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Sintering studies of magnesia-chromite refractory composites Zargar, Hamidreza 2014

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  Sintering Studies of Magnesia-Chromite Refractory Composites      by  Hamidreza Zargar    A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate and Postdoctoral Studies (Materials Engineering)        THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)      March 2014                     ? Hamidreza Zargar, 2014   ii  Abstract   The magnesia-chromite refractory composites are the best candidates for the lining of non-ferrous metal smelting and refining furnaces, due to their high melting temperature, chemical inertness, and excellent thermal shock resistance. However, their high sintering temperatures (>1700?C) increase the processing complexity and costs. In this investigation, the primary goal was to study the sintering of these composites, with the long-term engineering goal to reduce their sintering temperature to <1500?C in air.   The materials were synthesized via chemical methods using nitrates to assure chemical homogeneity. Al2O3, Fe2O3, and SnO2 affected the kinetics of the MgCr2O4 formation and increased the density of MgCr2O4 in the order Fe2O3>Al2O3>SnO2. The enhanced MgCr2O4 densification was attributed to the cation distribution in spinel structure (inversion phenomenon), caused by the inherent affinity of Fe+3 and Al+3 to tetrahedral sites. Fe2O3 and Al2O3 showed to form inverted spinel, while SnO2 resulted in the formation of normal spinel solid solutions.   Twelve magnesia-chromite composites were synthesized to study the effects of Al2O3, Fe2O3 and Cr2O3 on their sintering conditions; Cr2O3 decreased the density, while Fe2O3 and Al2O3 enhanced the densification of composites. The microstructural studies revealed that Fe2O3 and Al2O3 reduced the dihedral angle between MgO and spinel, while Cr2O3 increased it. The increased densification by Fe2O3 and Al2O3 was attributed to the decreased dihedral angle and formation of inverted solid solutions.   The optimized composition [MgO6.9Cr2O36.9Al2O32.7Fe2O3]mol% (MK) reached nearly full density in air at 1475?C for 70minutes; 1700?C is currently used for magnesia-chromite refractories.  iii   In order to study the effects of the particle size on densification, magnesia-chromite composites (NMK) with average particle size of ~20 nm were synthesized via Pechini's method. Reducing the particle size from 1.2 ?m for MK to 20 nm for NMK reduced the onset sintering temperature by 200?C to 1000?C.   The densification results were evaluated using master sintering curve theory for the first time for this kind of composites. The sintering activation energy was 443.7 and 302.6 kJ/mol for MK and NMK respectively. It was hypothesized that the oxygen diffusion through lattice and grain boundaries was rate controlling mechanism for MK and NMK respectively.   iv  Preface This research program was conducted within the collaborative research between Teck Metals Ltd., Trail, B.C., Clayburn Industries, Abbotsford, BC and the University of British Columbia, Vancouver BC (UBC), co-supported by NSERC-CRD grant. Teck metal provided UBC ceramic group (UBCeram) technical information on the performance of the refractories currently used in their facility. Clayburn provided UBCeram with the raw materials for making mag-chrome refractory castables.  One journal paper and 2 conference papers have been published so far based on the results of this project, and are included in the present thesis. Parts of Chapters 5 and 6 are submitted for publication in peer reviewed journals, as listed below. I am the primary contributor to the publications listed below, and the co-authors contributions are as follow: my supervisors, Drs. Tom Troczynski and George Oprea extensively commented on the experimental and analysis methods, and the results interpretation; C. Oprea contributed to editorial work on the papers.  1- H. Zargar, G.Oprea, T. Troczynski, Influence of solid solution formation on the solid state sintering MgCr2O4, Unitecr 2013, September , Victoria, Canada.    2- H. Zargar, C. Oprea, G. Oprea, T. Troczynski, The effect of nano-Cr2O3 in solid solution assisted sintering of MgO refractories, Ceramic International, 2012, 38, 6235?6241.  3- H. R. Zargar, G. Oprea, C.Oprea and T.Troczynski , Evaluation of the role of nano chromia in performance of magnesia chromite castables, Unitecr 2011, October  2011, Kyoto , Japan.  v  Table of Contents Abstract??????????????????????????????????????..ii Preface??????. ........................................................................................................................... iv Table of Contents .................................................................................................................................... v List of Tables ???????????????????????????????????.vii List of Figures. ..................................................................................................................................... viii Nomenclature??.. .............................................................................................................................. xii Acknowledgments ................................................................................................................................. xv Dedication???? ........................................................................................................................... xvii Chapter 1. Introduction ...................................................................................................................... 1 Chapter 2. Literature review .............................................................................................................. 4 2.1 Sintering theory overview ........................................................................................................ 5 2.1.1 Sintering mechanisms ............................................................................................................ 6 2.1.2 Sintering models and equations .............................................................................................. 8 2.1.3 Sintering of ionic compositions ............................................................................................ 14 2.2 Spinel structures ..................................................................................................................... 15 2.2.1 Chromite spinels .................................................................................................................. 17 2.2.2 Cation distribution in chromite spinels.................................................................................. 26 2.2.3 Sintering of chromite spinels ................................................................................................ 28 Chapter 3. Research scope and objectives ........................................................................................ 39 Chapter 4. Experimental .................................................................................................................. 42 4.1 Introduction ........................................................................................................................... 42 4.1.1 Synthesis of doped and undoped MgCr2O4 spinels ................................................................ 43 4.1.2 Synthesis of nano magnesia-chromite refractory composites ................................................. 44 4.1.1 Preparation of green ceramic bodies ..................................................................................... 45 4.2 Sintering of ceramic bodies .................................................................................................... 47 4.3 Materials characterization....................................................................................................... 48 4.3.1 Density, water absorption and apparent porosity ................................................................... 48 4.3.2 X-ray diffraction .................................................................................................................. 49 4.3.3 Scanning electron microscopy .............................................................................................. 50 4.3.4 Simultaneous thermal analysis (STA) .................................................................................... 50 4.3.5 Thermal etching ................................................................................................................... 51 4.3.6 Dimension change and weight loss ....................................................................................... 51 Chapter 5. The influence of spinel forming oxides on sintering of MgCr2O4..................................... 52 5.1 The influence of green density on sintering process ................................................................ 52 5.2 The influence of trivalent oxides (Fe2O3 and Al2O3) on the sintering of MgCr2O4 ................... 54 5.3 The effect of tetravalent oxides (SnO2) on the sintering of MgCr2O4 spinel ............................. 81 vi  5.4 The effect of Fe2O3 and SnO2 on sintering of Cr2O3 ................................................................ 85 5.4.1 The effect of SnO2 on densification of Cr2O3 ........................................................................ 86 5.4.2 The effect of Fe2O3 on the densification of Cr2O3 ................................................................. 90 Chapter 6. The effect of spinel forming oxides on the sintering of magnesia-chromite composites95 6.1 Introduction ........................................................................................................................... 95 6.1.1 The effect of Fe2O3 on the densification and grain growth of magnesia-chromite refractory composites ?????????????????????????????????????98 6.1.2 The effect of Cr2O3 on densification and grain growth of MK composites ........................... 107 6.1.3 The effect of Al2O3 on the densification and grain growth of MK composites ..................... 111 6.1.4 The effect of Fe2O3, Cr2O3, and Al2O3 on the microstructures of sintered magnesia-chromite refractory composites .......................................................................................................................... 115 6.2 The densification behavior of MK composite ....................................................................... 121 6.3 Kinetics of sintering of MK and NMK composites ............................................................... 136 Chapter 7. Conclusions and future work ........................................................................................ 148 7.1 The influence of spinel forming oxides (Fe2O3 and Al2O3) on sintering of MgCr2O4 ............. 148 7.2 The effects of spinel forming oxides on the sintering of magnesia- chromite composites ....... 151 References????? ....................................................................................................................... 156                 vii  List of Tables Table ?2-1. Estimated values for each sintering mechanism1 .................................................................... 11 Table ?2-2. Thermodynamic properties of selected chromite spinels; reprinted from2............................... 26 Table ?4-1.The summary of starting powders compositions ..................................................................... 46 Table ?5-1. Experimental conditions the measured parameters of the spinel formation kinetic studies ...... 60 Table ?5-2. Scattering factors for selected XRD reflections3 ..................................................................... 69 Table ?6-1. The composition of designed magnesia-chromite refractory composites ................................ 97 Table ?6-2. Particle size of selected magnesia-chromite composites after calcination at 850?C ................ 98 Table ?6-3. The theoretical composition of spinel solid solution in magnesia-chromite refractory composites .......................................................................................................................................... 116 Table ?6-4. Exponent values reported for different sintering mechanisms4, 5 ........................................... 137              viii  List of Figures Figure ?1-1. The schematic of a mag-chrome refractory6 ........................................................................... 2 Figure ?2-1. Illustration of various types of sintering4 ................................................................................ 6 Figure ?2-2. Different sintering mechanisms:1) Surface diffusion, 2) Volume diffusion from the surface, 3) Evaporation and condensation, 4) Grain boundary diffusion, 5) Volume diffusion from the grain boundary, and 6) Plastic flow (dislocation movement). All mechanisms lead to bond formation, but only the first 3 ones are accompanied by densification1.................................................................................... 8 Figure ?2-3. Schematic of the sintering process of a compacted powder, illustrating 3 stages of solid state sintering4. ................................................................................................................................................ 9 Figure ?2-4. Point defects in ionic structures4 .......................................................................................... 15 Figure ?2-5. Schematic of a spinel crystal4 .............................................................................................. 17 Figure ?2-6.  MgO-MgCr2O4 phase diagram7 ........................................................................................... 18 Figure ?2-7.  MgO-Al2O3 phase diagram8 ................................................................................................ 19 Figure ?2-8.  MgO-Fe2O3 phase diagram2 ................................................................................................ 21 Figure ?2-9. Spinel redox stability in MgO-Cr2O3-Al2O3-Fe2O3 at 1300?C a) in air and b) in reducing atmosphere. Open circles show unstable compounds; closed circles refer to stable compounds; bold lines illustrate the stable chromite spinel solid solutions; reprinted from2. ....................................................... 22 Figure ?2-10.  The schematic of spinel formation mechanism according to Wagner theory; reproduced from9 ..................................................................................................................................................... 25 Figure ?2-11. The effect of LiF concentration on activation energy of densification of MgAl2O4; the applied pressure was 33MPa10. .............................................................................................................. 30 Figure ?2-12. PO2 vs. density and weight loss of pure Cr2O3; the dominant species stable at various oxygen partial pressures are also indicated11....................................................................................................... 32 Figure ?2-13. Relative density of the samples obtained from MgCr2O4-TiO2 compacts by heating in a carbon bed and in air at 1500?C for 2h12. ............................................................................................... 35 Figure ?2-14. Bulk density and apparent porosity of magnesia-chrome grains developed from a) sintered magnesia, b) caustic magnesia13. ............................................................................................................ 36 Figure ?2-15. HMOR of magnesia-chrome aggregates developed from a) sintered magnesia and b) caustic magnesia14. ............................................................................................................................................ 37 Figure ?4-1. Schematic of chelation mechanism during synthesis of MKi composite15 ............................. 45 Figure ?5-1. The variation of density versus compacting pressure for as-pressed MK composites and MK composites sintered at 1500?C for 20 minutes; error bars are smaller than symbols ................................ 53 Figure ?5-2.  SEM images of synthesized spinel powders calcined at 850?C a) MgCr2O4, b) Mg[Cr0.8Fe0.2]2O4 and c) Mg[Cr0.8Al0.2]2O4 ............................................................................................. 55 Figure ?5-3.  XRD patterns of Mg[Cr0.8Fe0.2]2O4 samples calcined at various temperatures ....................... 56 Figure ?5-4.  The typical STA pattern of precursors for Mg[Cr0.8Fe0.2]2O4 composition ............................ 57 Figure ?5-5. The effect of heating rate on the STA peak position for Mg[Cr0.8Fe0.2]2O4 composition ........ 58 Figure ?5-6. Kissinger plot of       vs. 103/TP of MgCr2O4 as a function of composition ......................... 59 Figure ?5-7. The variation of relative density of sintered Mg[Cr1-xFex]2O4 compositions at different temperatures for 2 hours ........................................................................................................................ 62 Figure ?5-8. The MgO-Cr2O3-Fe2O3 phase diagram at 1300?C110 ............................................................. 63 ix  Figure ?5-9. SE-SEM image of fracture surface of a) MgCr2O4 sintered at 1250?C, b) MgCr2O4 sintered at 1500?C, c) Mg[Cr0.8Al0.2]2O4 sintered at 1250 ?C, d) Mg[Cr0.8Al0.2]2O4 sintered at 1500 ?C, e) Mg[Cr0.8Fe0.2]2O4 sintered at 1250?C, and f) Mg[Cr0.8Fe0.2]2O4  sintered at 1500?C ................................ 64 Figure ?5-10. a) XRD pattern of Mg[Cr1-xFex]2O4 quenched from 1475?C in air b) the variation of lattice parameter versus Al2O3 and Fe2O3 concentration; error bars are smaller than symbols ............................ 66 Figure ?5-11. The variation of the relative density of Mg[Cr1-xAlx]2O4 specimens sintered at different temperatures for 2hours; the lines connect the data points only for the purpose of easier readability ....... 67 Figure ?5-12. The comparison between the intensity ratios, I311/I220, of calculated and experimental results for inversion parameter mesurement. The results in this graph relate to Mg[Cr0.8Fe0.2]2O4 which was quenched from 1300?C. ......................................................................................................................... 71 Figure ?5-13. The variation of the inversion parameters in Mg[Cr1-xFex]2O4 and          Mg[Cr1-xAlx]2O4 with concentration of the sintering additives and sintering temperature (the lines represent the thermodynamic model and not the best fit ? refer to text) ................................................................................................ 72 Figure ?5-14. The variation of the lattice parameters of Mg[Cr0.8Al0.2]2O4 and Mg[Cr0.8Fe0.2]2O4 versus the sintering temperature ............................................................................................................................. 77 Figure ?5-15. a) The variation of compressive strength of samples sintered at various temperatures, b) weight loss of Mg[Cr1-xFex]2O4 and Mg[Cr1-xAlx]2O4 samples sintered at 1475?C ................................... 79 Figure ?5-16. The variation of relative density of Mg[Cr1-xSnx]2O4 (x=0, 0.05, 0.1, 0.15, and 0.2) compositions sintered in air at 1475?C for 300 minutes .......................................................................... 82 Figure ?5-17. XRD patterns of Mg[Cr1-xSnx]2O4 (x=0, 0.05, 0.1, 0.15, and 0.2) compositions sintered in air at 1475?C for 300 minutes; Sp: spinel solid solution .............................................................................. 83 Figure ?5-18. The change in lattice parameter of Mg[Cr1-xSnx]2O4 (x=0, 0.05, 0.1, 0.15, and 0.2) compositions sintered in air at 1475?C for 300 minutes .......................................................................... 84 Figure ?5-19. The variation in relative density of Cr2O3-vSnO2 (v=0.125, 0.25, 0.375, 0.5, 1 and 5 mol%) samples sintered in air at 1475?C for 300 minutes .................................................................................. 87 Figure ?5-20. XRD patterns of Cr2O3-vSnO2 (v=0.125, 0.25, 0.375, 0.5, 1, and 5 mol%) samples sintered in air at 1475?C for 300 minutes ................................................................................................................ 88 Figure ?5-21. The influence of SnO2 content on the lattice parameter of Cr2O3 sintered at 1475?C for 300 minutes in air. ........................................................................................................................................ 89 Figure ?5-22. Microstructure of the fracture surface of sintered Cr2O3-nSnO2 (n= 0.5 and 5 mol%) samples sintered in air at 1475?C for 300 minutes ............................................................................................... 90 Figure ?5-23. The variation of relative density of Cr2O3-vFe2O3 composition with Fe2O3 content sintered in air at 1475?C; the error bars are smaller than symbols ............................................................................ 91 Figure ?5-24. Cr2O3-Fe2O3 phase diagram; reprinted from Factsage results .............................................. 92 Figure ?5-25. The densification of Cr2O3 and MgCr2O4 versus Fe2O3 content. The samples were sintered at 1475?C in air for 300 minutes ................................................................................................................ 93 Figure ?6-1. The typical microstructure of synthesized magnesia-chromite composites; a) the lowest Cr/Al+Fe ratio (MK1), and b) the highest Cr/Al+Fe ratio (MK6) ............................................................ 97 Figure ?6-2. The variation of relative density of magnesia-chromite refractory composites versus Fe2O3 content; composites sintered at 1550?C for 300 minutes......................................................................... 99 Figure ?6-3. The XRD of MK3 composite sintered at 1550?C for 5 hours; .............................................. 100 Figure ?6-4. BSE image of MK3 sintered at 1550?C for 300 minutes; inset shows the EDS analysis of the selected points; the confidence intervals were obtained based on the ?/?3 equation for flat distribution, as each point has been analyzed 3 times ................................................................................................... 101 x  Figure ?6-5. Solid solubilities of sesquioxides in periclase at high temperatures2 ................................... 102 Figure ?6-6. The non-isothermal densification of MK3 and MK12 composite sintered in air at different temperatures for 300 minutes ............................................................................................................... 103 Figure ?6-7. Grain size of MK3 and MK12 composites sintered in air at different temperatures for 300 minutes ............................................................................................................................................... 106 Figure ?6-8. Variation of density of magnesia-chromite refractory composites as a function of Cr2O3 content; the error bars are smaller than the symbols sizes ..................................................................... 108 Figure ?6-9. The non-isothermal densification of MK3 and MK1 composite sintered in air at different temperatures for 300 minutes; error bars are smaller than symbols ....................................................... 110 Figure ?6-10. Average grain size of MK3 and MK1 composites sintered in air at different temperatures for 300 minutes ......................................................................................................................................... 111 Figure ?6-11. Variation of density of magnesia-chromite refractory composites as a function of Al2O3 content; error bars are smaller than symbols......................................................................................... 112 Figure ?6-12. The non-isothermal densification of MK3 and MK6 composites sintered in air at different temperatures for 300 minutes; error bars are smaller than symbols ....................................................... 113 Figure ?6-13. Average grain size of MK3 and MK6 composites sintered in air at different temperatures for 300 minutes ......................................................................................................................................... 114 Figure ?6-14. BSE images of a) MK3 and b) MK12 composites sintered at 1550?C for 300 minutes ...... 117 Figure ?6-15. The calculation of dihedral angle for the MK3 composite ................................................. 118 Figure ?6-16. The variation of the average dihedral angle of magnesia-chromite refractory composites versus oxide content; the composites were sintered at 1550?C for 300 minutes .................................... 119 Figure ?6-17. The variation of the density versus the dihedral angle for magnesia-chromite refractory composites .......................................................................................................................................... 120 Figure ?6-18. The non-isothermal densification and grain size of MK composite sintered in air at different temperatures for 300 minutes ............................................................................................................... 122 Figure ?6-19. The microstructure of MK composite at a)1150?C, b)1350?C, c)1475?C, and d)1600?C ... 125 Figure ?6-20. The SEM image of MK composite at 1600?C showing the exaggerated grain growth ........ 126 Figure ?6-21. Isothermal densification of MK composite sintered in air at different temperatures ........... 127 Figure ?6-22. The isothermal grain size versus relative density of MK composite sintered in air at different temperatures for 300 minutes ............................................................................................................... 128 Figure ?6-23. The non-isothermal densification and grain size of NMK composite sintered in air for 300 minutes ............................................................................................................................................... 130 Figure ?6-24. The microstructure of NMK composite at a)1150?C, b)1250?C, c)1350?C, and d)1475?C. 132 Figure ?6-25. The isothermal densification of NMK composite sintered in air at different temperatures.. 133 Figure ?6-26. The comparison between non-isothermal densification behavior of MK and  NMK composite sintered in air for 300 minutes ............................................................................................................. 134 Figure ?6-27. Sintering kinetics of the initial stage of sintering of MK composite; the 95% confidence intervals for n values are ? 0.02 (2?) ................................................................................................... 138 Figure ?6-28. Variation of relative density versus the sintering time during the initial stage of sintering . 139 Figure ?6-29. Calculation of activation energy of initial stage of sintering of MK composite using equations ?6-5 and ?6-6 .......................................................................................................................... 140 Figure ?6-30.  Kinetics study on the initial stage sintering of NMK composite according to the two sphere model (Kingery et al.5, 16) ..................................................................................................................... 141 Figure ?6-31. MSC of isothermally sintered MK composite ................................................................... 144 xi  Figure ?6-32. The variation of mean residual squares for estimated activation energies; the minimum was obtained at ~444 kJ/mol....................................................................................................................... 145 Figure ?6-33. MSC of isothermally sintered NMK composite ................................................................ 