized specimens. The effect was more pronounced at higher temperatures, as could be expected due to higher oxidation rate constants, and was more severe for finer microstructures such as found in MG0.2 specimens. In these cases, almost the entire pore structure seems to be filled with oxides resulting from oxidation (Figure 5.8). Some of the remaining open parts of pores 95  shown in Figure 5.8 may have resulted from detachment of the oxide that occurred during cross section preparation. The internal structure likely did not allow much of the embedding epoxy to impregnate the internal structure, even under vacuum, and consequently the oxide layers may not have been completely embedded in epoxy during specimen preparation. Figure 5.8 shows that oxides grew in the pores of MG0.2 specimens after 1000 h at 1073 K, reducing the free volume available for gas permeation.  Figure 5.7: SEM micrograph of a cross section of a pore in a MG5 specimen, heat treated for 10 h at 1273 K. The internal pathways for the reactant gases can be seen to be partially blocked due to oxide growth.  Figure 5.8: SEM micrograph of a cross section of multiple pores in a MG0.2 specimen, heat treated for 1000 h at 1073 K. The internal pathways for the reactant gases can be seen to be blocked due to oxide growth. 96  In Figure 5.9, the calculated gas permeabilities of the different oxidized porous AISI 430 specimens are shown. The high flow rate MFM20 could resolve the differences between the various porous specimens best, and was consequently used for all measurements. The minimum measurable flow rate in the chosen MFM20 was 0.01 dm3min‐1. If such a low flow rate was measured at 34.5 kPa, the detectability limit of the set‐up is approximately equivalent to κ=4x10‐16 m2. Gas permeability may continue to decrease even after the set‐up can no longer detect any gas flow. However, as porosity decreases, gas pathways that extend through the entire specimen become rare. Pavlovskaya et al., for example, found that for specimens with approximately 20% open porosity, less than 9% contributed to gas permeability [295]. Also, Kostornov et al. found that compared with porous powder materials, porous materials made from fibres exhibit a much more marked dependence of pore size on porosity, underlining the importance of tortuosity on gas permeability [296]. The graphs in Figure 5.9 show that the permeability of most of the porous AISI 430 specimens decreases with increasing oxidation duration and that the decreases are more noticeable at higher oxidation temperatures. The results are sorted by the permeability jig they were measured in. The permeabilities of the specimens oxidized at 873 K, 973 K, and 1073 K were measured in jig V3 and consequently have lower absolute permeability values than the permeabilities measured in jig V5. The permeability of the specimens oxidized at 920 K, 1020 K, and 1125 K was measured in jig V5. At 873 K, few changes occur in gas permeability up to 500 h for all specimens. From 500 h to 1000 h, MG0.2 specimens had a more noticeable decrease in gas permeability. At 920 K and at 973 K, the gas permeability of all specimens except MG40 and MG100 specimens decreases slowly with time, most noticeably for MG0.2, MG0.5, and MG1 specimens. At 1020 K (in the case of MG0.2 specimens), 1073 K (in the case of MG0.2 and MG0.5 specimens), and 1125 K (in the case of MG0.2, MG0.5, and MG1 specimens), the gas permeability drops below the measurable limit of the instrument within the duration of the oxidation measurements. In these cases, growth of oxides restricts gas flow below the detection limit of the MFM. At 1020 K and at 1073 K, gas permeability decreases for 97  all specimens except for MG40 and MG100 specimens. At 1125 K, significant decreases in permeability also appear for MG40 specimens. After 1750 h (for MG40 and MG100 specimens) and 2250 h (for MG5 specimens) at 1125 K, the specimens grew oxide scales (Fe2O3, as shown in Figure 4.32) to such an extent that the specimen diameter exceeded the jig diameter. It is consequently highly unlikely that such a high temperature will be used in metal supported SOFC operation. The gas permeability through the open structure of MG100 specimens was never influenced by oxide growths at any of the analyzed temperatures. Ideally for SOFC operation, the permeability should change as little as possible as a result of oxidation. The steeper the reduction in permeability as a function of oxidation time, the less likely it is that the particular combination of microstructure and temperature will be used in an SOFC. In SOFC testing, oxidation is not the only factor that may limit gas permeability through the stack. Carbon or sulphurous deposition from the fuels may also occur [297], [298]. Since these measurements are mass flow controlled, the pressure increases as the permeability decreases. In a 1 kW test stack at NRC IFCI, a pressure meter is installed into the system that will shut down the measurements if the pressure increases by 34.5 kPa [299]. The changes in permeability that such an increase in pressure by 34.5 kPa would cause were consequently calculated for the different types of specimens. If the measured permeability falls below the calculated value of permeability, the microstructure cannot be used in a 1 kW stack at the given temperature and duration, based on reduction of permeability due to oxidation, ignoring other effects that may also reduce permeability (such as carbon deposition). The gas flow chosen for this calculation was set to between 18 cm3/min per square centimetre of fuel cell surface area at NRC IFCI (designated "low flow rate", rLF, dotted lines in Figure 5.9) [293] and 160 cm3/min per square centimetre of fuel cell surface area (designated "high flow rate", rHF, dashed lines in Figure 5.9) [294] at ETH Zürich. The resulting flow rate in the geometry of the test design used in this work (Appendix J) was 1.2 ‐ 10 x 10‐6 cubic meters per second. The permeability values  98  corresponding to the resulting pressure at the targeted gas flow rates (18 ‐ 160 cm/min) are listed in Table 5.1. A detailed description of the calculation is given in Appendix K.  Table 5.1: Lower limit of permeability at which an NRC‐IFCI test station may shut down as a safety precaution due to an increase in pressure by 34.5 kPa. Specimen type (MG) 0.2 0.5 1 2 5 40 100  κ at 18 cm/min, rLF (m2) 2.2E‐15 2.5E‐15 2.4E‐15 2.7E‐15 2.6E‐15 3.4E‐15 3.8E‐15  κ at 160 cm/min, rHF (m2) 1.2E‐14 1.7E‐14 1.8E‐14 2.3E‐14 2.2E‐14 3.0E‐14 3.4E‐14  99  A  B  C  Figure 5.9: Gas permeability of porous AISI 430 specimens with varying microstructure oxidized at (A) 873 K, (B) 973 K, and (C) 1073 K (measured in jig V3). Inset italic numbers in (A) indicate the porous specimen media grade. Dashed lines and dotted lines indicate calculated maximum tolerable reduction in permeability for a 1 kW stack for a high flow rate and low flow rate operation, respectively. The dashed lines are shown only for the materials with the highest porosity for which the measured permeability was reduced below the tolerable limit. 100  D  E  F  Figure 5.9, continued: Gas permeability of porous AISI 430 specimens with varying microstructure oxidized at (D) 920 K, (E) 1020 K, and (F) 1125 K, (measured in jig V5). Dashed lines and dotted lines indicate calculated maximum tolerable reduction in permeability for a 1 kW stack for a high flow rate and low flow rate operation, respectively. The dashed lines are shown only for the materials with the highest porosity for which the measured permeability was reduced below the tolerable limit. 101  Since the gas permeabilities of specimens with finer microstructures (especially MG0.2, MG0.5, and MG1 specimens) are severely influenced at and above 1020 K, it appears that the porous AISI 430 specimens should not be used in operation at or above 1020 K, unless short operation times are envisioned. And while gas permeability through MG40 and MG100 specimens changes little due to oxidation, manufacturing of SOFCs is challenging on such substrates given the large surface pores present in the structures of the MG40 and M100 specimens. Consequently, specimens with a microstructure that comprises pores with a typical diameter of 11 µm (for example MG2 specimens with 28% porosity) appear to have a good combination of gas permeability and porosity in order to allow sufficient gas flow during operation.  5.5.  Conclusions ‐ Permeability of oxidized porous stainless steel  The gas permeability of MG0.2 specimens, with the finest microstructure analyzed in this work, was most affected by oxide growth, even at temperatures as low as 873 K. The permeability of MG0.2, MG0.5, and MG1 specimens decreased below the detection limit of the mass flow meter in less than the duration of the oxidation experiments presented here at temperatures of 1073 K and above. Only the gas permeability of specimens with very large microstructures (MG40 and MG100 specimens) was not limited by oxidation, even at 1125 K during Cr2O3 oxidation. For all specimens, growth of Fe2O3 significantly changed the microstructure. In the case of MG40 and MG100 specimens, the gas permeability could not be measured after 1750 h at 1125 K and in the case of MG5 specimens, the gas permeability could not be measured after 2250 h, since the specimens had grown in diameter beyond what could be measured in the permeability jig. The gas permeability through the microstructures of MG0.2‐MG5 specimens was found to significantly decrease due to oxide growth at and above 1020 K. Consequently, porous metal supported SOFC operation should be limited to temperatures below 1020 K. This finding supports the microstructure recommendations resulting from the calculated oxide scale thickness after 40,000 h  102  correlated with the available pore size diameter of the various porous AISI 430 microstructures (section 4.4.2, page 75). Of the analyzed specimens, MG2 specimens offered the most advantageous combination of low oxidation rate (k"(873 K)=1.8x10‐17 g2cm‐4sec‐1, k"(920 K)=5.0x10‐17 g2cm‐4sec‐1, or k"(973 K)=4.4x10‐16 g2cm‐4sec‐1) and low permeability reduction during oxidation. Combined with the fact that the surface roughness (Ra=4.9±0.2 µm, see section 4.2, page 39) is close to that of the denser MG1 (typical pore diameter of 7 µm, 23% porosity, Ra=4.2±0.1 µm), while the porosity (28%) is close to the porosity of the MG5 specimens (typical pore diameter of 14 µm, 31% porosity, Ra=6.5±0.5 µm), specimens with microstructures similar to that of the MG2 specimens combine good characteristics for use as SOFC substrates, making this particular microstructure a good candidate for SOFC manufacturing.  103  6. Oxidation of spherical surfaces and complete oxidation of stainless steel Section6, Tab:0, Fig: 0, Eq.: 0  6.1.  Introduction  Section 4 showed that porous AISI 430 (the alloy used in UBC SOFC manufacturing) material may experience two oxidation rates and reach a maximum relative mass gain at sufficiently high temperatures (1125 K). Taking a step away from the oxidation of complex sintered microstructures analyzed in section 4 and section 5, a set of experiments was designed to analyze the influence of surface curvature and particle size on oxidation. In this section the oxidation mass gain of different sieved size fractions of a sample alloy, in this case AISI 440C (the alloy used in NRC SOFC manufacturing) are measured. All particles exhibited complete oxidation with two distinct oxidation rates, but it was found that larger spheres exhibited the first, slower oxidation rate much longer than smaller particles. A model based on the spherical geometry (Msph) was proposed to explain the experimentally observed mass gain behaviour. As a reference for complete oxidation of sheet steel, the maximum relative mass gain of a metal alloy was calculated based on composition in Appendix L. This work takes a step back from the sintered microstructures analyzed in section 4, and investigates the oxidation behaviour of stainless steel powders, which may become a significant source of substrates for LT‐SOFCs. The material also serves as a model system to observe the effect of microstructure on oxidation behaviour of steel powder with spherical particles. While the oxidation of as‐prepared porous discs of steel has previously been studied [104], [124],  oxidation  behaviour  was  not  correlated  to  the  initial  microstructure. Published data on oxidation kinetics of stainless steel are often available only for flat sheet material. Little is known about the oxidation of steel when formed into porous structures regardless of the production method. The data are seldom related to the actual surface area of the system, but rather to the outside dimensions of the investigated specimens, making comparisons between different microstructures 104  difficult. Consequently, one of this work's objectives was to develop a new model that links oxidation kinetics to the powder particle size and the dynamically changing surface area of spherical steel powders (Msph, section 6.4). Likewise, the influence of the radius of curvature of the metallic particle on oxidation characteristics was investigated in this work. Furthermore, two reference models were developed that calculate the mass gain of stainless steel based on steel composition (Mel₁ and Mel₂, Appendix L). The experiments shown in Appendix L serve as a reference to the phenomena of complete oxidation observed for the spherical particles in section 6.3 and in porous AISI 430 materials at very high temperatures and long oxidation times (when exposed temperatures of 1125 K for several thousand hours, as described in section 4.4.2). Additional BET analysis was performed to characterize the surface pore structure prior to oxidation. This section reports on the mass change and crystal phase evolution of oxides formed on spherical AISI 440C powders heat treated at 873 K to 1073 K. Changes in the crystal phases and crystallite sizes were investigated by XRD in order to obtain knowledge about the changes of oxide crystallites under the influence of prolonged exposure to elevated temperatures. The oxidation behaviour of the steel was correlated with the substrate microstructure and particle size. Phase and microstructural changes of the metal and growing oxides in AISI 440C powders at elevated service temperatures are reported in this work for the purpose of understanding behaviour of stainless steel and its oxides under SOFC operating conditions.  6.2.  Experimental procedure  Stainless steel powders (UNS S44004 / AISI 440C micro melt, Carpenter Technology Corp., Wyomissing, PA, U.S.A.; Composition in mass %: Cr=17.70 , Mn=0.36, Ni=0.45, C=1.09, Mo=0.53, Si=0.46, P=0.016, S=0.009, Fe=balance) were sieved into different size fractions. A sieving column with 25 µm and 20 µm sieves was used (20.32 cm diameter, brass frame, Advantech Manufacturing, New Berlin, WI, U.S.A.) [300]. The powders were added to the top sieve, 10 g at a time, and shaken 105  (Ro‐tap, model RX‐29, W.S. Tyler, Mentor, Ohio, U.S.A.) for ten minutes each time to separate the powders into different size fractions. After the last quantity of powder was added, the assembly was shaken for another 198 minutes. The size fractions obtained by sieving were analyzed by laser light scattering (Malvern Mastersizer 2000, Spectris, Egham, U.K.) in distilled water. Since the gravimetric yield of the +25 µm size fraction was low, a special low‐volume dispersion system was used (Malvern Small Volume Dispersion Unit DIF2021 custom‐adjusted to a Hydro 2000MU scattering window). 1.0 ± 0.1 g of each powder was introduced into the unit while rotating the impeller at 3300 rpm. An external sonicator (Misonix Sonicator 3000 with HS‐306 probe, Misonix, Farmingdale, NY, U.S.A.) was used to disperse the particles in the suspension for 15 minutes at 84 W. Trapped air bubbles were allowed to escape prior to the measurement by briefly stopping the rotation of the impeller. Particle size distribution data were recorded ten times and averaged. The AISI 440C powders were deposited as thin layers on shallow cast alumina crucible pieces (AD‐94, Coorstek, Golden, CO, U.S.A., approximate dimensions 2x2x0.4 cm). The crucibles were prepared by cleaning them in an acidic mixture made of equivalent volumes of HCl (trace metal grade), HNO3 (American Chemical Society (ACS) reagent grade), and 30% H2O2 (ACS reagent grade, all obtained from Fisher Scientific, Nepean, ON, Canada) for 2 minutes, followed by 15 minutes of sonication (B‐42 Branson, Sheeton, CT, U.S.A.) each in ethanol (histological grade), acetone (histoprep), and distilled water. Finally, the cleaned crucibles were heat treated at 1373 K for one hour. The steel powders were placed on the alumina crucibles and heat treated at elevated temperatures in air (Thermolyne 48000, Thermo Fisher Scientific, Waltham, MA, U.S.A.). The mass gain of the powders was determined after oxidation at predetermined intervals. Before oxidation, the different AISI 440C stainless steel powder size fractions were analyzed by BET surface area analysis (SA3100, Beckman Coulter, Fullerton, CA, USA). A total of 0.50 ± 0.03 g of each powder particle size distribution was prepared in thin‐necked glass tubes with the smallest hollow volume possible. BET isotherms were 106  recorded for each of the sieved powder fractions. For the pore size distribution, the entire adsorption‐desorption isotherm was recorded twice and averaged. This analysis was performed in order to see if the unoxidized steel particles could be modelled as solid spheres with no or negligible surface pores. The crystal phases of the unoxidized and the oxidized materials were analyzed by XRD (D8 advance, Bruker axs, Karlsruhe, Germany) by grinding the materials into powders using an agate mortar and pressing thin, continuous layers of the different powders onto silica glass slides with the help of a stainless steel piston. The crystal structure of the powders was analyzed at defined time intervals during the cyclic oxidation. The XRD scans were performed from 2θ angles of 20° to 120° in 4715 steps with a 0.1 second/step scan rate, using a 0.2 mm emission slit, CuKα radiation, and a position sensitive detector (Våntec‐2000, Bruker axs, Karlsruhe, Germany). Some peaks (35.1° to 36.6° and 34° to 38° 2θ angles) were scanned with a five seconds/step scan rate for higher resolution. The data were background‐subtracted and Kα₂ stripped before analysis [301]. The peak shift of the XRD instrument was determined and all scans were adjusted accordingly. This was done by scanning a National Institute of Standards and Technology (NIST) 1976 standard corundum material at ambient conditions in the 34.2° to 35.8° range with a 0.5 second/step scan rate and 0.005° step widths using a 0.6 mm emission slit and comparing the resulting peak with the standard (012) peak at 35.139° [302]. The alignment of the XRD measurement was checked by mixing an internal reference material of highly crystallized LaB6 powder (Lot 046, calibrated against NIST standard reference material (SRM) 640c‐silicon, the Gem Dugout, State College, PA, U.S.A.) to the specimen powder. The XRD peaks found were aligned with the peaks of the reference materials in the database and adjusted for the instrument shift [303]. Then, the crystallographic peaks were compared with published diffraction data in the database such as AISI 410L [304], AISI 304 [305], γ‐CrFe7C0.45 [306], Fe2O3 [273], Cr2O3 [307], and (Fe,Cr)2O3 [308].  107  6.3.  Results and discussion of the mass gain experiments  The mass fraction distribution of the AISI 440C powder resulting from sieving is shown in Table 6.1. The majority of particles were smaller than 20 µm. Table 6.1: Mass fractions of the sieved AISI 440C powders Size fraction Mass fraction fm (%)  ‐20 µm 96.05  ‐25/+20 µm 3.53  +25 µm 0.42  Figure 6.1 shows the volume fraction distribution of the different size fractions of the AISI 440C powders as determined by dynamic laser light scattering (DLS).  Figure 6.1: Particle size analysis (PSA) of AISI 440C powder size fractions by dynamic laser light scattering. From the graphs in Figure 6.1, the mean particle diameter, Dmp, was calculated (Eq. 6.1). D  ∑  D ∑  f  ,  f  ,  ,  Eq. 6.1 108  Here, n is the number of diameters measured, Dm is the discretized diameter of each individual particle of the metal powder, and fv is the volume fraction (in %) of the particles having that diameter. The resulting average diameters of each sieved powder size fraction are listed in Table 6.2. The SEM micrograph of the AISI 440C powder in Figure 6.2 shows the spherical shape of the particles.  Figure 6.2: SEM micrograph of AISI 440C powders before oxidation. Reference density data for the AISI 440C alloy are in the range of ρm=7.65 gcm‐3 [309], ρm=7.70 gcm‐3 [310], and ρm=7.80 gcm‐3 [311]. For the purpose of these calculations, the density of the metal was assumed to be ρm=7.70 gcm‐3 [310]. In order to calculate the mass specific surface area and the relative mass gain of the material due to oxidation, the discreetly measured particle diameters Dm of the particle size distribution (Figure 6.1) were used to calculate the volume of each sphere, Vs,m, following Eq. 6.2. πD 6 The mass, ms,m, of each discretized particle was calculated using Eq. 6.3. V,  m  ,  V, ρ  Eq. 6.2  Eq. 6.3  The metal surface area, As,m, of these particles was calculated using Eq. 6.4.  109  A  πD  ,  Eq. 6.4  From Eq. 6.3 and Eq. 6.4, the mass specific surface area of each discretized particle size, SAs,m, was calculated using Eq. 6.5. SA  ,  A, m,  Eq. 6.5  The values calculated here in Eq. 6.2 to Eq. 6.5 were used in the model (section 6.4) and are summarized in Table 6.2.  