146 Figure ?6-34. The variation of mean residual squares for estimated activation energies; the minimum was obtained at ~303 kJ/mol....................................................................................................................... 147          xii  Nomenclature Latin Symbols m Numerical exponent n Numerical exponent H Temperature depended constant a Concentration of hydrogen L Length  C constant Ea Activation energy Ds Surface diffusion coefficient Dl Lattice diffusion coefficient Dgb Grain boundary diffusion coefficient P0 vapor pressure over a flat surface k Boltzman constant ma Mass of atom T Absolute temperature GB Grain boundary G Grain size ?G? Standard free of formation  ?G Free energy of formation ?H Enthalpy of  formation ?S Entropy of formation TD Theoretical density BD Bulk density WA Water absorption AP Apparent porosity Wi Weight of immersed specimen Ww Weight of saturated specimen Wd Weight of dry specimen RD Relative density Z number of molecules per unit cell M molecular weight of sample N Avogadro number V volume of unit cell nA Avarmi constant W1/2 Full width at half maximum F0 structural factor for normal spinel F1 numerical factor Ihkl Intensity F Structure factor P Multiplicity factor Lp Lorentz-polarization factor ?GD free energy of disordering cation distribution xiii  Na Mole fraction of MgFe2O4  Ma Mole fraction of MgAl2O4 r Cationic radios x The mole percent of trivalent and tetravalent cation substituted for Cr v The mole percent of Fe2O3 and SnO2 substituted for MgCr2O4 and Cr2O3 xd The diffusion depth ?0 initial density at time (t0) t time ? Surface energy CPFD cumulative percentage finer than, d Q Activation energy of sintering d Smallest [article size D Largest particle size  Greek Symbols ?S thickness of surface  ?gb grain boundary ?sv specific surface energy ? viscosity ? density ? Inversion parameter ?XRD Wave length ?XRD full width at half maximum of the intensity ? Heating rate ? Inversion parameter of divalent cation ? Inversion parameter of trivalent cation ? Related to the inversion parameter ?A-B the difference between site preference energies of A and B ?? constant Na numbers of molecules MgFe2O4  Ma numbers of molecules MgAl2O4 ?M/M Dihedral angle between magnesia grains ?S/M Dihedral angle between magnesia and spinel grains ?S/S Dihedral angle between spinel grains ?solid/liquid Grain boundary energy of solid liquid interface ?0 initial density at time (t0) ? Surface energy ?v Microstructure scaling factor for lattice ?b Microstructure scaling factor for grain boundary ? Atomic volume ?(?) Constant includes all the microstructure evolution during sintering ?(t,T(t)) Sintering parameters depending on the thermal history G(?) G function relates grain size to density xiv  Q Activation energy of sintering d Smallest particle size  Abbreviations FCC Face centered cubic FF FeFe2O4 MF MgFe2O4 FA FeAl2O4 MA MgAl2O4 FC FeCr2O4 MC MgCr2O4 TGA Thermal gravimetry analysis SSR Solid state reaction XRD X-ray diffraction HMOR Hot modulus of rupture MOR Modulus of rupture CCS Cold crushing strength MK Magnesia chromite composites (MgO-6.9Al2O3-2.7Fe2O3-6.9Cr2O3)[d: 1.27um] NMK Magnesia chromite composites (MgO-6.9Al2O3-2.7Fe2O3-6.9Cr2O3) [d: 20nm] STA Simultaneous thermal analysis BBOC Bottom blown oxygen convertor TCML Teckmetal Ltd CIP Cold isostatic pressing DSC Differential scanning calorimeter MK1 MgO-6.9Al2O3-2.71Fe2O3-4.9Cr2O3 MK2 MgO-6.9Al2O3-2.71Fe2O3-5.9Cr2O3 MK3 MgO-6.9Al2O3-2.71Fe2O3-6.9Cr2O3 MK4 MgO-6.9Al2O3-2.71Fe2O3-7.9Cr2O3 MK5 MgO-6.9Al2O3-2.71Fe2O3-8.9Cr2O3 MK6 MgO-4.9Al2O3-2.71Fe2O3-6.9Cr2O3 MK7 MgO-5.9Al2O3-2.71Fe2O3-6.9Cr2O3 MK8 MgO-7.9Al2O3-2.71Fe2O3-6.9Cr2O3 MK9 MgO-8.9Al2O3-2.71Fe2O3-6.9Cr2O3 MK10 MgO-6.9Al2O3-3.71Fe2O3-6.9Cr2O3 MK11 MgO-6.9Al2O3-1.71Fe2O3-6.9Cr2O3 MK12 MgO-6.9Al2O3-0.71Fe2O3-6.9Cr2O3    xv  Acknowledgments   I would like to express my sincerest gratitude to my supervisors, Dr. Tom Troczynski and Dr. George Oprea, for their insightful guidance and ongoing patience. They have helped me to improve my research quality and presentation skills by their constructive comments during the course of my study. I would like to thank them for their support and encouragement thorough out this research. It is not exaggeration if I say they are truly mentor for me.   I would like to recognize my supervisor committee members for their technical suggestions and guidance in the early stages of this thesis.  I would like to show gratitude to Dr. Akram Alfantazi for his permission to use his lab facilities. I would like to acknowledge Dr. Edouard Asselin who generously provided me with the access to use his STA instrument.   I would like to express thanks to Mrs. Carmen Oprea for her invaluable support during my experiments.   I would also like to express my appreciation to Mr. Dominic Verhelst and Mr. Terry Mills for their constructive advice and suggestions.  I would like to sincerely thank Mr. Ross Mcleod, Mr. Carl Ng, Mr. David Torok, Mr. Glenn Smith, Mr. Rudy Cardeno, Mr. Gary Lockart, and Mr. Roger Bennett for their technical supports. Special thanks to Mr. Wonsang Kim and Mr. Jacob Kabel for the time they spent to train me on instruments, repair furnaces and troubleshooting.   I would like to thank administration office personals Mrs. Fiona Webster, Mrs. Mary Jansepar, and Mrs. Michelle Tierney for their invaluable support from the day I arrived to UBC until my graduation day.   xvi   I would like to appreciate my aunts, cousins especially Isar, and their families for keeping my parents company during my studies in Canada. I would also like to acknowledge all my helpful and kind family and friends in Vancouver, Canada.  I would like to express my respect to Dr. Farhad Golestanifard, and Dr. Hamidreza Rezaei,  my previous supervisors at Iran University of Science and Technology, for their invaluable support. I would like to express my sincerest gratitude to Dr. Reza Bayati who always inspired me in both my academic and personal life.   This work was supported by Clayburn Refractories, Teckmetal Ltd and the Natural Sciences and Engineering Research Council (NSERC) of Canada.    xvii  Dedication        With love and respect to my dearests father Mahmood, mother Maryam, and brother Ehsan  for their eternal love and support during my entire life.  Without them I would not be here. & To my love Neda - her love inspired me and this thesis has been finalized with her unwavering  support and encouragement.         1  Chapter 1.  Introduction   Magnesia chromite refractories (called mag-chrome refractories) are widely used as refractory linings for the furnaces in steel, copper, nickel and lead industries. Mag-chrome refractories are a sub group of basic refractories preferentially used in the above applications due to their superior thermal shock resistance and chemical inertness in contact with molten metal and slags, in comparison to other basic refractories, including magnesia-spinel and magnesia refractories.   The mag-chrome refractories are usually made from fused magnesia chromite grains. The fused grains with the desired particle size distribution (typically 0.1 ?m to 7 mm) are mixed and then pressed to form a brick. The bricks are sintered in a tunnel kiln for about 48-72 hours, depending on its size. The sintering temperature is usually about 1700-1800?C and the sintering atmosphere is partially reducing to help the densification of fused grains.   Figure ?1-1 illustrates the schematic of a mag-chrome refractory microstructure. The large grains (>1 mm) called aggregates are bonded together by smaller particles (<1mm) called the matrix or binding system. During sintering the matrix would densify and form a bond with the aggregates, thus giving strength and integrity to the brick.   The matrix is the key component of the mag-chrome bricks because it is the first component of the brick which reacts with the corrosive environment. Therefore, the composition, the sintering behavior, and the interaction between binding system (matrix) and aggregates (fused magnesia chromite grains) are important in designing a microstructure for the refractory applications. The binding system for mag-chrome grains is usually fine fused grains and a small amount of MgO, Al2O3, and Fe2O3 to enhance the densification. These oxides react to form 2  spinel during the sintering and enhance the densification probably via synthesis and sintering process. No chromium oxide usually would be added because Cr2O3 reduces the densification of the binding system. Therefore, it is expected that the binding system would be vulnerable to fast corrosion especially when it is in contact with the molten slags used in the non-ferrous industry.  Figure ?1-1. The schematic of a mag-chrome refractory6    The phase analysis of fused mag-chrome grains indicates that they are composed of magnesia and a complex spinel solid solution. Therefore, a fully dense binding system (matrix) with the same composition or with high Cr2O3 composition would be ideal for the mag-chrome brick. Moreover, a composition with a spinel crystal structure is favorable because it may bond better to aggregate with the same crystal structure. In addition, reducing the sintering temperature of mag-chrome refractory from 1700?C to less than 1500?C via designing an appropriate binding system is significant for industry because high sintering temperature increases the production costs and contributes to the greenhouse effect by the CO2 emission associated with fossil combustible, commonly used for sintering.    Based on these rationales, the objective of this study was to design a binding system with the highest Cr2O3 content which reacts with aggregates and forms bond, and also a binding 3  system which sintered to densities above 95% at temperatures below 1500?C. Magnesia chromite spinel (MgCr2O4) and (Mg1-x-yAlxFey)[Mgx+yAlxFeyCr1-x-y]2O4 were selected as the base structures, and the effect of Al2O3, Fe2O3, and Cr2O3 on their crystal structure and densification were studied. The optimized composition, sintered to 96% density at 1475?C for 70 minutes in air, was selected as the binding system. The effect of reducing the particle size to nano scale (20 nm) on the sintering of selected binding system was evaluated. The sintering kinetics of this system was also studied. Attempts have been made to evaluate the effect of the designed binding system on the densification of the mag-chrome refractory. In this regard, a mag-chrome refractory was made using fused mag-chrome grains as aggregates and the designed composite as the binding system (matrix).             4  Chapter 2. Literature review   The sintering process has been used for thousands of years for the production of bricks, porcelains, etc.5. Its application is now also being directed to the manufacture of engineered microstructures suitable for certain applications, for instance dental implants, semiconductor substrates, turbine blades, etc.   The goal of sintering is to create a reproducible dense ceramic or metal part with a designed microstructure, which can be achieved through selecting and optimizing the processing variables. Therefore, sintering studies often focus on how the processing variables influence the final microstructure of the sintered body1. This is a measure of the microstructural and bulk parameters, or physical, mechanical and electrical properties, or their combinations, as a function of sintering parameters, including time and temperature5.    Magnesia-chromite* refractory composites have been used for more than 50 years as refractory linings in non-ferrous metal smelting and refining furnaces, owing to their high corrosion resistance against high silica and iron content slags and gaseous environments. However, the challenge of using them is the rapid oxidation of Cr during sintering. To avoid this, the sintering of magnesia-chromite refractory composites takes place at relatively high temperatures (~1750?C) and in a controlled atmosphere, which leads to high production costs. While the sintering mechanisms of MgO and chromite are separately well understood17-19, there is limited published work focusing on the sintering mechanism of magnesia-chromite refractory composites. Chromite is defined as a solid solution between two or more spinels, wherein one of                                                              * Chromite is the mineralogical name of FeCr2O4 (FC), however, it generally refers to any chromium-containing spinels or spinel solid solutions of [FeFe2O4(FF), MgFe2O4(MF), FeAl2O4(FA), MgAl2O4(MA), MgCr2O4(MC)]6. However, magnesia-chromite term in this context refers to MgO- MgCr2O4 composites and henceforth called MK composites. 5  them contains chromium in its composition6. The magnesia-chromite refractory composites contain spinel solid solutions that may experience different degrees of disordering, due to the cations movement between tetra and octahedral sites; thus the correlation between sintering properties and the degree of disordering has to be identified.  Many researchers have studied the structure of spinel solid solutions and evaluated the cations distribution in such structures20,21.  However, to the best of author?s knowledge, there are no published works correlating the extent of disordering to the sintering properties of spinel solid solutions, and there are only a few studies focused on the spinel solid solutions sintering.  This literature review will look at the sintering of magnesia-chromite refractory composites regarding three main research topics: sintering mechanisms of MgO-spinel composites, sintering mechanisms of Cr2O3 and Cr-containing spinels, and cation distribution in spinel solid solutions.  2.1 Sintering theory overview  Sintering can be defined as a thermally activated process that results in consolidation by bond formation between individual particles via mass transport mechanisms. It is accompanied by a lowering of the free energy of the system, due to reduced total interfacial energy4.   Sintering is categorized based on the mechanism by which the consolidation takes place. In solid-state sintering, the powder compact shrinks by the solid-state diffusion. In liquid-state sintering, the densification occurs in the presence of a liquid phase. If the liquid phase is only present in the early stage of sintering and the full densification occurs in the solid state, then this is a transient liquid-phase sintering4. Viscous sintering takes place in amorphous materials, where the volume fraction of liquid is high enough to lead to full densification by viscous flow of the grain-liquid mixture. Figure ?2-1 shows the temperature range for each sintering type1,4,5.  6   Figure ?2-1. Illustration of various types of sintering4  2.1.1 Sintering mechanisms  As mentioned in section ?2.1, sintering relies on mass transport mechanisms, which determine how mass transfers in response to the sintering driving force. There are two main mass transport mechanisms during sintering: bulk transport and surface transport. Although they both rely on the type and concentration of defects* in the crystal structure, and contribute to the bond formation, only the bulk mass transport mechanisms are responsible for densification.   The surface transport mechanisms indicate that mass flow initiates and terminates on the surface of the particles. It includes surface diffusion, evaporation, and condensation. As a result of the surface mass transport mechanisms, the particles contact area (neck) will grow, which leads to surface area reduction and bond formation, but no shrinkage (reduction in the distance                                                              * Crystal defects are displacement of an atom (point defect), arrays of atoms (line defect), atomic plan (planar defect) or cluster of atoms (volume defect) from the ideal arrangement of the crystal. 7  between the particle centers)4. Evaporation and condensation usually occur during the sintering of materials with high vapor pressure and are the dominating transport mechanism in sintering of the materials with small particle size and high surface area. In contrast, surface diffusion involves the atom movement between surface defects such as kinks and vacancies. The bond between the surface defect and the atom breaks first, then the atom moves and reattaches to the next available site, which is usually a kink. This is the initial mechanism of the sintering in almost all materials, and its contribution is higher for materials with highly curved surfaces and defective sites, where the concentration of vacancies is high due to the capillary forces1.  Bulk mass transport mechanisms are volume diffusion, mass diffusion and plastic flow, the latter usually occurring during pressure sintering22. The volume diffusion (or lattice diffusion) is the movement of vacancies through a crystalline structure, and accordingly, is influenced by temperature, composition and curvature. In contrast, the grain boundary (GB) diffusion indicates the mass flow between GBs. The GB is a narrow region (2-5 nm) between sintered grains, which is highly defected22. Thus the mass transport is faster than volume diffusion. The activation energy of GB diffusion is between that of the surface and volume diffusion. The summary of sintering mechanisms and their contribution to densification is depicted in Figure ?2-2.   8   Figure ?2-2. Different sintering mechanisms:1) Surface diffusion, 2) Volume diffusion from the surface, 3) Evaporation and condensation, 4) Grain boundary diffusion, 5) Volume diffusion from the grain boundary, and 6) Plastic flow (dislocation movement). All mechanisms lead to bond formation, but only the first 3 ones are accompanied by densification1  2.1.2 Sintering models and equations  Over the last five decades several models have been introduced to study the sintering kinetics of particles. They relate the sintering rate to the particle characteristics and compactness, and the sintering atmosphere and temperature. The derived models usually assume that the particles in the initial powder compact are spherical and of the same size, and that they are uniformly packed. These assumptions made the accuracy of the equations debatable23. The solid-state sintering process occurs in three overlapping stages, which are schematically shown in Figure ?2-3.  9   The first stage is called initial stage sintering, in which the particle rearrangement and the bond formation initiate at the primary contact points. The contribution of this stage to the densification is very limited, and is about 3 to 5 %.   The modeling of the initial stage sintering was first published by Kingery and Berg24, Coble25, and Johnson and Cutler26. According to their estimations, the relation between shrinkage and densifying mechanisms can be expressed as below:  (    )            2-1 where ?L is the change in the length, L0 is the initial length, m and n are numerical exponents indicating the mechanism of sintering, and H is a function of temperature that includes material and geometrical parameters. Table ?2-1 shows the value of m and n for different mechanisms. In practice, the sintering mechanism of the initial stage of sintering can be estimated by plotting    (    ) versus Log(t). The curve would be a straight line with the slope of (1/m).   Figure ?2-3. Schematic of the sintering process of a compacted powder, illustrating 3 stages of solid state sintering4.  10   However, when more than one sintering mechanism is active, then this method is no longer accurate enough to be used for the sintering mechanism estimation. The activation energy of densification in the initial stage of sintering can also be calculated by plotting the results of linear shrinkage vs temperature, and using the equations derived by Tietz27 and Younge28. (      )                 2-2  In the former equation, (    ) is the relative shrinkage at temperature T (limited to the initial sintering stage), Ea is the activation energy and n is a constant describing the sintering mechanism (n = 1, 0.5 and 0.33 for viscous, volume diffusion or grain-boundary diffusion respectively).   The second stage of sintering is called intermediate stage sintering and is the most important, since it determines the properties of the sintered compact. This stage covers about 90 % of the total densification that occurs during the whole sintering process5. The driving force is the reduction of surface energy due to the difference in surface curvature and consequent mass transport29.   The intermediate stage initiates after the grain growth and pore shape change, when pores and grain boundaries reach an equilibrium state and form dihedral angles. At this stage, the pore phase is considered as a continuous channel which shrinks afterward. In order to develop a model of this sintering stage, Coble30 approximated the complex shape of the pore by a continuous cylinder and applied diffusion equations. Equations ?2-3 and ?2-4 show the proposed models based on lattice and GB diffusion, respectively.   11                        2-3                            ?       2-4  In these equations ? is the density; Dl and Dgb are diffusion coefficients of the lattice and grain boundary diffusion, respectively;? ?gb is the thickness of the grain? boundary;? ?sv is the specific surface energy; k is the Boltzman constant; G is the grain size; T is the absolute temperature and      is the densification rate.   Table ?2-1. Estimated values for each sintering mechanism1   Mechanism m n Hb Surface diffusiona 7 4              Lattice diffusion from the surfacea  4 3            Evaporation and condensationa 3 2                 ?    Grain boundary diffusion 6 4                  Lattice diffusion from grain boundary 5 3              Viscous flow 2 1        a: denotes non-densifying mechanism, i.e., (    )     b: Ds, Dl, Dgb: diffusion coefficient of surface, lattice, and grain boundary diffusion;  ?s, ?gb; thickness of surface and grain boundary; ?sv: specific surface energy; P0: vapor pressure over a flat surface;  k: Boltzman constant; m: mass of atom; T: absolute temperature; ?: viscosity.   These assumptions introduced errors that resulted in predicted shrinkage rate higher than the experimental results. Kakar31 added two more assumptions to the previous model. The first was considering the shape and the second one was considering one active densifying mechanism, 12  i.e. volume diffusion or GB diffusion. In his model the pores and grains had certain geometries (polyhedral and cylindrical respectively), however the grain and pore sizes were set as constant during sintering. The model was criticized by Jorgensen32 for not considering the grain growth and the mathematical errors, respectively.  In 1970 Johnson33 proposed a model for intermediate-stage sintering in which the densification rate was related to the geometry of the compact during sintering, and to the bulk diffusion coefficients (Dv and Dgb). In this model, simultaneous grain and pore growth was assumed during sintering. In fact, the Johnson model is a modified version of the Coble model. The third stage is called final stage sintering, in which the elimination of the isolated pores continues until the theoretical density is reached. Although the grain growth initiates during the intermediate stage of sintering, this phenomenon is the main feature for the final stage. Due to the separation of GBs from pores, the pores move easier and faster than in the previous stage. As a result, the large grains tend to increase in size at the expense of the smaller grains, while simultaneously the pores shrink continuously until are totally eliminated33.   A final stage sintering model has also been developed by Coble25 and has become a standard, despite the fact that the effects of surface sintering mechanisms have not been included. In?addition?to?Coble?s?model, Herring?s?scaling?law?has been also used for studying the kinetics in the final stage sintering34,16. In this model, the effect of the pore size on the material transport at GB/pore interface was taken into account. According to the concept introduced by Herring?s?law, Kang and Jung16 derived the following equations to relate the densification rate to the volume diffusion and the GB diffusion, respectively:   13                           ?   2-5                         2-6 All parameters have been already introduced   In all the introduced models it is assumed that the grain size is constant, while it is changing during sintering, and it considerably changes the kinetics of sintering. For instance grain growth in the initial stage of sintering causes an increase in pore size locally and decreases the densification rate35. Grain growth is basically an increase in dimension of grains during sintering. The mechanisms of grain growth are usually different from those of densification; however, they are diffusion controlled. Grain growth occurs as atoms (ions) diffuse for a fraction of interatomic distance at grain boundary, resulting in dimensional increase of a grain at the expense of another1. The driving force of grain growth is the reduction of grain boundary area, as it is a high energy area.  There are two types of grain growth for porous ceramics, the normal and exaggerated growth. In normal grain growth the grain size is increasing, but the grain size distribution does not change considerably. Moreover, the pores remain attached to the grain boundary, especially for porous ceramics. In contrast, in exaggerated grain growth, a few grains grow very fast, eventually resulting in a bimodal distribution. Pores usually detach from the GB and remain inside the grain.   Although these sintering models are important in understanding the sintering process, they are impractical in terms of interpreting the experimental results. Therefore, few numerical and empirical models have been derived to help estimate the sintering kinetics.   14  2.1.3 Sintering of ionic compositions  The sintering mechanisms mentioned in section ?2.1.1 are active in systems where densification and grain growth occur by the movement of single type atoms or point defects of a component, whereas in polycrystalline ceramics, the matter transport may occur by diffusion of ions, or other charged species (point defects) rather than atoms. Accordingly, the type and concentration of defects can be influenced by the mobility and sinterability of ceramics.   There are two types of point defects in ceramics: intrinsic defects, which are formed during crystal growth and their concentration does not change with external influences; and extrinsic defects, which are caused by external influences, such as gaseous atmospheres, additives, etc36. Figure ?2-4 shows the different types of point defects in an ionic compound. The defects in ceramic structures would carry charges and they may react by ions and other defects*1. For instance, annealing metal oxide (MO) in a reducing atmosphere leads to the formation of an oxygen vacancy in the metal oxide structure (MO1-x). In contrast, annealing the same composition in an atmosphere with high oxygen partial pressure induces a metal vacancy (M1-yO) in the structure. In both cases the metal oxide seeks to equilibrate its components with the surrounding atmosphere. Solutes (dopants or additives) also change the structure of a ceramic compound by forming solid solutions. For example, Al+3 in Al2O3 may substitute for Mg+2 in MgO and forms vacant sites of Mg in MgO (     ).  As a conclusion, the rate of mass transport is a function of the point defect concentration in ceramic materials, and can be altered by temperature, oxygen partial pressure and dopant concentration. Since there is no clear controlling sintering mechanism for a ceramic compound, the correlation between the defect structure and the sintering rate is not straightforward and                                                              * Study of the interactions between defects is not within the scope of this thesis. 15  accurate. Therefore, the knowledge of defect chemistry may help predict the sintering of ceramic compounds under given conditions.        Figure ?2-4. Point defects in ionic structures4  2.2 Spinel structures  A spinel crystal is a FCC arrangement of anions where cations are filling tetrahedral and octahedral sites available between the anions, Figure ?2-5. A unit cell of spinel is composed of 56 atoms and includes 24 cations and 32 anions37,38. There are two types of cations in a unit cell of a spinel crystal, with two different valences. The general structural formula of a spinel crystal is AXBY2O4 where X and Y are the valences of cations; however, it should be mentioned that a spinel unit cell consists of 8 units, with the formula A8XB8YO32.   Type A cations are usually divalent e.g. Mg+2, Zn+2, Ni+2, Fe+2, Mn+2, etc. and fill 8 of the 64 available tetrahedral sites in the spinel crystal. In comparison type B cations are usually trivalent e.g. Al+3, Ti+4, Cr+3, Fe+3, etc. and are usually located at 16 of the 32 available octahedral sites37,39.  Depending on the valences of cations, two types of spinels are identified, including: 4-2 spinels where X= +2 and Y= +4 e.g. Mg2TiO4 16  3-2 spinels where X= +2 and Y= +3 e.g. MgAl2O4  A large group of industrially available spinels are crystallized in either type of spinels. For instance, spinels for refractory applications are (but not limited to) MgAl2O4, MgFe2O4, MgCr2O4, Mg2SnO4, etc.; for electronic applications include CoFe2O4, ZnCr2O4, etc39. Spinels with such cation arrangement where divalent and trivalent cations have filled tetrahedral and octahedral sites of a spinel crystal respectively are called normal spinels. However, the position of cations may change in a way that tri or tetravalent cations move to the tetrahedral sites and divalent cations locate into octahedral sites. In a certain situation, half of B type cations are located in tetravalent sites, and all A type cations are located in octahedral sites. A spinel crystal with this cation arrangement is called inverse spinel2. Therefore, the chemical formula of a 3-2 inverse spinel is B(AB)2O4. In naturally occurring spinels a fraction of cations change their positions between tetrahedral and octahedral sites; thus they are partially inversed. In order to understand the cation distribution in spinels, a general structural formula T(A1-?B?)M(B2-?A?)O4 is being used. In this formula, A and B refer to the two types of cations, T and M refer to tetrahedral and octahedral sites respectively and ? is the inversion parameter40.  The inversion parameter ? varies between 0 and 1, e.g. it is 0 for completely normal spinel and 1 for completely inverse spinel. The degree of inversion is a function of temperature, atmosphere, neighboring cation and anions, cation size and the electronic structure of the cation. For example, the inversion parameter (?) for CoAl2O4 is 0.055 at 850?C and 0.15 at 1400?C 41; this means that higher atomic mobility is present in the Co-Al spinel structure at higher temperature. Thus it can be concluded that the inversion parameter can be used to predict the relative cationic mobility in two spinels. In this regard, understanding the factors that control the inversion parameter is essential.   17    Figure ?2-5. Schematic of a spinel crystal4  2.2.1 Chromite spinels   Chromite is a mineralogical name for FeCr2O4; however, it generally refers to any chromium-containing spinels or solid solutions with spinel crystal structure6. There are six important chromite end-members including FeFe2O4 (FF), MgFe2O4 (MF), FeAl2O4 (FA), MgAl2O4 (MA), FeCr2O4 (FC), MgCr2O4 (MC); among them, MgCr2O4, MgAl2O4 and MgFe2O4 are stable in harsh environments where high temperature (>1300?C), thermal shock resistance, oxidizing-reducing atmosphere and corrosion resistance against molten slags are necessary. Due to these characteristics, MgCr2O4, MgAl2O4, MgFe2O4 and their solid solutions have been used as refractory materials for more than 50 years.   MgCr2O4 is a normal spinel (space group Fd3m) with a lattice parameter of 8.333?0.002 ?42,43 and theoretical density of 4.412 g/cm3. According to the MgO-MgCr2O4 phase diagram (Figure ?2-6), it is the only compound in this system, and its melting temperature is ~2350?C44. At high temperatures and in air atmosphere, the intrinsic defect in MgCr2O4 is the Cr vacancy, as 18  reported by Hiroki et al.45. Since the formation of Cr vacancies might be due to the evaporation mechanisms, the formed vacancies may improve the self-diffusion rate or the diffusion rates of other cations, but they cannot help the densification rate.  Figure ?2-6.  MgO-MgCr2O4 phase diagram7   The mechanism of vacancy formation has been was expressed by Kazumatomo46 as follows:                             2-7 where        is gaseous oxygen,     is oxygen lattice and               are negatively charged vacancy and electron hole, respectively. Calculating the self-diffusion coefficient of Cr at 19  different temperatures and partial pressures of oxygen, Kazumatomo demonstrated that self-diffusion was controlled by the Cr vacancies concentration.  MgAl2O4 is an isostructure of MgCr2O4 and is a normal spinel (space group Fd3m); its structure is described as a cubic lattice of oxygen atoms with Mg+2 occupying 12.5 % of tetrahedral sites and Al+3 occupying 50 % octahedral sites47. The lattice parameter and theoretical density are 8.0887 ? and the 3.59 g/cm3 respectively.   Figure ?2-7.  MgO-Al2O3 phase diagram8   As shown in MgO-Al2O3 phase diagram (Figure ?2-7) MgAl2O4 is also the only intermediate phase in MgO-Al2O3 system and its melting point is about 2135?C. Although MgAl2O4 and MgCr2O4 are isostructural compounds, the form different defects. Unlike MgCr2O4 in which Cr vacancy forms readily at high temperatures, Al vacancy in MgAl2O4 does not form very easily, due to the high vacancy formation energy (4.76 ev)45.  20   However, Murphy48 reported that the main defect type in stoichiometric MgAl2O4 spinel is the antisite disorder, as described in equation ?2-8, due to the lower formation energy of this process compared to other intrinsic defects. Such charged defects play a significant role in the accommodation of non-stoichiometry, foreign cations and also in the diffusional properties of spinel structure.                            2-8  Like two other chromites, MgFe2O4 is crystallized in spinel structure but unlike them it is an inverse spinel in which Fe+3occupies tetrahedral sites and Mg+2 octahedral sites; the inversion reaction may be triggered by heat49. The lattice parameter and theoretical density of MgFe2O4 are 8.3938 ?50 and 4.502 g/cm351 respectively. At temperatures above 1000?C, MgFe2O4 has an area of stability in the MgO-Fe2O3 phase diagram (Figure ?2-8), and its maximum melting temperature is ~1750?C. The main defect in the MgFe2O4 structure is disordering due to the lower octahedral site preference energy of Fe+3 than of Mg+2.    21   Figure ?2-8.  MgO-Fe2O3 phase diagram2    Alper2 showed that there was unlimited solid solubility between the chromite spinels at temperatures higher than 1000?C. It was also revealed that the chromite spinels, which are 2-3 type spinels, could also make solid solution with 2-4 spinels. The binary solid solutions of chromite spinels are generally considered as ideal solid solutions, although in few conditions (based on temperature and composition) they behave differently.  Chromite spinels (MgAl2O4, MgCr2O4, MgFe2O4 and their solid solution) have been usually considered as chemically stable compounds, however, their chemical stability is controlled by temperature, partial pressure of oxygen and composition. Ulmer43 graphically illustrated that the stability of the chromite spinel solid solutions was influenced by the partial 22  pressure of oxygen. Figure ?2-9 is a quaternary phase diagram of MgO-Cr2O3-Al2O3-Fe2O3 at 1300?C at different oxygen activities.    Figure ?2-9. Spinel redox stability in MgO-Cr2O3-Al2O3-Fe2O3 at 1300?C a) in air and b) in reducing atmosphere. Open circles show unstable compounds; closed circles refer to stable compounds; bold lines illustrate the stable chromite spinel solid solutions; reprinted from2.   As seen in Figure 2-9, in air atmosphere all sesquioxides were stable and iron was stable as hematite. No FeCr2O4 spinel would form in this condition since it would readily oxidize to parent oxides. Hence, MgAl2O4, MgCr2O4, MgFe2O4, and their solid solutions were stable in the mentioned conditions. Decreasing the oxygen partial pressure on the other hand made MgFe2O4 unstable and resulted in the hematite transformation into magnetite. In spite of these changes, no change in the stability of MgCr2O4, MgAl2O4 and their solid solutions was observed.  Walter42 reported that high temperature evaporation of Cr2O3 in MgAl2O4-MgCr2O4 solid solution and dissociation of MgFe2O4 above 1350?C in MgCr2O4-MgFe2O4 solid solutions 23  caused deviations from the Vegard?s law*. Paladino52 found that in equilibrated MgO-Fe2O3 mixtures, MgCr2O4 could be stable with hematite. Philips et al.42 also investigated the phase diagram of MgO-Fe2O3 by mineralogical identification process, and found that even at 1500?C and 1650?C MgFe2O4 decomposed into two phases Magnesiowustite (MW) + Magnesioferrite (MF). Speidel53 studied the stability of MgFe2O4 at different temperatures and oxygen activities using TGA, and found that the MgFe2O4 is a single phase up to 1300?C.   Ulmer et al. showed that the addition of Cr2O3 to MgO-Fe2O3 mixtures increased the stability of MgFe2O4, as implied by the reduction in ferrous iron content in response to Cr2O3 increase. Walter42 also found that the addition of MgCr2O4 into MgFe2O4 decreased the cell size of the formed solid solution spinel and increased the degree of normality of parent spinel structure. Therefore, it is generally considered that the MgCr2O4-MgFe2O4 solid solutions are binary up to 1400?C; however, above this temperature the deviation from binary behavior is significant.   The above review of chromite spinel structures and interactions between them shows that MgCr2O4, MgAl2O4, MgFe2O4 and their solid solution are isostructural;  however, depending on the cations involved in the spinel structures, the solid solution between them can be normal or inverse. Since the inversion involves cation mobility and also structural disordering, this phenomenon may affect the diffusion rates and densification behavior. Therefore, understanding the inversion mechanism and cation distribution in spinel solid solutions is essential for the analysis of the sintering mechanisms of spinel solid solutions.                                                               * Vegard?s?law states that the lattice parameters should vary linearly with composition for a continuous substitutional solid solution in which atoms or ions that substitute for each other are randomly distributed22. 24  2.2.1.1 Synthesis of chromite spinels  As described earlier, spinels such as MgAl2O4, MgCr2O4 and MgFe2O4 are categorized as chromite spinel materials. Chromite spinels are important materials due to their physico-chemical properties54, which them excellent candidates for refractories55,56, sensors57, catalysts, etc.   Chromite spinels have been traditionally synthesized by solid state reaction (SR), which involves high synthesis temperatures, usually above 1200?C58,59, resulting in low specific surface area and low reactivity. To avoid these shortcomings, several chemical synthesis techniques have been developed, including the sol?gel method (SG)60,61, co-precipitation (CP)44, solution combustion (SC)19,62, and hydrazine method (HM)61. The advantage of chemical routes compared to the solid state method was the ability to control the stoichiometry, particle size, and morphology of the synthesized spinel.   The basics of spinel formation have been explained by Wagner?s theory59: spinel formation initiates at the interface of primary oxides via counter diffusion of cations, and results in the formation of a spinel layer between Cr2O3 and MgO.  Due to the higher diffusion rate of Mg+2 in Cr2O3 in comparison to Cr+3 in MgO, the spinel layer grows toward Cr2O3 and leaves pores (termed? ?Kirkendall pores?), on the MgO site. The mechanism is schematically shown in Figure ?2-10; as seen, the spinel formation is accompanied by volume expansion. This mechanism was also reported by Greskovich63 for the formation of MgCr2O4, and by Watson59 for the formation of MgAl2O4.   25   Figure ?2-10.  The schematic of spinel formation mechanism according to Wagner theory; reproduced from9   Dilatometric studies of the reactions between spinel and sesquioxides in air confirmed the reduction of the sesquioxides to spinel at elevated temperatures. The studies also show that the reactions and phase transformations in chromite spinels involve volume change. For example, the isothermal reduction studies by Ulmer43 and dilatometry studies by Rigby and Culter64  pointed out where volume increase was observed during the reduction of sesquioxides to spinels. The volume increase was linked to the reduction of Fe+3 to Fe+2.  Although redox reactions were considered a reason for volume change in chromite spinels, Rigby64 introduced the Kirkendall effect i.e. pore formation due to different diffusion rates, as the main reason for such volume changes. Sako et al.65 also linked the pore formation to the Kirkendall effect during the formation of in situ spinel in Al2O3-MgO castables. In fact, larger pores were observed for higher MgO size in the microstructure of samples sintered at 1500?C for 5 h in air. Moreover, a spinel rim was seen around pores, emphasizing the presence of MgO in the existing pores before the spinel formation. In other words, MgO reacted with Al2O3 to form spinel and left a Kirkendall pore behind. The same results were also published by Braulio9, Yu et al.66, etc.   26  Table ?2-2. Thermodynamic properties of selected chromite spinels; reprinted from2  ?G? (1000-1227?C) (kcal/mol) ?G (kcal/mol) ?H (kcal/mol) ?S (cal/K) MgCr2O4 -10.27+1.7?10-3T (?0.5)    25?C -9.75?0.5 -9.9?0.5 -0.5 1000?C -8.10?0.5 -10.3?0.5 -1.7 MgAl2O4 -    25?C - - 0.53?0.2 1000?C -8.4 -6.9 +1.1 MgFe2O4 -5.75+0.32?10-3T (?0.4)    25?C -4.5?0.4 -4.8?0.4 1.1?1 1000?C -5.34?0.4 -5.75?0.4 -0.3?1   The thermodynamic properties of chromite spinels at 1000?C are summarized in Table ?2-2. As seen the ?G? values for the formation of MgCr2O4 and MgFe2O4 are negative, i.e. their formation is thermodynamically favorable. Moreover, the value of free energy of chromite spinels at 25?C and 1000?C indicates that MgCr2O4 should be the most stable phase both at low and high temperatures; MgAl2O4 followed by MgFe2O4 are the two most stable chromite phases after MgCr2O4. Therefore, understanding the solid solution formation between chromite spinels is essential, as they do not dissociate at high temperature, but react. As a result of the reaction between the chromite spinels, the crystal defects, disordering (cation distribution), and crystal distortion may occur, which affects the diffusional properties and densification behavior accordingly.   2.2.2 Cation distribution in chromite spinels  Spinels are important minerals and industrial materials and have been used as refractory, magnetic and semiconducting materials, and gems. Naturally occurring spinels consist of a variety of cations; the group of spinels which mainly consist of Mg+2, Al+3, Ti+4, Cr+3, Fe+2, and Fe+3 are categorized as chromite spinels. Since the type and position of cations involved in spinel 27  structure considerably change the physical and chemical properties of spinels, the determination of cation distribution is crucial in the characterization and prediction of the properties of either natural or synthetic spinels.   O'Neill and Navrotsky67 suggested that the inversion parameter describes the cation distribution in the case of binary spinels. Della et al.68 showed that the inversion parameter affected the static potentials in aluminate and ferrite spinels significantly. Kumar and Abbas69,70 showed that the magnetic properties in ferrite spinels, governed by super-exchange interactions, depended on the metal cations and their distribution over the two interstitial (tetrahedral and octahedral) sites. Francesco71 and Giovanni40 explained that knowledge of cation distribution process in spinels might provide important information on the cooling history of rocks, and elucidate constraints on diamond growth, since spinels were often found as inclusions in diamonds72.   Cation distribution in spinel solid solution was shown to strongly depend on the composition of the end-member spinels; for instance MgAl2O4, which has a normal structure over a wide range of temperatures, and MgFe2O4, which has an inverted structure with Mg+2 in the octahedral sites and Fe+3 in the tetrahedral sites, form inverted solid solutions [MgAl2-xFexO4 (0?x?2 ]73.   Nakatsuka et al.20 investigated the cation distribution in MgAl2O4-MgFe2O4 solid solutions using single crystal diffraction intensity, and showed that Al+3 and Fe+3 could occupy both the tetrahedral and octahedral sites. In contrast, Mg+2 occupied the tetrahedral sites in the MgAl2O4 rich compositions and octahedral sites in the MgFe2O4 rich compositions. Nakatsuka also showed that for the range of compositions 0.7?x?1.2 , two spinel phases were stable,  implying  a probable low temperature miscibility gap between MgAl2O4 and MgFe2O420. The same 28  phenomenon has been reported by Jacob74 in the MgO-Al2O3-Cr2O3 system. He demonstrated that the intracrystalline ion exchange was ruled by the site preference energies of the cations, and introduced a critical temperature (T=530?20?C) and a composition (                  ) above which some phase separation would occur.   Investigating the thermodynamics of complex spinel solid solutions,                           , Jacob and Behera75 explained that the cation distribution relied on temperature and composition; however, they developed a model predicting the cation distribution independent of these two factors, based on the octahedral site preference energies of the cations.  2.2.3 Sintering of chromite spinels  Sintering of ceramics is the most important stage of ceramic processing, since the properties of the final product, including mechanical, physical, electrical properties, etc., are influenced by the sintering parameters5. Sintering of MgAl2O4 spinels is well documented, due to the enormous potential for MgAl2O4 application in many industries1.  Pal et al.76 showed that there was about 40-50 wt% solubility of alumina in MgAl2O4 at 1600?C, which reduced rapidly with temperature decrease, implying precipitation of alumina during cooling. In spite of the high solid solubility of alumina in spinel, only 5-10 wt% alumina as a sintering additive is considered optimum76.  The addition of alumina in the mentioned range resulted in about 25% densification, and ~3.1g/cm3 bulk density at 1600?C. Although no microstructural evidence was shown in their report, the decreased density and increased open and closed porosity beyond these values were attributed to the precipitation of alumina during cooling.   Bratton77 has also investigated the initial stage sintering of MgAl2O4, and demonstrated that the volume diffusion was the controlling mechanism. In order to understand which species 29  was the rate-controlling one, the self-diffusion coefficients of O-2, Mg+2, and Al+3 in MgAl2O4, Al2O3 and MgO were compared to the measured data. It was shown that Al+3 and O-2 were the rate-controlling species in the initial stage of sintering. In another study, Rozenburg 78 studied the sintering kinetics of MgAl2O4 and LiF-doped MgAl2O4, using the master sintering curve techniques (MSC).  It was demonstrated that the addition of a small amount of LiF (0.5 wt%) reduced the activation energy of densification. Figure ?2-11 illustrates that increasing LiF up to 1 wt% decreased the densification activation energy from 470 to 190 kJ/mol. The activation energy for LiF-free samples is close to the lattice diffusion of oxygen in spinel, 430-490 kJ/mol, in agreement?with?Ting?and?Lu?s?results79. In addition, the activation energy of densification for the LiF-containing samples is very close to the activation energy of formation of MgAl2O4 in the presence of LiF (165 kJ/mol)80.     In a former study by Rozenburg10 it was explained that the reaction between LiF and MgAl2O4, which resulted in the formation of LiAlO2 and MgF2, may promote sintering of MgAl2O4 due to the liquid phase formation. However, the calculated activation energies in the later study proposed that the vacancy formation via the following reaction (Equation ?2-9) may be responsible for the reduced activation energy in the presence of LiF. Since sintering process was coupled with diffusion, the increased population of oxygen vacancies would reduce the activation energy.                  ?                               ?2-9  Bratton81 also studied the intermediate stage sintering of MgAl2O4 at 1300-1600?C and showed that volume diffusion was the active sintering mechanism; the activation energy of the 30  intermediate stage of sintering was 118 kJ/mol, close to that of the initial sintering stage, implying that the same mechanism was responsible for the densification.  Figure ?2-11. The effect of LiF concentration on activation energy of densification of MgAl2O4; the applied pressure was 33MPa10.      Investigation of the MgCr2O4 sintering was initiated by Anderson82 by studying the influence of the oxygen partial pressure. It was shown that MgCr2O4 could not densify to more than 70 % of theoretical density even at 1700?C, when the partial pressure of oxygen was higher than 10-10 atm, which is close to the equilibrium partial pressure for the following reaction 2-10 (                . Although it was shown that at           atm the MgCr2O4 densified to more than 98 % of theoretical density, it was also shown that MgCr2O4 might dissociate at 1600?C and            atm.                                      ?                                    2-10 0 0.2 0.4 0.6 0.8 1LiF concentration (wt%)150200250300350400450500550Activation energy of densification (kJ/mol)Activation energy of oxygen diffusion in spinel crystalActivation energy of MA spinel formation31   As a result of this decomposition, the small particles become smaller and large particles become larger, leading to MgCr2O4 grain growth with no densification82. The reaction showed in equation 2-10 plays two different roles in the densification of MgCr2O4: in the initial stages of sintering, the rapid grain growth results in pores entrapment inside grains, and these pores could not be eliminated82. In the final stage of sintering, when grains grow through lattice and grain boundary diffusion, the evaporation/condensation increases the grain growth rate more than the densification rate, leading to limited densification. A similar phenomenon was observed in the sintering of the Cr2O3 in air11, 83.   Studying the final stage of sintering of Cr2O3, Ownby11 showed that the densification of Cr2O3 was influenced by the oxygen partial pressure, and concluded that the maximum relative density (95%) was obtained when the oxygen partial pressure was equal with the equilibrium partial pressure of oxygen in the following reaction:                            ?                     2-11  As shown in Figure ?2-12, at PO2 higher or lower than PO2=10-12 atm (the equilibrium partial pressure for reaction ?2-11) the density of Cr2O3 decreases considerably; this behavior, according to Graham and Davis84, is related to the stability of different oxidation states of chromium. Cr+3 is the most stable form of chromium oxide, and its oxidation results in the formation of higher oxidation states Cr+4, Cr+6, which evaporate at PO2>10-3 atm as CrO2 and CrO3. At PO2<10-11 atm the metallic Cr leaves the sample; in the region between the mentioned pressures, evaporation was governed by the volatilization of CrO and CrO2. 32   Figure ?2-12. PO2 vs. density and weight loss of pure Cr2O3; the dominant species stable at various oxygen partial pressures are also indicated11.   Ownby et al. added 0.1 wt% and 1 wt% of MgO to retard grain growth during the final stage of sintering. The addition of 0.1 wt% of MgO at PO2=10-11 atm increased the density to 99.8 % of theoretical density, while adding 1 wt% of MgO limited the extent of densification to about 97 % of theoretical density, due to the formation of a continuous layer of MgCr2O4 at the grain boundary, resulting in reduced atom diffusion. -12 -8 -4 0Log PO2 (atm)6065707580859095100Relative density (%)01234Weight loss (%)Cr CrOCrO2CrO3CrO333   As reported by Graham84, Hench indicated that both the volume diffusion, and evaporation and condensation, were responsible for the sintering of Cr2O3. It was also shown that Cr+3 was the most stable oxidation state of Cr involved in the sintering of Cr2O3. Accordingly, the limited densification (relative density <75 %) of Cr2O3 in air and O2 atmospheres was attributed to the volatility of other oxidation states of chromium oxide, such as Cr+2, Cr+4, Cr+6. Roy85 found that the isothermal sintering of Cr2O3 in the presence of MgO was predominantly governed by grain boundary (GB) diffusion and simultaneous vapor transport at the sintering temperatures (1350-1500?C).   He also calculated the activation energy of sintering (125-272 kJ/mol) and stated that this very low value, compared to the activation energy for alumina sintering (628 kJ/mol), was caused by the GB diffusion as a result of departure of the oxide from the stoichiometric composition. Stone86 explained that the off-stoichiometry increased the lattice diffusion, which was very important in the sintering of Cr2O3. However, both studies pointed out that the role of the initial vapor transport should always be considered in Cr2O3. Stone87,86 investigated the effect of the reducing atmosphere, and found that the Cr2O4 layer formed on the Cr2O3 surface in oxygen atmosphere would be reduced in the presence of carbon, which resulted in enhanced densification at partial pressure of oxygen lower than 10-7 atm.  Hagel et al.88 studied the initial stage of sintering of Cr2O3 in Ar at PO2~10-2 atm, but they were not able to obtain more than 78 % of theoretical density. They concluded that the volume diffusion of lattice oxygen was the rate controlling factor. J.M. Neve and R. L. Coble83 studied the initial stage of Cr2O3 sintering at 1400?C and various oxygen partial pressures, and the maximum relative density of 75 % was obtained at the same PO2 as reported by Ownby11. Particle coarsening through the evaporation-condensation mechanism in the early stage of 34  sintering was attributed to poor densification. The results of sintering studies on MgCr2O4 and Cr2O3 show that the volume diffusion, grain boundary diffusion and evaporation-condensation govern the densification process and grain coarsening during sintering.  Several researchers investigated the role of sintering additives on the sintering temperature of MgCr2O4. Yamaguchi et al.12 investigated the role of TiO2 on the densification of MgCr2O4, and showed that the addition of up to 20 mol% of TiO2 can increase the extent of densification at 1500?C to 80 %TD in air and 96 %TD in reducing atmosphere. In spite of the limited density of samples sintered in air, the increase in density with increasing TiO2 content was also observed. Phase evolutions and lattice parameter calculations revealed that in both situations (sintering in air and carbon bed) the added TiO2 dissolved in MgCr2O4, although the solubility in air (15 wt%) was less than in reducing atmosphere (30 wt%) (Figure ?2-13). The formed solid solution was attributed to the better densification in reducing atmosphere. It was proposed that in reducing atmosphere at 1500?C the MgCr2O4 was thermodynamically unstable and decomposed by the following reaction:                    ?                           