Table 6.2: Mean particle diameters and mass specific surface areas of sieved powder fractions, calculated from the particle size distributions shown in Figure 6.1. Powder size fraction as‐received (unsieved) ‐20 µm ‐25/+20 µm +25 µm  Mean particle diameter Dmp (μm) 16.8 14.1 21.2 31.8  Mass specific surface area SAs,m (m2g‐1) 0.063 0.076 0.039 0.028  The crystal phases and crystallite sizes of the oxides formed on the surface of the AISI 440C powder at elevated temperatures were analyzed by XRD and compared with a literature database [254]. After ten hours at 1073 K, eskolaite (Cr2O3) and hematite (Fe2O3) oxide peaks appear in the recorded XRD spectra. Figure 6.3 shows the contributions of the two oxides to the diffraction peaks between 35.1° and 36.6°. After 90 additional hours of oxidation, the metallic peaks are very small compared with the oxide peaks. This indicates that the oxidation is almost complete. Further changes in XRD patterns may be due to changes in oxide composition and crystallite sizes. The ratio of both the volume of oxide phase compared to metallic phase and the ratio of hematite versus eskolaite phase increases during the first 100 hours of oxidation. This can be explained by the oxidation of the available chromium during the early stages of heat treatment, and oxygen reacting mainly with iron in the remaining bulk material at later stages during the first 100 h of oxidation. This means that Fe2O3 is already growing within the first 100 h of oxidation at 1073 K. 110  Figure 6.3: XRD pattern of AISI 440C powders after 10 h at 1073 K. 5 sec/step high resolution XRD scan of the 2θ region from 35.1° to 36.6°. Peaks indicated based on these references: Fe2O3: [273], Cr2O3: [307] An additional 900 hours at 1073 K resulted in little change in the XRD pattern (Figure 6.4), which agrees with the mass change findings: near‐complete oxidation of the powders appears to have occurred within the first 100 h. Table 6.3 shows the various oxidation conditions of the powders and the phases found in each case. The findings correlate well with results by Molin et al., who found ferrous oxide scales on AISI 430L spheres oxidized under similar oxidation conditions [104].  Figure 6.4: XRD pattern of AISI 440C powder, after 1000 h at 1073 K. The powder appears to be completely oxidized. All peaks fit the Fe2O3 phase described in reference [273]. In order to see if any further mass change after 1000 h at 1073 K could be observed, a set of thus pre‐oxidized powders of the unsieved powder fraction was exposed to 1173 K, 1273 K, and 1423 K for an additional 150 h each. Table 6.3 summarizes the oxidation conditions used and correlates them with the phases found by XRD.  111  Table 6.3: Phases found by XRD analysis of the oxidized metal powders. First oxidation (time (h) / Temp (K)) 10/1073 25/1073 50/1073 75/1073 100/1073 500/1073 1000/1073 1000/1073 1000/1073 1000/1073  Second oxidation (time (h) / Temp (K)) ‐ ‐ ‐ ‐ ‐ ‐ ‐ 150/1173 150/1273 150/1423  Phases BCC steel, eskolaite, hematite BCC steel, eskolaite, hematite BCC steel, eskolaite, hematite BCC steel, eskolaite, hematite eskolaite, hematite eskolaite, hematite eskolaite, hematite hematite hematite hematite  Using the Scherrer equation (Eq. 6.6) to determine the crystallite sizes of the oxides formed at the conditions outlined in Table 6.3, it was found that there was almost no change in crystallite size during heat treatment at 1073 K over 1000 h. Kλ βcosθ  phkl dhkl  thkl  Eq. 6.6  In Eq. 6.6, thkl is the crystallite thickness, phkl is the number of crystal planes per crystallite, dhkl is the distance between two crystal planes, λ is the wavelength of x‐ray radiation (0.154 nm for Cu‐Kα radiation), θ is the Bragg angle, and K is a form factor related to the shape of the crystallite. For unknown shapes, this factor can be approximated as 0.90 [312], [313]. The theoretical peak broadening, β, is a function of the full width (in degrees) of the recorded XRD peak at half maximum (FWHM2Θ), B, from which the effect of instrument broadening (also in degrees), bi, is subtracted, following Eq. 6.7 [314]. β  B  b  Eq. 6.7  The crystallite size of the oxides changed from 50±3 nm after 50 h at 1073 K (not shown) to 53±3 nm after 1000 h at 1073 K. After 1000 h at 1073 K, the oxidized specimens were heated for 150 h at 1173 K, 1273 K, and 1423 K, respectively. The oxide crystallite sizes increased to 56±3 nm, 82±5 nm, and 143±9 nm, at 1173 K, 1273 K, and 1423 K, respectively, as shown in Figure 6.5. This shows that the oxides formed at 112  1073 K do not change even when exposed to 1073 K for 1000 h. The XRD peak intensities and the reproducibility of the XRD results are discussed in Appendix M.  Figure 6.5: Scherrer crystallite sizes of oxidized AISI 440C powder, heat treated at different temperatures for 150 h each, after having been exposed to 1073 K for 1000 h (the initial crystallite size after the pre‐exposure is indicated by the value at 1073 K). One aim of increasing the temperature beyond 1073 K was to see if further mass gain could be observed, or if mass stabilization and complete oxidation had occurred after 100 h at 1073 K. The unsieved AISI 440C powders oxidized at 1073 K gained 0.16 mass% between 500 h and 1000 h. When exposed to temperatures exceeding 1173 K, a small mass loss was observed. Heated to 1173 K for 150 h, the mass change was approximately ‐0.1 mass%, after 150 h at 1273 K, the mass change was approximately ‐0.2%, and when heat treated at 1423 K, the mass change was approximately ‐0.8 mass%. Only the mass loss at 1423 K was larger than the deviation in average maximum relative mass gain of 41.3 ± 0.2 mass% averaged across specimens of all AISI 440C powder size fractions oxidized for 1000 h at 1073 K. Some metals, for example chromium, may volatilize from the analyzed materials at elevated temperatures [48]. Specimens oxidized at 1073 K still gained mass between 500 h and 1000 h, and even after 1000 h at 1073 K, the overall observed mass gain was lower than 113  what would be expected from the elemental oxidation models described in Appendix L. Based on the elemental composition, the relative mass gain of the AISI 440C powders should be between 42.1 ‐ 43.3 mass%. Some metallic material may have been retained in the oxidized particles, as there was still an increase of 0.16 mass% between 500 h and 1000 h at 1073 K. Even after long times at elevated temperatures, the different size fractions still increased their overall mass due to oxidation, albeit slowly, as shown in Figure 6.6 to Figure 6.8. The small difference between the calculated (Appendix L) and the experimentally observed mass gain could be due to some of the elements forming oxides of mixed stoichiometry and due to some of the species volatilizing over time. Also, the composition of the particles may have changed from the initial elements that were added during powder production, potentially due to volatilization of some elements during the production process. Figure 6.6 shows the relative mass gain (mrel, in %, calculated from Eq. 6.8) of the different AISI 440C size fractions oxidized at 1073 K as a function of the square root of time. In Eq. 6.9, mtot(t) is the measured mass of the oxidized powder at time t, and mm(t=0) is the initial mass of the unoxidized metal powder. m  m  t m  m t t 0  0  x100  Eq. 6.8  From the data shown in Figure 6.6, it appears that the relative oxidation mass gain during the first hours was slower than during later times, before approaching the maximum relative oxidation mass gain. This effect was more pronounced for larger spheres. Since the mass fractions of the different powder sizes show that most of the powders were 20 µm in diameter or smaller (Table 6.1), the difference in relative mass gain between unsieved and the ‐20 µm powder size fractions could be expected to be small. The ‐25/+20 µm powder size fraction had a slower initial relative oxidation mass gain, but reached a plateau of near‐maximum oxidation mass gain after 80 h. The +25 µm powder size fraction had an even slower relative oxidation mass gain up to 100 h compared with the other powder size fractions.  114  Figure 6.6: Comparison of mass gain relative to unoxidized mass at 1073 K between the different AISI 440C powder size fractions. The reduction in the remaining metal core diameter due to oxidation affects the metal surface area of small particles more strongly than the metal surface area of larger particles. Consequently, the surface area changes more slowly on larger spheres (such as the +25 μm size fraction) than on smaller spheres (such as the ‐20 μm size fraction). Powders with smaller spheres contain more initial surface area per unit mass of powder (Table 6.2) and relative oxidation mass gain is therefore more rapid. Also, larger spheres contain a larger overall molar quantity of chromium, delaying the onset of iron oxidation. Figure 6.6 also shows that a slower initial mass gain is followed by a rapid mass gain. This shows that at least two distinct stages of oxidation can be detected in the oxidation of AISI 440C powder (Figure 6.6), which may correlate to different types of oxide forming on the different spheres. On larger spheres, it takes a longer time until the second, rapid mass gain occurs. The maximum relative mass gain is determined by the elements in the alloy and the oxides formed (Appendix L). 115  As the differences between the different oxidation rate constants could not be easily observed at 1073 K, oxidation experiments were also performed at 920 K and 1023 K for all sieved size fractions, and at 873 K and 973 K for the unsieved size fraction. The temperature of the furnace operating at 920 K was confirmed by a NIST certified thermocouple. The relative oxidation mass gain of the different AISI 440C powder size fractions are shown Figure 6.7 (920 K) and Figure 6.8 (1023 K).  Figure 6.7: Comparison of relative mass gain of the different AISI 440C powder size fractions at 920 K.  116  Figure 6.8: Comparison of relative mass gain of the different AISI 440C powder size fractions at 1023 K. The oxidation mass gain of the different powder size fractions at 1023 K, and even more so at 920 K, shows at least two distinct oxidation rates, more distinctively visible than at 1073 K. The first oxidation rate is slow, and can be observed much longer for larger sphere diameters. Also, the first oxidation rates of the different sieved size fractions are more similar at low temperatures (920 K, Figure 6.7) than at higher temperatures (1073K, Figure 6.6), which may indicate that at higher temperatures there may already be an influence of Fe oxidation during this initial oxidation stage. The error bars in Figure 6.6 ‐ Figure 6.8 are noticeable for the fast oxidation region. This is due to the difference in the onset of this fast Fe2O3 oxidation between the different individual powder specimen crucible pieces. While pouring the powders onto the dishes, small differences in the size distribution of the powders on each individual dish may have occurred.  117  The oxidation experiments at 873 K and 973 K were carried out with only the unsieved powder size fraction, over too short a time period, and with too few mass measurements to observe the fast oxidation rates observed at 920 K, 1023 K, and 1073 K. Consequently, they were only used for the SEM and EDX analyses of the microstructure and composition. As a reference, the published mass gain of flat AISI 440C sheet oxidized at 1073 K is shown in Figure 6.9 [174]. The oxidation mass gain of this flat sheet also seems to change with time. The oxidation of the AISI 440C sheet was, however, not analyzed long enough to observe how the oxidation mass gain of the flat sheet would progress until reaching the maximum theoretical relative mass gain. Also, the authors did not report the relative mass gain.  Figure 6.9: Oxidation mass change of AISI 440C sheet at 1073 K as a reference from published literature. Data reprinted from [174] with permission of Elsevier. In order to correlate the mass gain observed experimentally to physical phenomena, cross sections of the oxidized steel particles were prepared by embedding them in epoxy resin, cutting by diamond saw, and polishing of the surface with a 1 μm surface finish. Figure 6.10 shows the surface of unsieved AISI 440C powder after 10 h and 100 h at 873 K. Few oxide scales are visible. After 100 h, individual, discontinuous oxide crystals appear on the surface (bright spots in the micrograph). Figure 6.11 shows the surface of unsieved AISI 440C powder after 10 h and 100 h at 973 K. After 100 h, the 118  surface of the particles is covered in a continuous oxide layer. Oxidation at 1073 K is more noticeable (Figure 6.12). After 10 h, the spheres are covered in a continuous oxide scale, which grows thicker and into a slightly less regular spherical shape after 100 h.  A  B  Figure 6.10: SEM micrograph of unsieved AISI 440C powder after (A) 10 h at 873 K and (B) 100 h at 873 K. Some oxide crystals (bright spots) can be seen on the surface of the particles after 100 h.  A  B  Figure 6.11: SEM micrograph of unsieved AISI 440C powder after (A) 10 h at 973 K and (B) 100 h at 973 K, showing the oxide surface of the particles.  A  B  Figure 6.12: SEM micrograph of unsieved AISI 440C powder after (A) 10 h at 1073 K and (B) 100 h at 1073 K, showing severe oxidation of a particle.  119  The surface micrographs (Figure 6.10 to Figure 6.12) were correlated with the cross sections of the oxidized particles after longer oxidation times (Figure 6.13 to Figure 6.18). Figure 6.13 shows the cross section of AISI 440C particles oxidized for 100 h and for 1500 h at 873 K. Little oxidation can be observed after short times (100 h), and even after 1500 h, only a thin oxide scale forms on the surface of the steel particles. The EDX elemental maps of the same region after 100 h are shown in Figure 6.14. Little oxygen is present at the surface of the particles, and none of the smaller particles examined have oxidized throughout. Figure 6.15 shows the cross section of AISI 440C particles oxidized for 100 h and for 1000 h at 973 K. After 100 h, a continuous surface oxide scale is visible on the spheres and some of the smaller particles contain oxide throughout their entire cross sectional area, which can be seen in the EDX elemental map shown in Figure 6.16. Also, the larger spheres show a high Cr content in the oxide layer on the surface of the sphere, a Cr depleted region inside that circumference, and again a higher Cr content towards the centre of the sphere. This indicates that some Cr depletion occurs in the unoxidized alloy due to the formation of a surface chromia layer, as also reported by Wohlfromm et al. [151]. If the sphere is sufficiently large, the Cr cation diffusion may not occur all the way to the centre of the sphere, where the Cr content observed in cross section may increase again. After 1000 h at 973 K, some of the oxidized material has started to grow together. Figure 6.17 shows the cross section of AISI 440C particles oxidized for 100 h and for 1000 h at 1073 K. The particles appear to be oxidized throughout their entire cross sectional area. This correlates well with mass gain experiments, which show little additional mass gain after 100 h. Figure 6.18 shows the EDX elemental map for the same region as in Figure 6.17 A, which shows the presence of oxygen throughout the particles. The morphology of the materials changes little between 100 h and 1000 h at 1073 K, but different regions of the oxide may have grown together more strongly, as shown in Figure 6.17 B.  120  A  B  Figure 6.13: SEM micrograph of unsieved AISI 440C powder after (A) 100 h at 873 K and (B) 1500 h at 873 K. After 100 h, there is little evidence of oxidation on the surface of the particles. After 1500 h, a thin oxide film has formed on the surfaces.  Figure 6.14: EDX elemental maps of unsieved AISI 440C powder cross sectioned after 100 h at 873 K (Figure 6.13 A). Maps: SE=secondary electron image, O=oxygen, Cr=chromium, Fe=iron.  A  B  Figure 6.15: SEM micrograph of unsieved AISI 440C powder after (A) 100 h at 973 K and (B) 1000 h at 973 K. After 100 h, a surface oxide film is visible on the spheres, after 1000 h, some of the oxide layers have grown together.  Figure 6.16: EDX elemental maps of unsieved AISI 440C powder cross sectioned after 100 h at 973 K (Figure 6.15 A). Maps: SE=secondary electron image, O=oxygen, Cr=chromium, Fe=iron. 121  A  B  Figure 6.17: SEM micrograph of unsieved AISI 440C powder after (A) 100 h at 1073 K and (B) 1000 h at 1073 K. Oxidation products are already visible throughout the spheres after 100 h, and after 1000 h, most of the oxides have grown together.  Figure 6.18: EDX elemental maps of unsieved AISI 440C powder cross sectioned after 100 h at 1073 K (Figure 6.17 A at a lower magnification). Maps: SE=secondary electron image, O=oxygen, Cr=chromium, Fe=iron. The microstructural and compositional analyses of the oxidized AISI 440C spheres show that the initial oxide formed on the surface of the spheres is a Cr‐rich oxide. This can be seen best in the cross sections of the AISI 440C powder oxidized for 1000 h at 873 K (Figure 6.13 B) or for 100 h at 973 K (Figure 6.15 A). The EDX elemental map of Cr in the cross section of the AISI 440C powder oxidized for 100 h at 973 K displays ring‐shaped high concentrations of Cr on the surface of the larger spheres (Figure 6.16). Once most of the chromium has oxidized, the remaining metal atoms oxidize, too, likely through a mixture of (Fe,Cr)2O3 and Fe2O3 oxidation. This secondary oxide growth proceeds with the second, fast oxidation observed in the mass gain measurements (Figure 6.7 to Figure 6.9). At 1073 K, oxidation occurs very quickly, and after 100 h, the particles are mostly oxidized throughout (Figure 6.17). During the oxidation of spherical particles, the surface area of the metal changes with time, as the diameters of the remaining metal cores shrink. Consequently, a theoretical model (Msph, described in detail in section 6.4) was developed to calculate 122  the area‐normalized mass gain based on a dynamically changing metal surface area of spherical particles during oxidation.  6.4.  Model (Msph) describing the oxidation of spherical particles  Based on SEM image analysis (Figure 6.2) and the results of BET surface pore analysis (Appendix N), the AISI 440C particles were modelled as perfect spheres. The initial surface area was calculated based on the geometrical dimensions of the sieved powder size fractions. Spherical particles typically oxidize from the outside to the inside as shown in section 6.3. Any mass gain can be assumed to derive from oxygen atoms being added to the metallic structure of the spheres. On a flat sheet, this changes the metal surface area very little. However, on small spheres, the volume of metal oxide formed translates into a thickness of an oxide layer which depends on the radius of the sphere and the metal surface area of the spheres, which changes during oxidation [179]. For simplification, the composition of the oxide and the metal core were calculated only on the basis of the Fe and Cr content of the alloy, and the oxides formed were assumed to be of the M2O3 type as indicated by the XRD results shown in section 6.3. The density of the AISI 440C alloy was assumed to be ρm=7.7 gcm‐3 [310]. For the calculations of the molar volumes of the metal and the oxides, the alloy was approximated as a Fe‐Cr compound with a molar ratio of fFe:fCr = 0.81:0.19, where fFe and fCr are the molar fractions of the metals, and fn is the composition. Table 6.4 shows reference values for the density, ρm, and molar mass, Mm, of the metals and the density, ρox, and molar mass, Mox, of the metal oxides, as well as the molar volumes of the metals, VM,m, and their oxides, VM,ox, calculated from Eq. 6.9 and Eq. 6.10. V  V  ,  ,  M ρ  Eq. 6.9  M ρ  Eq. 6.10  123  Table 6.4: Density, molar mass and molar volume of Fe, Cr (m) and their oxides (ox). Substance  Density ρm and ρox (gcm‐3) [17]  Molar mass Mm and Mox (gmol‐1) [17]  Fe Cr Fe2O3 Cr2O3  7.87 7.14 5.25 5.21  55.85 51.99 159.6 152.0  Molar volume VM,m and VM,ox (10‐6 m3mol‐1) 7.09 7.23 30.5 29.1  Figure 6.19 shows the oxidation model in a cross section of one oxidizing metal sphere. The initial radius of the metal sphere is Rinit, the total (growing) radius of the oxidizing sphere is Rtot, the remaining (diminishing) radius of the metal core is Rm, and the total thickness of the oxide is δox. The Thiele modulus, correlating chemical activity with a shape, and determining a size below which activity is only related to the amount of materials present, and no longer to the surface area, were not used in this work [315]. Future extensions of the model will incorporate those theories.  Figure 6.19: Oxidizing sphere model schematic, cross section.  124  The following equations describe the characteristics of the spherical oxidation model Msph. Eq. 6.11 shows how the change in oxide scale thickness, δox, and the metal surface area at any given time, As,m, are related to an oxidation mass gain rate constant ks and the oxidation time t. At t=0, no oxidation was assumed to have occurred on the powders (Rm = Rinit). d  δ A, dt  A  k  ,  Eq. 6.11  δ  As a first approximation, the mean particle diameter, Dmp, of the steel particles in each of the different particle size distributions was calculated from Figure 6.1 (Table 6.2). The mass changes observed in the mass gain experiments were correlated to the ns spheres with the mean particle diameter (Eq. 6.12) present in each measurement by calculating the metal volume of each individual sphere, Vs,m (Eq. 6.2), the metal mass of each sphere, ms,m (Eq. 6.3), and the metal surface area of each sphere, As,m (Eq. 6.4), at each point in time using the time‐dependent remaining metal radius of the particles, Rm=0.5Dmp.  n  m /m  Eq. 6.12  ,  The change in metallic volume due to oxidation can be calculated from the mass gain experiments as follows. For each steel sphere, the mass (mO, Eq. 6.13) and molar quantity (NO, Eq. 6.14) of the oxygen added during the oxidation experiments were calculated. Here, mtot(t) is the measured mass of the oxidized powder at time t, and mm(t=0) is the initial mass of the unoxidized metal powder. MO is the molar mass of oxygen (16.0 g/mol). m  m  t  N  m m M  t  0  Eq. 6.13  Eq. 6.14 125  The molar quantities of metal oxide, Nox, relate to the molar quantities of oxidized metal, Nm,ox, and oxygen, NO, as shown in Eq. 6.15. 