2-12  Moreover, TiO3 also became unstable in reducing atmosphere and reduced to TiO2. In the early stage of sintering, this instability acts as driving force for the higher diffusion rates of cations and enhanced densification. In oxidizing atmosphere, MgCr2O4 vaporized according to the equation ?2-12, and resulted in grain growth through evaporation of Cr species and their condensation on the neck area. This decreased the driving force of sintering and suppressed the densification.  35   Figure ?2-13. Relative density of the samples obtained from MgCr2O4-TiO2 compacts by heating in a carbon bed and in air at 1500?C for 2h12.    Ghosh et al.13 investigated the effect of magnesia reactivity and unstabilized ZrO2 on the sintering of magnesia-chrome ceramics. Two types of magnesia grains with 95 wt% purity and different grain sizes (sintered magnesia with 1 m2/g) and caustic magnesia with 13.5 m2/g) were used. The chromium oxide was provided by chrome ore, which contained Cr2O3:62 wt%, MgO:15 wt%, Fe2O3:12 wt% and Al2O3:10 wt%. Figure ?2-14 shows the variation of bulk density and apparent porosity of magnesia-chrome samples sintered at 1700 and 1750?C versus the ZrO2 content.  Regardless of the type of magnesia grains, the addition of zirconia progressively increased the bulk density and decreased the apparent porosity of the magnesia-chrome samples. However, the bulk density of the compositions made with caustic magnesia was considerably lower than the one with sintered magnesia. Sintering was accompanied by spinel formation along with densification. Therefore, since caustic magnesia was finer than sintered magnesia, spinel 0 10 20 30 40 50 60TiO2(mol%)5060708090100Relative density (%)Carbon bedair36  formation was enhanced, which delayed densification. The authors correlated the densification with the effect of ZrO2 on changing the grain boundary of magnesia-chrome samples, which decreased the dihedral angle. According to the investigation by Halder89, it appears that ZrO2 decreases the dihedral angle in the magnesia chromite spinel, which facilitates the direct bond (grain-grain contact) formation.   As shown in Figure ?2-14, increasing the sintering temperature to 1750?C did not increase the density in samples containing caustic magnesia and 5 wt% ZrO2, but decreased the apparent porosity. Unfortunately, the authors did not explain these observations; hence the mechanism which resulted in this behavior must be further investigated. Moreover, the hot modulus of rupture at 1300?C was also evaluated. As seen in Figure ?2-15 the HMOR increased about 80% in samples containing 5 wt% ZrO2 compared to the samples without ZrO2. This behavior is correlated with increased densification as well as the grain-to-grain bonding, due to the ZrO2 addition. In both cases the HMOR rose progressively by increasing the ZrO2 content, and reached a plateau at 3 %ZrO2.   Figure ?2-14. Bulk density and apparent porosity of magnesia-chrome grains developed from a) sintered magnesia, b) caustic magnesia13.  37   It can be concluded that higher amounts of ZrO2 increase the direct bond between magnesia-magnesia or chrome grains, which resulted in improved high temperature strength. The temperature influenced more the samples containing caustic magnesia grains than the ones with sintered magnesia grains; also, the rate of increase in HMOR with increasing ZrO2 for the samples containing sintered grains was higher than that of the ones with caustic magnesia grains13. This behavior correlates well with the spinel formation rate in caustic magnesia grains and sintered magnesia grains. In fact, the smaller crystal size of caustic magnesia grains compared to that of sintered magnesia grains resulted in higher activity of caustic grains and higher spinel formation rate compared to sintered magnesia grains. The same results have been reported for the hot modulus of rupture (HMOR) by Singh14.   Figure ?2-15. HMOR of magnesia-chrome aggregates developed from a) sintered magnesia and b) caustic magnesia14.   Zhao90 studied the addition of nano Fe2O3 into the matrix of magnesia-chrome ceramics and reported that the sintering temperature was reduced by about 150?C. The bulk density of samples containing 1.5 wt% nano Fe2O3 sintered at 1550?C (3.06 g/cm3) was 0.7 % higher than 38  that of samples without nano Fe2O3 (3.04 g/cm3). It was also shown that the amount of nano Fe2O3 up to 2 wt% progressively increased the CCS (cold crushing strength) and MOR (modulus of rupture) at every sintering temperature. For instance, MOR of the samples sintered at 1550?C (6.5 MPa) was considerably higher than that obtained in samples without nano Fe2O3 (4.75 MPa).   Recently, Azhari et al.56 found that adding nano iron oxide can enhance the formation of magnesioferrite spinel at temperatures as low as 1350?C compared to 1550?C for samples without nano Fe2O3. The dilatometry results showed that the onset sintering temperature, where the shrinkage started, was ~1150?C for samples without nano Fe2O3 and it was ~1100?C for samples containing 4 wt% nano Fe2O3. The low sintering temperature of the samples containing nano Fe2O3 was attributed to the decrease in the dihedral angle between magnesia grains.   To the best of our knowledge, there is very limited information about the application of nano particles to lower the sintering temperature of Cr2O3 containing ceramics. Moreover, existing sources are only limited to the application of nano Fe2O3, with no mechanism being proposed by the authors. Reviewing the literatures on sintering MgCr2O4 also indicates that there is a lack of studies on the lattice changes during the densification of MgCr2O4 and MgCr2O4 containing composites. Information on the lattice changes during sintering would help us evaluate transformation assisted sintering, which could considerably reduce MgCr2O4 and MgCr2O4 composite sintering temperatures. Reducing the sintering temperature of MgCr2O4-containing composites is very important for steel and non-ferrous industries, where they are extensively being used as refractory linings.   39  Chapter 3. Research scope and objectives     Sintering of magnesia-chromite refractory composites (MgO-MgCr2O4), is currently a viable process to make ceramics for refractory linings in non-ferrous metal smelting and refining furnaces. The goals of sintering of the magnesia-chromite refractory composites are to (i) achieve significant densification (i.e. 85-95% relative density) and (ii) to achieve engineered microstructure of a desired phase composition, with the highest MgCr2O4 content which can withstand the harsh working environments. The challenge of processing magnesia-chromite refractory composites is the required high sintering temperature (~1750?C) that increases the complexity of the production processes and costs. While much attention has been paid to sintering of Cr2O3, there are only a few recent publications addressing the sintering and densification of magnesia-chromite refractory composites19, 91.   The broad goal of the present work was to determine the kinetics of sintering and microstructural development of magnesia-chromite refractory composites and based on these results, to reduce their sintering temperature below 1500?C in air. Within this broad scope, the specific objectives of this research were as follows: 1. Investigation of the influence of trivalent ions (used as Al2O3, Fe2O3) on the sintering behavior of MgCr2O4.   2. Study of the effects of the spinel-forming tetravalent metal oxide (SnO2) as sintering additives, on the sintering behavior and crystal structure of the MgCr2O4.   3. Investigation of the role of the inversion phenomenon on the densification of MgCr2O4 by comparing the effects of SnO2 and Fe2O3 on the densification of MgCr2O4 and Cr2O3.   4. Study of the effect of Al2O3 and Fe2O3 as spinel forming sintering additives on the densification of magnesia-chromite refractory composites.  40   5. Investigation of the sintering mechanisms of micron sized and nano sized magnesia-chromite refractory composites, in particular the kinetics of sintering of the nano and micron sized magnesia-chromite refractory composites to understand the sintering rate controlling mechanisms.  The following activities have been carried out within the scope of this research in order to address the above objectives: ? The effects of the sintering additives including Fe2O3, Al2O3, and SnO2 on the formation and the densification of MgCr2O4 were investigated by simultaneous thermal analysis (STA: DSC/TGA). To explain the mechanism through which the sintering additives affected the densification of MgCr2O4 their influence on the MgCr2O4 unit cell including the lattice parameter and cation distribution (inversion degree) were investigated based on the XRD method. ? The effects of the Cr2O3, Fe2O3 and Al2O3 on the densification of magnesia-chromite refractory composites were investigated by comparing the microstructure and densification results of 12 compositions called MKi (1?i?12). The composition with the density above 95% at the lowest sintering temperature was considered as the best composition and was used for sintering kinetics studies. ? The best composition of magnesia-chromite refractory composites powders was synthesized with two different particle sizes via two different methods including (i) sol-gel (termed "nano" magnesia-chromite refractory composite powders (NMK)) and (ii) conventional powder processing (termed "micro" magnesia-chromite composite powders (MK)). The powders synthesized by these two methods had average particle sizes of ~20 nm and ~1.27 ?m respectively. The phase analysis, 41  microstructure and particle size of prepared composites were investigated by XRD and SEM.  ? The densification and the kinetics of sintering the synthesized NMK and MK composites were investigated via isothermal sintering techniques. The composite powders were pressed uniaxially and sintered at different temperatures (950-1750?C), for various durations (20-300 minutes) in air. The densification behavior of magnesia-chromite refractory composites has been investigated by comparing the density and the microstructure of the sintered composites. The activation energy of sintering was calculated based on the isothermal sintering technique results and applying the master sintering curve theory on the data. ? The best magnesia-chromite refractory composition, selected according to the criterion of the maximum density (~95 % of theoretical density) at optimum microstructure, was used as a binding system in refractory brick samples containing additionally fused mag-chrome grains. The bricks were sintered at 1475?C for 5 hours. The physical and mechanical properties of the bricks were used to estimate their in-field performance.   It is anticipated that the findings of this project will contribute to the fundamental understanding of sintering magnesia-chromite composites, and will also provide the Canadian non-ferrous industry with a new technology for the low-temperature sintering of magnesia-chromite composites.  42  Chapter 4. Experimental  4.1 Introduction  This chapter describes in detail the techniques and procedures employed to study the sintering of magnesia-chromite refractory composites. The role of Al2O3, Fe2O3, and SnO2 on the formation and the densification of pure MgCr2O4 were first thoroughly investigated. To understand the effects of the inversion phenomenon on the sintering of MgCr2O4, the densification results of Cr2O3-Fe2O3 and Cr2O3-SnO2 were compared with MgCr2O4-SnO2 and MgCr2O4-Fe2O3.  Based on the results of the above experiments with the intension of designing a refractory grade magnesia-chromite composite, 12 compositions (called MKi; 1?i?12) were designed in order to investigate the effect of the Fe2O3, Cr2O3 and Al2O3 on the densification of magnesia-chromite refractory composites. The composition with the relative density above 95% at the lowest sintering temperature and time was considered as the best composition and used for sintering kinetics analysis. The best composition was synthesized in two particle sizes, 1.27 ?m and 20 nm. The micron and nano sized composite powders were called MK and NMK composites and were used to study the sintering kinetics and understand the sintering mechanism of magnesia-chromite refractory composites and optimize their sintering conditions, including time, temperature, and additives, as well as to produce refractory grade magnesia-chromite refractory composites at temperatures below 1500?C in air.   43  4.1.1 Synthesis of doped and undoped MgCr2O4 spinels  These materials were prepared in order to study the effect of trivalent (Al2O3 and Fe2O3) and tetravalent oxide (SnO2) in the densification of MgCr2O4, to test our hypothesis that Fe2O3 or Al2O3 induces inversion in the MgCr2O4 lattice. Analytical grade magnesium nitrate hexahydrate (Mg(NO3)2.6H2O, purity >99.9%), chromium nitrate nonahydrate (Cr(NO3)3.9H2O, purity >99.9%), aluminum nitrate nonahydrate (Al(NO3)3.9H2O, purity >99.9%) and ferric nitrate nonahydrate (Fe(NO3)3.9H2O, purity >99.9%), and nano tin oxide (SnO2, purity> 99.9%) have been used as raw materials, in order to minimize the introduction of impurities during processing. The required amounts of raw materials were dissolved in 100 cm3 of distilled water.   The solution was stirred at 400 rpm and evaporated until the formation of a dark ?spongy??mix of salts that was later dried at 250?C for 24 hours and calcined at 850?C for 6 hours, in order to form synthetic powders. The average particle size of such processed oxides was determined through SEM observations to be about 0.7 ?m. The general formula of these specimens is Mg[Cr1-xMex]2O4, where x is the amount of Me cation (Me = Al, Fe, Sn) replacing chromium, and varies between 0 and 0.2 with 0.05 mol% intervals. It has been verified that in all cases the whole amount of magnesia used reacted with the sintering additive to form spinel.   Based on the results of analyzing the effect of sintering additives on the sintering of MgCr2O4, and the intention of designing a magnesia-chromite composite for refractory applications 12 compositions called MKi (1?i?12) were designed and synthesized following the same procedure. The chemical compositions of all the synthesized samples are presented in Table ?4-1.  44  4.1.2 Synthesis of nano magnesia-chromite refractory composites   These sets of samples were prepared to investigate the effect of particle size on the densification of MK composites. Nano-particles of MK composites?were?prepared?via?Pechini?s?method15. Magnesium nitrate hexahydrate (Mg(NO3)2.6H2O, purity >99.9%), chromium nitrate nonahydrate (Cr(NO3)3.9H2O, purity >99.9%), aluminum nitrate nonahydrate (Al(NO3)3.9H2O, purity >99.9%) and ferric nitrate nonahydrate (Fe(NO3)3.9H2O, purity >99.9%), citric acid (C6H8O7?H2O), and ammonia solution (NH4OH, 30%) were used as the starting materials. All starting materials were purchased from Fisher Scientific Ltd. The required amounts of raw materials were first dissolved in 100 ml of distilled water. Then citric acid was added to the solution, with the ratio of citrate to metal ions of 0.5:1. Citric acid plays two major roles: (1) as a chelating agent it binds metal ions and preserves them from precipitation during pH changes (the schematic of chelation mechanism is shown in Figure ?4-1); (2) as a fuel, owing to the presence carbohydrate chains in its structure, burns fast in air and generates heat, thus reducing the synthesis temperature.  In?order?to?increase?the?efficiency?of?citric?acid?as?a chelating agent, pH of the solution was adjusted to 6 by adding ammonia92. The solution was homogenized for half an hour on a hot plate while mixing with a magnet stirrer, and then it was heated to achieve evaporation of water and formation of a concentrated viscous solution. The solution was heated at 200?C for 24 hours. As a result, a dark brownish sponge-like precursor formed; this was pulverized with pestle and mortar and calcined at 850?C in order to form a nano size magnesia-chromite refractory composite.  45   Figure ?4-1. Schematic of chelation mechanism during synthesis of MKi composite15   It is expected that due to the chelating effect of citric acid, the particle size remains in the range of nano size, and in fact a particle size in the range of 20 nm was obtained. With respect to the? formation?of? the? sol?and?gel?during? the?Pechini?s? synthesis?procedure,? Jeng92 reported that during heating, a polyacrylamide network would form in the primary sol at 120?C. Further heating melts the citric acid at about 173?C and convert it to aconitic acid, then itaconic acid, which undergoes polymerization and swells with the decarboxylation at higher temperatures60. Since the decarburization at high calcination temperature involves CO2 evolution, the resulting powder would form soft agglomerates. 4.1.1 Preparation of green ceramic bodies  In all cases except for the laboratory scale bricks, the calcined powder was de-agglomerated using pestle and mortar, mixed with 5 wt% polyvinyl alcohol (PVA) solution, and subsequently pressed uniaxially to form cylindrical specimens, 14 mm in diameter and 2-4 mm in height. The compaction pressure was selected on the basis of achieved maximum density of pressed composites sintered at 1500?C for 2 hours.  46  Table ?4-1.The summary of starting powders compositions         MgO (mol%) Al2O3 (mol%) Cr2O3 (mol%) Fe2O3 (mol%) SnO2 (mol%) Mg[Cr]2O4 50  50   Mg[Cr0.95Fe0.05]2O4 50  47.5 2.5  Mg[Cr0.9Fe0.1]2O4 50  45 5  Mg[Cr0.85Fe0.15]2O4 50  42.5 7.5  Mg[Cr0.8Fe0.2]2O4 50  40 10  Mg[Cr0.95Al0.05]2O4 50 2.5 47.5   Mg[Cr0.9Al0.1]2O4 50 5 45   Mg[Cr0.85Al0.15]2O4 50 7.5 42.5   Mg[Cr0.8Al0.2]2O4 50 10 40   Mg[Cr0.95Sn0.05]2O4 50  47.5  2.5 Mg[Cr0.9Sn0.1]2O4 50  45  5 Mg[Cr0.85Sn0.15]2O4 50  42.5  7.5 Mg[Cr0.8Sn0.2]2O4 50  40  10 Cr2O3-2.5Fe2O3   97.5 2.5  Cr2O3-5Fe2O3   95 5  Cr2O3-7.5Fe2O3   92.5 7.5  Cr2O3-10Fe2O3   90 10  Cr2O3-2.5SnO2   92.5  2.5 Cr2O3-5SnO2   95  5 Cr2O3-7.5SnO2   92.5  7.5 Cr2O3-10SnO2   90  10 MK 83.5 6.9 6.9 2.7  NMK 83.5 6.9  6.9 2.7  MK1 85.49 6.9 2.71 4.9  MK2 84.49 6.9 2.71 5.9  MK3 83.49 6.9 2.71 6.9  MK4 82.49 6.9 2.71 7.9  MK5 81.49 6.9 2.71 8.9  MK6 85.49 4.9 2.71 6.9  MK7 84.49 5.9 2.71 6.9  MK8 82.49 7.9 2.71 6.9  MK9 81.49 8.9 2.71 6.9  MK10 81.49 6.9 3.71 6.9  MK11 82.49 6.9 1.71 6.9  MK12 84.49 6.9 0.71 6.9     The influence of green density on the densification of composites has been discussed in Section ?5.1. All compositions have been pressed with the same pressure of 120 MPa, since the same materials with similar particle size and particle size distribution (except NMK) have been used in all experiments. The difference between composites is limited to their compositions.  47   To prepare the specimens for the sintering studies, all formed pellets were heat treated at 850?C for 1 hour and furnace cooled to assure a complete dissociation of PVA and burning of the residual carbon from PVA58,93. To minimize moisture absorption by the pellets, they were kept at 150?C before sintering. 4.2 Sintering of ceramic bodies   In order to study the effects of Fe2O3, Al2O3 and SnO2 the sintering of MgCr2O4, pellets made of Mg[Cr1-xMex]2O4 compositions were heated in a box furnace with 5?/min up to the sintering temperatures (1250-1500?C with 50?C intervals), soaked for 2 hours and cooled inside the furnace to room temperature. From each composition, one specimen was air quenched to room temperature after being soaked at the sintering temperature, to preserve the phase composition and the microstructure at the sintering temperature. This enabled us to determine any changes taking place during materials cooling, to calculate the inversion parameter at the sintering temperature and to correlate it to the sintering behavior of MgCr2O4 spinel.   A  series  of  isothermal  sintering experiments  was  carried  out  to  study the densification  and  grain  growth  of  magnesia-chromite refractory composites. The isothermal sintering was conducted at 850-1600?C with 50?C intervals. The temperature of the furnace was first increased to the desired sintering temperature, and the pellets were placed in the hot furnace for 20, 70, 180 and 300 minutes. The samples did not show any signs of thermal shock experience in this process, as no micro cracks were observed on the surface and cross section of sintered samples. The samples used for each condition were air-quenched to preserve the high temperature structure, for the phase evolution. The characteristics of the sintered samples were determined and used for the sintering mechanism analysis, as described in the following sections.   48   The densification behavior of magnesia-chromite refractory composites was evaluated both non-isothermally and isothermally. As described in section ?4.2, each data point including density, grain size, porosity, etc. is representative of an average value for 3 samples quenched from the sintering temperature. This indicates that all sintering experiments were performed isothermally, but some of the results were reported in the form of non-isothermally collected data. 4.3 Materials characterization  4.3.1 Density, water absorption and apparent porosity  Polished samples were used for bulk density (BD), water absorption (WA), and apparent porosity (AP) measurements, using the Archimedes immersion test. The test was performed on the furnace-cooled sintered samples. The weight of the dry samples (Wd) was measured first.   The samples were impregnated with a wetting agent solution (Kerosene; ?k: 0.78 g/cm3) in a vacuum chamber for 2 hours, to ensure that all pores were filled with the solution. The impregnated samples were then suspended in the solution and the immersed weight (Wi) was measured. The samples were removed from the solution and wiped with a piece of kerosene-saturated paper, to ensure that the excess solution was removed only from the surface, but not from the surface pores. The weight of the kerosene-saturated samples (Ww) was then measured quickly. All density measurements were performed at room temperature. The bulk density, water absorption and apparent porosity were calculated using the equations ?4-1 to ?4-3 respectively:                 4-1     [          ]          4-2 49                   4-3  The standard error of the density determination was about ? 0.1%. In order to compare the results, the relative density (RD) was calculated by dividing the measured bulk density by the theoretical density of the composition. The theoretical density of each composition was calculated from the XRD-determined unit lattice parameter for the samples sintered at 1500?C and quenched in air. It was assumed that the microstructure consists of a single phase spinel solid solution, with no excess spinel-forming oxides. This assumption was XRD-validated for all the samples sintered above 1250?C. The calculated theoretical densities of all compositions used in the present study are presented in Table ?4-1. 4.3.2 X-ray diffraction  Phase analyses were performed on pulverized specimens (d< #200 mesh) using a Rigaku-Multiflex X-ray diffractometer (Tokyo, Japan), with Cu-K?? radiation? (?:? 0.154056? nm)?functioning at a voltage and current of 40 kV and 20 mA respectively. The XRD patterns were built from data collected for?2?? in? the?15-80 degrees range, with a scan rate of 0.5 degree per minute. All the X-ray diffraction (XRD) patterns were analyzed with the JADE program for phase identification.  4.3.2.1 Lattice parameter measurement The lattice parameter was calculated using the following equation.   ?                     4-4 where ? is the wavelength of the incident beam (0.1542 nm), h, k, and l are the plan indexes and ??is?the?Bragg's??diffraction?angle.  50  4.3.2.2 XRD density measurement  Knowing the value of the unit cell and the number of atoms per unit cell, the theoretical density of samples was calculated as follow:     ?    ?   4-5 where ?A is sum of the atomic weights of the atoms in the unit cell, M is molecular weight of sample, N is the Avogadro number, and V is the volume of unit cell. The XRD data was used for inversion parameter measurements as detailed in section  5.2.  4.3.3 Scanning electron microscopy   Due to the non-conductivity of the samples, they were coated with 5 nm of gold using a spattering machine to prevent the charging effect caused by the ceramics and electron beam interactions. The microstructures were then studied using a scanning electron microscope (SEM, Hitachi S-3000N, Japan) with an accelerating voltage of 15 kV. The average grain size (G) was measured based on the conventional image analysis technique of the linear intercept method (ASTM E112)95. For each sample at least three images were assessed by drawing 5 line segments.  The average grain size of the sintered samples (G) was determined by multiplying the average linear intercept by 1.57196. 4.3.4 Simultaneous thermal analysis (STA)  To determine the activation energy (Ea) for the MgCr2O4 spinel formation in the presence of sintering additives, 25 mg of precursors were used for STA analysis. The precursors were heated to 900?C in air with three different heating rates (10, 20 and 25?/min) using PerkinElmer 51  STA 6000. The data was fitted to the Kissinger106 model in order to find the activation energy of spinel formation.        ?        ?            4-6 where ? is heating rate, Tp is the temperature of the maximum DSC formation peak and R is the universal gas constant. The activation energy (Ea) was calculated from the slope of the plot of        ?  vs. 1/TP.  4.3.5 Thermal etching   The sintered samples were polished using 6 and 1 micron diamond solutions, and returned to the box furnace for thermal etching to reveal the grain boundaries. This was accomplished at a temperature 50-300?C lower than the sintering temperature, for a short duration of 15 minutes in air. Both the heating and cooling rates for the etching treatment were 10?C/min.   4.3.6 Dimension change and weight loss  The dimensions were measured by a digital caliper with the precision of ?0.001 mm. The weight loss was measured with the precision of ?0.001 g.    52  Chapter 5.   The influence of spinel forming oxides on sintering of MgCr2O4  5.1 The influence of green density on sintering process   It is well known that the processing of primary powders before sintering significantly affects the densification and the physical properties of sintered ceramics97,98. Krell et al.98 sintered submicron alumina grains and showed that the conventional sintering of submicron alumina was affected by the shaping procedure. They compared the density of uniaxially pressed submicron alumina with the density of the same composition shaped by CIP (Cold Isostatic Pressing) in addition to uniaxial pressing. It was shown that addition of CIP shaping procedure reduced the sintering temperature from 1450?C to 1400?C and also increased the final density from 98% to 99%. The enhanced densification was attributed to the higher homogeneity of particle coordination in the CIP processed specimens.   In the present study, the uniaxial pressing has been used to form pellets for densification studies. As shown in Figure ?5-1, no considerable change in both the green and sintered densities was observed at compaction pressure of above 120 MPa. Due to the similarity between the pressing pattern of magnesia chromite refractory composites and other samples, only the variation of density versus compacting pressure for the best magnesia-chromite refractory composite (MK) is presented. In the case of NMK composites, which were made of nano composite particles, cracks in specimens were observed at compacting pressures higher than 100 MPa. It is expected that the very small particle size of NMK sample (<20 nm) generates large friction forces between the nano sized particles99,100, which limits the particle rearrangement, resulting in a very low green density of 35%?0.1%. Increasing the compaction pressure in this 53  situation increases the stress and eventually forms cracks in the compact. Figure ?5-1 also shows that the final density of the MK composite is affected by their green density, as also reported by others. Woolfrey101 showed that the final density of UO2 powder decreased considerably for the compacts with green densities below 40%. He related this behavior to a critical value of the ratio of pore size to the particle size, above which pores stabilized and inhibited local shrinkage. He also showed that the green density did not change the sintering mechanism and the activation energy of sintering.    Figure ?5-1. The variation of density versus compacting pressure for as-pressed MK composites and MK composites sintered at 1500?C for 20 minutes; error bars are smaller than symbols     In contrast to MK, densification of NMK composite was not affected by the green density. The same phenomenon has been reported by Neves et al.100; they found that the green density had no influence on the densification of the nano ZnO, while a significant reduction in the final density was recorded for the micro ZnO with the low green densities. They attributed this to the 20 60 100 140 180Compacting pressure (MPa)102030405060708090100Density (g/cm3)Sintered at 1500 ?CAs pressed54  higher specific surface area and also to the higher rate of grain boundary diffusion of nano particles in comparison to micron sized particles.   Based on the results obtained in this section, specimens made by nano and micron sized powders were pressed uniaxially under the 100 MPa and 125 MPa respectively.  5.2 The influence of trivalent oxides (Fe2O3 and Al2O3) on the sintering of MgCr2O4  SEM images of the powder calcined at 850?C are shown in Figure ?5-2. Grains with the average size of 0.2, 0.7, and 0.3 ?m were observed for Mg[Cr]2O4, Mg[Cr0.8Fe0.2]2O4 and Mg[Cr0.8Al0.2]2O4 compositions calcined at 850?C. Since the calcination temperature was significantly higher than the decomposition temperature of nitrates, it is believed that fewer agglomerates were formed. In fact, the formation of NOX gas did not allow the formation of agglomerates, assured a homogenous compaction, and reduced stress development during sintering.  The typical XRD patterns of Mg[Cr0.8Fe0.2]2O4 composition calcined at various temperatures are shown in Figure ?5-3. It is seen that spinel starts to form at 550?C and is accompanied by MgO, Fe2O3 and Cr2O3 at 650?C, indicating that nitrates first oxidize and then react to form spinel or spinel solid solutions. When the calcination temperatures were increased to 850?C and 1050?C, the oxides reacted further to form spinel products, therefore, the intensities of identification peaks decreased for the unreacted oxides and increased for the spinel products.  A -0.352?0.003 degree shift in the position of the (311) identification peaks of spinel is also observed, which can be attributed to the formation of spinel solid solutions. There are similarities between the XRD patterns of Al2O3 and Fe2O3 containing compositions, but at 1050?C a comparison in the peak intensities ratios indicates that the unreacted oxide content in 55  the Mg[Cr0.8Al0.2]2O4 compositions (ICr2O3(104)/IMgCr2O4(311):0.072) is higher than that of Mg[Cr0.8Fe0.2]2O4 compositions (ICr2O3(104)/IMgCr2O4(311): 0.033).  In addition, the shift in the position of (311) spinel peaks in Mg[Cr0.8Al0.2]2O4 composition is +0.214?0.003 degree smaller than that of Mg[Cr0.8Fe0.2]2O4. The difference between the formation of spinel products in Al2O3 and Fe2O3 containing compositions is explained by the formation mechanism and kinetics of spinel formation.   Figure ?5-2.  SEM images of synthesized spinel powders calcined at 850?C a) MgCr2O4, b) Mg[Cr0.8Fe0.2]2O4 and c) Mg[Cr0.8Al0.2]2O4   The formation mechanism of spinels has been explained by the Wagner theory59. According to it, spinel formation initiates at the interfaces of the primary oxides and continues by 56  counter diffusion of cations at the interface of oxides. In this mechanism the formed spinel layer is considered as a barrier to the cations diffusion, and suppresses the formation of spinel, therefore decreasing the formation rate. In the presence of Al2O3, MgAl2O4 spinel forms faster than MgCr2O4 due to its lower activation energy of formation (171 kJ/mol)102. This layer, therefore, should decrease the diffusion rate of cations and decrease the rate of spinel or spinel solid solution formation. However, in the case of Mg[Cr0.8Fe0.2]2O4 a solid solution formation between MgFe2O4 and MgCr2O4 should be faster than the Mg[Cr0.8Al0.2]2O4 formation, since MgCr2O4 and MgFe2O4 form almost in the same time due to their similar activation energies (337 and 323 kJ/mol)103,104.   Figure ?5-3.  XRD patterns of Mg[Cr0.8Fe0.2]2O4 samples calcined at various temperatures  57   Simultaneous thermal analysis (DSC/TGA) was used to study the effect of Al2O3 and Fe2O3 on the kinetics of MgCr2O4 formation. The typical STA plot of MgCr2O4 is shown in Figure ?5-4. The first two endothermic peaks at 150 and 350?C with the corresponding weight loss are attributed to the oxidation of nitrates to magnesium and chromium oxides respectively105. The exothermic peak at about 650?C with no weight loss is attributed to the formation of pure MgCr2O4 formation, since the XRD patterns have shown the presence of MgCr2O4 at 650?C.     Figure ?5-4.  The typical STA pattern of precursors for Mg[Cr0.8Fe0.2]2O4 composition    To determine the activation energy (Ea) for the MgCr2O4 spinel formation in the presence of sintering additives, 25 mg of Mg[Cr]2O4, Mg[Cr0.8Fe0.2]2O4 and Mg[Cr0.8Al0.2]2O4 precursors were used for STA analysis. The precursors were heated to 900?C in air with three different heating rates (10, 20 and 25 ?/min). It was observed that increasing the heating rate moved the 100 300 500 700 900Temperature(?C)-30-20-100102030Heat flow; Endo down (?J/mg) 0102030405060Mass (mg) DSCTGNitrates decompositionSpinel formation58  correlated exothermic peak of spinel formation toward higher temperatures. Figure ?5-5 shows the position change with increase in heating rate.  Figure ?5-5. The effect of heating rate on the STA peak position for Mg[Cr0.8Fe0.2]2O4 composition   The maximum temperature of the exothermic peak was recorded and analyzed using the Kissinger equation in order to find the activation energy (Ea) of spinel formation 106:         ?         ?            5-1 where Tp (K) is the temperature of the maximum DSC formation peak, R(J/K.mol) is the universal gas constant, and   (K/min) is the heating rate. The activation energy (Ea) was calculated from the plot of        ?   vs. 1/TP. The Kissinger plot of MgCr2O4 as a function of composition is shown in Figure ?5-6. Based on these plots, the activation energy of the formation of Mg[Cr]2O4, Mg[Cr0.8Fe0.2]2O4 and Mg[Cr0.8Al0.2]2O4 are 329?7 kJ/mol, 298?11 kJ/mol and 206?3 kJ/mol respectively. Since the reported activation energies are the average of 2 400 500 600 700 800Temperature(?C)010203040DSC; Down Endo (?v)???25??min ???20??min ??10??min Tp Tp Tp 59  measurements, the confidence intervals were set as 2?*. The crystallization mechanism is determined by calculating the Avrami constant (n)107 of the exothermic peak using equation?5-2:    (           ?   )  5-2 where w1/2 is the full width at half maximum (semi-breath) of the exothermic peak. When nA is low value (i.e. nA <2) it implies that surface crystallization is the dominant crystallization mechanism. In contrast, high n value is the indication of high nucleation rate, i.e. n>2.5 for diffusion controlled reactions or nA >4 for polymorphic transformation107.  Figure ?5-6. Kissinger plot of   (    ? )vs. 103/TP of MgCr2O4 as a function of composition   Table ?5-1 shows the kinetic parameters of the three studied compositions. As seen the Avrami constant of all compositions is above 2.5, as an indication of diffusion controlled spinel formation reaction. The obtained activation energies for MgCr2O4 and Mg[Cr0.8Fe0.2]2O4 are close to the value reported by Paik et al. for MgCr2O4 (323 kJ/mol)103. This indicates similar                                                              * ?: Standard deviation 1.02 1.06 1.1 1.14 1.18 1.22Tp-1 (103K-1)-11.2-11-10.8-10.6-10.4-10.2In[??Tp2] (K-1S-1) Mg[Cr0.8Al0.2]2O4Mg[Cr0.8Fe0.2]2O4MgCr2O4Ea/R=-39.628R=0.9918Ea/R=-24.738R=0.9929Ea/R=-35.859R=0.990660  kinetics and mechanism of the formation of these spinels. For the Mg[Cr0.8Al0.2]2O4 the activation energy is close to the pure MgAl2O4 (171 kJ/mol)102, but much lower than for pure MgCr2O4. In order to find out the reasons, the activation energies of diffusion of cations involved in spinel formation, in their oxides, are compared to the obtained activation energies for each composition.   Table ?5-1. Experimental conditions the measured parameters of the spinel formation kinetic studies  ? (?/min) Tp (K) W1/2 (K) Ea (kJ/mol) nA Average(nA) Mg[Cr0.8Al0.2]2O4 25 858 28.3 206?3 2.6 2.6 20 849 29 2.5 Mg[Cr0.8Fe0.2]2O4 25 853 22 298?11 2.4 2.6 20 846 19 2.8 Mg[Cr]2O4 25 934 22 329?7 2.5 2.5 15 930 27 2.5   The spinel forms by the counter diffusion of cations, so the activation energy of the whole reaction should be close to the activation energy of the diffusion of the slowest cation. A comparison between the activation energies of diffusion of Mg+2(327 kJ/mol), Fe+3(419 kJ/mol)102, Al+3(477kJ/mol)108, and Cr+3 (~500 kJ/mol)46 in their oxides and the activation energy of the formation of pure MgCr2O4 (323 kJ/mol), MgFe2O4 (337 kJ/mol) and MgAl2O4 (171 kJ/mol) indicates that the formation of spinel is mostly controlled by the diffusion of trivalent oxides.   The difference in the activation energy of the formation of MgAl2O4 and MgCr2O4, or MgFe2O4 and MgCr2O4, can be attributed to the type of the trivalent cations. As reported by Fernandez et al.102 the rate of formation of aluminate spinels is influenced by the site preference energies of divalent cations. They showed that MgAl2O4 formed faster than ZnAl2O4 and 61  NiAl2O4 because on the one hand, the tetrahedral site preference energy of Mg+2 was less than of Zn+2 and on the other hand, the octahedral site preference energy of Ni+2 was very high (-59 J/mol). As a result, Mg+2 moved more readily than Zn+2 and Ni+2 and increased the rate of MgAl2O4 formation.  Considering the same analogy, MgAl2O4 would form before MgCr2O4 because of the smaller size of Al+3 (0.54 ?)109 than Cr+3 (0.62 ?)109, and because of the smaller octahedral site preference energy of Al+3 (-41.9 kJ/mol) than of Cr+3 (-87.9 kJ/mol)38. The same reason is considered for the small activation energy of MgCr2O4 in the presence of Fe2O3 298 kJ/mol. According to the above discussion, it is hypothesized that MgAl2O4 and MgFe2O4 form before MgCr2O4 via an exothermic reaction60. Therefore, the reduction in the activation energy could be attributed to the compensation of part of the activation energy of MgCr2O4 with the generated heat from the formation of MgFe2O4 and MgAl2O4.   The results of kinetic studies of spinel formation indicate that during the formation of both Mg[Cr0.8Al0.2]2O4 and Mg[Cr0.8Fe0.2]2O4 solid solutions, the diffusion of Cr+3 is controlling the spinel formation rate; however, in Mg[Cr0.8Al0.2]2O4, due to the fast formation of MgAl2O4, the MgCr2O4 formation was more suppressed and resulted in the higher concentration of unreacted oxides at the calcination temperature (850?C).       The influence of the sintering temperature and Fe2O3 content on the relative density of the Mg[Cr1-xFex]2O4 (x=0, 0.15 and 0.2) is presented in Figure ?5-7. The results show that for the Fe2O3 free samples (x=0), practically no significant densification (<7 % of theoretical density) was observed at 1250?C-1500?C. However, densification increased by ~20% in the same sintering temperature range, for the Mg[Cr0.8Fe0.2]2O4 specimens. Figure ?5-9 shows the typical microstructure of the samples sintered at 1250 and 1500?C. It is observed that the higher 62  sintering temperature reduced the overall porosity of both types of sintered samples; however, the effect of Fe2O3 on increasing the density was more significant than the sintering temperature.  This can be explained based on the MgO-Cr2O3-Fe2O3 phase diagram110, where there is unlimited solid solubility between MgCr2O4 and MgFe2O4, Figure ?5-8. Considering 100% conversion of Fe2O3 to MgFe2O4 at the sintering temperatures, the Mg[Cr0.95Fe0.05]2O4 and Mg[Cr0.8Fe0.2]2O4 compositions contain about 8.8 and 12.5 wt% MgFe2O4 respectively.   Figure ?5-7. The variation of relative density of sintered Mg[Cr1-xFex]2O4 compositions at different temperatures for 2 hours    Since the phase diagram, Figure ?5-8, predicts that MgCr2O4-MgFe2O4 solid solution is the thermodynamically stable phase at the sintering temperatures of 1250 and 1500?C, the solid solution should also form during the sintering process studied in this work.    1225 1275 1325 1375 1425 1475 1525Temperature(?C)455055606570Relative density (%) X = 0X = 0.15X = 0.263   Figure ?5-8. The MgO-Cr2O3-Fe2O3 phase diagram at 1300?C110   The XRD patterns of specimens containing Fe2O3, Figure ?5-10a, show indeed the formation of MgCr2O4-MgFe2O4 solid solution since no peaks other than shifted MgCr2O4 peaks are detected. Similar results were also observed in the XRD patterns of Al2O3 added samples. Figure ?5-10b displays the change in MgCr2O4 lattice parameter with increased sintering additives contents, confirming the formation of solid solutions between MgCr2O4 and the sintering additives. Considering ?0.0002? (equivalent to 2?) error for lattice parameter values, the linear change indicates? that? the? formed? solid? solutions? obey? the?Vegard?s? law111,112. It has not been reported that MgCr2O4-MgAl2O4 or MgCr2O4-MgFe2O4 solid solutions indeed obey the Vegard?s?law, although it has been reported by Amelie111 for MgAl2O4-Cr2O3 solid solutions. Since the solid solution obeys the Vegard?s? law, it can be inferred that that the MgFe2O4 and MgAl2O4 substitutionally dissolved in MgCr2O4.  64   Figure ?5-9. SE-SEM image of fracture surface of a) MgCr2O4 sintered at 1250?C, b) MgCr2O4 sintered at 1500?C, c) Mg[Cr0.8Al0.2]2O4 sintered at 1250 ?C, d) Mg[Cr0.8Al0.2]2O4 sintered at 1500 ?C, e) Mg[Cr0.8Fe0.2]2O4 sintered at 1250?C, and f) Mg[Cr0.8Fe0.2]2O4  sintered at 1500?C    Figure ?5-10b also shows that the addition of Fe2O3 increases the lattice parameter, while Al2O3 addition results in lattice parameter decrease. In both cases, due to the presence of the solute cation in the host structure, MgCr2O4 lattice is expected to be under stress caused by the cation size mismatch1. The generated stresses could make the host lattice unstable, causing the 65  cations to move in a way that reduces the stress. In other words, the stress in the lattice generated due to solid solution formation could work as an additional driving force for sintering1.  It has been previously shown by Anderson82 that the MgCr2O4 spinel cannot be fully densified in air due to its decomposition according to the reaction ?2-10. On the contrary, Yamaguchi12 showed that by introducing TiO2 to MgCr2O4, a solid solution would form between MgCr2O4 and TiO2 that causes the increase of the cationic mobility and densification. Figure ?5-11 shows the variation of the relative density of Mg[Cr1-xMex]2O4; (Me: Al and Fe; 0?x?0.2) with the sintering temperature. Although the same trend is observed for both compositions, the obtained relative density for the specimens containing Al2O3 was smaller than for the specimens containing Fe2O3. This suggests different interaction mechanisms between the sintering additives (Fe2O3 and Al2O3) and MgCr2O4. There is unlimited solid solubility between MgCr2O4 and sintering additive derived spinels (both MgFe2O4 and MgAl2O4), which indicates that the formation of solid solution is not the only reason for the enhanced densification.   Later in this thesis it is discussed that the unit cell volume of the spinels increases in the presence of Fe2O3, and decreases in the presence of Al2O3. As a result, it is estimated that cation mobility in Al2O3 containing samples is less than in the samples containing Fe2O3, and thus the densification rates change in the same manner.  66    Figure ?5-10. a) XRD pattern of Mg[Cr1-xFex]2O4 quenched from 1475?C in air b) the variation of lattice parameter versus Al2O3 and Fe2O3 concentration; error bars are smaller than symbols  10 20 30 40 50 602? (?)MC (111)MC (331)MC (511)MC (400)MC (311)MC (222)MC (220)MC (111)ax=0x=0.15x=0.20 0.05 0.1 0.15 0.2 0.25x 8.2868.3228.3588.3948.438.466lattice parameter (A?) Mg[Cr1-xFex]2O4Mg[Cr1-xAlx]2O4b67   MgAl2O4 is a normal spinel while MgFe2O4 is an inverse spinel3,49,113. Therefore, in the presence of Fe+3, some degree of inversion in MgCr2O4 lattice should also occur. Since at the sintering temperatures the inversion process of MgCr2O4 in the presence of Fe2O3 is thermodynamically favorable and inversion is a diffusion controlled process, then it likely adds to the driving force of sintering. It is therefore suggested that Fe+3 increases the cationic mobility in MgCr2O4 to a higher degree than Al2O3 because it forms an inverse solid solution, while Al2O3 forms a normal solid solution with MgCr2O4.    Figure ?5-11. The variation of the relative density of Mg[Cr1-xAlx]2O4 specimens sintered at different temperatures for 2hours; the lines connect the data points only for the purpose of easier readability     To investigate the influence of inversion on the densification behavior of Mg[Cr1-xMex]2O4 (Me: Al and Fe; 0?x?0.2) compositions, the XRD patterns of sintered specimens were analyzed using the method introduced by Porta3. The specimens quenched from the sintering temperature were pulverized to less than 5 ?m particle size to assure the homogenous distribution of planes in 1225 1275 1325 1375 1425 1475 1525Temperature(?C)444648505254565860Relative density (%)X = 0X = 0.15X = 0.268  the XRD specimens. The distribution of cations between the tetrahedral and octahedral sites was estimated by comparing the intensity ratios of the experimental and the calculated data.   It was described by Patange et al.114 that a comprehensive information on the distribution of cations between the tetrahedral and octahedral sites of a spinel structure can be achieved by comparing the experimental and theoretical intensities of peaks whose intensities were (i) independent of oxygen parameter, (ii) did not differ dramatically, and (iii) were proportional to the reciprocal of cation distribution. In spinels, the (220), (311), (400), and (422) planes have such characteristics; therefore in this work the inversion parameter was estimated based on the comparison between the intensity ratios of the peaks related to these planes. The theoretical intensities were calculated using the following equation94:      | |           5-3 where Ihkl is the intensity, F is the structure factor, P is the multiplicity factor and Lp is the Lorentz-polarization factor. The values for the F, P and Lp factors were extracted from literature94. As mentioned by Cullity94, the equation ?5-3 gives the peaks intensity for 0 K, where there is no atomic vibration.   For accurate intensity measurement at room temperature, several authors3,94 studied the effect of the temperature factor on the calculated intensity and reported that for high melting point crystals the thermal vibration of  atoms at room temperature is low enough that would not influence the calculated intensity. For this reason the effect of temperature on the intensity has not been investigated in this study. The structural factors were calculated using the equation used by Porta3 as follows:             5-4 69  where Fo is the structural factor for normal spinel; ? is related to the inversion parameter (equals 0.5 and zero for inverse and normal spinels), ? is the atomic scattering factor and F1 is defined as a numerical factor. Table ?5-2 shows the scattering factors for selected reflections as reported by Porta3.   Table ?5-2. Scattering factors for selected XRD reflections3 Reflection h2+k2+l2 P FO F1 311 16n+11 24 fy+fx/?2 -(?2-1) 400 16(2n+1) 6 2fy-fx+4fox 4 220 16n+8 12 fx -2 422 16n+8 24 fx -2 fx*, fy, fox are atomic scattering factor of cations in tetrahedral and octahedral sites, and oxygen ions; n is an integer    Based on the model developed by Porta3, the composition of MgAl2O4-NiFe2O4 solid solution is considered as Nix?Mg(1-x)?Al2?[Nix(1-?)Mg(1-x)(1-?)Al2-2?]O4 in which ?, ?, and ? were the fractions of Ni+2, Mg+2, Al+3 in the tetrahedral sites respectively. Porter related ? to ?, ?, and x as follows:                               5-5  It should be mentioned that based on the definition, the inversion parameter is the fraction of trivalent cations in tetrahedral site; therefore ? has the same definition in both ?5-4 and ?5-5 equations.   In our study, to further simplify the inversion parameter calculation, it was assumed that the final spinel solid solution maintained the stoichiometric composition of the spinel structure. The Cr+3 was assumed to fill only the octahedral sites due to its high octahedral site preference                                                              * Weighted values were used for calculation of  fx and fy.  70  energy (-87.6 kJ/mol). Based on these assumptions the composition of solid solution in the studied systems, MgCr2O4-NAMgFe2O4 and MgCr2O4-MAMgAl2O4, is defined as                   (Mg1-?Me?)[Mg?Me2NA-?Cr2-2NA]O4 in which ? and NA are the fractions of Me+3 in the tetrahedral sites and MA is the mol fraction of MgFe2O4 and MgAl2O4.  The intensity ratios for I311/I220 were calculated by changing ? for various intervals for compositions with x=0, 0.05, 0.2. The intervals for ? were selected between 0.01 and 0.1 based on the convergence of the calculated and experimental data. The resulting inversion parameter was considered the value at which the closest fit with the experimental results was obtained.   The typical graphs that were constructed to estimate the inversion parameter are shown in Figure ?5-12. At ? values close to 0.24 the calculated intensity ratio curves converge with the experimentally obtained intensity ratio curves. As we defined the inversion parameter as the fraction of trivalent cations in the tetrahedral sites, the inversion parameter equals ?. The value inversion parameter in this study is an average of three values obtained from I311/I220, I400/I220, and I311/I422 intensity ratios. The confidence intervals for inversion parameter is estimated based on ?/?3 (i.e. assumes uniform distribution of the results) and was about the same value (0.0003) for all three measurements.  71   Figure ?5-12. The comparison between the intensity ratios, I311/I220, of calculated and experimental results for inversion parameter mesurement. The results in this graph relate to Mg[Cr0.8Fe0.2]2O4 which was quenched from 1300?C.   The inversion parameter for other selected compositions was calculated in a same way as described above, and plotted as a function of temperature in Fig.5-13 for different concentrations of sintering additives (Al2O3, Fe2O3). It is clear that the inversion parameter increases with temperature regardless of the type of sintering additives.  The same behavior was also observed by Martingo et al.115 investigating the kinetics of natural and synthetic Mg(Al,Fe)2O4 system. They showed increasing the temperature increased the degree of inversion. 0 0.2 0.4 0.6 0.8 1?00.61.21.82.43I311/I220??= 0.24 Experimental data72   Figure ?5-13. The variation of the inversion parameters in Mg[Cr1-xFex]2O4 and          Mg[Cr1-xAlx]2O4 with concentration of the sintering additives and sintering temperature (the lines represent the thermodynamic model and not the best fit ? refer to text)    Figure ?5-13 also illustrates that the degree of inversion is higher for samples containing Fe than for those containing Al, and the increase in the concentration of sintering additives has a significant influence on the degree of inversion. This behavior can be explained by considering the effect of site preference energies of Cr+3, Fe+3 and Al+3. Martignago and Negro116 showed that the degree of inversion of Mg(Cr,Al)2O4 was lower than that of Mg(Fe,Al)2O4 at each temperature. Also they showed that the inversion parameter was inversely proportional to the Cr+3 content. They attributed this to the high octahedral site preference energy of Cr+3, which limits the Mg-Al cation exchange.     Due to the inversion phenomenon in a spinel structure, (A+2)tet[B+3]oct2O4, a fraction of trivalent cations (?) move from the octahedral sites to the tetrahedral sites. Based on this 600 800 1000 1200 1400 1600Temperature (?C?00.050.10.150.20.250.3Inversion parameter x=0.2Fe x=0.2Al x=0.05Fe x=0.05Al 73  relocation, the chemical formula of the spinel would change to (A1-?B?)tet[B2-?A?]octO4 and the inversion reaction could be written as (1-?)(A)tet+(2-?)[B]oct ? ?(B)tet+?[A]oct.    In the study by O?Neil?et. al39, the equilibrium constant for the above reaction was related to the site preference energy of cations and the entropy change during cations site changes. According to this study, the change in free energy of disordering cation distribution (?GD) is zero at equilibrium, and the equilibrium constant of the interchange reaction between tetrahedral and octahedral sites (1-?)(A)tet+(2-?)[B]oct = ?(B)tet+?[A]oct, is as follows:    (?    ?    ? )            ?      5-6 where ? is the inversion parameter, ?A-B is the difference between site preference energies of A and B respectively and is an indication of configurational entropy, and ?? is a constant of about    -20 kJ/mol for all 2-3 spinels49.   The accuracy of the results obtained in our work has been judged by comparing them with the above thermodynamic model, developed? by? O?Neil? et? al.39 In this regard, the chemical formulas of the spinel solid solutions in MgCr2O4-MAMgAl2O4 and MgCr2O4-NAMgFe2O4 systems before inversion were estimated as (Mg+2)tet[Cr+32-2MAAl+32MA]octO4 and (Mg+2)tet[Cr+32-2NA Fe+32NA]octO4 respectively. NA and MA were the mole fractions of MgFe2O4 and MgAl2O4 in the solid solution, respectively. The chemical formula of the solid solutions after inversion was also estimated based on the assumption that the Cr+3 cations remain in the octahedral site in any conditions. Based on this assumption the chemical formula of the solid solutions after inversion would be (Mg1-?Al?)tet[Cr2-2MAAl2MA-?Mg?]octO4 and (Mg1-?Al?)tet[Cr2-2NAFe2NA-?Mg?]octO4. The cation distribution reactions between MgCr2O4 and NAMgFe2O4 and MgCr2O4 and MAMgAl2O4 can be therefore written as follows:  74  (1-?)(Mg+2)T + (2MA-?)[Al+3]O   ?  ?[Mg+2]O + ?(Al+3)T    5-7 (1-?)(Mg+2)T + (2NA-?)[Fe+3]O    ?  ?[Mg+2]O + ?(Fe+3)T  5-8  According to these reactions, a part of Mg+2 in tetrahedral sites is replaced by Fe+3 or Al+3, and Mg+2 enters into the octahedral sites of the spinel lattice. The resulting increase in the inversion parameter therefore means that more cations are exchanged between the tetrahedral and octahedral sites. Thus the inversion phenomenon likely increases the cation mobility and therefore the sintered density of these materials. A comparison between the values of inversion parameters for Al and Fe containing samples clearly illustrates that the inversion could be an influential factor in the higher densification of (Mg+2)tet[Cr+32-2NA Fe+32NA]octO4 solid solutions than (Mg+2)tet[Cr+32-2MA Al+32MA]octO4.       The? ONeil?s thermodynamic model was modified in this work for the MgCr2O4-NAMgFe2O4 and MgCr2O4-MAMgAl2O4. As mentioned earlier, in order to simplify the calculation of cation distribution, it was assumed that the Cr+3 remains in the octahedral site due to its very high octahedral site preference energy (-160 kJ/mol)49. Based on this assumption,  the equilibrium constant for the cation distribution via equations ?5-7 and ?5-8 would be the following:   (?    ?      ? )                   ?      5-9   (?    ?      ? )                   ?      5-10 where NA and MA are the mole fractions of MgFe2O4 and MgAl2O4. The values of ?Mg-Al (26.6 kJ/mol), ?Mg-Fe (23 kJ/mol), ??Mg-Al(-21.7 kJ/mol), and ??Mg-Fe (13 kJ/mol) were extracted from literature39, 49, 67.   It is seen in Figure ?5-13 that the experimental results (symbols) correlate well with the thermodynamic model developed by Hugh and?O?Neill?(lines)39 at temperatures below 1250?C. 75  At temperatures above 1300?C there is a small deviation from the model, which is attributed to changes in the materials due to insufficient cooling rates. In fact, the cooling rate usually is not high enough to quench the cation distribution at the soak temperature. This phenomenon is more significant in Fe containing sample as reported by Walters and Wirtz117. Fe+3 and Al+3 substituted for Cr+3 occupy both tetrahedral and octahedral sites. The presence of Cr+3, which has the highest octahedral site preference energy among other cations109, is expected to intensify this site interchange process. Thus Fe+3 preferred tetrahedral sites and therefore forced Mg+2 to move to the octahedral sites.    The ionic radius of Fe (rFe+3 = 0.67?) is larger than of Mg+2 (rMg+2 = 0.57?); therefore, it is expected that Fe+3expanded the tetrahedral site size and displaced the oxygen ions toward the octahedral sites and consequently shrank them. The same phenomenon could happen for Al+3 but, as its ionic radius (rAl+3 = 0.54 ?) is smaller than that of magnesium and chromium ions, it would have caused opposite effect, i.e. shrinkage of the tetrahedral sites and expansion of the octahedral sites. Despite the opposite effect of Al+3 and Fe+3 on the MgCr2O4 lattice, it appears that they both caused the displacements, thus increasing ionic mobility, which in turn enhanced the densification of these spinels.   In order to study whether the solid solution formation rate affects the densification, the variation of MgCr2O4 lattice parameter versus sintering temperature for both types of additives is plotted in Figure ?5-14. For the Mg[Cr0.8Fe0.2]2O4 composition, a solid solution formed at temperatures below 1250?C as no changes in lattice dimension was observed. In contrast, the lattice dimension decreased continuously with the increase in the sintering temperature for Mg[Cr0.8Al0.2]2O4.  76   This indicates that at the same sintering temperature more solid solution formed in Fe2O3 containing samples than in Al2O3 containing samples. This is expected based on the earlier results on the kinetics of spinel formation. As shown later, in the presence of iron oxide both MgFe2O4 and MgCr2O4 form almost in the same time. In contrast, in the presence of aluminum oxide, MgAl2O4 spinel forms faster than MgCr2O4 and creates a MgAl2O4 spinel barrier between chromium oxide and magnesium oxide. Thus, it is expected that the solid solution formation rate in the MgCr2O4-NAMgFe2O4 samples is higher than in the MgCr2O4-MAMgAl2O4 samples.   Wang et al.118 showed the same result studying the effect of solid solution formation on the sintering of ZrC. He demonstrated that the rate of solid solution formation influenced the extent of ZrC densification. It was shown that VC with 1.3 vol% solid solubility limit with ZrC was more effective in sintering and densification of ZrC than TaC and NbC with unlimited solid solubility in ZrC, due to the faster formation of VC solid solution than TaC and NbC. At 1250?C-1500?C, i.e. at early stages of sintering, a weight loss of 0.08 to 0.1% was observed for all compositions. It is therefore believed that??evaporation-condensation??was?the?main?mass?transportation mechanism during the densification in this temperature range, and caused the grain growth in all samples regardless of the type and concentration of additives86.  The weight loss and the compressive strength of the samples versus the sintering additives content are plotted in Figure ?5-15. Each data point in these plots is the average value of the measured property for 3 specimens. The increase in additive content did not change the weight loss considerably but it raised the compressive strength of specimens. The enhancement of the compressive strength, where no significant densification was involved, confirmed that the evaporation-condensation was the mass transfer mechanism5.The same behavior was observed in 77  sintering of materials with a high vapor pressure at sintering temperatures, for example Si3N4 and SiC with a covalent bond nature4.   Figure ?5-14. The variation of the lattice parameters of Mg[Cr0.8Al0.2]2O4 and Mg[Cr0.8Fe0.2]2O4 versus the sintering temperature   In order to better understand how the sintering is influenced by the sintering additives in the systems under consideration, the influence of the possible mechanisms of solid solution formation and the crystalline structures of the solid solutions is discussed. At elevated temperatures, Fe+3 and Al+3 should diffuse into the MgCr2O4 lattice through the available tetrahedral and octahedral sites. Assuming that the synthesized MgCr2O4 has no defects, it would consist of 72 unoccupied lattice sites per unit cell, including 16 octahedral and 56 tetrahedral, available for the introduced sintering additive119. Due to this lattice structure, the interaction between the sintering additives and lattice sites can happen in three different scenarios. In the first scenario, substituting Fe+3 or Al+3 for Mg+2 results in the formation of        and       due to the high affinity of Cr+3 to octahedral sites, through the following reactions:  1200 1300 1400 1500Temperature (?C)8.258.2868.3228.3588.3948.438.466Lattice parameter (A) Mg[Cr0.8Fe0.2]2O4Mg[Cr0.8Al0.2]2O478              ?         ?               5-11             ?         ?                5-12    The formation of vacancies facilitates the overall diffusion rate and eventually the densification. However, the vacancy formation is expected to increase the lattice parameter of MgCr2O4 when there is an increase in Fe2O3 and Al2O3 content. Figure ?5-10b shows that the addition of Fe2O3 resulted in increase in lattice parameter as predicted in reaction ?5-12, while a decrease in the lattice parameter was observed when Al2O3 was added, implying that the reaction (?5-12) may not happen.    In the second scenario, Fe+3 and Al+3 could substitute for Cr+3. In case of Fe+3 this is unlikely, as the octahedral site preference energy* (OSPE) of Cr+3 [-87.9 kJ/mol] is higher than that of Fe+3[18.8 kJ/mol], which makes substitution process thermodynamically impossible38. Therefore in this scenario, Fe+3 can form a solid solution with MgCr2O4 only where there is a partial reduction of Fe+3 to Fe+2 by the conversion of Cr+2 to Cr+3, as predicted by the Ellingham diagram120. Only in this case Fe+2 could enter either octahedral or tetrahedral sites, or substitute for Mg+2. Due to their very low OSPE [4.2 kJ/mol] the Fe+2 ions would not be able to enter into octahedral sites in the presence of Cr+3, thus they would rather occupy the available tetrahedral sites, which should increase the lattice parameter of MgCr2O4 due to the larger tetrahedral bond distance of Fe+2 than that of Mg+2113.                                                               * OSPE is defined as the difference between crystal field stabilization energy (CFSE) of octahedral and tetrahedral sites109.  79   Figure ?5-15. a) The variation of compressive strength of samples sintered at various temperatures, b) weight loss of Mg[Cr1-xFex]2O4 and Mg[Cr1-xAlx]2O4 samples sintered at 1475?C    As mentioned above, the Fe+2 could also replace Mg+2, as the size difference between Fe+3 (0.67 ?) and Mg+2 (0.57 ?)109 is less than 15 %; therefore, an increase in lattice parameter is expected at higher Fe2O3 content. However, the mechanisms under scenario 2 were less probable since the sintering was performed in air, where the chance of iron reduction was very low.    As shown in Figure ?5-10b the lattice parameter of MgCr2O4 increased linearly with increasing the Fe2O3 content. Based on the above scenarios and the change in the trend of the lattice parameters, the mechanism of the solid solution formation in Mg[Cr1-xFex]2O4 system could include diffusion of Fe+3 into tetrahedral sites of the MgCr2O4 lattice. The same behavior was also elucidated by Walter et al.42; in their study of Mg[Cr1-xFex]2O4 solid solution series, they reported that the lattice parameter grew linearly with increasing the MgCr2O4 content. Moreover, they have shown that the normality of MgCr2O4 decreased by increasing the MgFe2O4 content. Francesco71 also showed that the increase in Fe+3 reduced the activation energy for inversion of MgAl2O4 spinel from 274 to 265 kJ/mol. Therefore, based on above discussion and 80  plots of inversion parameter versus temperature and composition (Figure ?5-13), it was concluded that the increase in Fe2O3 introduced inversion to MgCr2O4 and subsequently enhanced the densification.  Al+3 has the OSPE of [-41.9 kJ/mol] which is 5 times higher than OSPE of Fe+3 and also is the second highest OSPE, implying the higher possibility of substitution of Al+3 with Cr+3 than of Fe+3 with Cr+3 in the octahedral sites38. The presence of Al+3 in the octahedral sites was also observed in the study by Ulf 121, where the color change in MgAl2O4- MgCr2O4 solid solution was studied. Moreover, the size difference between Al+3 (0.39 ?) and Mg+2 (0.57 ?)109 is more than 30 %, which indicates that the Al+3 cannot be substituted for Mg+2 in tetrahedral sites. Therefore, Al+3 cations occupy other available octahedral sites in MgCr2O4 unit cell. If this scenario happens, then due to the smaller octahedral bond distances of Al+3 (M-O: 1.915 ?) in comparison to that of Cr+3 (M-O: 1995 ?)122, the lattice parameter of MgCr2O4 should be reduced when Al2O3 content increased. Considering the above discussion and the results observed in Figure ?5-10b and Figure ?5-13, it is concluded that the Al+3 is probably located in the octahedral sites and the formed solid solution is a normal spinel.      According to the experimental observations and theoretical analysis, it is concluded that the addition of trivalent oxides enhanced the densification of MgCr2O4 in air at temperatures below 1500?C. The increased densification is attributed to the increased cationic mobility due to the solid solution formation and to the inversion phenomenon in the MgCr2O4 crystal structure. The difference between the performance of Fe2O3 and Al2O3 as sintering additives is explained by the manner in which each trivalent cation changed the MgCr2O4 unit cell. It is shown that the Fe2O3 is more effective than Al2O3, as it creates an inverse solid solution. In addition, the weight 81  loss results showed that the addition of Al2O3 and Fe2O3 did not change the oxidation kinetics of Cr+3 and accordingly did not change its vaporization.  In order to understand the contribution of solid solution formation and the proposed inversion phenomenon on the densification behavior of MgCr2O4, the effect of SnO2 as a sintering additive for MgCr2O4 was also studied. The SnO2 was selected for two reasons:  because it forms Mg2SnO4 spinel in reaction with MgO, and because as a tetravalent cation has a different effect on the MgCr2O4 lattice.  5.3 The effect of tetravalent oxides (SnO2) on the sintering of MgCr2O4 spinel  In the previous section, several mechanisms were discussed and an explanation for the change in the sintering behavior of MgCr2O4 in the presence of Fe2O3 and Al2O3 was proposed. It was concluded that the addition of Al2O3 and Fe2O3 enhanced the densification of MgCr2O4 through solid-solution formation, creation of lattice imperfections, and distortion of the host structure. It was shown that the solid-solution formation during sintering not only resulted in the increased density, but also raised the cold crushing strength of specimens due to the higher atomic mobility at the grain boundaries, which eventually resulted in the bond formation.  In this section, the influence of SnO2 on the densification of MgCr2O4 is studied. In comparison to Al2O3 and Fe2O3, SnO2 is a tetravalent oxide and its addition to MgCr2O4 increases the concentration of cation vacancies in the host structure, because there is a charge difference between Sn+4 as solute and Cr+3 and Mg+2 as host cations122. According to literature, there is unlimited solid solubility between MgCr2O4 and Mg2SnO437. Therefore, it is expected that the addition of SnO2 should improve sintering, thus increasing the density of MgCr2O4. Figure ?5-16 shows the effect of SnO2 on the relative density of MgCr2O4 sintered in air at 1475?C for 5 hrs. Each data point in this figure represents the average value calculated for 3 82  samples. As shown, the increase of the SnO2 content to 10 mol% considerably increased the relative density of MgCr2O4 from ~51% to ~64%.  Figure ?5-16. The variation of relative density of Mg[Cr1-xSnx]2O4 (x=0, 0.05, 0.1, 0.15, and 0.2) compositions sintered in air at 1475?C for 300 minutes   There is an analogy between this system and the MgCr2O4-MgFe2O4 and MgCr2O4-MgAl2O4 systems, as there is unlimited solid solubility between the end members; therefore, the same explanations can be used to describe the mechanism by which SnO2 enhanced the densification of MgCr2O4.   The XRD patterns of SnO2 containing compositions are shown in Figure ?5-17. No new peaks could be identified in XRD patterns at higher SnO2 content. However, the peaks shifted toward the lower angle, indicating that a solid solution has been formed and increased the lattice parameter of MgCr2O4. This can be explained by the larger effective cationic radius of Sn+4 (0.69 ?) than of Cr+3 (0.62 ?) and Mg+2 (0.57 ?). Mg2SnO4 spinel is a normal spinel in which Sn+4 occupies octahedral positions and Mg+2 tetrahedral sites37.  0 0.05 0.1 0.15 0.2X5153555759616365Relative density (%) 83   Figure ?5-17. XRD patterns of Mg[Cr1-xSnx]2O4 (x=0, 0.05, 0.1, 0.15, and 0.2) compositions sintered in air at 1475?C for 300 minutes; Sp: spinel solid solution   The octahedral site preference energy of Sn+4 is relatively high; hence it is expected that it sits in the octahedral sites next to Cr+3, or substitutes for Cr+3. The size mismatch causes lattice distortion, which enhances the densification123. The addition of SnO2 results in the formation of cation vacancy in the MgCr2O4 structure to compensate for the excess charge on Sn+4.   The hypothesized vacancy formation reaction is shown in equation ?5-13, which proves that the addition of tin oxide increases the population of vacancies in the spinel structure. It is expected that the increase in the concentration of vacancies enhance both the cation diffusion and densification. Park124 reported the same results for the sintering of In2O3, in which Zn substituted for In and resulted in the formation of oxygen vacancy; subsequently it increased the density of In2O3 through increased ionic diffusivity.  84             ?         ?                    5-13  Figure ?5-18. The change in lattice parameter of Mg[Cr1-xSnx]2O4 (x=0, 0.05, 0.1, 0.15, and 0.2) compositions sintered in air at 1475?C for 300 minutes   Based on the above, it is concluded that SnO2 increases the lattice parameter of MgCr2O4 and enhances the densification of MgCr2O4 via solid solution formation mechanism. The comparison between the addition of Fe2O3, Al2O3 and SnO2 indicates that the formation of solid solution enhances the densification. However, these explanations are not satisfactory to conclude how the inversion phenomenon contributes to the densification of MgCr2O4. Therefore, the effect of Fe2O3 and SnO2 on the densification of Cr2O3 has also been studied.   This experiment was designed since Cr2O3 and MgCr2O4 have similar sintering behaviors and unlimited solid solubility with Fe2O382,110. In the presence of the sintering additives, the inversion phenomenon does not occur in Cr2O3; however, it should occur in MgCr2O4 because this phenomenon is defined for spinel structures37.  0 0.05 0.1 0.15 0.2x 8.2868.3228.3588.3948.438.466lattice parameter (A?) 85  5.4 The effect of Fe2O3 and SnO2 on sintering of Cr2O3   In this section the effect of tin oxide and iron oxide on the densification of pure Cr2O3 has been evaluated. This study is carried out to clarify the contribution of the inversion phenomenon, which is caused by the presence of Fe2O3 and Al2O3, on the sintering of pure MgCr2O4. The selection of Cr2O3 for the study was due to the fact that on the one hand it has the same sintering behavior and also identical sintering mechanisms with MgCr2O482, and on the other hand the two compounds crystallize in two different crystal structures: MgCr2O4 has a spinel crystal structure, while Cr2O3 has a hexagonal structure82,125.   In addition, both have a substantial solid solubility with Fe2O3 and limited solubility with SnO22. Therefore, a comparison between the densification of MgCr2O4-SnO2 and Cr2O3-SnO2, and MgCr2O4-Fe2O3 and Cr2O3-Fe2O3 could explain the contribution of the solid solution formation to the densification of MgCr2O4. In addition, the comparison that has been made between the densification of MgCr2O4-Fe2O3 and Cr2O3-Fe2O3 could also elucidate the contribution of inversion process to the densification, since inversion phenomenon is only characteristic to the spinel structures. Therefore, if in identical sintering conditions the density of MgCr2O4-Fe2O3 is higher than the density of Cr2O3-Fe2O3, the excess density is achieved due to the inversion phenomenon induced by Fe2O3 in the lattice structure of MgCr2O4.   Cr2O3, Fe2O3, and SnO2 grains with particle size of 1.2?m, similar to particle size of synthesized (1.5?m) MgCr2O4, were mixed and pressed to make pellets with ~48% green density, identical to that of Mg[Cr1-x(Fe/Sn)x]2O4 samples. The pellets were then sintered at 1475?C for 300 minutes, i.e. in the same sintering conditions as for Mg[Cr1-x(Fe/Sn)x]2O4. 86  5.4.1 The effect of SnO2 on densification of Cr2O3  The variation of the relative density of specimens sintered in air at 1475?C for 300 minutes versus the SnO2 content is shown in Figure ?5-19; the relative density of specimens slightly increased from 51.92% (2.70?0.27 g/cm3) to 58.93% (3.07?0.22 g/cm3) by increasing the SnO2 to 0.5 mol%. The further increase in SnO2 content to 5 mol% decreased the density to a value less than for the pure Cr2O3 sample.   The same phenomenon was reported by K.A. Berry126: the addition of MgO to alumina raised the density of alumina up to the solid-solubility limit of MgO in Al2O3, and then reduced tit below this limit, which was attributed to the solid solution formation as a result of dissolution of the sintering additive in the host structure.   In order to find out if this phenomenon also occurred in the Cr2O3-vSnO2 compositions, the XRD patterns of the samples with 0.125, 0.25, 0.375, 0.5, 1, and 5 mol% SnO2 were compared to the pure Cr2O3. Figure ?5-20 shows the X-ray diffraction patterns of the samples sintered at 1475?C in air for 300 minutes.   A very small shift toward higher angle (by 0.24 degree) is observed in the XRD patterns, which is proportional to the SnO2 content for samples with less than 0.5 mol% SnO2. This is an indication of the formation of a solid solution between Cr2O3 and SnO2. Since the XRD peaks shifted toward high angles, it is concluded that the lattice parameter of the solid solution is smaller than that of Cr2O3. Considering the cationic radius of Cr+3 (0.62 ?) and Sn+4 (0.69 ?)109, the addition of SnO2 to Cr2O3 resulted in the substitution of Sn+4 for Cr+3, accompanied by an increase in the Cr2O3 lattice parameter. For compositions with SnO2 beyond 0.5 mol%, this trend is not valid. An identification peak of SnO2 is also observed in the diffraction pattern of Cr2O3-5mol% SnO2. 87   Figure ?5-19. The variation in relative density of Cr2O3-vSnO2 (v=0.125, 0.25, 0.375, 0.5, 1 and 5 mol%) samples sintered in air at 1475?C for 300 minutes    The variation of lattice constant of Cr2O3 versus SnO2 content is presented in Figure ?5-21. As shown, the lattice parameter increased to a=4.9653?0.0005 ? and c=13.6948?0.0005 ?, and reached a plateau at 0.5 mol% of SnO2. The increase in the lattice parameter is attributed to the solid solution formation between Cr2O3 and SnO2. The fact that the lattice parameter is not changing with the increase in SnO2 content beyond 0.5 mol% is attributed to the precipitation of tin oxide, Figure ?5-21. In other words, the solid solubility limit of SnO2 in Cr2O3 is about 0.5 mol% under the sintering conditions. Similar results were reported by D. H. Park et al.124 who investigated the effect of zinc oxide and defect chemistry on the sintering of In2O3.   For compositions with more than 0.5 mol% SnO2, tin oxide would precipitate on the Cr2O3 grains or the grain boundaries. The SEM images of the fracture surface of Cr2O3-0.5 SnO2 and Cr2O3-5SnO2 sintered at 1475?C are shown in Figure ?5-22.  0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5SnO2 (mol%)505254565860Relative density (%)88   These images demonstrate that 0.5mol% tin oxide is dissolved in to the Cr2O3 lattice; in contrast, for the Cr2O3-5SnO2 compositions, SnO2 precipitated inside the grains and at the grain boundaries of Cr2O3.  Figure ?5-20. XRD patterns of Cr2O3-vSnO2 (v=0.125, 0.25, 0.375, 0.5, 1, and 5 mol%) samples sintered in air at 1475?C for 300 minutes   According to these results, up to 0.5 mol% tin oxide formed a solid solution with Cr2O3 and enhanced its densification. SnO2 possibly formed cation vacancies in chromia and thus enhanced the diffusion and densification. The following reaction is proposed for the cation vacancy formation:             ?      ?                5-14  Further increase in SnO2 resulted in the precipitation of SnO2 on Cr2O3 grains and grain boundaries and adversely affected the densification process. The presence of the precipitates 89  could have decreased the grain boundary energy127. Since the maximum density in this set of samples is less than 60?0.1 %, the precipitation could not enhance the densification. For the Cr2O3-vSnO2 system, the chromium vapor pressure at temperatures above 1200?C is relatively high (i.e. 0.232 Pa at 1400?C). For the processing conditions?where?the?material?s?porosity?is?still?high (40-50%) and the fraction of grain/grain contacts is limited, surface diffusion and evaporation/condensation mechanisms could dominate the mass transport mechanism, and thus control the sintering process. For this reason, for compositions with more than 0.5 mol% SnO2, the densification decreases.     The comparison between these results and the densification behavior of MgCr2O4 in the presence of SnO2 sheds light on the effect of solid solution formation on the densification of Cr2O3 and MgCr2O4.   Figure ?5-21. The influence of SnO2 content on the lattice parameter of Cr2O3 sintered at 1475?C for 300 minutes in air.   0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5SnO2 (mol%)4.94374.94734.95094.95454.95814.96174.96534.96894.97254.9761lattice parameter"a" (?) 13.591613.607613.623613.639613.655613.671613.687613.7036lattice parameter"c" (?)ca90   The increase in SnO2 content continuously increased the density of MgCr2O4 as a result of the unlimited solid solubility between MgCr2O4 and Mg2SnO4. In contrast, density increased to a maximum with the increase in tin oxide content up to 0.5 mol%, and decreased with further SnO2 additions. This behavior is attributed to the effect of the solid solution formation on the sintering of ceramics, since the solid solubility of SnO2 in Cr2O3 is shown to be 0.5 mol%.    Figure ?5-22. Microstructure of the fracture surface of sintered Cr2O3-nSnO2 (n= 0.5 and 5 mol%) samples sintered in air at 1475?C for 300 minutes   5.4.2 The effect of Fe2O3 on the densification of Cr2O3  Figure ?5-23 shows the variation of relative density of Cr2O3-vFe2O3, (v: 1, 2.5, 5, 7.5 and 10 mol%) compositions sintered at 1475?C in air for 300 minutes. The reported relative density is the average density of three samples. The errors are calculated based on ?/?3 and are about 0.5%. Considering the experimental errors, the relative density gradually increased with the increase in Fe2O3 content, indicating that the Fe2O3 enhances the sintering of Cr2O3.  91   A phase diagram of Cr2O3-Fe2O3 was constructed using the Factsage software to find out the reasons for this behavior. Based on the phase diagram, shown in Figure ?5-24, there is unlimited solid solubility between these oxides.    Figure ?5-23. The variation of relative density of Cr2O3-vFe2O3 composition with Fe2O3 content sintered in air at 1475?C; the error bars are smaller than symbols   Formation of solid solution can improve the densification in two ways. First, the formation of solid solution creates lattice distortion due to the size mismatch between solute and host atoms/ ions; this affects their diffusivity and densification. Second, it can create lattice imperfections such as ion vacancies or interstitials of both ion types, if there is a charge difference between solute and the host ion in the ceramic material. In the case of Cr2O3 and Fe2O3, since there is no charge difference between Cr and Fe, no vacancy would form in Cr2O3 as a result of Fe2O3 addition. However, due to the size difference between Fe+3 (0.67 ?) and Cr+3 (0.62 ?) a substantial lattice distortion is induced in Cr2O3, which could possibly enhance 0 2 4 6 8 10Fe2O3(mol%)52545658606264Relative density (%) 92  densification. Therefore, the increase in the solid solution content as a result of Fe2O3 addition is attributed to this sintering behavior.   Figure ?5-24. Cr2O3-Fe2O3 phase diagram; reprinted from Factsage results   As explained earlier, the main purpose of this experiment was to explore the contribution of the inversion phenomenon to the sintering of MgCr2O4. In this regard, the effect of solid solution formation on the sintering of MgCr2O4 was explained by comparing the results of the sintering of MgCr2O4-SnO2 and Cr2O3-SnO2. In order to differentiate between the contribution of solid solution formation and the inversion during sintering of MgCr2O4, a comparison between the results of the densification of MgCr2O4-Fe2O3 and Cr2O3- Fe2O3 has been made.   In both systems there is unlimited solid solubility between the end-members. They also form different crystal structures. MgCr2O4 crystallizes in the spinel form and Cr2O3 in the hexagonal form. In addition, MgCr2O4 and Cr2O3 have similar sintering behaviors; therefore, any 0 20 40 60 80 100mole Fe2O3/(Cr2O3+Fe2O3)11001300150017001900210023002500Temperature (?C)Solid solution (SS)LiquidL+SS93  differences between their densification behaviors in the presence of Fe2O3 can be attributed to the inversion phenomenon. Figure ?5-25 shows the densification of Cr2O3 and MgCr2O4 versus Fe2O3 content; the density of both MgCr2O4 and Cr2O3 has shown to be proportional to the Fe2O3 content. Although the density of pure MgCr2O4 is similar to the density of Cr2O3, the rate of increase in density of MgCr2O4 with Fe2O3 is considerably higher than that of Cr2O3. In other words, the density of MgCr2O4 is more than that of Cr2O3 for the samples with same Fe2O3 content. According to the above discussion, the difference between the densities is attributed to the inversion phenomenon, which only occurred in spinel structure.   Figure ?5-25. The densification of Cr2O3 and MgCr2O4 versus Fe2O3 content. The samples were sintered at 1475?C in air for 300 minutes   It is concluded that the inversion process is considerably important in the sintering of MgCr2O4 with a spinel structure. In Section ?5.2 it was demonstrated that the inversion process 0 1 2 3 4 5 6 7 8 9 10Fe2O3(mol%)505458626670Relative density (%) MgCr2O4-nFe2O3Cr2O3-nFe2O394  could result in either the reduction or the increase in the volume of tetrahedral and octahedral sites in the spinel lattice, depending on the size of the interchanging cations.  