1 1 Eq. 6.15 N , N 2 3 Consequently, the mass of the metal cations in the oxide, ms,m,ox (Eq. 6.16) can be N  calculated for each individual sphere with the molar mass of the metal, Mm (55.1 g/mol), and the number of spheres present (ns, Eq. 6.12). m  2 3N M n  , ,  Eq. 6.16  The mass of the oxide formed on each individual sphere, ms,ox, can then be calculated by adding the mass of the oxygen added to the stainless steel due to oxidation to the metal cations involved in the oxidation, assuming an M2O3‐type oxide formation (Eq. 6.17). 2 3N M Eq. 6.17 m, n The remaining mass of unoxidized metal in each sphere, ms,m,r, can be calculated by m  subtracting the mass of the oxidized metal of each sphere from the initial mass of each sphere (Eq. 6.18). m  0 m, , n The total mass of each sphere, ms, can be calculated from Eq. 6.19. m  t  , ,  m  m  t n  Eq. 6.18  Eq. 6.19  In order to calculate the time dependent total thickness of the oxide, δox, and the time dependent metal surface area, As,m, the masses calculated in Eq. 6.14 to Eq. 6.19 can be converted into volumes, in this case the time dependent metal volumes (Vs,m, Eq. 6.2) and oxide volumes (Vs,ox, Eq. 6.20) of the oxidizing steel spheres. The volume of the M2O3 oxide on each sphere, Vs,ox, can be calculated by subtracting the volume of the remaining metal core inside each sphere, Vs,m, from the total volume of the oxidizing sphere, Vtot, following Eq. 6.20. 126  m, Eq. 6.20 ρ Based on the mass gain observed during the oxidation measurements, the volume of V,  V,  4 π R 3  V,  δ  R  the remaining metal spheres can be calculated following Eq. 6.21, and the unoxidized radius of the steel spheres can be calculated following Eq. 6.22. V,  R  m, ρ  Eq. 6.21  3 V 4π ,  Eq. 6.22  The oxide scale thickness can then be calculated following Eq. 6.23, derived by inserting Eq. 6.22 in Eq. 6.20. R  δ  3 V 4π ,  V,  Eq. 6.23  The total volume occupied by each oxidized sphere, Vs,tot, can be calculated following Eq. 6.24, using the overall radius of the sphere Rtot described in Eq. 6.25. 4 π R 3  V, R  R  δ δ  Eq. 6.24 Eq. 6.25  The linear scaling of δox/As,m with t0.5 (Figure 6.20, justifying Eq. 6.11) allows the calculation of an oxidation growth rate constant, which can later be used to predict mass change under conditions similar to those of this experiment. An example of the slopes chosen for the calculations of the oxidation growth rate constants in the model is shown in Figure 6.20 for the ‐25/+20 µm powder size fraction oxidized at 1023 K. In addition, the two different slopes evidenced in the plot of Figure 6.20 further reveal the presence of two distinct growth rate constants. This observation indicates the presence of two different oxidation processes. The oxidation rate constants ks for the first oxidation process of the spheres (Cr2O3, ks,1) are shown in Table 6.5 and for the second oxidation process (Fe2O3, ks,2) are shown in Table 6.6. 127  Figure 6.20: Time‐dependent oxide scale thickness over time‐dependent metal surface area as a function of square root of time, indicating the two linear sections from which the oxidation constants ks were extracted, at the example of the ‐25/+20 µm size fraction of AISI 440C powder oxidized at 1023 K. Table 6.5: Cr2O3 oxidation growth rate constants (ks,1, in h‐0.5m‐1) for different AISI 440C sieved powder size fractions. Size fraction ‐20 μm unsieved ‐25/+20 μm +25 μm  920 K  1023 K  1073 K  44 30 13 8.3  339 264 70.6 39.1  646 487 103 60.0  Table 6.6: Fe2O3 oxidation growth rate constants (ks,2, in 103 h‐0.5m‐1) for different AISI 440C sieved powder size fractions. Size fraction ‐20 μm unsieved ‐25/+20 μm +25 μm  920 K  1023 K  1073 K  0.7 0.5 0.5 0.4  5.7 3.5 3.9 3.0  5.6 3.5 3.9 3.0 128  The oxidation growth rate constants ks are dependent on the activation energy for diffusion of rate limiting species (metal cations or oxygen anions), and follow an Arrhenius‐type relation, shown in Eq. 6.26. Here, A* is a pre‐exponential factor, EA is the activation energy for oxidation, R is the universal gas constant (8.314 JK‐1mol‐1), and T the temperature. k  A∗ e  Eq. 6.26  The activation energies of the oxidation rate constants shown in Table 6.5 were calculated from the slope of an Arrhenius‐type graph of ln(ks,1) as a function of 1/T and are shown in Figure 6.21. It can be seen that the oxidation rates of smaller sieved size fractions (such as ‐20 μm) are slightly more influenced by temperature than the oxidation rates of larger size fractions. The variations in the activation energy shown in Figure 6.21 derive from the statistical analysis described in detail in Appendix O. Future work is necessary to determine the exact contributions of metal cation and oxygen vacancy diffusion to the overall observed oxide growth rate, as well as the effect of grain boundaries and microstructural defects on diffusion [152‐156]. The connecting lines between data points in Figure 6.21 are inserted for better readability, and do not suggest a physical model.  Figure 6.21: Arrhenius‐type graph showing the activation energy of ks,1 (Cr2O3) with different size fractions of spherical AISI 440C particles. 129  The temperature dependence of the Cr2O3 oxidation rate (ks,1) on the surface of steel spheres with a known mean diameter shown in Figure 6.21 can be used as a predictive tool to calculate the oxidation rate constant at other temperatures, following Eq. 6.26. The changes in oxidation growth rate constant ks,1 as a function of mean particle diameter show that the oxidation rate is significantly faster for small particles than for larger particles, but the trend could not be correlated to a simple functional relationship (Figure 6.22). Future work is necessary to evaluate this phenomenon in further detail.  Figure 6.22: Influence of the mean particle diameter, Dmp, on the oxidation growth rate constant ks,1 (Cr2O3) at the analyzed temperatures. The Arrhenius‐type graph of ln(ks,2) as a function of 1/T of the oxidation rate constants shown in Table 6.6 are shown in Figure 6.23. The variations in the activation energy shown in Figure 6.23 derive from the statistical analysis described in detail in Appendix O. Since the oxidation rate constants at 1023 K and 1073 K were very similar, and only three temperatures were analyzed, no activation energy was calculated for ks,2. More closely spaced data acquisition points could be used in order to be able to resolve 130  the fast second oxidation rates at the different temperatures better. Additionally, oxidation mass gain should be analyzed at additional temperatures in order to improve the prediction tool suggested here by the fitting parameters shown in Figure 6.23. Clearly, further research is necessary to analyze the oxidation rate ks,2 in further detail.  Figure 6.23: Arrhenius‐type graph of ks,2 (Fe2O3) with different size fractions of spherical AISI 440C particles. Due to the similar values of ks,2 at higher temperatures (1023 K and 1073 K), the error in the slope is large. The connecting lines between data points in Figure 6.23 are inserted for better readability, and do not suggest a physical model. The temperature dependence of the Fe2O3 oxidation rate (ks,2) on the surface of steel spheres with a known mean diameter shown in Figure 6.21 can be used as a predictive tool to calculate the oxidation rate constant at other temperatures, following Eq. 6.26. However, due to the similar values of ks,2 at 1023 K and 1073 K (resulting from the data acquisition method used in this work), this predication has a high error. There is currently insufficient experimental data to accurately predict the changes in ks,2 as a function of temperature. Future oxidation 131  experiments at more temperatures and more acquisition data points will be carried out in the future to address obtain a more precise prediction tool for the fast iron oxide growth rate. The changes in oxidation growth rate constant ks,2 as a function of mean particle diameter (Figure 6.24) show that iron oxide formation is also significantly faster for smaller particles, and that the iron oxide growth rate seems to stabilize for larger particles. Similar trends were observed for all temperatures.  Figure 6.24: Influence of the mean particle diameter, Dmp, on the oxidation growth rate constant ks,2 (Fe2O3) at the analyzed temperatures. The time at which the switch from the first to the second oxidation rate constant occurs was determined experimentally. Figure 6.25 shows the oxidation rate switch time for the different sieved powder size fractions listed in Table 6.7. It can be seen that the switch occurs much later for the large (+25 μm) size fraction than for the other three smaller size fractions. Also, the switch time was very similar for the ‐20 μm and the unsieved size fraction, which is probably due to the similarity in particle size for these two size fractions.  132  Table 6.7: Cr2O3‐Fe2O3 oxidation rate switch time, in hours, for the different sieved powder size fractions constants. Size fraction ‐20 μm unsieved ‐25/+20 μm +25 μm  920 K  1023 K  1073 K  545 641 1424 5553  138 161 246 545  26 27 39 94  Figure 6.25: Arrhenius‐type graph of oxidation duration at which ks,1 switches to ks,2, as determined by the mass gain measurements of AISI 440C powders with different sieved size fractions. The variations in the activation energy shown in Figure 6.25 derive from the statistical analysis described in detail in Appendix O (Figure O.1). The connecting lines between data points in Figure 6.25 are inserted for better readability, and do not suggest a physical model. By using the curve fitting shown in Figure 6.25, the oxidation type switch times of similar powder size distributions can be calculated for other temperatures. However, it can be seen in Figure 6.25 that the projection of the 133  oxidation rate time switch at other temperatures involves significant error. The oxidation type switch time (Figure 6.25) did not follow the Arrhenius‐type behavior described in Eq. 6.26 very well. The analysis of the oxidation type switch time at additional temperatures may help to improve the accuracy of this prediction. However, the oxidation type switch time can be calculated as a function of mean particle diameter, as shown in Figure 6.26. It appears that the oxidation time at which Cr2O3 oxidation changes to Fe2O3 oxidation can be predicted as a function of mean particle diameter indicated in Figure 6.26.  Figure 6.26: Oxidation time, ts, at which ks,1 switches to ks,2, as determined by the mass gain measurements of AISI 440C powders with different sieved size fractions. The prediction tools of the oxidation behaviour of stainless steel spheres as a function of either mean particle diameter or temperature are summarized in Table 6.8‐ Table 6.11. Table Table 6.8, Table 6.9, and Table 6.10 assume a thermally activated process as described in Eq. 6.26. Table 6.11 follows the fit of the data presented in Figure 6.26. 134  Table 6.8: Parameters for the prediction of oxidation behavior of Cr2O3 on spherical steel particles (ks,1) based on curve fitting results performed in this work. Size fraction ‐20 μm unsieved ‐25/+20 μm +25 μm  ‐0.5  m‐1) 22.9 23.4 17.8 16.3  A* (h  EA (kJ/mol)  146±8 153±12 116±13 108±9  Table 6.9: Parameters for the prediction of oxidation behavior of Fe2O3 on spherical steel particles (ks,2) based on curve fitting results performed in this work. Size fraction ‐20 μm unsieved ‐25/+20 μm +25 μm  ‐0.5  m‐1) 22.9 21.1 21.1 21.0  A* (h  EA (kJ/mol)  125±29 114±25 113±25 113±27  Table 6.10: Parameters for the prediction of the time (in hours) until the surface oxidation of stainless steel spheres changes from ks,1 to ks,2, depending on oxidation temperature (large error). Size fraction ‐20 μm unsieved ‐25/+20 μm +25 μm  ‐0.5  m‐1) ‐13.4 ‐14.1 ‐16.4 ‐18.9  A* (h  EA (kJ/mol)  152±34 159±38 182±35 211±25  Table 6.11: Parameters for the prediction of the time (in hours) until the surface oxidation of stainless steel spheres changes from ks,1 to ks,2, depending on mean particle diameter Dmp. Size fraction 920 K 1023 K 1073 K  Pre‐exponential factor (h)  Slope (exponential factor)  75.0 44.6 8.12  0.136 0.079 0.076  In order to model the oxidation behaviour of spheres of different diameters, the oxidation constants ks obtained by mass gain experiments were used to predict the 135  mass gain of the powders. In a case where the mass gain was not measured, and only the oxidation growth rate constant and initial metal radius of an oxidizing sphere are known, the relationship between δox/As,m can be expressed in terms of the metal radius Rm at time t. Assuming that the metal mass is conserved throughout the oxidation, the mass of the metal in a sphere ms,m at time t=0 h is the same as the sum of the mass of the remaining unoxidized metal, ms,m,r, and the metal in the oxide, ms,m,ox, at any time t. m  t  ,  0  m  m  , ,  ρ  , ,  πR  Eq. 6.27  Knowing how the molar quantities of metal oxide, Nox, oxidized metal, Nm,ox, and oxygen, NO, relate to each other from Eq. 6.15 allows the mass of the oxidized metal (ms,m,ox, which is related to the oxide scale thickness, δox) to be calculated following Eq. 6.28, in which Mm is the molar mass of the metal (Table 6.4). m  N , ,  M  ,  2N M n  n 8π ρ 3  M M  R  2M m M δ  ,  Eq. 6.28  R  Using Eq. 6.28, Eq. 6.27, can be rearranged to Eq. 6.29, which expresses δox as a function of the remaining metal radius Rm. m  δ  ,  t 0 ρ 8π M ρ M 3  πR  R  R  Eq. 6.29  For a spherical system in which Rm and As,m change over time, the relationship between the thickness of the oxide and the remaining metal surface area was found to be linear with the square root of time (Figure 6.20) and can be expressed following Eq. 6.30 (as a solution to Eq. 6.11), for 0<Rm<Rinit, and 0<t<tox, where tox is the overall duration of the oxidation. m δ A,  ,  t 0 ρ 8π M ρ M 3 4πR  πR  R  R  Eq. 6.30 k √2t 136  By inserting possible values for Rm, and knowing ks from mass gain experiments (for example Figure 6.20), values for the time t at which Rm has the specified value were calculated for all temperatures (920 K, 1023 K, 1073 K) for the analyzed sieved particle size fractions. The resulting calculated relative mass gain was compared with the relative mass gain observed in experiments for each powder size fraction at 920 K (Figure 6.27), 1023 K (Figure 6.28), and 1073 K (Figure 6.29).  A  B  C  D  Figure 6.27: Calculated relative mass gain compared with measured relative mass gain for a spherical oxidation curve fitting model Msph at 920 K. (A) unsieved, (B) ‐20 μm, (C) ‐25/+20 μm, (D) +25 μm powder size fraction of AISI 440C powders.  137  A  B  C  D  Figure 6.28: Calculated relative mass gain compared with measured relative mass gain for a spherical oxidation curve fitting model Msph at 1023 K. (A) unsieved, (B) ‐20 μm, (C) ‐25/+20 μm, (D) +25 μm powder size fraction of AISI 440C powders.  A  B  C  D  Figure 6.29: Calculated relative mass gain compared with measured relative mass gain for a spherical oxidation curve fitting model Msph at 1073 K. (A) unsieved, (B) ‐20 μm, (C) ‐25/+20 μm, (D) +25 μm powder size fraction of AISI 440C powders. 138  The relative mass gain calculated with the present spherical oxidation model Msph at all temperatures confirms that there is an initial time duration during which oxidation occurs on the spherical particles with the first, slow oxidation rate constant, and then switches to a faster oxidation rate constant. The present model, Msph, shows that the changes in mass are influenced by the initial diameter of the spheres. The first oxidation stage, fitted by the spherical oxidation model, Msph, in Figure 6.27 to Figure 6.29, can be attributed to the formation of one species of oxide, in this case a Cr‐ rich oxide, as indicated by the occurrence of Cr and O on the outside shell of AISI 440C particles oxidized for 100 h at 973 K (Figure 6.16) and the eskolaite phases found by XRD (Table 6.3). A second type of oxidation occurred, as can be seen by the step‐like increase of the experimentally measured relative mass gain with time (Figure 6.27 to Figure 6.29), which can be fitted using a second oxidation rate constant. This second oxidation likely involves the formation of Fe‐rich oxides such as Fe2O3, as indicated by the occurrence of Fe and O in the formed oxides of AISI 440C particles oxidized for 100 h at 1073 K (Figure 6.18) and the high temperature oxidation XRD data shown in Figure 6.3, indicating the formation of M2O3‐type oxides. It can be observed from Figure 6.27 to Figure 6.29 that the calculated relative mass gain is in good agreement with the measured relative oxide mass gain. However, some deviations are visible during the switch from the first oxidation growth rate constant to the second, for example for the relative oxidation mass gain of the +25 μm AISI 440C powder size fraction between 450 h and 550 h at 1023 K. There may be other mixed (Fe,Cr)2O3 species oxidizing in this region. However, the model proposed here (Msph) physically only assumes the creation of two distinct oxide species. In the time span between the two different assumed oxide growth regions, an oxide growth region with oxide growth rates in between the first and second region could exist. Additionally, there is a small difference between the maximum relative mass gain calculated and the experimental measurements. The final calculated maximum relative mass gain is slightly higher than the measured maximum relative mass gain. Reasons for a higher calculated mass gain could be variations in powder composition from the reported average 139  composition of the powders, variations in density of the oxides formed, variations in the average density of this particular composition of AISI 440C, the distribution of particle sizes in each sieved size fraction that was simplified to one average diameter in this model, and possibly due to volatilization of some of the elements [316]. While calculations based on the assumptions of different oxide densities could be performed with the effect that the calculated maximum relative mass gain would be more closely matched to the measured maximum relative mass gain, such a treatment is unlikely to provide further scientific insight about oxidation rate kinetics of spherical particles. The model proposed here (Msph) shows that the oxidation mass gain observed on spherical particles is influenced by its non‐planar microstructure, and by the effect of at least two different oxidation rate constants. Future refinements of the model could include using the entire particle size distribution in the calculations.  6.5.  