In the case of Fe2O3, as Fe+3(0.67 ?) is larger than Mg+2 (0.57 ?), it induces stress on the cations in octahedral sites and thus perhaps increases the driving force for movement of the cations from neighboring octahedral sites to other sites. In contrast, the addition of Fe2O3 to Cr2O3 could only enhance the densification, as it only slightly induces distortion to the Cr2O3 lattice due to the size mismatch. Therefore, it is hypothesized that the inversion phenomenon enhanced the sintering of the MgCr2O4.                     95   Chapter 6. The effect of spinel forming oxides on the sintering of magnesia-chromite composites  6.1 Introduction  In the previous section the effect of various sintering additives on the crystal structure and the sintering of MgCr2O4 have been studied. It was shown that the effectiveness of sintering additives increases with the increase in solid solubility and the degree of inversion induced by the additive. Based on the results of this study, Fe2O3 is selected as the most effective and SnO2 as the least effective sintering additives. The main reason for the different performance of SnO2, Al2O3 and Fe2O3 is explained by the induced degree of inversion.   SnO2 forms a normal spinel solid solution, Mg[Cr1-x,Snx]2O4 with MgCr2O4 regardless of temperature and SnO2 content. Al2O3 and Fe2O3 both form partially inverted spinel solid solutions, (Mg1-?,Al?)[Cr2-2NA,Mg?,Al2NA-?]2O4 and (Mg1-?,Fe?)[Cr2-2NA,Mg?,Fe2NA-?]2O4  respectively, but Fe+3 introduced more inversion to the MgCr2O4 structure and resulted in more atomic mobility and eventually more densification under similar sintering conditions.   The main purpose of this study was to sinter magnesia-chromite composites at temperatures below 1500?C for refractory applications. Therefore, the reduction in the sintering temperature, the phase assemblage and the microstructure of the sintered composite should be all considered in the composite design. MgCr2O4 can withstand the contact with bottom blown oxygen convertors (BBOC)* slag at 1100-1200?C, but MgO, MgAl2O4 and especially MgFe2O4 dissolve very fast in the slag in the same conditions. In magnesia-chromite refractory composites                                                              * The average composition of the BBOC slag is: Ag: 37%, As: 0.2%, Sb: 3.3%, Pb: 7.4%, Bi: 47%, and Cu: 0.4%. It should be mentioned that these elements are in oxide form due to the working conditions of BBOC.  96  MgO, MgAl2O4 and MgFe2O4 form a solid solution with the host structure, MgCr2O4, and therefore are expected to have less reactivity with the slag than the pure compositions. The higher the content in the solid solution, the more the formed solid solution is prone to dissolve in the slag.       Based on the obtained knowledge of the influence of the selected sintering additives and of the crystal structure on the densification of MgCr2O4, as well as on the sintering behavior of MgO and chromite from literature, 12 magnesia-chromite composites, coded MK1 to MK12, were designed (Table 5-2). The primary goal of designing the 12 composites was to understand the effects of Fe2O3 and Al2O3 on their sintering behavior, and to optimize the Fe2O3, Al2O3 and Cr2O3 content in the compositions. As shown in Table ?6-1, MK1-MK4, MK5-MK9 and MK10-MK12 were designed to evaluate the effect of Cr2O3, Al2O3, and Fe2O3 content on the sintering of magnesia-chromite composites respectively. The range of the Cr2O3, Fe2O3, and Al2O3 content was set based on the composition of industrially available fused chromite grains, and with the intention of keeping the value of Fe2O3 below 10 wt% in the composition. Based on the previous studies, the presence of more than 10wt% Fe2O3 in the refractory composites negatively affects their performance.  In order to study the effect of each oxide on the densification of magnesia-chromite refractory composites, a comparison has been made between the relative densities of all magnesia-chromite refractory compositions which were sintered at 1550?C for 300 minutes. Based on these results, 4 composites were selected for further non-isothermal sintering studies. The best composition was nominated based on the densification results and used for the sintering kinetics studies.  97   Table ?6-1. The composition of designed magnesia-chromite refractory composites   MgO (mole%) Al2O3 (mole%) Fe2O3 (mole%) Cr2O3 (mole%) MK1 85.49 6.9 2.71 4.9 MK2 84.49 6.9 2.71 5.9 MK3 83.49 6.9 2.71 6.9 MK4 82.49 6.9 2.71 7.9 MK5 81.49 6.9 2.71 8.9 MK6 85.49 4.9 2.71 6.9 MK7 84.49 5.9 2.71 6.9 MK8 82.49 7.9 2.71 6.9 MK9 81.49 8.9 2.71 6.9 MK10 81.49 6.9 3.71 6.9 MK11 82.49 6.9 1.71 6.9 MK12 84.49 6.9 0.71 6.9   The typical morphology of the synthesized magnesia-chromite refractory composites is shown in Figure ?6-1. For compositions with high content of Fe2O3 or Al2O3 the particles are in the form of hexagons and cubes with rounded edges. In contrast, samples with high Cr2O3 have sharp corners and are slightly smaller. The particle and grain size of selected magnesia-chromite refractory composites are measured by SEM and XRD respectively, and the results are listed in Table ?6-2.  Figure ?6-1. The typical microstructure of synthesized magnesia-chromite composites; a) the lowest Cr/Al+Fe ratio (MK1), and b) the highest Cr/Al+Fe ratio (MK6)  98   As expected, the differences between the particle sizes of different composites are in the range of 15-20 % of the smallest particle. For this reason the effect of initial particle size on the densification of magnesia-chromite refractory composites was not incorporated in the interpretation of the results.    Table ?6-2. Particle size of selected magnesia-chromite composites after calcination at 850?C  Particle size (?m) MK1 1.12 MK3 1.27 MK6 1.34 MK12 1.19  6.1.1 The effect of Fe2O3 on the densification and grain growth of magnesia-chromite refractory composites  Figure ?6-2 illustrates the density variation versus the Fe2O3 content of the composites. The increase in Fe2O3 increases the density of magnesia-chromite refractory composites sharply from 83% to 95% of theoretical density. The same behavior was observed during sintering of pure MgCr2O4 and was attributed to the solid solution formation and the inversion process of the formed spinel solid solution.  The microstructure of the magnesia-chromite refractory composites consists of two phases which are soluble in each other; therefore, the same analogy can be considered for this behavior. 99   Figure ?6-2. The variation of relative density of magnesia-chromite refractory composites versus Fe2O3 content; composites sintered at 1550?C for 300 minutes    Figure ?6-3 shows the XRD patterns of the MK3 composite air quenched from the sintering temperature of 1550?C. The formation of spinel (Sp) solid solution can be confirmed by the shift toward high diffraction angles recorded for the [101] peak of MgO. The BSE microstructure of polished and thermally etched MK3 composites is shown in Figure ?6-4. It is seen that the microstructure is composed of two phases; the darker phase is MgO with 3% Fe2O3, 0.2% Al2O3 and 3.6% Cr2O3 as solutes, and the brighter phase is a spinel solid solution.  0 1 2 3 4Fe2O3(mol%)8084889296100Relative density (%) Sintering temperature/ time/ atmosphere: 1550?C/ 300 min/ Air100   Figure ?6-3. The XRD of MK3 composite sintered at 1550?C for 5 hours;  Sp: (Mg1-x-y,Fey,Alx)[Cr2-x-y,Alx,Fey,Mgx+y]O4; ? = x+y   A closer examination of the chromite grains, Figure ?6-4, shows the presence of a brighter rim around the spinel grains; the Fe2O3 content is higher in the spinel grains and at the MgO/spinel interfaces (rim). Al2O3 is concentrated in the spinel grains and its concentration is ~0.22% in the center of the selected MgO grains. Similar observations were reported by Stubican and Menezes128. They presented that there was a difference between the diffusion of Fe, Cr, and Al from chromite grains to magnesia grains.  The large amount of iron, limited amount of chromium and almost no aluminum was reported to have diffused from chromite into magnesia at 1400?C128. This phenomenon can also 10 20 30 40 50 60 70 802? (?)MgO (100)SpMgO (101)MgO (002)MgO (110)SpSpSpSpSpSpSpSpSpSpSpSpSpSpSpSpSpSp101  be predicted from the respective phase diagrams. Figure ?6-5 shows a part of the phase diagrams of MgO-MgAl2O4, MgO-MgFe2O4, and MgO-MgCr2O42.   Figure ?6-4. BSE image of MK3 sintered at 1550?C for 300 minutes; inset shows the EDS analysis of the selected points; the confidence intervals were obtained based on the ?/?3 equation for flat distribution, as each point has been analyzed 3 times    It is observed that at high temperatures Al2O3, Cr2O3 and Fe2O3 are partially soluble in MgO and their solubility increases with temperature, while the solubility decreases in the order  Fe2O3>> Cr2O3> Al2O3 at temperatures above 1000?C. Therefore, the shift in the MgO peak is attributed to the formation of MgO solid solutions at the sintering temperature. At 1550?C, some of Fe2O3 and Cr2O3, which are in the form of spinel, are dissolved into MgO and form a MgO solid solution. The diffusion of Fe and Cr into MgO results in the formation of V??Mg vacancy in MgO through the following reaction, in which Me is Fe or Cr, and increases the diffusion rate of cation in the MgO lattice, and subsequently the densification: 102          ?     ?                6-1  Figure ?6-5. Solid solubilities of sesquioxides in periclase at high temperatures2   Figure ?6-6 illustrates the variation of the relative density of MK3 and MK12 composites during non-isothermal sintering from 900 to 1600?C at an approximate heating rate of 20 deg/min). For both composites the density increases with temperature, but at temperatures above 1250?C the density of MK3 is significantly higher than the density of MK12. In addition, the increase in density for MK3 can be fitted to the ?S??curve, but not for MK12 (i.e. it appears that the density increase saturation at 98-99% could occur at temperatures significantly higher than 1600?C).   The? ?S?? curve? pattern? of? density? with? sintering? temperature? indicates? that? the MK3 composite experienced all three steps of the sintering process4. At temperatures below 1150?C, 103  density barely changed with an increase in the sintering temperature resembling the initial stage of sintering. In the intermediate stage, the density sharply rose to 90% of theoretical density with a 250?C increase in the sintering temperature (from 1200 to 1450?C) and in the final stage it reached 98% of the theoretical density above 1500?C. In contrast, for MK12 the initial stage of sintering extended to about 1300?C, and the density increased to 84% of theoretical density at 1600?C. This indicates that two different mechanisms control the densification of MK3 and MK12.    Figure ?6-6. The non-isothermal densification of MK3 and MK12 composite sintered in air at different temperatures for 300 minutes   In the interpretation of the densification and grain growth results for these composites, it should be considered that there is about 40 wt% spinel in the composition of the magnesia-chromite refractory composites; according to Karpinos et al.129 this affects the kinetics of magnesia-chromite refractory composites densification. They showed that the kinetics of sintering of two-phase composites depends on both the volume fraction and the morphology of 900 1050 1200 1350 1500 1650Temperature (?C)44526068768492100Relative density (%) MK3MK12104  the second phase. For instance, they presented that for copper-ZrC composites the higher the ZrC content and ZrC particles aspect ratio, the lower the final density of the composite129. Boltona et al.130,131, and Fan et al.131 also showed that densification and the grain growth were affected by the presence of the second phase in the microstructure. They stated that the sintering behavior of the second phase must be taken into account when studying of kinetics of densification and grain growth of a composite.  In this regard, the effect of the composition on the densification of the second phase, which is a solid solution of MgCr2O4-MgAl2O4-MgFe2O4, must be considered when analyzing the results of the densification of the magnesia-chromite refractory composites. Earlier in this work in ?Chapter 5, it was described that the solid solution formation increases the cation mobility via different mechanisms, including vacancy formation, stress induction, etc., and this increases the densification. In this case, since Fe2O3 has high solubility in MgO, the higher the Fe2O3 content in magnesia-chromite refractory composites, the more solid solution is formed in the composite, which results in higher densification. In Section ?5.2 we have shown that the Fe2O3 not only enhances the densification of pure MgCr2O4 via solid solution formation, but it also contributes to densification due to the induced inversion?in?the?host??MgCr2O4??structure.   We showed that regardless of the sintering temperature, an inverse spinel solid solution (Mg1-?, Fe?) [Cr1-x, Mg?, Fe?-x]2O4 forms . Since the inversion is associated with the short range of cation mobility, we proposed that this reduces the activation energy of the sintering of MgCr2O4. The same analogy can be applied for magnesia-chromite refractory composites. The only difference is that in the magnesia-chromite refractory composites, both Al2O3 and MgO are present in the composition. As a result, the contribution of Al2O3 in the inversion of the spinel should be taken into account.  105   A comparison between the compositions of MK3 and MK12 shows that they both have the same Cr2O3 and Al2O3 content, and the difference between them is limited to the Fe2O3 content. Based on the above explanations, the higher content of Fe2O3 in the composition of MK3 resulted in a better densification of MK3 than of MK12. As shown in Figure ?5-13, the presence of about 2 mol% excess Fe2O3 in MK3 significantly increases the inversion parameter in the spinel. Considering the kinetics of sintering of the two-phase magnesia-chromite refractory composites and the enhancement of densification of MgO and spinel by Fe2O3, it can be concluded that the composites with higher Fe2O3 content densify better than the others.   The variation of the grain size of MK3 and MK12 with the sintering temperature is presented in Figure ?6-7. The grain size increased with temperature for both composites; however, the final grain size of MK3 is larger than in MK12. In fact, considering the ?0.7 ?m confidence interval for the average grain sizes for the two compositions, it appears that the materials are similar at low temperatures and the differences are visible only at 1600?C. Considering the errors in grain size measurements, Figure ?6-7 demonstrates that increasing Fe2O3 from 0.71 (MK12) to 2.71 mol% (MK3) resulted in about 10% increase (dave: 5.5 to 6 ?m) in the average grain size of both spinel and magnesia; however, an opposite trend, reduction in grain size by adding solute, is expected. According to the classic theory of the grain growth4, the presence of a second phase, here the spinel, should have also suppressed the grain growth of MgO. This anomaly can be explained from two perspectives.  Let's consider the grain growth via the interface migration under the chemical non-equilibrium status. At high temperatures, multiphase polycrystalline solids become chemically unstable, and as a result equilibration reactions occur to reach the new equilibrium condition. These reactions usually occur by diffusion, effecting boundary movement from one grain to 106  another, and causing grain growth in the first grain at the price of consuming the second grain; this results in the formation of a new solid solution behind the migrating boundary1,4. In MK3 composites, as shown in Figure ?6-14, the grain boundaries are curved, indicating the non-equilibrium conditions at the grain interfaces. The chemical analysis of the grains, displayed in Figure ?6-4, shows a difference in the chemical potential of Fe at the spinel/MgO interfaces, which acts as a driving force for the grain growth. As a result, the increase in Fe2O3 content increases the driving forces for grain growth and increases the grain size.  Figure ?6-7. Grain size of MK3 and MK12 composites sintered in air at different temperatures for 300 minutes   The second perspective proposes that in two-phase composites the activation energy for grains coarsening is related to the reduction of the grain boundary energy between the same-phase grains, and also to the reduction of the interphase boundary energy between unlike grains131. This occurs via grain growth through grain boundary migration and Ostwald ripening 850 1000 1150 1300 1450 1600Temperature (?C)12345678910Grain size (?m) MK3MK12Error bar: ??????m107  processes. The Ostwald ripening is a long range diffusion process, while the grain boundary migration requires a short distance diffusion of atoms between two sides of the grain boundary. Therefore, Oswald ripening is the rate controlling mechanism of grain growth in two-phase composites. As a result, the solid solubility of the two phases in each other plays a significant role in the grain growth of the composite. It is therefore proposed that the slightly larger grain size in MK3 composites could be caused by the higher Fe2O3 content in comparison to the MK12 composites.   As shown in Figure ?6-5, the high amount of Fe2O3 in the spinel results in a high degree of solid solubility, and hence more active Oswald mechanism, and larger grain sizes of both MgO and spinel. Due to the errors in grain size measurement and limited data, at the present stage of this research it is not possible to reach definite conclusions from the above results.  6.1.2 The effect of Cr2O3 on densification and grain growth of MK composites  The variation of relative density of magnesia-chromite refractory composites with the Cr2O3 content is shown in Figure ?6-8. It should be mentioned that in this series the compositions of Fe2O3 and Al2O3 are constant, and the changes in Cr2O3 content are balanced with MgO. The effect of Cr2O3 on the densification of magnesia-chromite composites and on the microstructure features of the spinel and MgO have been evaluated and used as a base for the interpretation of the results.   Two different trend-lines are fitted to the results in Figure ?6-8. Based on the first trendline, density decreases with the increase in Cr2O3 content. According to the second trendline, dash line, the trend of change in density with Cr2O3 content is also diminishing, but there is a sharp increase in the density of the magnesia-chromite refractory composite with 6.9 mol%. The density dropped from 96?0.3% to ~92?0.3% with 1 mol% increase in Cr2O3 content, and then 108  rose sharply to 96?0.3% and dropped to ~84% of theoretical density with the continuous increase of Cr2O3 to 8.9 mol%.   This behavior can be explained by the different oxidation rates of chromia in the presence of other composite constituents. In an investigation by Warshaw and Keith132, it has been shown that temperature, partial pressure of oxygen, Cr2O3 content, and the composition of the composites containing Cr2O3 solid solutions influence the vaporization intensity of Cr2O3.   Figure ?6-8. Variation of density of magnesia-chromite refractory composites as a function of Cr2O3 content; the error bars are smaller than the symbols sizes   In the same study, it was reported that at a given condition, the presence of Al2O3 and MgO increases the evaporation of chromium. In contrast, the addition of the SiO2 reduced chromium evaporation. They explained this observation based on MgO increasing the ratio of Cr+3 to Cr+2 in a composition. Cr+3 is unstable at both high temperatures and oxygen partial pressures, oxidizes to Cr+4 and leaves the composition; therefore, the increase in MgO causes the enhanced 4.5 6 7.5 9Cr2O3(mol%)8084889296100Relative density (%) Sintering temperature/ time/ atmosphere: 1550?C/ 300 min/ Air109  vaporization of Cr2O3132. Sata and Lee133 reached the same conclusion when studied the vacuum vaporization of MgCr2O4. They showed that at a given condition the vaporization of MgCr2O4 is higher than that of MgO and Cr2O3.     Based on the above discussion, the reduced density due to the increase in Cr2O3 content is attributed to the higher vaporization of chromium, which is detrimental for density. However, at 6.9 mol% Cr2O3, it seems that the reduction of chromium vaporization due to the reduced MgO in the composition was large enough to enhance the densification and to result in the final density of 96%.   In order to evaluate the influence of Cr2O3 on the sintering behavior of magnesia-chromite refractory composites, a comparison has been made between the densification and the grain growth behavior of MK1 and MK3. Figure ?6-9 illustrates the S curve densification plot for MK1 and MK3 composites, which indicates that in both materials sintering occurred in three stages. The only difference between the densification of MK1 and MK3 is the maximum achieved density, which is higher for MK3 (99?0.1 %) in comparison to MK1 (95?0.4 %). In fact at temperatures above 1350?C, the density of MK3 has dominated MK1. This is explained by the fact that MK1 has more MgO than MK3.  As mentioned, MgO increases chromium evaporation significantly at any given condition. The sintering of Cr containing ceramics is very sensitive to the partial pressure of oxygen82. This sensitivity is due to the intensified chromium evaporation at high oxygen partial pressures. It is concluded that the higher density of MK3 in comparison to MK1 is due to the enhanced chromium evaporation in MK1.    Figure ?6-10 shows the variation of grain growth versus sintering temperature for the MK3 and MK6 composites. The increase in the sintering temperature increased the grain size for both 110  composites, and also the grain size of MK3 is larger than that of MK1 at temperatures above 1500?C. As explained earlier, the vaporization of chromium from MK6 composite is perhaps higher than from MK3, and for this reason a larger grain size was expected for MK1. Other influential parameters on the grain growth of composites were first identified and used to explain this behavior. In the case of Fe2O3, the classic theory of grain growth4 is not applicable due to the variety of solutes in the composition. For this reason, it is considered that the grain growth is controlled by the Ostwald mechanism in both MK1 and MK3 composites131.    Figure ?6-9. The non-isothermal densification of MK3 and MK1 composite sintered in air at different temperatures for 300 minutes; error bars are smaller than symbols   The smaller grain size of the MK3 composites is due to the higher Cr2O3 content in its composition. In fact, according to the phase diagram2, Cr2O3 is less diffusive in MgO grains; therefore, in any given condition the grain growth for MK3 is always lower than for MK1. In other words, the spinel in MK3 is rich in Cr2O3 and its solubility in MgO is less than in MK1. As a result, the grain growth via the Ostwald mechanism is suppressed in MK3.  900 1050 1200 1350 1500 1650Temperature (?C)44526068768492100Relative density (%) MK3MK1111   In contrast, MK1 contains 4.9 mol% Cr2O3; hence, it has higher Fe/Cr+Al ratio. For this reason, the spinel solid solution in the microstructure of MK1 is more soluble in MgO than the spinel in MK3. In addition, the MgO content of MK3 is less than that of MK1. As explained earlier this would reduce the chromium vaporization rate in MK3 in comparison to MK1. This reason also explains the smaller grain size of MK3 in comparison to MK1 composite.   Figure ?6-10. Average grain size of MK3 and MK1 composites sintered in air at different temperatures for 300 minutes    6.1.3 The effect of Al2O3 on the densification and grain growth of MK composites  The density variation with the Al2O3 content in the magnesia-chromite composites is plotted in Figure ?6-11. The density of magnesia-chromite composites rose sharply from 81% to 96% of theoretical density with the increase in Al2O3 content and reached a plateau at ~6.9 mol% Al2O3. In order to explain this curve two subjects should be considered.  850 1000 1150 1300 1450 1600Temperature (?C)12345678910Grain size (?m) MK1MK3Error bar(MK1): ??????mError bar(MK3): ??????m112   First, like in the previous section ?6.1.1 discussing the effect of Al2O3 on the densification of both magnesia-chromite microstructure features, the effects of spinel and MgO must be evaluated. Second, in these compositions Al2O3 has been replaced with MgO; therefore, any changes in the densification behavior were attributed only to Al2O3 content. In the first part of the curve, where Al2O3 increases to 6.9 mol%, the increase in density can be explained by the formation of excess solid solution in compositions with the higher Al2O3 content.  Figure ?6-11. Variation of density of magnesia-chromite refractory composites as a function of Al2O3 content; error bars are smaller than symbols   As shown in section ?5.2, Al2O3 enhances the densification of pure MgCr2O4, as it forms an inverse spinel solid solution with it47. The same analogy can be considered here. For the second part of the curve, where the density reached a plateau, two reasons could be considered. First adding more Al2O3 to the composite reduces the Cr/Al+Fe ratio, and secondly it also reduces the Fe/Cr+Al ratio.  4.5 6 7.5 9Al2O3(mol%)8084889296100Relative density (%) Sintering temperature/ time/ atmosphere: 1550?C/ 300 min/ Air113   The low Cr content promotes densification through the mechanism explained in the previous section, but as discussed earlier, reduction in the Fe content deteriorates the density. In fact, Fe is the only cation in this series of composites that significantly enhances the densification of both MgO and spinel in magnesia-chromite refractory composites; therefore, the addition of Al2O3 contributes in two opposite ways to the densification of the magnesia-chromite refractory composites. On the one hand it enhanced the density, as it reduces the total Cr content. On the other hand, it reduces the densification, as it reduces the total Fe content and enhances the vaporization of Cr from the system. In the concentration range used in this study, 4.9 ? Al2O3 ? 8.9, for composites with Al2O3 concentration above 6.9 mol%, these two effects must have balanced off each other, and for this reason the density-concentration curve reached a plateau. In order to analyze the effect of Al2O3 on the densification and grain size of magnesia-chromite refractory composites, the densification curves of MK6 and MK3 were compared. In Figure ?6-12, both composites show a trend of increasing density with temperature.   Figure ?6-12. The non-isothermal densification of MK3 and MK6 composites sintered in air at different temperatures for 300 minutes; error bars are smaller than symbols  900 1050 1200 1350 1500 1650Temperature (?C)44526068768492100Relative density (%) MK3MK6114   For MK3 the density increases slowly with the sintering temperature until 1150?C, then it rises sharply from ~55% to 96% with a ~250?C increase in sintering temperature, and reaches a plateau of 96-99% for sintering temperatures above 1450?C. In contrast, density of MK6 increases linearly with a relatively small slope up to ~1350 C, then with a sharper slope up to ~1600?C, when density reaches ~86 %.  The change in the grain size of MK3 and MK6 composites at different temperatures is shown in Figure ?6-13. There is the same pattern for both composites; however, the grain size of MK6 is slightly larger than that of MK3. This is explained by the higher ratio of Cr/Fe+Al in MK6 in comparison to MK3.    Figure ?6-13. Average grain size of MK3 and MK6 composites sintered in air at different temperatures for 300 minutes   As any change in alumina content in these samples has been balanced with MgO, the low alumina content in MK6 means that there is more magnesia in this composition in comparison to 850 1000 1150 1300 1450 1600Temperature (?C)12345678910Grain size (?m) MK3MK6Error bar(MK6): ??????mError bar(MK3): ??????m115  MK3. The higher MgO content increases the vaporization of chromium from the composite, as it increases the Cr+3/Cr+2 ratio132. The larger grain size of MK6 is attributed to the evaporation/condensation mass transport mechanism, which is possibly more active in MK6 than in MK3. 