Conclusions ‐ Oxidation of spherical steel particles  This section analyzed the oxidation behaviour of spherical AISI 440C stainless steel powder. It was found that due to the small particle sizes of the analyzed powders, the oxidation of the AISI 440C particles was almost complete after 100 h at 1073 K, indicated by a significant reduction in mass gain from 100 h to 1000 h as compared with the mass gain from 20 h to 100 h. Very little mass loss was observed when powders that were oxidized for 1000 h at 1073 K were heat treated at 1273 K or 1423 K for an additional 150 h, which indicates that mass loss due to volatilization at lower temperatures likely has little effect on the measured mass gain of the materials. XRD spectra of the unsieved oxidized AISI 440C powders showed no metallic peaks from 100 h oxidation time at 1073 K onwards (section 6.3). This correlated well with mass gain measurements and showed that oxidation was almost complete after 100 h at 1073 K for all sieved size fractions of AISI 440C powder. The average mass gain of approximately 0.16 mass% from 100 h to 1000 h at 1073 K indicated that only very little further oxygen was added to the material. The ratio of both the volume of the 140  oxide phase compared to the metallic phase and the ratio of hematite phase versus eskolaite phase increased during high temperature treatment. This implies that almost complete oxidation of the available chromium occurs during the early stages of oxidation, and that oxygen reacts mainly with iron in the remaining bulk material in the later stages. The experimentally observed maximum relative mass gain at 1073 K was slightly lower than the expected theoretical maximum mass gain based on elemental composition (Appendix L), possibly indicating that either the mass gain had not yet been completed after 1000 h at 1073 K or that some volatilization occurred. Oxides found by XRD matched Cr2O3 and Fe2O3. Scherrer crystallite size calculations showed little changes in oxide crystallite size over 1000 h at 1073 K (section 6.3). However, significant crystallite growth was observed when the material that was oxidized for 1000 h at 1073 K was heat treated at temperatures above 1173 K. For the operation of an SOFC this means that no such changes in crystallite growth occur at typical operating conditions. The surface nanostructure of the steel powders was found to be very similar for all the different sieved size‐fractions, with the bulk volume of nano‐pores smaller than 5 nm (Appendix N). This observation means that the particles can be modelled as smooth spheres without having to account for additional features such as protrusions or cavities, thus simplifying the modelling of surface oxidation for this set of spherical particles. Changes in oxidation growth rate were observed for the different sieved particle size fractions (section 6.4). An initial, slow oxidation rate of a Cr‐rich oxide on the surface of the spheres was observed. This behaviour was more pronounced at low temperatures and for the large AISI 440C size fractions. This is in good agreement with Alitavoli et al., who found that oxidation layer thicknesses increased slower on larger spheres (106 µm versus 39 µm average powder diameter) of copper and steel (of undisclosed composition) [123]. This also matches the EDX elemental maps of cross sectioned AISI 440C powders after 100 h at 973 K (Figure 6.16) that showed that smaller spheres oxidized throughout while larger spheres formed a protective Cr‐rich surface 141  layer. After the chromium content underneath this surface oxide layer was depleted, a faster second oxidation rate could be observed. Likely, this second oxidation process mainly involved the oxidation of Fe, with only small remaining quantities of Cr oxidizing. The larger the initial steel spheres, the longer the first oxidation rate was observed and the lower the Cr2O3 oxidation activation energy, indicating that the oxidation of larger spheres may be less susceptible to temperature changes. At 920 K, for example, the first, slow oxidation rate was dominant for more than 4900 h for the +25 µm size fraction, much longer than for any of the other analyzed size fractions. This behaviour may be related to the overall molar quantity of Cr present in the spheres. In larger spheres, more Cr was present, and consequently Cr depletion in the metal may have occurred later than in smaller spheres. It is also possible that the oxides formed on the surface of larger spheres are more protective. Very small spheres could have a curvature that is too large for the chromium oxide to cover protectively, resulting in an earlier appearance of iron containing oxides. This phenomenon has direct implications on SOFC technology, as it means that very thin (<20 μm) metallic features should be avoided in metal‐supported SOFCs, in order to prevent an early occurrence of Fe2O3 formation. Further work is necessary in order to evaluate this phenomenon in detail. At higher temperatures, for example 1073 K, the faster oxidation of Fe‐rich oxides occurred early, within the first tens of hours of the experiments, so that a differentiation between the two different oxidation rates was difficult. It may be beneficial in future work to observe the behaviour of all sieved size fractions for longer times at lower oxidation temperatures. The model describing metal oxidation on spherical surfaces proposed in this section, Msph, is based on a two‐step oxidation behaviour observed for the AISI 440C alloy (section 6.4). The switch between these two oxidation rates was determined experimentally. The model can be used as a validation tool to explain the mass gain observed during oxidation of metallic spheres and showed that during the oxidation of metallic spheres, δox/As,m scales linearly with the square root of time. It was found that there was a region between the first and the second oxidation rate in which the relative 142  mass gain appears to occur with an oxidation rate that ranged in between the two oxidation rates (of Cr2O3 and Fe2O3). Such a difference could result from a different oxidation rate constant, for example resulting from the formation of mixed (Fe,Cr)2O3 oxides. Also, the model Msph slightly overestimated the final relative mass gain. The oxides formed may have a lower density than the oxide density that was assumed in these calculations, some materials may have volatilized at elevated temperatures, and the mass gain, even after the long oxidation times investigated in this work, may not have been complete. It is possible that some metallic material, less than detectable by XRD, remained throughout the oxidized material. Future refinements of the model could include using the entire particle size distribution, rather than just an average particle size, and calculating a volume‐averaged particle size. The curve fitting performed in this work was used to create a predictive tool that can be used to calculate the oxidation behavior of materials with similar mean particle diameters at different temperatures and of materials oxidized at the same temperatures, but with different mean particle diameters. Future work is still necessary to reduce the errors in the predictions. For practical purposes, devices such as SOFCs would ideally not be run at temperatures that are so high as to ever reach the second fast oxidation rate. The presence of large quantities of oxide may reduce the permeability in porous structures, as described in section 5.4, and may lead to reduced mechanical stability of the material and to a reduced electronic conductivity, especially in the case of Fe2O3. In order to prevent the occurrence of Fe2O3, reduce the oxidation rate of all oxides, and reduce the migration of Cr to the electrochemically active parts of the fuel cell, protective coatings can be applied to the metal surface (section 7).  143  7. Chromium diffusion in protective spinel coatings for intermediate temperature solid oxide fuel cells Section7, Tab:0, Fig: 0, Eq.: 0  7.1.  Introduction  One degradation mechanism of solid oxide fuel cells (SOFCs) is the poisoning of cathodes by chromium. Chromium migrates to the electrolyte‐electrode interface, resulting in reduced electrochemical activity and reduced performance. Sources of chromium in the fuel cell stack include steel components such as metal fuel cell substrates and interconnects. In order to reduce chromium poisoning of the SOFC cathode and to slow the growth of resistive oxide scales, the steel surfaces can be coated with protective ceramic coatings. This section investigates chromium diffusion through protective coatings with a spinel crystal structure to evaluate the suitability of the coatings for protection of SOFC metallic components such as interconnects or cell supports. The aim here is to calculate a minimum thickness for protective spinel coatings that will sufficiently reduce chromium migration towards the SOFC over the projected operation lifetime.  7.2.  Experimental procedure  An ammonium‐assisted coprecipitation method from sol was chosen to produce the spinels. Ammonium hydroxide (ACS Grade, Assay 28w/w, Thermo Fisher Scientific, Hampton, NH, U.S.A.) was used as the precipitating agent to avoid saturating the solution and the spinel lattice with sodium ions, as would be the case using precipitation agents such as NaHCO3. Aqueous solutions of desired composition and concentration were produced as outlined in Table 7.1. The cation source materials were all nitrates (Fe: ACS grade, 98‐101% purity, Cu: ACS grade, 98‐102% purity, Mn: ACS grade, 98% purity, Mg: ACS grade, 98% purity, Al: ACS grade, 100% purity) [317].  144  Table 7.1: Spinel preparation by coprecipitation method. Cation1‐Cation2  Cation1 (mol)  Cation2 (mol)  Water added (mol)  Mol[NH3]/ Mol [CationsTOT]  Cu‐Mn ("low" NH3) Cu‐Mn Mg‐Al Mn‐Fe Mn‐Co Mg‐Fe  0.036  0.064  2.75  1.5  Water in 2nd precipitation solution (mol) 1.7  0.033 0.033 0.066 0.05 0.033  0.066 0.066 0.133 0.05 0.066  2.75 2.75 2.75 2.75 2.75  10 10 10 10 10  ‐ ‐ ‐ ‐ ‐  The nitrates were dissolved in 2.75 mol water and stirred with a Teflon‐coated magnetic stirrer at 300 rpm until no solid material or concentration gradients were visible. Stirring continued for a minimum of one hour. In a separate beaker, the ammonium hydroxide solution was prepared, and a magnetic stirrer was added. The cation solution was transferred to the ammonium solution in distinct aliquots using a 1000 ml pipette. The resulting precipitate was left stirring for one hour. All precipitates and solutions were filtered (Whatman Ashless‐42 filter paper, GE Healthcare, Maidstone, U.K.) a total of four times. The filtered solutions were sonicated and analyzed by laser light scattering (Zetasizer nano, Malvern Instruments, Worcestershire, U.K.) to analyze if any particles remained suspended in the filtered suspensions. The filtered precipitates were dried at 373 K for 24 h. Then, the filter paper was removed and the filtrate was ground in a mortar. These powders were then dried at 623 K (6 K/min heating and cooling, 1 h dwell time) and ground again. This temperature was chosen to start the reaction of the powders, while being low enough to allow sintering of the powders as pellets later. The thermal characteristics of the resulting powders were investigated by thermogravimetric analysis (TGA) and differential thermal analysis (DTA) in a thermal balance (L81/1750, Linseis, Selb, Germany) while circulating a volume of 40 l/h air up to 1273 K. The specimens were heated at a rate of 10 Kmin−1 and the temperature was controlled by a type B thermocouple.  145  The powders were pressed into pellets using a hydraulic press (Carver Inc., Wabash, IN, U.S.A., model 3912) with a diameter of 15 mm by applying a pressure of 11.3 MPa to a Teflon‐coated stainless steel die for two minutes while evacuating the compression chamber using an electric pump. The resulting discs were heat treated to different temperatures up to 1773 K, depending on the material. The phases formed at each sintering temperature were determined by x‐ray diffraction (XRD D8 Advance, Bruker AXS, Karlsruhe, Germany) and the microstructure and compositional distribution determined by scanning electron microscopy (SEM, S ‐3500 Kabushiki Kaisha Hitachi Seisakusho, Tokyo, Japan) and energy dispersive x‐ray spectroscopy (EDX, Oxford Instruments, Oxford, U.K.). The surfaces of the sintered specimens were carefully polished by hand using 4000 grit SiC paper. The coefficient of thermal expansion (CTE) of the sintered specimens was measured between 473 K and 1273 K by thermomechanical analysis (TMA) (Setaram Setsys Evolution S60, Caluire, France), at a heating and cooling rate of 3 Kmin‐1. Due to the small batch production, thin (approximately 1 mm) sintered specimens were used in these measurements, leading to larger error margins than if sintered cylinders with a longer shaft length were used. Sintered specimens of yttria stabilized (8 mol%) zirconia were produced by tape casting and sintering of cut‐out discs at 1873 K for 4 h, to serve as TMA reference materials. The resulting CTEs were compared with literature values. Values of electronic conductivities of the spinels were obtained from the literature. A layer of chromia was deposited by spray pyrolysis. The precursor solutions used for depositing Cr2O3 coatings were prepared by dissolving Cr(NO3)3.9xH2O (99.99% purity, Alfa Aesar, Ward Hill, MA, U.S.A.) in butyl carbital (99%, Alfa Aesar, Ward Hill, MA, U.S.A.), with a final concentration of 0.1 mol/l. Electrostatic spray deposition was used with no additional air flow. Figure 7.1 schematically shows the setup of the spray pyrolysis deposition apparatus, which utilized a positively charged stainless steel nozzle (inner diameter of 0.6 mm, flat outlet) for the atomization and spraying of the precursor solution. Because of the electrostatic field (12 kV) between the nozzle and the grounded substrate, a certain distribution of pressure develops on the solution surface, 146  overcomes the surface tension, and causes the disintegration of the solution into micron‐sized droplets. The charged droplets subsequently accelerate along the lines of electrostatic force to the grounded substrate. The nozzle‐to‐substrate distance was set to 25 mm and the solution flow rate to 1 ml/h. The spinel substrates were heated to 873 K for the Mn‐Co spinels and 973 K for all other spinels. After the evaporation of the solvent and the pyrolytic decomposition of solute taking place at or near the substrate, an oxide film was formed on the substrate surface. The as‐deposited Cr2O3 coatings consisted of an up to 5 µm thick dense layer on the surface of the spinel substrates, and an approximately 25 µm thick powdery porous chromia deposit on top of the dense chromia layer.  Figure 7.1: Schematic drawing of the spray pyrolysis apparatus. The chromia surface and the interface between spinel and chromia were investigated by SEM, EDX and XRD. For interfacial studies, the specimens were immersed in epoxy under vacuum, and cured for 24 h in air at room temperature. The resulting material was sectioned with a diamond blade and polished to a 1 µm surface finish with diamond suspensions. The diffusion couples were heat treated to different temperatures from 1073 K to 1473 K (Thermolyne 48000B furnace, Thermo Fisher Scientific, Waltham, MA, U.S.A.) in air. The oxygen activity aO₂=pO₂/p0 was approximated as log(aO₂)=‐0.68, with the pressure under standard conditions p0 = 1 atm and pO₂ the oxygen partial pressure. Cross 147  sections of the diffusion couple were prepared from specimens cooled after 6000, 9600, 15000, 30000, and 60000 minutes. The diffusion of the chromium ions was traced by x‐ray CrKα₁ energy emissions at 5.415 keV. The traces of the other elements were measured at 0.277 keV (C Kα₁), 0.525 keV (O Kα₁), 1.254 keV (Mg Kα₁,₂), 1.487 keV (Al Kα₁), 5.899 keV (Mn Kα₁), 5.947 keV (Cr Kβ₁), 6.404 keV (Fe Kα₁), 6.491 keV (Mn Kβ₁), 6.930 keV (Co Kα₁), 7.058 keV (Fe Kβ₁). The Cr Kα₁ EDX traces were fit to the following mathematical diffusion model of a thin surface film on bulk material following Shewmon [318]. The concentration c(x,t) of solute α deposited on the surface after diffusion time t at elevated temperature and at depth x in the material along the spinel bar is given by Eq. 7.1 [238], [318], where D is the diffusion coefficient of the solute. At t=0, the solute can only be found in the surface film, and the concentration of solute within the substrate material is zero. c x, t  α √4πDt  exp  x 4Dt  Eq. 7.1  While the solute spreads into the surrounding solute‐free material, the overall solute material, α, remains constant. Thus, if plotted in a concentration versus depth graph, the area under the graph remains constant independently of time and temperature, assuming only negligible solute volatilization. Strictly, some solute may volatilize; for example, the vapour pressure of chromium at 1394 K is 13 mPa, but this is still negligibly small [319]. In order to determine how long the bar needs to be in order for the diffusing solute to not reach the other end of the bar during the experiment, Shewmon recommends to arbitrarily use 0.1% as a sufficiently insignificant solute density at a distance x’ [318]. This is done by dividing the solute beyond x’ in an infinite bar by the total solute in the bar (Eq. 7.2) [318].  10  exp exp  x 4Dt dx x dx 4Dt  Eq. 7.2  148  In the present diffusion study, the diffusing chromia never reached the other end of the sintered spinel bars, regardless of the time or temperature investigated. The data obtained from EDX traces (y1) were fitted to the thin film diffusion model (Eq. 7.1). The concentration profiles were normalized by dividing the solute concentration at depth x by the maximum solute concentration found in the solute surface layer (indicated by a subscript n), and by moving the surface of the spinel to x=0 (indicated by a subscript z). The resulting concentration profile (y2) is mathematically described in Eq. 7.3.  y  c  c x , ,t x , 0, t  α exp √4πDt α exp √4πDt  x , 4Dt  x , 4Dt  exp  0 4Dt  Eq. 7.3  The two datasets y1 (the EDX trace data) and y2 (the calculated concentration profile values) were compared by linear regression analysis. The correlation coefficient, Rc, was calculated following Eq. 7.4. In Eq. 7.4, n is the number of data‐points recorded.  n∑  R n∑  y  ,  y ,y ∑  ∑  ,  y  ,  y n∑  ,  ∑ y  y ,  ,  ∑  y  Eq. 7.4 ,  The highest value of Rc2 was used to determine the closest match between the EDX trace data and the mathematical fit. The solute concentration, α, was determined by image analysis of polished cross sections. The thickness of the surface layer of Cr2O3 was determined by measuring the thickness of the layer in 16 positions on ten different SEM images.  7.3.  Results and discussion  In the case of the prepared Cu‐Mn solutions, the mixed nitrate solution was brown and the filtered solution was blue; the same color as copper nitrates dissolved in 149  water. In order to facilitate more precipitation, a second beaker with 1.7 mol distilled water and 2.55 mol ammonia (as outlined in Table 7.1) was prepared, and the filtered solution was dripped into this second beaker. Some additional precipitation was observed. It is possible that insufficient ammonia ions were present to completely precipitate the cations. However, the filtered solution remained blue, even after this second titration step. Schweizer et al. have shown that copper nitrates and ammonia can form a soluble component (Schweizer's reagent, Cu(NH3)4(H2O)2)2+) under the conditions used in this production method, which could prevent copper from precipitating [320], [321]. Dynamic laser light scattering was done to find particles smaller than the filter opening. No particles could be detected in the filtered blue copper ammonia nitrate solution after filtration. A second precipitation reaction with low NH3 content was prepared (Table 7.1) to see if Schweizer's reagent would not be formed when using lower NH3 concentration. However, some copper remained in solution as evidenced by its blue color after filtration. Tanaka et al. showed that the production of Cu‐Mn spinels by ammonia or sodium bicarbonate precipitation can yield spinel crystals with the smallest amount of manganese oxide phase as a by‐product, but the exact production parameters are unknown [322]. According to XRD information found in literature, Cu‐Mn spinels tend to occur with at least a small presence of other phases visible in XRD analysis [323], [324], [325], [326], [327], [328], [329], [330], [331], [332]. Among these other phases, hausmannite and tenorite are prominently featured in most XRD patterns reported. A list of phases typically found in Cu‐Mn spinels is shown in Table 7.2.  150  Table 7.2: Phases found in addition to spinel phases in the Cu‐Mn system, depending on preparation method. Abbreviations used: CoPNa – Coprecipitation with (Na) carbonates, CoPK – Coprecipitation with (K) carbonates, EG – Ethylene glycol, EtOH – Ethanol, EtAcH – Ethoxy acetylacetone, CIT – Citric acid organic complex method, MAL – Malic acid organic complex method, CoPUr – Urea coprecipitation, PEC – Pechini method. Phase CuO (tenorite)  MnO Mn2O3 Mn3O4 (hausmannite) Mn5O8 CuCl (nantokite) Mn8O10Cl3 Na2Mn5O13  Preparation method (Reference) CoPNa [326], [333], Sol‐Gel Acetate [331], Sol‐Gel EG/EtOH [331], Sol‐Gel EtAcH [325], Sol‐Gel Acetate/Chloride [330] CoPK [327] CoPNa [326], CIT [332], MAL [332], CoPUr [332], PEC [332] CoPNa [326] CoPNa [326] Sol‐Gel Acetate [331] Sol‐Gel Acetate/Chloride [330] CoPNa [326]  Reduced copper content in the dried Cu‐Mn powders resulting from incomplete copper cation precipitation in NH3 was also observed in the EDX maps showing very little copper, and the XRD pattern mostly showing hausmannite phase. Since the final copper content in the oxides formed from the Cu‐Mn solutions was too low to form desired spinel phases, these compounds were not used for diffusion studies. In the case of the Mg‐Al solution, precipitates formed as a white, gel‐like substance. The filtered solution was slightly milky, and particles with a size of 0.7‐1.2 µm were found by laser light scattering. In the case of the Mn‐Fe solution, the precipitates were dark red‐brown, the precipitates of the Mn‐Co solution were dark green/brown, and the precipitates of the Mg‐Fe solution were dark brown/black. The filtered Cu‐Mn solution was blue, the Mg‐Fe and Mn‐Fe solutions were clear after filtering. No particles could be detected in these solutions by laser light scattering. The precipitates were dried and analyzed by TGA. Figure 7.2 shows the results of the TGA analysis of the Mn‐Fe and Mg‐Al powders following a drying step for 1 h to 623 K. The overall mass loss of the Mg‐Al powder reaches almost 30%, whereas the Mn‐Fe powder loses approximately 7%. The slightly (approximately 0.25 mass%) 151  reduced mass loss plateau between 917‐1231 K is due to irregularities in the baseline. Mg‐Al powder has a precipitous mass loss starting at 650 K, with the steepest decrease in mass at 700 K, with a corresponding endothermic peak in the DTA signal. Mass loss stabilizes above 875 K. The more gradual mass loss of the Mn‐Fe powder stabilizes after reaching 875 K, with a corresponding exothermic DTA peak which may indicate crystallization.  A  B  Figure 7.2: Thermogravimetric analysis of (A) Mg‐Al, and (B) Mn‐Fe powder following drying to 623 K. In order to obtain an idea of the precision of the EDX measurements, the EDX interaction volumes were calculated. The depth of electron interaction (in µm), del, was estimated from Eq. 7.5 [334], and the width of electron interaction (in µm), wel, from Eq. 7.6 [334], where Eac is the accelerating voltage (in keV) and ρ is the material density (in gcm‐3) [335]. d  w  0.1E ρ  .  0.077E ρ  Eq. 7.5  .  Eq. 7.6  152  The range of an electron interacting with a material, rel, which is determined by the straight line distance between the electron's point of entry into a material and its final resting place, was estimated from Eq. 7.7 [336], where A is the atomic mass (in gmol‐1), and Z is the atomic number.  r  0.0276AE ρZ ⁄  ⁄  1 1  0.978x10 E 1.957x10 E  ⁄  Eq. 7.7  ⁄  The interaction width of electrons with the target determines the precision of the EDX measurement. Based on the calculated interaction data shown in Table 7.3, the interaction widths range from 4.0 µm for Mg to 0.8 µm for Co. This contributes to the error of the measurements. It may be argued that as a result of this imprecision, the exact value for the diffusion coefficient cannot be determined. However, erring on the side of caution, this work is aimed at analyzing the maximum diffusion of chromium in spinel materials at a given temperature. If the protective spinel layer is of sufficient thickness to prevent chromium from reaching the spinel surface, it will not migrate towards the electrochemically active regions of the SOFC. Protective spinel coatings should be of sufficient thickness to prevent chromium from reaching the spinel surface even under the fastest diffusion observed in this work for each spinel material.  Table 7.3: Calculated electron interaction depth and width in solids. Material C Mg Al Cr Mn Fe Co  del (µm) 3.8 5.1 3.3 1.3 1.2 1.1 1.0  wel (µm) 2.9 4.0 2.6 1.0 0.9 0.9 0.8  rel (µm) 4.3 6.2 4.2 1.8 1.7 1.6 1.4  153  Chromium can also form spinel structures with the bulk material elements under investigation. The Cr‐spinel ternary phase diagrams of the investigated materials are shown in Appendix Q. After forming the substrate discs by dry powder compression, the specimens were sintered at elevated temperatures. The sintering shrinkage of the diameter of the sintered specimens, measured using callipers, is shown in Figure 7.3. If materials reach a plateau in the sintering shrinkage curve such as above 1473 K in the case of MgAl2O4, most of the densification of the material will have occurred. Phase compositions as a result of thermal treatment (shown in Figure 7.4‐Figure 7.7) also have to be taken into account when choosing spinel sintering temperatures.  Figure 7.3: Sintering shrinkage of the diameter of various sol gel derived pressed ceramic powders. The components of the solid oxide fuel cells should have closely matched coefficients of thermal expansion (CTE), in order to reduce the stresses in the stacks and prevent damages such as spallation, which may result in reduced efficiencies of the system. The coefficient of thermal expansion (CTE) of the sintered specimens was measured and is shown in Table 7.4 and related to literature values. 154  Table 7.4: Measured CTE compared with literature values for CTE and electronic conductivity. Nominal spinel substrate composition  CTE (10‐6 K‐1)  Temp. range (K)  CTE Ref. value (10‐6 K‐1)  Ref. Temp. range (K)  8.8 [338] 9 [248] 9 [339] 11.5 [340] 12.3 [248] 12.3 [339]  Electrical conductivity σel, ref. value (Scm‐1) CoMn2O4: 6.4 [248] MnCo2O4: 60 [248] MnCo2O4: 36 [337] ‐ ‐6 10 [248] ‐ ‐ 0.08 [248] ‐  CoMn2O4: 7 [248] Mn1.5Co1.5O4  7.1±0.3  523‐ 1273  MnCo2O4: 9.7 [248]  1073 1073 1073 293‐1093 1073 298‐1273 373‐1273 1073 298‐1273  MgAl2O4  8.5±1.1  523‐ 1273  MgFe2O4  12.6±1.4  423‐ 1073  MnFe2O4  12.2±1.0  523‐ 1273  12.5 [248]  8 [248]  1073  9.4±0.9  523‐ 1273  9 [341], 9‐10 [342], 10 [343], 10.3 [344], 10.5 [345]  ‐  1073‐1273  YSZ  XRD spectra taken after drying at 373 K showed no presence of spinels. Following a heat treatment at 623 K, the XRD patterns showed some oxide structures. In the case of Cu‐Mn spinel, the only phase present was Mn3O4 hausmannite, and EDX results showed only minor (<5 at%) copper content in the resulting compound. After pressing the sol‐gel derived powders into discs, the specimens were sintered. It was found that the Cu‐Mn compound produced a copper‐rich liquid phase at temperatures as low as 1473 K, indicating that further work is necessary in the investigation of the phase diagram of the Cu‐Mn mixture at high temperatures. The Cu‐Mn phase diagram shows a eutectic below 1473 K with a Cu‐rich melt of MnO, Mn2O3, and Cu2O. Cu2O is liquid at 1493 K, and can oxidize to CuO tenorite during cooling. The presence of molten copper oxide phase at temperatures as low as 1473 K indicates that oxidation to CuO may occur at temperatures below 1493 K [346]. 155  Silica from impurities in the refractory plates started to appear in the spinel specimens sintered at 1773 K. Consequently, such high sintering temperatures were avoided for the spinel materials, and only used for the YSZ reference. MnFe2O4 co‐existed with (Mn,Fe)2O3 phases in the sintered Mn‐Fe materials. Figure 7.4 shows that the MgAl2O4 phase is stable at all investigated temperatures and contains only minor amounts of Al2O3 at 1723 K. Minor amounts of MgO were found at all temperatures. Consequently, the material was sintered at 1723 K before applying the chromia layer.  Figure 7.4: XRD patterns of MgAl2O4 sintered at 1273‐1723 K. Crystal structures were determined based on these references: Rectangles: MgAl2O4 [347], circles: Al2O3 [348], [349], diamonds: MgO [350]. The sintering temperature of the material increases upwards in the graph. 347  348  349  350  156  From Figure 7.5 it appears that the best temperature for making a substrate from Mn‐Fe material is 1723 K, since the phases present do not change significantly from 1648 K to 1723 K. Consequently, 1723 K was chosen as the sintering temperature for this material.  Figure 7.5: XRD patterns of the Mn‐Fe material, sintered at 1273‐1773 K. Crystal structures were determined based on these references: Rectangles: MnFe2O4 [351], circles (only at 1273 K): (Mn0.37Fe0.63)2O3 [352], diamonds: α‐Fe2O3 [353], x: FeMn2O4 [354], # (at T=1773 K): Al2O3 from refractory [348], circles (at T≥1648 K): Mn2O3 [355]. No information available for peaks 2θ>90° in the reference databases. The sintering temperature of the material increases upwards in the graph. 351  352  353  354  355  157  Figure 7.6 shows the XRD patterns of MgFe2O4 at 1623 K, 1673 K, and 1723 K. MgO, if present, cannot be distinguished by XRD due to peak overlay with MgFe2O4. For densification purposes, 1723 K was selected as the sintering temperature.  Figure 7.6: XRD patterns of MgFe2O4. The MgFe2O4 phase appears stable at the investigated temperatures. Crystal structures were determined based on these references: XRD peaks of MgO (circles) [350] overlay the MgFe2O4 (rectangles) [356] peaks and cannot be distinguished by this method, diamonds: (Al2O3)1.333 [357]. No evidence of Fe2O3 [353] was found. The sintering temperature of the material increases upwards in the graph. 356  357  158  Figure 7.7 shows the XRD patterns of Mn1.5Co1.5O4 at 1373 K, 1423 K, and 1473 K. The spinel XRD peaks were most defined at 1473 K, but the underlying refractory showed evidence of staining from the spinel material, so in order to not change the surface composition by cation migration, no higher sintering temperature was investigated. 1473 K was chosen as the sintering temperature before Cr2O3 deposition.  Figure 7.7: XRD patterns of Co1.5Mn1.5O4. Crystal structures were determined based on these references: Rectangles: (Mn,Co)(Mn,Co)2O4, Mn:Co ratio 1:1 [358], [359], diamonds: (Mn,Co)(Mn,Co)2O4, Mn:Co ratio 1:0.5 [358]. No evidence of Mn3O4 [360] was found. The sintering temperature of the material increases upwards in the graph. 358  359  360  Cross sections of the interface between spinel and Cr2O3 of the as‐sprayed specimens are shown in Figure 7.8. The spinel materials are shown to the left of the images. The Cr2O3 layer can be seen on the surface of the spinel, and the powdery Cr2O3 material deposited on top of the Cr2O3 surface layer can be seen embedded in the epoxy to the right of the images. 159  A  B  C  D  Figure 7.8: Polished cross section of as‐deposited Cr2O3 layer on spinel substrates. A dense Cr2O3 layer formed at the surface and an up to 25 µm porous layer formed above the dense layer. (A): Mn1.5Co1.5O4, (B): MgAl2O4, (C): MgFe2O4, (D): MnFe2O4. After 100 h at 1273 K most of the powdery Cr2O3 material is not present anymore to the original extent. Even the low vapour pressure of chromium [319] combined with the potential formation of volatile compounds such as CrO2(OH) [361] and the small particle size of the powders may contribute to some volatilization. A crack parallel to the surface appeared in the MgFe2O4 specimens between the initial spinel and the Cr containing spinel material (not shown). The compositional profiles resulting from EDX linescans were used to determine the diffusion parameters. Figure 7.9 shows three examples of the recorded composition profiles.  160  A  B  C  D  Figure 7.9: EDX elemental analysis of MgAl2O4 spinel in contact with a spray‐pyrolized Cr2O3 surface layer. A: Micrograph of a polished cross‐section after 500 h at 1273 K indicating three linescans recorded in this micrograph, B, C, D: EDX linescans corresponding to A.  The recorded EDX CrKα₁ traces were fit using Eq. 7.3. Figure 7.10 compares the graphs of the recorded EDX CrKα₁ trace shown in Figure 7.9D with the best calculated diffusion profile.  161  Figure 7.10: Example of a normalized EDX CrKα₁ linescan data (diamonds) overlaid with the closest normalized fit (rectangles). In order to find the best fit, the values for D were varied and the maximum in Rc2 was recorded. The value of D that resulted in the highest Rc2 value was chosen. At lower temperatures and short investigation times, the error of the measurement technique itself is more dominant, as the average diffusion coefficient calculated on as‐sprayed specimens can be similar in magnitude to the diffusion coefficient of the cation at the investigated temperatures. The reason for this is mainly the spread of the electrons in the specimens as calculated in Eq. 7.5‐Eq. 7.7, but it may also be influenced by the elevated Cr2O3 deposition temperature which may have facilitated some initial diffusion. At the higher testing temperatures, this influence becomes negligible, and measurement error is dominated by differences between the linescan measurements on the same material. The diffusion coefficients were then plotted in an Arrhenius‐type graph of the natural logarithm of the diffusion coefficients plotted as a function of 1/T (Figure 7.11). Some of the spinels may form chemical reactions with the chromia, which could influence the diffusion characteristics. 162  Figure 7.11: Arrhenius‐type graph showing the diffusion constants calculated in this work. The slopes of the graphs in Figure 7.11 were used to calculate the activation energy (EA) of the diffusion of chromium ions through the respective spinel (Table 7.5). Table 7.5: Activation energy EA of Cr cation diffusion in different spinels. Cr2O3 layer in contact with this spinel MgAl2O4 MgFe2O4 Mn1.5Co1.5O4 MnFe2O4  EA (kJ mol-1) 177 263 201 348  Since the activation energy and the diffusion coefficient D are known, the pre‐ exponential factor D0 in Eq. 7.8 can be calculated for each temperature T. R is the universal gas constant (8.314 JK‐1mol‐1). D  D e  Eq. 7.8 163  Using the values for D and EA, the diffusion profile of Cr ions in the spinel materials investigated in this work were calculated at the targeted operating temperatures of intermediate temperature SOFCs (IT‐SOFCs, 873 K – 1123 K). The U.S. Department of Energy (DOE) has set a lifetime target for stationary fuel cells to 40,000 h [19], [20], [21]. Since the appearance of Cr ions in the electrochemical layers of the SOFC may lead to performance degradation, no Cr ions should diffuse through a protective coating over the entire targeted lifetime. The depth profiles (Eq. 7.1) of Cr solute in the various spinels were calculated using t=40,000 h and the diffusion constants shown in Figure 7.11, resulting in the diffusion profiles shown in Figure 7.12. The graphs in Figure 7.12 show the concentration depth profiles of Cr solute (in terms of Cr concentration cCr) as a function of depth within the material at different proposed IT‐ SOFC operating temperatures.  164  A  B  Figure 7.12: Diffusion depth profiles after 40,000 h based on the calculated diffusion coefficients for different proposed IT‐SOFC operating temperatures. (A): Mn1.5Co1.5O4, (B): MgAl2O4. The profile changes with temperature are indicated in (A). 165  C  D  Figure 7.12, continued: Diffusion depth profiles after 40,000 h based on the calculated diffusion coefficients for different proposed IT‐SO FC operating temperatures. (C): MgFe2O4, (D): MnFe2O4. 166  Diffusion to the depth at which the solute concentration was less than 0.1% (as recommended by Gilewicz‐Wolter [219]) of the surface concentration was calculated for the different spinels at the proposed IT‐SOFC operating temperatures. These values represent minimum thickness requirements for protective coatings and are summarized in Table 7.6. Table 7.6: Recommended minimum thickness, in μm, of spinel coatings based on Cr cation diffusion at 873‐1123 K. Temperature (K) Spinel material MgAl2O4 MgFe2O4 Mn1.5Co1.5O4 MnFe2O4  873  923  973  1023  1073  1123  3 3 5 2  5 5 10 2  7 10 18 5  12 21 31 10  18 41 53 25  27 77 87 57  Table 7.6 shows the recommended minimum thickness of spinel coatings at various targeted IT‐SOFC operating temperatures for the prevention of Cr ion diffusion. This does not take into account microstructural effects such as surface scale spallation, which could potentially destroy the integrity and protectiveness of the surface coating.  7.4.  Conclusions ‐ Cr diffusion in spinels  Spinel materials were created by coprecipitation from sol‐gel, followed by drying and sintering. In the case of Cu‐Mn solutions, the produced solid material contained mainly manganese oxides, with only little evidence of Cu found by EDX analysis. Copper seems to form a soluble ammonium complex (Schweizer's reagent) and does not completely precipitate under the investigated conditions [324]. This material was consequently not investigated in the Cr diffusion analysis. Spray pyrolysis of Cr2O3 onto Mn1.5Co1.5O4, MnFe2O4, MgFe2O4, and MgAl2O4 spinel substrates resulted in an up to 5 μm thick, dense layer of Cr2O3 on the surface of the spinel as well as a thicker (up to 25 μm) layer of Cr2O3 nano powder. During thermal treatment, the thickness of the layer of powdery chromia material was reduced at elevated temperatures over time. Possible reasons include Cr volatilization, nano‐particle agglomeration, and sintering. 167  From the diffusion distances observed, Cr ions diffuse slowest in MnFe2O4 spinel at the targeted IT‐SOFC operating temperatures. The diffusion coefficients of Cr ions in MgAl2O4 spinel at 1273 K – 1473 K were several orders of magnitude lower than for any of the other investigated spinel materials, which may be due to differences in atomic radii of the different cations. However, the activation energy of Cr ion diffusion in MgAl2O4 was also lower than in any of the other analyzed spinel materials. The calculated diffusion profile at SOFC operating temperatures below 973 K showed that an MgAl2O4 spinel thickness of at least 10 μm may prevent detrimental Cr ion diffusion. In the case of the MgFe2O4 spinel, chromium interacted with the spinel to form a layer that physically separated from the bulk spinel by cracking parallel to the surface. The magnesium level is the same in both layers and the iron levels are lower throughout the diffusion layer. Observation of the interaction between chromium and manganese‐ iron spinels was difficult. The x‐ray energies of the Cr Kβ₁ (5.947 keV) and Mn Kα₁ (5.899 keV), and of the Mn Kβ₁ (6.491 keV) and Fe Kα₁ (6.404 keV) emission peaks are very similar, and could not be resolved with the instrument used. However, Cr Kα₁ (5.415 keV) had a very distinct energy, and was investigated individually. Chromium diffused into Mn1.5Co1.5O4 was not morphologically distinct from as‐sintered Mn1.5Co1.5O4 in SEM analysis. The diffusion volume contained equally reduced amounts of Mn and Co, indicating that both atoms were similarly displaced by Cr atoms. Protective spinel coatings of the investigated compositions with thicknesses of approximately 31 µm (Mn1.5Co1.5O4), 21 µm (MgFe2O4) 12 µm (MgAl2O4), or 10 µm (MnFe2O4) can significantly reduce Cr ion diffusion through the entire thickness of the spinel layer at targeted IT‐SOFC operating temperatures of up to 1023 K. At 1123 K, a very high operating temperature for metal supported SOFCs (section 5.5), Mn1.5Co1.5O4 layer thicknesses of 90 µm may limit the Cr ion diffusion through the entire spinel layer, MnFe2O4 and MgFe2O4 layers may prevent Cr ion diffusion through the entire thickness of the spinel layer at a thickness of 60‐80 µm, and MgAl2O4 layers at a thickness of 30 µm.  168  8. Summary and conclusions of the work presented This work investigated the degradation of porous stainless steel specimens proposed for the application in low and intermediate temperature solid oxide fuel cells as support materials. The oxidation mass gain (section 4) and change of gas permeability (section 5) due to cyclic oxidation were measured. Traditionally, the oxidation mass gain of porous stainless steels has been correlated with the outer geometric surface area of the material [122], [124], [125], and the findings typically indicate that the higher the porosity, the faster the oxidation mass gain. This work used a novel approach by utilizing image analysis on polished cross sections in order to calculate the surface area of the porous stainless steel specimens. The mass gain then was normalized with the overall metal surface area of the materials. It was found that the oxidation mass gain does not increase with porosity, as is often claimed in literature [124], [125]. While there may be other factors influencing the oxidation mass gain, there was no clear trend that would have indicated that specimens with higher porosity oxidize faster than specimens with lower porosity. Typically investigated porous materials have <25% porosity, if the porosity value is reported. The oxidation rates of the porous AISI 430 stainless steel specimens were found to be slower than for comparable dense materials. The oxidation rate constants (k") for MG0.2‐MG100 specimens ranged between 0.9‐3.2*10‐13 g2cm‐4sec‐1 at 1125 K compared with 13*10‐13 g2cm‐4sec‐1 at 1123 K for AISI 430 sheet [401], 2.3*10‐13 g2cm‐4sec‐1 for E‐brite (24 mass% Cr, 1 mass% Mo) [284], and 8.7*10‐13 g2cm‐4sec‐1 for E‐brite coated with lanthanum doped strontium cobaltite (LSCo) [284], and compared well with published approximate k" values for porous AISI 434L and AISI 316L materials which are approximately 10‐13 g2cm‐4sec‐1 [129]. It was concluded that the porous structures have a slower oxidation rate than flat sheets of similar composition. During the oxidation of porous structures, some surfaces may become difficult to reach for oxide ions as pores close due to oxidation. Even when compared with flat sheets of higher chromium content (24 mass% Cr, 1 mass% Mo) [284] at a lower temperature (1073 K), the oxidation rate constants found in this work 169  range from 2.1‐5.9*10‐14 g2cm‐4sec‐1 and are lower than the k"=8.8*10‐14 g2cm‐4sec‐1 found for a 24 mass% Cr steel, yet of similar range as AISI 444 coated with LaCrO3 with an oxidation rate of k"=5.8*10‐14 g2cm‐4sec‐1. However, spinel coatings such as MnCo2O4 were found to lower the oxidation rate of AISI 430 steels by two orders of magnitude at 1123 K [401].  The influence of oxidation on gas permeability through the porous AISI 430 specimens  was  analyzed  (section 5).  Gas  permeability  can  be  determined  experimentally by measuring the velocity of the gases flowing through porous specimens [140], or by applying a constant pressure and measuring the resulting mass flow through the specimens [295]. In this work, a constant pressure was applied to the specimens, and the resulting mass flow of the gas through the specimens in a jig specifically designed during the course of this project was recorded. Measurements of gas permeability through porous specimens often focus on different materials and production methods [295]. It is, however, at least equally important to record the permeability of porous materials under operating conditions that may change the microstructure. Consequently, this work analyzed the influence of oxidation on the gas permeability of porous AISI 430 specimens. The gas permeability of MG0.2 specimens, with the finest microstructure analyzed in this work, was most affected by Cr2O3 oxide growth, even at temperatures as low as 873 K. The permeability of MG0.2, MG0.5, and MG1 specimens decreased below the detection limit of the mass flow meter at 1073 K and above. Only the gas permeability of specimens with very large microstructures (MG40 and MG100 specimens) was not significantly influenced by oxidation, even at 1125 K. For all specimens, growth of Fe2O3 significantly changed the microstructure at 1125 K. Some of the specimens grew so much in diameter that the gas permeability through these specimens could no longer be measured in the permeability jig. This means that metal supported SOFCs should definitely not be operated at such a high temperature. The gas permeability through the microstructures of MG0.2‐MG5 specimens was found to 170  significantly decrease even during Cr2O3 oxidation due to oxide growth at and above 1020 K. Consequently, porous AISI 430 supported SOFC operation should be limited to temperatures below 1020 K. This finding supports the microstructure recommendations resulting from the calculated oxide scale thickness after 40,000 h based on oxidation rate kinetics (section 4) correlated with the available pore size diameter of the various porous AISI 430 microstructures. Of the analyzed specimens, MG2 specimens offered the most advantageous combination of low oxidation rate (for example k"(873 K)=1.8x10‐17 g2cm‐4sec‐1, k"(920 K)=4.0x10‐17 g2cm‐4sec‐1, and k"(973 K)=4.0x10‐16 g2cm‐4sec‐1), low permeability reduction during oxidation combined with reasonably high porosity (28%) and a low surface roughness (Ra=4.9±0.2 µm) compared with the other analyzed specimens, making this particular microstructure a good candidate for SOFC manufacturing.  In order to get a more detailed understanding of the oxidation behaviour of curved steel surfaces, without the added complexity of sintering necks present, as in the case of sintered stainless steel discs, the oxidation behaviour of stainless steel powders was analyzed (section 6). The powders were sieved into different size fractions in order to determine the effect of metal particle size and surface curvature on oxidation. The powders typically oxidized to a specific maximum oxidation value. Metal powders can be produced, for example, by gas, water, and oil atomization [362]. Nyborg et al. found that as‐sprayed powders always contain an oxide layer, even in very low oxygen atmospheres [363]. The thickness of the oxide layer, containing up to 8 nm thick scales of mainly Cr2O3 and small amounts of MnO and SiO2 was found to depend on the atmospheric content during production [363]. Such 8 nm thick oxide scales are of similar thickness as the surface nanostructure found by BET analysis in this work, with the bulk volume of nano‐pores smaller than 5 nm in diameter, possibly resulting from surface oxidation during production [363]. This observation means that the particles can be modelled as smooth spheres without having to account for additional features such as protrusions or cavities, thus simplifying the modeling of 171  surface oxidation for this set of spherical particles. Scherrer crystallite size calculations showed little changes in oxide crystallite size over 1000 h at 1073 K. However, significant crystallite growth was observed at temperatures above 1173 K. For the operation of an SOFC this means that no such changes in crystallite growth occur at typical operating conditions. It was furthermore found that due to the small particle sizes, the oxidation of the AISI 440C particles was almost complete after 100 h at 1073 K, indicated by a significant reduction in mass gain from 100 h to 1000 h as compared with the mass gain from 20 h to 100 h oxidation time. XRD spectra of the unsieved oxidized AISI 440C powders showed no metallic peaks from 100 h oxidation time at 1073 K onwards. This correlated well with mass gain measurements and showed that oxidation was almost complete after 100 h at 1073 K for all sieved size fractions of AISI 440C powder. It was found that almost complete oxidation of the available chromium occurs during the early stages of oxidation, and that oxygen reacted mainly with iron in the remaining bulk material during the later stages of oxidation. The oxides found by XRD matched Cr2O3 and Fe2O3. Changes in oxidation growth rate were observed for the different sieved particle size fractions. An initial, slow oxidation rate of a Cr‐rich oxide on the surface of the spheres was observed. This behaviour was more pronounced at low temperatures and for the larger size fractions. This is in good agreement with Alitavoli et al. who found that oxidation layer thicknesses increased slower on larger spheres of copper and steel [123]. This also matches the EDX elemental maps of cross sectioned AISI 440C powders after 100 h at 973 K that showed that smaller spheres oxidized throughout, while larger spheres formed a protective Cr‐rich surface layer. After the chromium content underneath this surface oxide layer was depleted, a faster second oxidation rate related to the oxidation of iron could be observed. Lawless et al. also observed an induction period of surface oxides on copper surfaces, lasting until oxide nuclei were first observable on the metal surface, followed by lateral growth of the oxide until the  172  surface was covered by the oxide, and finally followed by uniform growth of the oxide film [364]. The first oxidation rate was observed longer for larger spheres. This behaviour may be related to the overall molar quantity of Cr present in the spheres. In larger spheres, more Cr was present, and consequently Cr depletion of the sphere and the resulting time until the oxidation rate changed to the fast rate, was longer as a result. Additional effects of surface curvature may be present. The surface curvature of small could be too large for Cr‐oxides to form protectively, resulting in an earlier oxidation of Fe‐containing oxides. This phenomenon has direct implications on metallic components used in oxidative or corrosive environments, such as SOFCs. In these technologies, very thin (<20 μm) metallic features should be avoided in ferritic steel components, in order to prevent an early occurrence of Fe2O3 formation. Further work is necessary in order to evaluate this phenomenon in detail. At higher temperatures, for example 1073 K, the faster oxidation of Fe‐rich oxides occurred early, within the first tens of hours of the experiments, so that a differentiation between the two different oxidation rates was difficult. It may be beneficial in future work to observe the behaviour of all sieved size fractions for longer times at lower oxidation temperatures. The model of spherical oxidation (Msph) developed in this work confirmed that at least two different oxidation rate constants were present in the oxidation of stainless steel powder. It was found that there was a region between the first and the second oxidation rate in which the relative mass gain occurred with an oxidation rate that ranged in between the two oxidation rates of Cr2O3 and Fe2O3, likely involving the oxidation of (Fe,Cr)2O3, leading to a small deviation between predicted and observed relative oxidation mass gain. Also, the model Msph slightly overestimated the final relative mass gain. The oxides formed may have a lower density than the oxide density that was assumed in these calculations, some materials may have volatilized at elevated temperatures, and the mass gain, even after the long oxidation times investigated in this work, may not be complete. It is possible that some metallic material, less than detectable by XRD, remained throughout the oxidized material. Future work is still 173  necessary to identify the exact source of this small deviation. Additionally, the model could be expanded to include the full spectrum of particle sizes in the particle size distributions of each sieved size fractions, rather than just using an average particle size diameter for the distribution. However, the deviations between model Msph and experimental data were small and limited to the described effects. Consequently, the present model is a good characterization tool of spherical oxidation of Fe‐Cr based steels. Such an oxidation type can be expected for typical SOFC metal support materials at IT‐SOFC operating temperatures. The curve fitting performed in section 6.4 was used to create a predictive tool to calculate the oxidation behavior of materials with similar mean particle diameters at different temperatures and of materials oxidized at the same temperatures, but with different mean particle diameters. It was found that the Cr2O3 oxidation rate of spherical particles, ks,1, showed a thermally activated behavior. Fe2O3 oxidation rate on spherical particles, ks,2, also appeared to be thermally activated, but the frequency of data acquisition points with time in the cyclic oxidation experiments may not have been sufficient to completely resolve the values of ks,2, especially at the higher analyzed temperatures. The time, ts, at which the oxidation changed from ks,1 to ks,2, could be predicted well for different mean particle diameters at the analyzed temperatures. However, the prediction of the oxidation type switch time was more challenging as a function of temperature, since the data did not follow an Arrhenius‐type behavior well. Future work is still necessary to reduce the errors in the predictions. In practice, devices would ideally not be run at temperatures that are so high that they would lead to the second fast oxidation rate of iron oxidation. The presence of large quantities of oxide may reduce the permeability in porous structures, may lead to reduced mechanical stability of the material, and to a reduced electronic conductivity, especially in the case of Fe2O3. Both the oxidation experiments of porous sintered AISI 430 and of spherical AISI 440C showed a significant increase in oxidation rate for metal features smaller than 20 µm (MG0.2 specimens in the case of the sintered AISI 430 and ‐20 µm sieved 174  particles in the case of the AISI 440C powders). It appears that this is a particle size below which significantly faster oxidation occurs. This may be due to geometric effects, and a large curvature, for which the Pilling Bedworth ratio of Cr oxidation is no longer protective, or due to the presence of insufficient quantities of Cr, resulting in rapid oxidation of all Cr present, and consequently an early onset of iron oxidation.  One degradation mode of SOFCs is Cr poisoning of the electrochemically active parts of the cell. Spinels are desired protective materials due to their high electronic conductivities at SOFC operating temperatures and their ability to prevent or reduce Cr leakage into the cell [346]. Spinel coatings such as MnCo2O4 may also reduce the oxidation rate constants of stainless steels by two orders of magnitude compared with uncoated steels [401]. In this work, Mn1.5Co1.5O4, MnFe2O4, MgFe2O4, and MgAl2O4 spinel materials were created by sol‐gel coprecipitation, followed by drying and sintering. A layer of Cr2O3 was deposited on the surface by spray pyrolysis, and the resulting diffusion couple was heat treated at various high temperatures. The diffusion coefficients of Cr ions in MgAl2O4 spinel at 1273 K – 1473 K were found to be lower than for any of the other investigated spinel materials (section 7). The activation energy of Cr ion diffusion in MgAl2O4 was also lower than in any of the other analyzed spinel materials. At 1123 K, a high operating temperature for metal supported SOFCs that may lead to excessive oxide formation as shown in the oxidation analysis of porous AISI 430 specimens in this work (section 4 and section 5), Mn1.5Co1.5O4 layer thicknesses of 90 µm may limit the Cr ion diffusion through the entire layer. MnFe2O4 and MgFe2O4 layers may prevent Cr ion diffusion through the entire thickness of the layer at a thickness of 60 µm to 80 µm and MgAl2O4 layers at a thickness of 30 µm. Even though such thick layers may be produced for example by surface deposition from solution [346], this is yet another indication that 1123 K is a too high operating temperature for metal supported IT‐SOFCs.  175  9. Future work The oxidation characteristics of stainless steel powders and of porous sintered stainless steels were characterized and correlated to the surface area of the materials. For the stainless steel powders, the continuous changes in surface area during oxidation were taken into account in the Msph model. Similar work can be done for sintered materials, by cross sectioning the oxidized porous specimens at regular intervals and by repeated analysis of the overall remaining metal surface area through the measurement of the Sv values by image analysis. Typically, oxidation analysis correlates oxidation mass gain with only the outer geometric surface area and also assumes constant surface area with time. This work showed that such an analysis is incomplete, and that the change of the surface area with time has to be taken into account in future standardized analyses of porous metal oxidation. The gas permeability through porous metal specimens was shown to decrease as a result of oxide scales growing in the pores. This reduction in permeability could be related to a numerical relationship between the changes in gas permeability, the temperature and duration of the experiments, and the initial microstructure of the porous stainless steel specimens. As the particle size distribution of the unsieved and the ‐20 µm powder size fractions analyzed in this work were closely related, future work should address separating such small powders better. The finest ASTM standard sieve available today has a mesh with a nominal opening of 20 µm (ASTM Mesh No. 635) and costs several times more than even the second finest mesh with a nominal opening of 25 µm (ASTM Mesh No. 500). Ideally, mono‐dispersed powders [365] with a single diameter or narrow size distributions should be analyzed in order to properly attribute the oxidation mass gain effects observed to the microstructure and surface curvature. The mathematical models used in this work assume material densities from literature references. The composition, phase, and density of SOFC alloys and the oxides formed on the alloy surface could be analyzed in‐situ during high temperature measurements. Also, mass gain experiments should be performed at additional temperatures in order to obtain a better predictive tool from the curve fitting developed in this work. 176  The oxidation mass gain model Msph could be refined by using the particle size distribution in the calculations rather than assuming particles with a mean particle diameter. It would also be beneficial to observe the oxidation behaviour of the first oxidation rate constant for all sieved size fractions for longer times. This could be achieved experimentally by oxidizing the different sieved size fractions of the stainless steel powder at oxidation temperatures below 920 K and for longer (>9000 h) times. The results from such an investigation could be used to determine the similarities of the first oxidation growth rate of the different particle sizes at various temperatures. The mass transfer coefficient of the ions involved in the oxidation of stainless steels analyzed in this work should be measured, in order to improve the oxidation models. Coating of stainless steel with spinel coatings can increase the oxidation resistance of the metallic substrates for IT‐SOFC operation [401]. However, coating porous stainless steel will also reduce the volume of pores in the material. This can have a limiting effect on the mass transport of reactant gases toward the SOFC. A balance has to be found between successfully protecting the surfaces of the metal, and allowing sufficient gases to reach the reactive region in the fuel cell. Oxidation mass gain, changes in gas permeability and electrical conductivity of complete metal‐supported SOFCs with protective coatings applied should be analyzed in the future. SOFCs based on spinel‐coated porous metal support structures then have to be tested in long term tests (>10,000 h). The cell performance and degradation even of completely ceramic‐based SOFCs are only in few cases satisfactory over the entire 40,000 h targeted lifetime. Shorter operating times may be advisable for metal supported SOFCs, if low degradation rates can be demonstrated over these shorter lifetimes. Thermal cycling capability and tolerance of metal supported SOFCs towards fuel impurities and diverse fuel types have to be demonstrated. 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Umino, Process for producing alloy steel powder, U.S. Patent 4448746 (1984). [363] L. Nyborg, I. Olefjord, surface oxidation of steel powder during atomization, Key Engineering Materials 29‐31 (1988) 9‐20. [364] K.R. Lawless, the oxidation of metals, Reports on Progress in Physics, 37 (1974) 231‐316. [365] M. Ramamurthi, K.H. Leong, Generation of monodisperse metallic, metal oxide and carbon aerosols, Journal of Aerosol Science 18 (1987) 175‐191.  208  Appendices Appendix A  Fe‐Cr phase diagram  Section0, Tab:0, Fig: 0, Eq.: 0  Figure A.1: Fe‐Cr phase diagram showing which phases can be expected at equilibrium for different combinations of chromium content and temperature [366]. The shaded area indicates typical compositions of ferritic stainless steels and operating temperatures for metal supported SOFCs. Lower operating temperatures have also been proposed (e.g. [31]). α: Ferrite phase, γ: Austenite phase, σ: Intermetallic Fe‐Cr phase leading to embrittlement. Phase diagram used with permission of Dr. A. Kajinic and Computational Thermodynamics Inc [366]. 366  209  Appendix B  Elemental analysis of the AISI 430 specimens  Section0, Tab:0, Fig: 0, Eq  .: 0  The elemental compositions of the different media grades are shown in Table B.1 as reported by the manufacturer, based on the initial metal powders prior to sintering. Inductive coupled plasma mass spectrometry was performed using cleaned, sintered specimens to analyze the average composition of the material prior to commencing the oxidation study. The results of that analysis are shown in Table B.2. The error reported for this measurement was 5%. The measurement error derives from the precision of the calibration curves used for each individual element. It can be seen that the Cr content is lower than that of the initial material. This may be due to Cr volatilization during the sintering of the AISI 430 discs. The measured Cr content is discussed in section 4.1.  Table B.1: Elemental compositions (at%) of the AISI 430 discs, as reported by the manufacturer (Fe=balance). MG C Cr Si Mn S P O, B, Co, Ni, Cu, Mo, W  0.2 0.069 17.054 0.880 0.230 0.012 0.018  0.5 0.132 17.635 1.615 0.090 0.017 0.035  1 0.114 17.603 0.821 0.230 0.038 0.018  2 0.114 17.603 0.821 0.230 0.038 0.018  5 0.082 17.905 1.015 0.130 0.012 0.018  40 0.073 18.042 1.132 0.060 0.015 0.018  100 0.073 18.042 1.132 0.060 0.015 0.018  ‐  ‐  ‐  ‐  ‐  ‐  ‐  210  Table B.2: Elemental compositions (at%) of the AISI 430 discs, analyzed by inductive coupled plasma mass spectrometry (5% measurement error, Fe=balance). MG Cr Al Sb As Ba Be Bi Cd Ca Co Cu Pb Li Mg Mn Mo Ni P K Se Ag Na Sr S Tl Sn Ti V Zn Zr  0.2 16.05 4.2E‐03 4.4E‐04 5.9E‐03 5.6E‐04 1.9E‐04 9.7E‐03 4.5E‐05 4.0E‐03 1.4E‐02 4.7E‐02 8.3E+01 3.8E‐04 2.3E‐02 4.7E‐02 1.0E‐01 1.1E‐02 1.5E‐01 9.9E‐03 8.7E‐02 3.4E‐04 1.5E‐04 1.7E‐02 2.5E‐05 4.1E‐02 1.7E‐04 1.0E‐03 3.2E‐03 3.1E‐04 8.7E‐04  0.5 16.18 9.9E‐03 5.2E‐04 5.8E‐03 5.0E‐04 1.8E‐04 9.7E‐03 4.7E‐05 4.7E‐03 1.3E‐02 6.0E‐02 8.3E+01 3.3E‐04 1.5E‐02 4.4E‐02 7.3E‐02 9.0E‐02 1.5E‐01 2.2E‐02 9.5E‐02 3.9E‐04 1.7E‐04 7.0E‐03 2.8E‐05 4.0E‐02 1.6E‐04 2.3E‐03 3.3E‐03 3.6E‐04 1.4E‐03  1 16.13 5.9E‐03 4.8E‐04 5.7E‐03 5.6E‐04 1.8E‐04 1.0E‐02 4.7E‐05 4.5E‐03 1.3E‐02 3.5E‐02 8.3E+01 3.3E‐04 1.1E‐02 4.4E‐02 8.7E‐02 6.7E‐02 1.8E‐01 1.5E‐02 8.1E‐02 3.8E‐04 1.7E‐04 4.6E‐03 2.8E‐05 3.6E‐02 1.6E‐04 2.5E‐03 2.8E‐03 3.6E‐04 1.6E‐04  2 15.74 4.0E‐03 4.2E‐04 5.1E‐03 5.8E‐04 1.8E‐04 9.6E‐03 4.3E‐05 3.8E‐03 1.3E‐02 7.1E‐03 8.4E+01 4.7E‐04 1.0E‐02 4.5E‐02 1.2E‐01 9.6E‐04 3.5E‐01 4.0E‐03 8.3E‐02 3.2E‐04 1.9E‐04 7.1E‐03 2.4E‐05 2.9E‐02 1.3E‐04 2.1E‐03 2.8E‐03 3.0E‐04 6.6E‐04  5 16.15 5.9E‐03 7.5E‐04 5.0E‐03 5.8E‐04 3.0E‐04 1.0E‐02 9.5E‐05 6.7E‐03 1.4E‐02 7.6E‐03 8.3E+01 2.6E‐04 1.4E‐02 6.6E‐02 1.2E‐01 1.0E‐03 3.0E‐01 3.5E‐03 6.8E‐02 5.4E‐04 2.5E‐04 7.0E‐03 4.1E‐05 5.8E‐02 2.6E‐04 2.0E‐03 3.1E‐03 5.3E‐04 7.4E‐04  40 15.50 7.5E‐03 8.7E‐04 5.2E‐03 4.8E‐04 3.4E‐04 9.6E‐03 9.0E‐05 8.0E‐03 1.2E‐02 2.8E‐02 8.4E+01 4.9E‐04 7.3E‐03 8.3E‐02 1.1E‐01 1.3E‐02 2.5E‐01 3.3E‐03 6.4E‐02 6.4E‐04 3.0E‐04 8.8E‐03 4.9E‐05 6.3E‐02 2.5E‐04 3.4E‐04 4.5E‐03 6.3E‐04 5.4E‐04  100 15.85 4.2E‐03 5.6E‐04 6.6E‐03 5.5E‐04 2.5E‐04 9.9E‐03 6.1E‐05 5.0E‐03 4.7E‐01 3.4E‐02 8.3E+01 4.1E‐04 8.2E‐03 4.7E‐02 1.2E‐01 1.2E‐02 4.3E‐01 1.1E‐02 7.3E‐02 4.3E‐04 1.9E‐04 5.0E‐03 3.1E‐05 3.6E‐02 2.5E‐04 3.9E‐04 1.6E‐03 4.0E‐04 1.2E‐03  211  Appendix C  Discussion of common porosity measurements  Section0, Tab:0, Fig: 0, Eq  .: 0  Various methods to measure porosity exist, and for each method many different experimental procedures have been developed. There is no single measurement which could be identified to have the best characteristics of all available measurement methods. Each measurement has its own set of advantages and drawbacks, including cost, availability of instruments, or porosity type analyzed. This section elaborates on the different methods, and explains that it is important to always quote measured porosity values with regards to their measurement method. Bruckschen et al. reported that synchrotron X‐ray microfocus computed tomography achieved the highest resolution of analyzed three dimensional images of bone replacement scaffolds with open pores in the range of 100‐500 μm, with a significantly  better  image  quality  than  standard  microfocus  computed  tomography [367]. Furthermore, the authors noted that SEM image analysis showed the poorest results due to difficulties with specimen preparation, image artefacts, and ambiguous interpretation of the images. Faidi et al. noted that current methods for evaluating SOFC layer flatness, gas permeability, and porosity are limited in that they cannot distinguish the effects of different micro‐features on overall surface quality, and the effects of cracks, seal defects, and porosity on gas permeability [368]. Furthermore, Bodosci et al. found that permeability tests of liquids through concrete were significantly influenced by the position and method of the test, and varied between tests in the laboratory and in the field [137]. These research results underline the need for further fundamental understanding of how to standardize permeability and porosity analysis methods and apply them to different fields of research. Table C.1 gives a brief overview of commonly used porosity measurement methods.  212  Table C.1: Summary of various porosity measurement methods. *Cost unknown, **Argonne National Lab (ANL) [369], ***PMI Analytical [370], ****University of Calgary, Dept. Cell Biology. 369370  Measurement method  Features  X‐ray diffraction ‐ Obtains porosity from volumetric and mass combined with measurements and compares these with volumetric and calculations using XRD unit cell volumes; mass ‐ Depends heavily on precise volumetric and XRD measurements measurements Archimedes ‐ Measures porosity by mass gain of a solid when method a liquid (or microspheres [371]) is infiltrated into its pores; ‐ Easy and low cost [372]; ‐ Requires reproducible preparation and measurement standards (e.g. ASTM C373‐88 [373]) Image analysis ‐ Measures porosity of polished cross sections; ‐ Can give information about shape and feature distribution and dimensions within a material; ‐ Lengthy specimen preparation and potential introduction of artefacts; ‐ Data interpretation depends on specimen and acquisition conditions Liquid injection ‐ Measures porosity by infiltrating a specimen porosimetry with liquid, for example Hg (toxic); ‐ Can analyze pore size distribution and tortuosity; ‐ Specimen size limited He pycnometry ‐ Measures the volume of gas (He) displaced by a known mass of substance Chemisorption/ ‐ Measures the volume of cryogenic gas Physisorption/ adsorbing at particle surfaces [374]; BET ‐ Particles with low surface area cannot be measured; ‐ Pore size distributions measured to a maximum diameter of 150 nm Capillary flow Gas pressure and flow rate through wet and dry porometer porous specimens are compared. Measures pore size distribution, flow rate through specimen Microfocus Three dimensional reconstruction of a scanned computed structure with ~10 μm resolution [367] tomography Synchrotron X‐ray Three dimensional reconstruction of a scanned microfocus structure with <4 μm resolution [367] computed tomography Gamma ray Measures the radiation reduction of gamma rays transmission through a porous specimen and compares this to attenuation in dense specimens  Porosity Approx. type capital cost 103 $CAD total 230‐320  Estimated usage cost $CAD 50‐200/h  open  6  0‐10/item  total  40  0‐20/item  open  115  300/item***  open  80  open  70‐110 BET: 25‐30  60‐ 100/item*** 150‐ 200/item  open  65  100‐ 500/item***  total  120  100/h****  total  *  1000/h**  total  *  *  213  Computer‐aided analysis of cross sections following metallographic preparation is a common method to evaluate porosity [373], [375], [376], [377], [378]. Nicholl et al. noted that different methods of preparation may lead to measurement artefacts in optical image analysis. For example, pull‐outs of sections of material from the specimens during polishing, especially of ceramic materials, may result in increased measured porosity levels [375]. Also, this method assumes that the material is isotropic, that the features in the images are representative, and that the features are distributed evenly throughout the material. Mercury porosimetry can be used to obtain information about the porosity and pore size distribution of a specimen [379], [380], [381], [382], [383]. Lee et al. found that mercury porosimetry may not be sensitive enough for pores with thin necks, and combined the method with optical image analysis to follow the effect of deformation on pore size distribution and porosity [381]. Combining mercury porosimetry with a capillary flow porometer technique, Du et al. found that many blind pores (which may be detrimental to gas diffusion) may exist within an SOFC electrode material [384]. Porous materials may contain three kinds of pores: through pores that are open to the outside and permit flow, blind pores that terminate inside the material and do not permit flow, and closed pores that are not accessible. The Archimedes method is a low‐cost, quick method to measure open porosity [385], [386]. However, Rampon et al. found that thin specimens may crack during measurement, creating additional artificial porosity [387]. Appoloni et al. reported that the gamma ray transmission methodology can analyze the total porosity over spatially well defined volumes of a specimen with smaller experimental deviations than Archimedes measurements [388]. Helium pycnometry can be used as an additional measurement of density to Archimedes measurements [389], [390]. Dividing the bulk density (calculated from the mass of the specimen divided by its bulk dimensions), by the skeletal density (the ratio of the sum of the masses of all discrete pieces of solid material to the sum of the volumes of the solid material in the pieces and closed pores within the pieces [391]) of 214  the materials measured by helium pycnometry yields the total porosity of the specimen [382]. Brunauer‐Emmett‐Teller (BET) measurements can give additional information about pore size distribution and surface area of small pores on material surfaces up to a maximum pore diameter of 150 nm [392]. Kivi et al. used the BET method to determine the surface area of these very small (<5 nm) surface features on SOFC cathode powders [393]. Porosity can also be estimated by measuring the volume, mass, and density of a specimen [394]. These measurements are very sensitive to the exact knowledge of the theoretical density of a given material, which is sometimes taken from literature values [394]. Theoretical density, the ratio of the mass of a collection of discrete solid materials to the sum of the volumes of these solid pieces, can also be calculated if the unit cell volume is known from crystallographic analysis [395]. This analysis can be done very quickly and with a minimal amount of materials preparation.  215  Appendix D Specimen holder for Archimedes measurement preparation Section0, Tab:0, Fig: 0, Eq.: 0 Section0, Tab:0, Fig: 0, Eq.: 0  Figure D.1: Porous steel specimen holder for Archimedes measurement preparation. 216  Appendix E  Specimen holder for oxidation experiments  Section0, Tab:0, Fig: 0, Eq.: 0 Section0, Tab:0, Fig: 0, Eq.: 0  Figure E.1: Porous steel specimen holder for oxidation experiments.  217  Appendix F  Confidence intervals of porous AISI 430 oxidation EA  Section0, Tab:0, Fig: 0, Eq.: 0  The confidence intervals of the linear least squares regression analysis of the slope in the Arrhenius‐type graphs of ln(k") as a function of 103/T (from section 4.4.2) were calculated. This section describes the mathematical statistical analysis. The resulting  graphs  including  95%  confidence  intervals  are  shown  in  Figure F.1 [396], [397], [398], [399], [400]. The sums of the squares of deviations of x values (Sxx, Eq. F.1) and y values (Syy, Eq. F.2) from the mean of x̅ and y̅, and the sum of the cross‐product of the deviations of x and y from x̅ and y̅ (Sxy, Eq. F.3) were calculated, using n as the data sample size.  S  S  x  x  x  1 n  x  Eq. F.1  S  y  y  y  1 n  y  Eq. F.2  x y  y  xy  1 n  x  x  y  Eq. F.3  The correlation coefficient Rc was calculated from Eq. F.4. S  R  S S  Eq. F.4  The sample distribution (tα,ν) of the data sample was calculated from Eq. F.5, with s as the sample standard deviation, n is the sample size (with n‐2 as the degrees of freedom, ν), x̅ as the sample mean value of x, and µ as the population mean. t  ,  x μ sn .  Eq. F.5  The values for t for select confidence intervals (for example 95%, within two standard deviations of the center of the distribution) were taken from reference 218  tables [397]. The slope of the linear regression curve, m, was estimated following Eq. F.6. m  n∑  ∑ x ∑ ∑ x  xy ∑ x  y Eq. F.6  The y‐axis intercept, by, was calculated following Eq. F.7. ∑  b  m∑ N  y  x  Eq. F.7  The standard deviation of the regression in y‐direction, sy, was calculated following Eq. F.8. S  s  m S n 2  Eq. F.8  The standard deviation of the slope, sm, was calculated following Eq. F.9. s S  s  Eq. F.9  The standard deviation of the y‐axis intercept, sb, was calculated following Eq. F.10. s  1 ∑ x ∑ x  s n  Eq. F.10  The distance, Δy, between the y‐values of the linear regression line, ypred, and the outer boundaries defined by the confidence interval, CI, was calculated for every ith datum following Eq. F.11. Δy  t  ,  s  1 n  x  x S  Eq. F.11  219  A  B  C  D  E  F  G  Figure F.1: Linear least squares regression analysis of the oxidation activation energy data presented in section 4.4.2. The solid line shows the predicted slope in the Arrhenius‐type graph, the dotted lines show the 95% confidence interval of the data. A: MG0.2, B: MG0.5, C: MG1, D: MG2, E: MG5, F: MG40, G: MG100.  220  Appendix G  Oxidation rates of sintered porous AISI 430  Table G.1: Measured oxidation rates (k’’ and k’) calculated in this work (section 4.4.2). Specimen type MG0.2  MG0.5  MG1  MG2  MG5  MG40  MG100  Temp. (K) 873 920 973 1020 1073 1125 873 920 973 1020 1073 1125 873 920 973 1020 1073 1125 873 920 973 1020 1073 1125 873 920 973 1020 1073 1125 873 920 973 1020 1073 1125 873 920 973 1020 1073 1125  k" (g2cm‐4sec‐1) 7.35E‐17 2.56E‐16 2.17E‐15 3.50E‐14 5.87E‐14 1.83E‐13 3.26E‐17 3.90E‐17 2.19E‐16 3.34E‐15 2.34E‐14 9.51E‐14 4.37E‐17 8.27E‐17 1.23E‐15 8.08E‐15 3.32E‐14 1.30E‐13 1.83E‐17 3.95E‐17 3.95E‐16 4.86E‐15 2.13E‐14 8.63E‐14 3.88E‐17 6.94E‐17 9.67E‐16 7.38E‐15 4.41E‐14 1.41E‐13 3.12E‐17 7.52E‐17 8.05E‐16 1.68E‐14 4.35E‐14 3.24E‐13 2.28E‐17 3.25E‐17 2.88E‐16 7.17E‐15 3.15E‐14 2.43E‐13  k' (cm2sec‐1) 2.71E‐17 9.45E‐17 8.03E‐16 1.29E‐14 2.17E‐14 6.76E‐14 1.20E‐17 1.44E‐17 8.11E‐17 1.23E‐15 8.64E‐15 3.51E‐14 1.61E‐17 3.05E‐17 4.53E‐16 2.98E‐15 1.23E‐14 4.79E‐14 6.76E‐18 1.46E‐17 1.46E‐16 1.80E‐15 7.88E‐15 3.19E‐14 1.43E‐17 2.56E‐17 3.57E‐16 2.73E‐15 1.63E‐14 5.22E‐14 1.15E‐17 2.78E‐17 2.97E‐16 6.21E‐15 1.61E‐14 1.20E‐13 8.43E‐18 1.20E‐17 1.06E‐16 2.65E‐15 1.16E‐14 8.98E‐14  221  Table G.1 lists the oxidation rates calculated for all AISI 430 specimens analyzed in this work (described in Section 4.4.2 and displayed graphically in Figure 4.39, Page 79). Table G.2 lists some literature reference values of oxidation rate constants for comparison.  Table G.2: Reference values for oxidation rates (k’’, k’) and for expected oxide scale thicknesses after 40,000 h. Percentage values are given in mass%. Material AISI 430 AISI 430 & MnCo2O4 AISI 444 & LaCrO3 E‐Brite (26%Cr, 1%Mo) E‐Brite (26%Cr, 1%Mo) E‐Brite (26%Cr, 1%Mo) E‐Brite (26%Cr, 1%Mo) E‐Brite LSCo Porous AISI 434L&316L  Temp. (K) 1123 1123 1073 1073 1123 1173 1273 1123 1173  k" (g cm‐4sec‐1) 1.28E‐12 1.48E‐14 5.80E‐14 8.80E‐14 2.30E‐13 9.80E‐13 3.10E‐12 8.70E‐13 1.00E‐13 2  k' (cm sec‐1) 4.73E‐13 5.47E‐15 2.14E‐14 3.25E‐14 8.50E‐14 3.62E‐13 1.15E‐12 3.21E‐13 3.69E‐13 2  δox,40kh (μm) 117 13 25 31 49 102 182 96 33  Ref [401] [401] [402] [284] [284] [284] [284] [284] [129]  222  Appendix H  Calculations of gas pressure, temperature and density  Section0, Tab:0, Fig: 0, Eq.: 0 The influence of water content on air density and viscosity were calculated in this section. The density ρgas of the air supplied to the permeability measurements was calculated from Eq. H.1. ρ  m V  p R T  Eq. H.1  In Eq. H.1, Vgas is the gas volume, mgas is the mass of the gas occupying that volume, pgas is the partial pressure of the gas, Rgas is the specific gas constant for each gas (287.1 Jkg‐1K‐1 for dry air Rdry [403], 461.5 Jkg‐1K‐1 for water vapour RH₂O [403], and 2077 Jkg‐1K‐1 for helium RHe [404]), and T is the dry bulb temperature (in K). Helium was supplied from a bottle (Praxair Canada). Air was supplied to the permeability measurement chamber via a compressor connected to a pressure swing adsorption system. The remaining water vapour in the air had a dew point range of TDP = 218‐231 K, as determined by the pressure swing adsorption system (Ingersoll Rand dryer model T7400‐EMS). The density of moist air ρgas,mix was calculated using Eq. H.2. ρ  ,  p R T  1 1  x R x R  Eq. H.2  In Eq. H.2, xh is the specific humidity (mH₂O/mdry), where mH₂O is the mass of the water vapour, and mdry is the mass of the dry air at pressure pdry. Outdoors, air density can be estimated using the standard pressure, p0 (101,325 Pa), and temperature, Ts = 288.15 K, at sea level [405], [406], [407], [408], [409], universal gas constant R (8.314 Jmol‐1K‐1), and the molar mass of dry air Mdry (28.964 gmol‐1). These equations are provided as a theoretical calculation reference to compare with the measured values of pressure and temperature. The average temperature and absolute pressure inside the measurement instrument (Alicat MFM) were measured over 20 non‐consecutive days. The resulting average atmospheric pressure was pgas,inst = 101.35 ± 0.80 kPa. The measurement 223  precision of the instrument was the larger error of ±0.8% of each reading or ±0.2% of the full scale. The temperature inside the MFM measured by a thermocouple installed inside the instrument was Tgas,inst = 296.2 ± 2.5 K, the higher end of which was reached after leaving it on for several hours due to heating of internal electronics, independent of any gas flow. Due to this heating effect of the MFM, a separate measurement of the gas temperature was taken, and averaged over 60 days, resulting in Tgas=294.4±0.9 K. The theoretical calculations of Eq. H.2 yield a dry gas pressure of pdry=100,604 Pa. This is just 0.78 kPa below the average pressure pgas,lab measured in the lab, and consequently within the standard deviation of the gas pressure measurement. Therefore, the average measurements of temperature Tgas (294.4±0.9 K), and pressure pgas,inst (101.35 ± 0.80 kPa) were used when required in calculations. To find out how much the density and viscosity of the air used in the gas permeability measurements was influenced by the water present in the air supply, the water evaporation pressure pvap was calculated. To do so, the saturation water vapour pressure psat was used [410], [411], [412], [413]. It can be calculated using an approximation of the empirical Wobus formula [414], [415], [416] (Eq. H.3). p c  10  Eq. H.3  In Eq. H.3, the constants are c0 = 6.1078, c1 = 7.5, c2 = 237.3. Using the dew point as the temperature in Eq. H.3 yields water vapour pressure pvap (Eq. H.4). p  p  p  p  Eq. H.4  The results from Eq. H.4 were then used to calculate the density of the gas in Eq. H.2. Table H.1 shows the density and saturation pressure of the humid air at the upper and lower dew point. Table H.1: Density of moist air, ρgas, based on the dew point of the air stream. TDP (K) 218 231  psat (Eq. H.4) (Pa) 3.4 15  ρgas,mix (kgm‐3) 1.1992 1.1990  224  The theoretical density of air in the dew point range of 231‐218 K is 1.1992‐1.1990 kgm‐3. This shows that the small addition of moisture has little influence on air density. The molar content of water in air at the two different dew points was calculated. The saturation vapour pressure can be empirically calculated following Eq. H.5 with Tc as the gas temperature in degrees centigrade [417]. p  610.78 exp 17.29  T  T 238.3  Eq. H.5  The water vapour pressure relates to the saturation pressure and the relative humidity, RH, as shown in Eq. H.6. RH⁄100  p  p  Eq. H.6  At the dew point (TDP), calculated in Eq. H.7, psat=pvap. p 610.78 Eq. H.7 T p 17.29 ln 610.78 Solving Eq. H.7 for pvap yields Eq. H.8 [418]. In this equation, TDP is expressed in degrees 238.3 ln  centigrade. T p  17.29  exp  ln  T  p 610.78  238.3  ln 610.78  Eq. H.8  Using Eq. H.1, the molar concentration cw,mol and the concentration by mass cw,mass of water in air can now be calculated following Eq. H.9 and Eq. H.10 with MH₂O as the molar mass of water. c c  ,  ,  n V c  ,  p RT  Eq. H.9  ∗M  Eq. H.10  225  Converting this concentration into molar and mass ratios of water vapour to air leads to Eq. H.11 and Eq. H.12. n n  p p  m m  M M  p  Eq. H.11  p  ,  p  Eq. H.12  p  ,  Here, nH₂O and ndry are the molar quantities of water vapour and dry air, respectively, and mH₂O and mdry are the mass of water vapour and dry air, respectively. Using Tgas=294.4 K, TDP=218 K (lower limit) or TDP=231 K (upper limit), R=8.314 JK‐1mol‐1, and pgas,tot=pgas,inst=101.35 kPa, the values shown in Table H.2 were calculated. Table H.2: Calculations of molar composition and relative humidity of the analyzed water/air gas mixture system. Dew Point (K) 218 231  pvap (Pa) 3.4 15  cw,mol (10 mol m‐3) 1.4 6.2 ‐3  cw,mass (10‐3 g m‐3) 25.1 111  RH (%)  nH₂O/ndry  0.14 0.60  3x10‐5 15x10‐5  Table H.2 shows that little water remained in the air stream (nH₂O/ndry <15x10‐5). This has been shown in Table H.1 to have little influence on gas density. However, small additions of water have been hypothesized to have large effects on friction [419], [420], [421], [422] and sliding wear [423]. As a consequence, the influence of the polar molecule water on the non‐polar molecules of the gases used in these experiments could potentially be significant for the viscosity of the gas, and should therefore be calculated. The dynamic viscosity of gases is dependent on temperature, which can be accounted for using the Sutherland formula [424], [425], [426], [427]. μ μ  T T  S T S T  .  Eq. H.13  Here, μ0 is the reference viscosity at reference temperature T0. Tgas is the temperature of the gas and S is the Sutherland constant. Table H.3 contains a list of Sutherland constants for the different gases used for permeability measurements in this work. 226  Table H.3: Sutherland constants, and applicability ranges for a number of gases. * Information not available. μ0 Gas S (K) T0 (K) Temperature Pressure References (10‐6 Pa•s) range for <2% limit error (K) (MPa) * * Air 120 291.15 18.27 [428], [429] * * Air 120 305.37 18.968 [426] Air 111 273 17.16 170‐1900 ≤1.8 [428], [430] H2O 1064 350 11.2 360‐1500 ≤10.0 [430] * * He 79.4 273.00 19 [424], [431] * * * He 79.4 20 [432] * * He 79.4 305.37 20.113 [433] 186.4 * He 79.4 273 200‐1500 [425], [428] (likely 18.64)  Based on the calculations in Eq. H.13, and estimating the average gas temperature as 294.4 K, a helium gas viscosity μHe of (20.07 ± 0.40)*10‐6 Pa•s and a dry air viscosity μdry of (18.44 ± 0.37)*10‐6 Pa•s were calculated. For further refinement, the gas viscosity can be adjusted for the fact that non‐polar gas molecules are mixed with polar water molecules. The viscosities of single gases have been calculated over large temperature ranges by Svehla (Figure H.1) [434] and Brokaw [435], [436], [437], and the viscosities of water/air mixtures have been calculated by Studnikov [438] (Figure H.2), who found less than 1% error compared with their experimental data.  Figure H.1: Change of viscosity of single gases with changes in temperature. Graph drawn with data from [434], with permission of Dr. B. Ulrich and NASA. 227  Figure H.2: Change of viscosity of air/water mixtures with changes in temperature. Water contents are given in (0‐30) mol%. Graph drawn with data from [438], with permission of Springer Science and Business Media. Figure H.2 shows that the addition of water results in only small reductions of the viscosity of the air‐water mixture. While large quantities of polar water molecules could have been expected to have a significant impact on gas viscosity, for the very small quantities of water present in this work, the changes in viscosity were small enough to be within the error margins calculated for μHe and μdry. Consequently, the values of viscosity calculated with data from Table H.3 (helium gas viscosity μHe of (20.07 ± 0.40)*10‐6 Pa•s and a dry air viscosity μdry of (18.44 ± 0.37)*10‐6 Pa•s) and the value of density calculated with data from Table H.1 (ρgas = 1.1991 ± 0.0001 kgm‐3) were used in the calculations in this work.  228  Appendix I  Friction and pressure loss in the gas permeability set‐up  The gas friction in the tubes and pressure drop caused by the entire permeability measurement set‐up (section 5) was calculated in order to find out how much the permeability measurements were influenced by a given set‐up. Knowing the inner diameter Di of a tube, the inner cross sectional area Ai of the tube can be calculated (Eq. I.14). A  0.25πD  Eq. I.14  The gas speed vgas can be calculated from Ai and Qgas, known as gas discharge or volumetric flow rate. Q Eq. I.15 A The Reynolds number Re, a measure of the ratio of inertial forces to viscous forces, is v  defined as shown in Eq. I.16. Re  v  ρ μ  D  Eq. I.16  Here, ρgas is the gas density, and μgas is the gas viscosity. Flow changes from laminar to turbulent in the Reynolds region of 2000‐2500 [439], [440], [441], [442] as shown in Figure I.3.  Figure I.3: Change of flow regimes with change in Reynolds number. Reproduced from [442] with permission of Dr. Glenn Elert. Several components in the system such as 90 degree bends, valves, etc. can be characterized in terms of equivalent lengths Leq=L/Di, where L is the length of a 229  component with inner diameter Di. The values of these equivalent lengths can be found in the literature [443]. The total length of the tube system Ltot can then be calculated as the sum of all equivalent lengths of mt components and nt straight tubes (Eq. I.17). L  L D  L  Eq. I.17  In order to evaluate the friction of a gas in the set‐up, the Darcy‐Weisbach friction factors Flam (laminar flow) and Ftur (turbulent flow) of the gas in the tube can be calculated [444]. In the case of laminar flow, the laminar friction factor Flam can be estimated as follows in Eq. I.18. 64 Eq. I.18 Re In case of turbulent flow, which can be found even for small gauge pressures if F  small (<1 mm diameter) pores are investigated, the turbulent friction factor Ftur can be calculated with the iterative Colebrook equation for completely turbulent flows [445]. 1  R 3.7D  2log  F  2.51 Re F  Eq. I.19  In Eq. I.19, RA is the surface roughness, taken from tabulated values. RA only influences turbulent flows. An approximation for the Colebrook equation was proposed by Serghides [446]. The author proposed the method shown in Eq. I.20 ‐ Eq. I.23 to calculate Ftur. A  R 3.7D  2log  12 Re  Eq. I.20  B  2log  R 3.7D  2.51A Re  Eq. I.21  C  2log  R 3.7D  2.51B Re  Eq. I.22  F  A  B C  A 2B A  Eq. I.23  The surface roughness has no influence on laminar flows. Table I.4 contains several average RA values for different materials. 230  Table I.4: Average surface roughness of various tube materials. Material Glass, polymer Glass, polymer  RA (10‐6m) "Smooth" 1.5 ‐ 7  Copper, brass  1‐2  Stainless steel Steel (American National Institute of Standards (ANSI) schedule 40) Polymer coated steel  15 45 – 90 0.5 – 2.4  Reference [447] [448] [447], [448], [449], [450] [448] [447], [448], [449], [450] [451]  The friction in the tube Kw (Eq. I.24), the total inner tube volume Vi (Eq. I.25), and the residence time tres of the gas in the tube (Eq. I.26), can then be calculated using the gas velocity vgas, and the equivalent length of the pipe components Leq. Specific friction factors for valves and fittings were ignored in these calculations. K  L  F D  Eq. I.24  V  AL  Eq. I.25  t  L v  Eq. I.26  From these calculations, the pressure drop in the tube system Δp (Eq. I.27) and the power loss P (Eq. I.28) can be calculated (g is the gravitational constant, 9.81 ms‐1). Δp  ρgΔh P  0.5K ρ  v  ΔpQ  Eq. I.27 Eq. I.28  The calculations in this section were applied to the gas permeability set‐up, using the density of the gas ρgas = 1.1991 kgm‐3 (as calculated in Appendix H) and a gas flow rate of 6 dm3min‐1, and using the viscosity of dry air μair = 18.44 ± 0.37*10‐6 Pa•s (as calculated in Appendix H). The pressure drop in the measurement set‐up was calculated for various flow rates. The resulting values were used to subtract the influence of the tube system on the gas permeability measurement. For the jig designed specifically for this work, the influence of the set‐up was found to be negligible. 231  Gas permeability through the porous AISI 430 discs was tested with the initial gas permeability set‐up that was open to the environment (V1). The mass flow meter (MFM) downstream of the analyzed specimens received little gas flow when low porosity specimens were inserted and none when specimens with more open pore structures were inserted. Gas permeability theory would attribute no gas flow to absolutely dense materials through which no gas permeates. In this case, however, the gas likely escaped into the atmosphere around the o‐ring seals. It is not recommended to use this set‐up for any kind of permeability measurement. Consequently, novel gas permeability jigs were designed and tested as described in section 5.2.1. It was found that both the o‐ring sealing configuration and overall tube length and inner tube diameter have an influence on measured gas flow rate. As a consequence, the pressure loss inside such tube systems was calculated in Appendix H. Furthermore, it was found that the maximum gas flow rate of the MFM had an influence on the measurements. When using an MFM0.05 (maximum flow rate of 50 cm3/min), the flow rates of gas through the different porous AISI 430 specimens were similar, with the exception of the least porous microstructure (MG0.2 specimens). For the MFM0.3 (maximum flow rate of 300 cm3/min), the flow rates of MG1 specimens and MG2 specimens were similar, and the flow rates of MG40 specimens and MG100 specimens could not be differentiated. In the case of the largest MFM20 (maximum flow rate of 20 dm3/min), the individual specimens could be differentiated by flow rate. Additionally, this configuration allowed flow rates larger than flow rates typically used in SOFC stack testing [293], [294]. Consequently, the MFM20 was used, the tube system was changed to larger inner diameters and shorter lengths, and the specimen jig V5 was designed (Appendix J). Also, in order to be able to measure the permeability of the cathode gas that is used in SOFC operation, the gas was changed from helium to air. Helium was initially used since it is a small, non‐polar molecule that may be more suited to detecting gas permeability through small pores and pinholes such as those typically found in electrolytes. The gas flow rates measured with inadequate designs (<2 dm3/min at 10 kPa) are still low compared with industrial SOFC stack systems that can transport 232  10 dm3 min‐1 of reactant gases, although the overall volume of gas flow depends on the size of the stack [452]. This deliberation led to the development of the larger permeability jigs (such as V5, described in Appendix J), which allowed much higher gas flow rates to be measured, and to reduce the influence on the permeability measurements due to gas flow restrictions of the jig and the gas flow tubes. In order to test the influence of the tube system on gas flow measurements experimentally with no specimen holder jig, the gas flow through the tubes was measured (Figure I.4). 90 degree angle bends and orifices with a diameter of 406 μm (16/1000 of 1 inch, designated 16t) were inserted. As expected, when inserting two orifices into the gas stream, the gas flow rate was reduced more than with just one single orifice. The length of the tubes had no influence on the measurements when at least one such small orifice was present (Figure I.4, where Di is the inner diameter of the tubes), as this orifice became the most restricting part of the permeability measurement set‐up.  Figure I.4: Air flow rate through tubes (Di=3.2 mm) of various lengths and connected with one or two 406 μm diameter orifices. Lengths: short = 6 cm, medium = 8 cm, long = 38 cm. It was found that tubes with an inner diameter of less than 5.6 mm were too restricting for gas flow measurements at the observed gas flows. Consequently, tubes with an inner diameter of at least 5.6 mm were used in the improved jig set‐up V5. Steel 233  tubes with an inner diameter of 5.6 mm and a length of 17 cm were evaluated. However, repeated consecutive opening and closing of the Swagelok fittings on steel tubes is not recommended as the seal surface wears significantly on steel tubes. Consequently, polymer tubes (pressure rated up to 1.9 MPa [453]) with an inner diameter of 9.3 mm and a total length of 6 cm each were used for measuring the gas flow through the porous AISI 430 specimens. The gas permeability jig V5 was machined with the same minimum inner diameter. Also, any Swagelok parts used were drilled open to a minimum inner diameter bore of 6.4 mm, the same as the maximum inner diameter on the entrance and exit slots of the MFM and pressure controller. The following experiments describe the testing of the characteristics of the tube system including the specimen holder jig V5. Figure I.5 shows the observed range of air flow rates as a function of gauge pressure of the permeability set‐up with and without a MG0.2 specimen inserted. The graph also shows a slight increase in gas flow rate resulting from using different tubes. Using the inner diameter and length of each component in the set‐up, the overall pressure loss of the system was calculated (see section Appendix H for details of the calculations). The values of residence time from exiting the pressure controller to entering the MFM, total power loss, and pressure loss were calculated for each of the gas flow rates observed in Figure I.5. The results are shown in Figure I.6. The flow regime changed from laminar to turbulent in the set‐up using a V5 jig at a gas flow rate of approximately 10.7‐10.8 dm3min‐1. The same calculations were performed for helium flow through the empty V3 jig using a low‐flow MFM with a maximum flow rate of 5x10‐4 dm3min‐1 (Figure I.7).  234  Figure I.5: Air flow rate as a function of gauge pressure for an empty set‐up (V5) and a set‐up with an MG0.2 specimen inserted. The difference in air flow rate between using two 17 cm long steel tubes (Di=5.6 mm) and two 6 cm long polymer tubes (Di=9.3 mm) were small and were only noticeable at gauge pressures above 5 kPa.  Figure I.6: Calculated theoretical values of residence time, total power loss and pressure loss in the V5 set‐up using a MFM20. Errors include the errors from the calculation of gas viscosity. Differences in the turbulent range result from using different surface roughness values in the calculations; Circles: 15 µm (typical for the insides of stainless steel tubes (Table I.4), Upwards triangles: 40 µm. 235  Figure I.7: Calculated theoretical values of residence time, total power loss and pressure loss of the V3 set‐up using an MFM0.05. The values of the total pressure drop due to tube constrictions shown in Figure I.6 were subtracted from the measured gauge pressure. The corrected values can be seen in Figure I.8 for an empty V5 jig. It shows that the latest implementation of the gas permeability testing jig (V5) has been improved to the point where the influence of pressure loss due to set‐up constrictions on the measurements of gas flow rate become negligible. The corrected values (shown in Figure I.8 as "Jig V5, empty, corrected") do not deviate significantly from the measured values due to the open structure of the entire set‐up and the resulting low pressure loss.  236  Figure I.8: Air flow rate as a function of gas gauge pressure applied across an empty jig V5 and two 6 cm length tubes (Di=9.3 mm) (rectangles) compared with the pressure values corrected for the pressure loss due to the entire set‐up. Inset: Magnification of the highest recorded datum. The pressure drop across one or two 406 μm diameter orifices with a length of 1.52 mm is more noticeable. The calculated air flow versus gauge pressure graphs resulting from applying the pressure drop corrections from Figure I.6 to Figure I.4 are shown in Figure I.9. The graph shows that for set‐ups that restrict gas flow, such as tubing that includes a 406 µm diameter orifice, the measured air flow rate as a function of applied gas gauge pressure can be influenced by the measurement set‐up.  237  Figure I.9: Air flow rate through a set‐up that includes either one or two 406 μm diameter orifices, corrected for the pressure loss due to the single (or double) orifice using the calculations shown in Figure I.6.  238  Appendix J  Mechanical design of gas permeability jig V5  Section0, Tab:0, Fig: 0, Eq.: 0  Figure J.1: Gas permeability measurement jig V5, top part.  239  Figure J.2: Gas permeability measurement jig V5, bottom part.  240  Appendix K  Influence of oxidation on permeability  Section0, Tab:0, Fig: 0, Eq.: 0  Setting the boundary limits for flow rates in between the flow rates reported by two research groups, 18 cm3/min/cm2 at NRC IFCI (designated "low flow rate", rLF, lower horizontal dotted line in Figure K.1) [293] and 160 cm3/min/cm2 (designated "high flow rate", rHF, upper horizontal dashed line in Figure K.1) [294] at ETH Zürich, flow rates based on the geometry of the fuel cell permeability measurement outlined in Appendix J were calculated. The increase in pressure that would lead to an automatic safety shut down of a typical 1 kW station, 34.5 kPa, was added to the pressure observed at the respective flow rates. The resulting slopes of gas flow versus gauge pressure can be observed in Figure K.1 at the example of a MG0.2 specimen. The permeability values calculated from these slopes based on the calculations shown in section 5.4 (page 99) were used as the threshold values below which the permeability should not fall during operation.  Figure K.1: Air flow rate through MG0.2 specimens, and the change in gas flow versus gauge pressure slopes resulting from increasing the pressure by 34.5 kPa, which would cause a typical 1 kW stack to shut down. 241  Appendix L Oxidation mass gain model based on elemental composition Section0, Tab:0, Fig: 0, Eq.: 0 In order to create a model of complete oxidation of steel (observed, for example, for small AISI 440C spheres in section 6.4), the maximum oxidation mass gain of sheet steel was measured as a reference and modelled based on composition. This section proposes a model of complete oxidation based on elemental composition and correlates the calculations with the mass gain of 0.66 ± 0.01 mm thick AISI 430 steel sheets of composition (in mass%) Cr=16.32, Mn=0.310, Ni=0.176, C=0.039, Mo=0.04, Si=0.240, P=0.024, S=0.001, N=0.043, Cu=0.110, Fe=balance. The AISI 430 sheets were oxidized at elevated temperatures (1223 K and 1473 K) in order to compare the maximum mass change observed for the stainless steel sheets with the maximum mass change that could be expected to result from complete oxidation. Figure L.1 shows the measured relative mass change of the AISI 430 sheets as a function of time.  Figure L.1: Relative mass change of dense AISI 430 specimens oxidized at 1273 K and 1473 K in air.  242  After 20 hours at 1473 K, the relative mass gain of the AISI 430 sheet was 43.53 mass%. After 40 hours at 1473 K, this value had decreased by 0.06 mass% to 43.47 mass%. After 400 hours at 1223 K, the sheet had gained 43.40 mass%. Based on the graph in Figure L.1, the oxidation may not yet have been completed after 400 h at 1223 K, the mass still increased by 0.04 mass% from 350 h to 400 h oxidation at 1273 K. The mass gain after 400 h at 1273 K was 0.07 mass% lower than the mass gain after 40 hours at 1473 K. Theoretical maximum mass gain of the analyzed AISI 430 steel specimens was calculated using two oxidation models. This was done to observe if the maximum mass gain of sample materials such as AISI 430 sheet could be explained by one of the two following models of oxidation. In the first model, it was assumed that excess oxygen was available and that each cation completely oxidized into a species as defined in Table L.1. Cation vacancies or oxygen vacancies could potentially form in an iron oxide host lattice (elemental oxidation model Mel₁). In the second model, it was assumed that only stoichiometric M2O3 oxide was produced, and that non‐Fe cations occupied the Fe lattice sites in a solid solution; Fe cations may become reduced or oxidized or other charge carriers may be produced (elemental oxidation model Mel₂). In lattices that contained cations with a lower oxidation state than 3+, the lattice may take up additional oxygen, and in lattices that contained cations with higher oxidation states than 3+, oxygen may be released from a Fe2O3 host lattice. In each case, the elements C, N, and S were assumed to either volatilize or to not form any compounds during oxidation. In reality, the phases of the alloying elements are likely to be more complicated. Some may form crystal structures such as spinels or react with impurities from the atmosphere such as water [454]. These phenomena were disregarded here, however. Some of the relevant phase diagrams that include elements found in the AISI 430 sheet are shown on pages 250‐253, outlining the complexity of the analyzed systems. The Fe/Fe2O3/SiO2 phase diagram shown in Figure L.3 on page 251 indicates that no reaction between silica and a Fe2O3 host lattice occurs, and that silicon oxides always exist as SiO2 phase in such a mixture. This was consequently taken into  243  account in both oxidation models. The resulting maximum theoretical mass gain was very similar for oxidation models Mel₁ and Mel₂. The calculated mass gain of a completely oxidized material with the AISI 430 sheet composition analyzed in this work was 43.59 mass% (Mel₁) or 43.62 mass% (Mel₂), assuming that every atom except C, N, and S oxidized and did not volatilize and a mass gain of 43.51 mass% (Mel₁) or 43.54 mass% (Mel₂), assuming that C, N, and S volatilized, which is a very low difference. For a steel with a hypothetical composition of 17.32 at% Cr and the balance made up of iron with no other elements present, the theoretical mass gain was calculated to be 43.49 mass%. The average mass gain predicted by model Mel₁, including the mass gain values calculated with C, N, and S as either oxidizing or as volatilizing elements, was 43.55 ± 0.06 mass%, and the average mass gain predicted by model Mel₂ was 43.58 ± 0.06 mass%, so the results of the models are very similar. The average of the maximum mass gain predicted in both models was 43.57 ± 0.05 mass%. This fits closely with the observed mass gain (43.53 mass% after 20 h at 1473 K, 43.47 mass% after 40 h at 1473 K, and 43.40 mass% after 400 h at 1273 K). Consequently, it was shown that average mass gain calculations of the models (Mel₁ and Mel₂) can predict the observed maximum theoretical mass gain of completely oxidized steels to within 0.2 mass%. The proposed reactions of the two oxidation models are shown in Table L.1 (oxidation model Mel₁) and Table L.2 (oxidation model Mel₂). Table L.1: Assumptions made for oxidation model Mel₁ Atomic species Cu  Oxidation model Mel₁: Kröger‐Vink notation [455] 2CuO  2Cu  V ∙∙  2O  Mo  2MoO  2Mo  V ∙∙  2O  Ni  2NiO  2Ni  V ∙∙  Cr  Cr O  2Cr  Mn  Mn O  2Mn  P Fe  3P O  6P ∙∙  4V  2O 3O 3O 15O  Host lattice 244  Table L.2: Assumptions made for oxidation model Mel₂. Atomic species Cu  Mo  Ni  Oxidation model Mel₂: Kröger‐Vink notation A: 2CuO B: O g A: 2MoO B: O g A: 2NiO B: O g  V ∙∙  2Cu V ∙∙  2e′ → O  2Mo  V ∙∙  V ∙∙  2e′ → O  V ∙∙ 2Cr  Mn  Mn O  2Mn  Fe  6P ∙∙  2O  2e′ → O  Cr O  A: 3P O  2O  V ∙∙  2Ni  Cr  P  2O  3O  3O  4V  15O  2V ∙∙  4e′  B: 2 O → O g  Possible defect reaction under influence of pO₂: 2Fe  O g → 2Fe ∙  V  O  Both the surfaces and the fractured cross sections of the AISI 430 specimens oxidized at 1273 K and 1473 K were analyzed by SEM and XRD. Figure L.2 shows an SEM micrograph of the fractured cross section of an AISI 430 specimen oxidized for 40 h at 1473 K. A dense oxide layer formed on the outside of the specimens (outer oxide) while the inner part of the oxidized steel (core oxide) was more porous.  245  Figure L.2: SEM micrograph of a fractured cross section of an AISI 430 specimen oxidized for 40 h at 1473 K. The image shows two microstructurally distinct oxide layers. The outer oxide scale (left and right in the image) was comprised of a dense iron‐rich oxide layer and the core oxide was comprised of a porous chromium‐rich oxide. Two morphologically and compositionally distinct layers were observed in the SEM analysis in specimens oxidized for 40 h at 1473 K (Figure L.2). The two layers were physically separated using a spatula. Each layer material was ground in a mortar for further XRD crystal structure analysis. The two oxides appeared to have the same basic Fe2O3–type crystal structure (Figure L.3 and Figure L.4).  246  Figure L.3: XRD spectrum of ground core oxide powder of an AISI 430 specimen oxidized for 40 h at 1473 K. The oxides had a Fe2O3 crystal structure (rectangle markers) such as described in this reference: [273], adjusted for the specimen's lattice parameter by multiplying the d‐spacing by 0.9957, likely resulting from a solid solution of Fe2O3, Cr2O3 and the other alloying elements.  Figure L.4: XRD spectrum of ground outer oxide powder of an AISI 430 specimen oxidized for 40 h at 1473 K. The oxides had a Fe2O3 crystal structure (rectangle markers) as described in this reference: [273] Figure L.5 shows an SEM micrograph of a fractured cross section of an AISI 430 specimen oxidized for 400 h at 1273 K. The outer oxide formed with a dense 247  microstructure, while the inner core part of the oxidized steel consisted of a porous oxide. The microstructurally distinct oxide layers could not be physically separated and were ground together for XRD phase analysis (Figure L.6). The oxide had an Fe2O3–type crystal structure.  Figure L.5: SEM micrograph of a fractured cross section of an AISI 430 specimen oxidized for 400 h at 1273 K showing two microstructurally distinct porous oxide layers.  Figure L.6: XRD spectrum of ground oxide of an AISI 430 specimen oxidized for 400 h at 1273 K. The oxides had a Fe2O3 crystal structure (rectangle markers) as described in reference [273], adjusted for the specimen's lattice parameter by multiplying the d‐spacing by 0.9937, likely resulting from a solid solution of Fe2O3, Cr2O3 and the other alloying elements. 248  The XRD analyses performed on the specimens oxidized at 1473 K (Figure L.3) and 1273 K (Figure L.6) indicated the formation of an Fe2O3‐type crystal lattice.  Summary ‐ Compositional oxidation models (Mel₁, Mel₂) and related experiments on AISI 430 sheet The maximum relative mass gain of dense AISI 430 specimens was measured and compared with the maximum theoretical mass gain based on two oxidation models Mel₁ and Mel₂ proposed in this section. The resulting mass gain of the dense AISI 430 specimens analyzed could be predicted with the models presented in this section (Mel₁ and Mel₂) to within ±0.2 mass%. The complete oxidation of the metal atoms in the material was observed by XRD, within the detection limit of the XRD. The two morphologically distinct oxides observed after 400 h at 1223 K could not be separated. The specimens oxidized for 40 h at 1473 K also exhibited two microstructurally distinct oxides. Separation of these oxides of the AISI 430 specimens was easy, as the outer oxide shell had almost completely spalled off. The XRD spectra of the ground oxides showed that the crystal structure of both regions was based on a Fe2O3‐type lattice structure. While different oxide microstructures occur at different temperatures, for example a dense outer layer at 1473 K (Figure L.2) and needle‐shaped growths on the surface of specimens oxidized at 1273 K (Figure L.5), ultimately all metal atoms in a material may oxidize under suitable conditions. Knowledge of the maximum theoretical mass gain can be applied to explain the maximum oxidation mass gain for example of porous AISI 430 specimens oxidized at 1125 K for long times, exhibiting a second, fast oxidation rate (Fe2O3, section 4.3) and the mass gain of oxidized steel microspheres (section 6.4).  Phase diagrams of possible AISI 430 oxide mixtures Section0, Tab:0, Fig: 0, Eq.: 0 The phase diagrams presented in this appendix represent only some of the possible combinations of oxides that could be encountered during the oxidation of 249  AISI 430 steel. The oxides shown in Appendix L all have M2O3‐like crystal structures, so if other phases occurred, they occurred with less than 5 volume percent. The oxidation models presented in Appendix L do not take into account any more complex chemical interactions than those shown in Table L.1. However, the deviation between observed and theoretical mass gain is small for AISI 430 sheets and may be explained with the occurrence of some of the phase interactions shown here, as well as interactions with other atmospheric contents such as water, or the volatilization of some of the species.  Figure L.1: Phase diagram of FeO/Fe2O3 and P2O5. Wus = Wustite (FeO), Q = iron phosphate phase with 10 ± 1.5 at% P. Reprinted with permission of Dr. A. Schommers, copyright 1963 Verlag Stahleisen GmbH, Düsseldorf, Germany [456]. 456  250  Figure L.2: Phase diagram of Mn2O3 and Cr2O3. Reprinted with permission of John Wiley and Sons, Blackwell, and the American Ceramic Society. [457]. 457  Figure L.3: Phase diagram of Fe, SiO2, and Cr2O3 [458]. (Fa = fayalite (Fe2SiO4); Fe = metallic iron; Hem = hematite (Fe2O3); Mag = magnetite (Fe3O4); S = silica (SiO2); Wus = wustite (FeO)). Along the Fe2O3/SiO2 axis it seems that SiO2 coexists with Hem and Mag, rather than in a solid solution. Reprinted with permission of Dr. K. Noland and AIME [458]. 251 458  Figure L.4: Phase diagram of the system Fe2(MoO4)3‐NiMoO4 [459]. Reprinted with permission of B.V. Straalen and Springer Science and Business Media. 459  Figure L.5: Phase diagram of the system CuO‐Cu2O‐Fe2O3‐Fe3O4 on the CuO‐Fe2O3‐T plane at pO₂ = 2.1 x 104 Pa and Ptot = 1