6.1.4 The effect of Fe2O3, Cr2O3, and Al2O3 on the microstructures of sintered magnesia-chromite refractory composites  In the previous section the influence of chromite constituents on the sintering of synthetic chromite were investigated. It was shown that each of the three considered oxides can change the densification and the grain growth behavior in a certain way. This makes the studying of the sintering mechanism of magnesia chromite composite challenging. In this section we will study the effect of each oxide on the final microstructure of the magnesia chromite composite with respect to the morphology of the grains. Moreover, the influence of the oxide on the dihedral angle, as well as the grain boundary energy of the magnesia chromite composite are reported, in order to verify the results of densification of magnesia chromite composite provided in the previous section.   The microstructures of MK1 and MK3 composites quenched from 1550?C after 300 minutes sintering are shown in Figure ?6-14. In the MK3 composite, which is enriched in Fe2O3, the spinel grains are mostly equiaxial. In contrast, the spinel grains in the microstructure of MK12 with high alumina and chromia are generally angular. This difference in the morphology of these spinels can be explained with respect to the strain energies due to the lattice mismatch between MgO and spinel solid solution94.   The phase composition of the spinel in MK3 and MK12 is calculated theoretically, assuming that all trivalent oxides react with an equal mole percent of magnesia to form spinel. 116  The results are reported in Table ?6-3.  MK12 contains only 6 wt% MgFe2O4. Contrary to MK12, MK3 consists of 19 wt% MgFe2O4. Since the interface between MgO and MgFe2O4 is reported to be coherent, then the formed spinels in MK3 are more rounded134.   The interface between MgAl2O4 and MgCr2O4 is not coherent and makes the spinel more irregular and angular134. Goto and Lee134 reported that in the microstructure of magnesia chromite refractories the chromite precipitates with different morphologies on the magnesia grains. They attributed this phenomenon to the contribution of the strain energy to the microstructure of chromite refractories.  Table ?6-3. The theoretical composition of spinel solid solution in magnesia-chromite refractory composites  MgFe2O4 (wt%) MgAl2O4 (wt%) MgCr2O4 (wt%) MK3 19 40 52 MK12 9 36 45   The dihedral angle of the 12 designed composites has been calculated from the SEM images. The dihedral angle was selected as the angle with the maximum frequency of repetition. Since the designed composites consist of two phases, three different dihedral angles have been defined: MgO/MgO (?M/M), spinel/spinel (?S/S), and spinel/MgO (?S/M). In this study, the dihedral angle between spinel and MgO was considered for the analysis of the effect of dihedral angle on the densification of the composites.   The reason was that the ?M/M and ?S/S varied very little with the composition. The average calculated ?M/M and ?S/S values were almost the same, ~114 and 109? respectively. Theoretically, the value of ?M/M and ?S/S for a single crystal MgO and spinel should have been 120?4; however, these composites consist of two polycrystalline phases, with different orientations of the grains, 117  as well as variation of composition along the grain boundaries. As a result, the calculated values are acceptable. Figure ?6-16 shows the frequency of repetition of dihedral angles for the MK3 composite. According to the above definition, the dihedral angle for this composition is 96?.   Figure ?6-14. BSE images of a) MK3 and b) MK12 composites sintered at 1550?C for 300 minutes   The change in the dihedral angle (?S/M) versus the R2O3 content is shown in Figure ?6-16. The increase in the Al2O3 and Fe2O3 decreases the dihedral angle. In contrast, the value of ?S/M is proportional to the Cr2O3 content. The same trend has been reported by White et al. 2 measuring the effect of the same oxides on the dihedral angle in MgO-15 wt% monticellite. The main difference between the results of the present study and the one reported by White is the measure of dihedral angle. The values reported by White are considerably lower than those calculated in the present study.   For instance, (?M/M) was reported to increase from 25 to 45? for MgO-15 wt% monticellite with a 10mol% increase in the Cr2O3 content. Also, (?M/M) was reported to decrease from 25 to 20? with a 10mol% increase in the Fe2O3 content.  118     Figure ?6-15. The calculation of dihedral angle for the MK3 composite   This difference can be explained by considering the fact that White measured the dihedral angle between magnesia grains in a matrix of melted monticellite. The interfacial energy (?solid/solid ) is usually 1 to 2 orders of magnitude lower than (?solid/liquid )4, thus the dihedral angle decreases according to the equation ?6-2. In contrast, in the present study the dihedral angle was measured in the solid state. The grain boundary energy of the oxides and spinels has similar values, 1-2 J.m-2; therefore, the dihedral angle is relatively high. The increase and decrease in the dihedral angle can be translated to increase and decrease in the interfacial energy between the MgO/spinel grains according to the following equation:          ?             6-2 where ?M/M and ?S/M are the grain boundary energy of MgO/MgO and the interfacial energy between  MgO and spinel grains respectively. The grain boundary energy of the MK3 composite 75 85 95 105 115 125 135 145Angle (?) 01020304050Frequencyffff119  was calculated using the above equation; the grain boundary energy of pure MgO (?M/M = 1.411 J.m-2) was obtained from literature135. Using the average dihedral angle between MgO and spinel ?S/M = 95 in the equation ?6-2, the resulted interfacial energy was about 1.04 J.m-2 for MK3 with 2.71 mol% Fe2O3 sintered at 1550?C. The ?S/M decreased to 0.965 J.m-2 with the increase in the Fe2O3 content of the composite to 4.9 mol%.   This reduction in the interfacial energy can be correlated to the higher solubility of Fe2O3 in both magnesia and spinel solid solution, which enhanced the densification and reduced the strain energy between spinel and MgO. It also resulted in the formation of a rounded second phase between the MgO grains in the microstructure of high iron oxide content magnesia-chromite refractory composites. The uncertainty of these measurements is estimated at ?5?.   Figure ?6-16. The variation of the average dihedral angle of magnesia-chromite refractory composites versus oxide content; the composites were sintered at 1550?C for 300 minutes  0 2 4 6 8 10R2O3 (mol%)7288104120136152Dihedral angle "?S/M" (?) Al2O3Cr2O3Fe2O3120   The change in the relative density of the magnesia-chromite refractory composites with the dihedral angle is shown in Figure ?6-17: the relative density is higher for the composition with the smaller dihedral angle. Similar results have been reported by Alper2, who reviewed a study by White et al. and showed that Fe2O3, Al2O3, and TiO2 improved the densification of the basic refractories by decreasing the dihedral angle between the magnesia grains.  Gosh et al.13 also reported that the addition of ZrO2 to the magnesia chromite refractories increased the densification due to the decrease in the dihedral angle. To the best of our knowledge, there is however no published information about the effect of Fe2O3, Al2O3, and Cr2O3 on the dihedral angle of magnesia or chromite spinel. In this section the effect of trivalent oxides on the densification, grain growth behavior, and microstructure of magnesia-chromite composites were investigated. For this purpose, 12 compositions were prepared and compared with each other, with respect to the density and grain growth.  Figure ?6-17. The variation of the density versus the dihedral angle for magnesia-chromite refractory composites  80 90 100 110 120Dihedral angle "?S/M" (?)8084889296100Relative density (%)121   Based on the results, the MK3 composition was selected for studying the kinetics of sintering. For the sake of simplicity, the MK3 is called MK composite hereafter. In addition, nano sized MK called, NMK, was also prepared?via?Pechini?s?method (section ?2.2.1.1) and was used to evaluate the effect of particle size on the densification behavior of the magnesia-chromite refractory composites.  6.2 The densification behavior of MK composite  Figure ?6-18 shows the variation of the relative density and the grain size of the MK composite for sintering temperatures between 850?C and 1600?C. The plot of the relative density versus sintering temperature exhibits a sigmoidal shape. The density increased only 4% up to 1150?C, but increased significantly, up to 92%, at sintering temperatures between 1150 and 1450?C. The densification rate was lower for sintering temperatures above 1450?C, and the maximum density of the composite was 98% of the theoretical density at 1600?C.   The variation of grain size with the sintering temperature showed a parabolic shape. While the density was significantly increasing between 1150? and 1450?C, no considerable increase in the grain size was observed in this range of temperatures. In contrast, at temperatures above 1475?C the grain size increased dramatically, i.e. by ~140%, whereas the density increased only by ~5%. The average grain size of the MK composite was ~7 ?m, and the standard deviation of the measured grain size was ?0.9 ?m, for the fully dense (?~98%) composite. According to the classic theory of sintering, this curve shows the three stage of sintering4: the first stage, where no significant densification occurred (<4%), the intermediate stage, where the density increased dramatically from ~52% to 92%, and the final stage, where the density increased slightly from 92 to 98 % and the grain size increased significantly from ~3 to ~7?m.  122   Figure ?6-18. The non-isothermal densification and grain size of MK composite sintered in air at different temperatures for 300 minutes    The reduced densification rate in the 3rd stage can be linked to the grain growth16 and the presence of insoluble gas entrapped in the closed pores5. This behavior can be attributed to the distribution of open pores in the 2nd stage of sintering and to their contribution on the grain growth inhibition. During the intermediate stage, pores are usually located at the triple junctions and would pin the grain boundaries, consequently suppressing the grain growth.  However, as the temperature increases, the pores would become thermodynamically unstable136 and form closed ones at the beginning of the final stage. As a result, the grain size increases sharply, as there is no resistance to the grain boundary migration. This phenomenon has been addressed by several researchers. Mazaheri et al.137 investigated the two-step sintering of nano ZnO and showed that in a certain sintering condition it was possible to densify nano ZnO to the full density with about 200% smaller grain size in comparison with the same composition 850 1000 1150 1300 1450 1600Temperature (?C)3644526068768492100Relative density (%) 13579111315Grain size(?m) DensityGrain sizeInitial stageIntermediate stageFinal stage123  sintered in a conventional sintering profile. Li et al.138 reported the same phenomenon by comparing the conventional sintering procedure to the two-step sintering procedure.   Another reason for the limited grain growth at the intermediate stage of the sintering of MK composite could be the presence of the second phase in the microstructure. In the MK composite, ~30 vol% of the microstructure consists of the spinel phase. The presence of spinel affects the grain growth rate during the 2nd stage of sintering, when the grain boundary migration is controlled by volume and by the grain boundary diffusion mechanisms. However, it should be mentioned that due to the solid solubility between magnesia ?matrix? and spinel ?inclusion?, the grain boundary pinning has probably occurred due to the size factor.   According to the Zener drag effect theory1, 4 the exerted drag force on the grain boundaries is proportional to the grain boundary surface area that is occupied by the 2nd second phase. In this regard, the fewer and the smaller the 2nd phase particles are at the grain boundaries, the more drag forces they create, and become more effective in the hindrance of the grain growth. In addition, it is known that any phenomenon which increases the movement of the 2nd phase would increase the grain growth5. The MK composite powder has been synthesized through the chemical route to ensure the uniformity of the mixing at molecular level44,139,140. In addition, the grain sizes of spinel (dSP:1.28 ?m) and magnesia (dMg:1.34 ?m) are relatively identical.   Therefore, the slight increase in the grain size of the MK composite is attributed to the increased mobility of MgO grain boundaries at high temperature, due to the solid solubility between MgO and spinel. Moreover, the increase in temperature also increased the spinel grain size and reduced its effect on the grain boundary movement. At temperatures above 1450?C, the pores were collapsing and the inclusions were large enough to not be able to inhibit the grain growth, allowing for a ~140% grain size increase. The influence of inclusions on the density of 124  ceramics has been studied for several systems. Haroun141 theoretically and experimentally proved the inclusions would suppress the grain growth during the densification of ceramics. He also showed that the grain growth inhibition depends on the size and the movability of the inclusion. Lange et al.142 studied the Al2O3-ZrO2 system and reported that although ZrO2 hindered the grain growth of Al2O3, it became more effective when its concentration was ~5 vol%.  The typical microstructure of the MK composite at the different stages of sintering is shown in Figure ?6-19a-d. The microstructure of the specimen sintered at 1150?C (Figure ?6-19a) contains? a? large? amount? of? pores,? which? reflects? the? low? density? of? the? composite? (?=54%). Increasing the sintering temperature to 1350?C (Figure ?6-19b) resulted in the reduction of the pore content and the formation of a relatively dense structure with ~80% density. The sintering at 1475?C  (Figure ?6-19c) provided a near fully dense microstructure ~96%, with larger grains of 6.4 to 7.3 ?m; however, a further increase in the sintering temperature (T=1600?C, Figure ?6-19d) only increased the grain size from ~4 ?m to ~7 ?m, at 98 % relative density.  Figure ?6-19 also shows that the spinel phase is composed of smaller equiaxial sub-grains. This microstructure can be explained by the fact that the composites used in this study were made via a chemical method, which is homogeneous at the molecular level. In Section ?5.2 it was shown that spinels such as MgAl2O4, MgCr2O4, and MgFe2O4 would form in such homogenous mixtures at relatively low temperatures (T<1000?C). It was also shown that the formation mechanism involves the oxidation of nitrates to oxides, followed by the spinel-forming reaction between the oxides. Therefore, the microstructure of the MK composite at the calcination temperatures and also at low sintering temperatures (T<1350?C) is composed of MgO and 125  spinels or spinel solid solutions. Figure ?6-19a,b illustrate this microstructure, consisting of small cubic and equiaxial grains with rounded edges,  randomly distributed in the microstructure.  Figure ?6-19. The microstructure of MK composite at a)1150?C, b)1350?C, c)1475?C, and d)1600?C   As determined by EDX, the cubes are rich in magnesia and the equiaxial grains are rich in spinel forming oxides. At high sintering temperatures (T >1400?C) there is unlimited solid solubility between spinel structures (MgCr2O4- MgFe2O4- MgAl2O4); as a result, they form a solid solution with a composition close to (Mg1-x-y,Fey,Alx)[Cr2-x-y,Alx,Fey,Mgx+y]O4.   In contrast, there is a limited solid solubility between the spinel solid solution               (Mg1-x-y,Fey,Alx)[Cr2-x-y,Alx,Fey,Mgx+y]O4 and magnesia. Therefore, at the sintering temperature, 126  when the concentration of spinels gets beyond the solid solubility limit in magnesia, the spinel solid solution exsolves from magnesia grains and changes the microstructure of the MK composite to the one shown in Figure ?6-19c and d. A very similar microstructure was also observed in the sintered microstructure of BaTiO3-SrTiO3 solid solutions143.  Figure ?6-20 also shows the SEM image of the MK composite sintered at 1600?C in the regions where the exaggerated grain growth has occurred. The exaggerated grain growth can be attributed to the inhomogeneous distribution of the pores and to the second phase in the MK microstructure. This was caused by the reduced pore volume at high temperatures, and also by the high solid solubility of MgO and spinel, which resulted in the ongoing local composition change. As a result, the grains at the dense locations grew faster than in the rest of the MK microstructure. The same phenomenon has been reported by Lange et al.142 in the studying of the effect of ZrO2 on the densification of Al2O3. Roy14, 85 also reported the effect of the solute on the densification and the grain growth of Cr2O3.   Figure ?6-20. The SEM image of MK composite at 1600?C showing the exaggerated grain growth  127   The isothermal experiments were performed at 1200?C-1600?C with 50?C intervals. The evolution of the relative density over the sintering schedule at different holding temperatures is shown in Figure ?6-21. This set of experiments has been executed to understand the densification behavior of the MK composite at the different stages of sintering.   As expected based on the theory of densification4, the density did not change at temperatures below 1150?C, in the initial stage of sintering. The densification rate was increasing in the temperature range of 1200-1450?C. At temperatures above 1450?C the densification rate was increasing at holding times below 70 minutes, but it was almost zero beyond that time limit. In other words, at temperatures above 1475?C no change in the density was recorded after 70 minutes, indicating that this was the optimum sintering time for the MK composite.   Figure ?6-21. Isothermal densification of MK composite sintered in air at different temperatures   0 50 100 150 200 250 300Time (minute)405060708090100Relative density (%) 1600?C1550?C1475?C1400?C1150?C900?CInitial stage128   Figure ?6-22 illustrates the variation of the grain size with the relative density of the MK composite. The grain size did not change considerably until the density reached the critical value of ~60% of the theoretical density, which indicates the initial stage of sintering. Above this critical density, the grain size increased slightly until the density reaches ~90%, and it rose dramatically to the maximum average grain size value. The 90% is the critical density above which the grain growth accelerates, indicating the transition from the intermediate to the final stage of sintering. Correlating the densification and the grain size results with the microstructures of the sintered composite supports the division of the sintering process of MK composite into the three stages.    Figure ?6-22. The isothermal grain size versus relative density of MK composite sintered in air at different temperatures for 300 minutes   In the initial stage, the neck formation, with no densification and no grain growth occurred; this stage was followed by the intermediate stage, when the grain growth happened above the 40 50 60 70 80 90 100Relative density (%)12345678910Grain size (?m) 900?C1000?C1100?C1150?C1200?C1250?C1300?C1350?C1400?C1450?C1475?C1500?C1525?C1550?C1600?C129  critical relative density due to the collapse of some pores, in spite of the presence of the 2nd phase and a continuous network of pores.  The main characteristic of the final stage of sintering was the rapid grain growth. During the final stage, the densification did not change considerably, although the grain size did change; however, only closed pores and the secondary phase remained in the final sintered microstructure.   As mentioned in the literature, one parameter which could affect the densification behavior is the initial particle size of the ceramic powder. According to Herring?s scaling law144, the particle size is proportional to the reciprocal sintering rate; the smaller particles sinter faster than the larger ones.  Reducing the particle size increases the surface area of the system and substantially increases the driving force for the sintering process, which could result in a considerable reduction in the sintering145-148. In spite of this achievement, reducing the particle size also increases the chance of agglomeration, contamination and grain coarsening, which negatively affects the physical and the mechanical properties of a certain ceramic149-151.   Since one of the main objective of this study was to reduce the sintering temperature of the magnesia-chromite composites in air from 1750?C to below l500?C, nano particles of the MK composite were prepared?via?Pechini?s?method, as described in the experimental section ?4.1.2. The sintering studies were performed on the pellets made of the nano MK composite particles (called NMK), and the results were compared to those obtained by the micron sized MK composite.   Figure ?6-23 shows the densification and the grain growth change of the NMK composite at sintering temperatures in the 900-1600?C range; the plot of the density exhibited a sigmoidal 130  behavior, implying the occurrence of the three stages of sintering. The density increased slowly from ~35% to 44% at 1000?C, dramatically increased from 44 to ~92% at 1300?C, and reached a plateau at almost 1350?C. The three stages of sintering are inserted in Figure ?6-23.   The grain size followed a parabolic profile, rising sharply from ~700 nm at 1300?C to ~2000 nm at 1475?C. The microstructures of specimens, marked as A, B, C, and D on Figure ?6-23, are shown in Figure ?6-24. As expected, the pore volume decreased from ~30% at 1100?C to zero at 1350?C. However, the grain size increased dramatically to 100 times the grain size?of?the?primary??synthesized?grains?,?and to 10 times the grain size of the specimen sintered at 1150?C+-.   Figure ?6-23. The non-isothermal densification and grain size of NMK composite sintered in air for 300 minutes    Three mechanisms could be attributed to the high grain growth in the microstructure of NMK composite. It is well known that the reduction in the particle size increases the surface area of a system, and the surface related phenomenon will be affected by the increased surface area. 850 1050 1250 1450 1650Temperature (?C)3644526068768492100Relative density (%) 010002000300040005000600070008000Grain size(nm) DensityGrain sizeInitial stageIntermediate stageFinal stageABCD131  In the case of the NMK composite, the high surface area has probably increased the evaporation of Cr2O3 from the system at the sintering temperature, and enhanced the non-densifying evaporation/condensation mass transport mechanisms, resulting in the grain growth. The evaporation of Cr2O3 is known to be detrimental for the densification of Cr2O3 containing ceramics11,88. We have also showed that the spinel forming additives such as Al2O3 and Fe2O3 would not affect the evaporation rate of Cr2O3 in the designed magnesia-chromite composite. Considering the above explanations plus the fact that the sintering was carried out in air, the very high surface area of the nano sized NMK composite could be attributed to the high grain growth rates, especially at temperatures above 1350?C. This statement is verified by the fact that the oxidation and evaporation of Cr2O3 exponentially increased with the temperature, as reported by Graham84.   The second reason of the high grain growth rate is also related to the small size of the powder in NMK. The grain growth might have occurred through the Ostwald mechanism, like for the MK composite. The smaller particle size of the NMK grains created the short diffusion paths and resulted in the high dissolution of small grains and the growth of large grains. According to the?Fick?s?second?law, the penetration depth (xd) is relative to the square root of the product of the diffusion coefficient (Dd) and time (t), (xd=2?Dd.t)1. In the NMK composite the penetration depth is very short, 20 nm; therefore, the time required for the diffusion of cations from one grain to another is short, and the grain growth rate is high. The extensive grain growth of nano ceramics has been studied by several investigators99, 146, 149, 152-156.   They all showed that grain growth occurred as a result of the grain boundary mobility and the full densification occurred when the grain boundary mobility was suppressed. The grain boundaries are also known as sinks for vacancies; therefore, the separation of the grain boundary 132  from pores is detrimental to the densification146,156. Several techniques have been used to sinter the nano ceramics with limited or no grain growth, but the review of these techniques is not in the scope of this study.   Figure ?6-24. The microstructure of NMK composite at a)1150?C, b)1250?C, c)1350?C, and d)1475?C   The isothermal densification behavior of the NMK composite is shown in Figure ?6-25. It is similar to the one presented for the MK composite in Figure ?6-21. At high sintering temperatures, above 1350?C, the variation of density with the sintering time reaches a plateau relatively fast, i.e. after about 20 minutes.  133   In the mid sintering temperature range from 1100?C to 1300?C, the density increases continuously. There are some similarities between the isothermal densification behavior of NMK and MK at the low sintering temperatures, where the density was below 60%; however, the density increased linearly with time for NMK, while it did not change significantly in the MK composite. This different behavior can be explained by the different sintering kinetics for the nano and micro sized MK grains.    Figure ?6-25. The isothermal densification of NMK composite sintered in air at different temperatures    A comparison has been made between the densification behavior of MK and NMK composite in Figure ?6-26. It is observed that the onset sintering temperature of the nano sized particles is ~200?C below the onset sintering temperature of micron sized MK grains. In the intermediate stage, the sintering process of NMK composite also continued faster than that of the MK composite; however, they both reached their full density.  0 50 100 150 200 250 300Time (minute)30405060708090100Relative density (%) 1600?C1450?C1350?C1200?C1100?C900?CInitial stage134   This is attributed to the fact that at higher sintering temperatures, the difference between the densities of specimens with low green densities decreases, and results in the convergence of densification curves of both set of samples to the same value. Despite the fact that the green density of specimens made of NMK grains was lower, they reached the full density even faster than the MK grains. As mentioned in the beginning of this chapter, the same phenomenon has been observed by Neves100.   The driving force of sintering is the reduction of the interfacial energy4. This is caused by the reduction in the interfacial energy and in the surface area, through the decrease in the densification and grain growth respectively. By reducing the particle size to the nano range, the surface energy of the system and the sintering driving forces are higher than for the micro size grains.   Figure ?6-26. The comparison between non-isothermal densification behavior of MK and  NMK composite sintered in air for 300 minutes   850 1050 1250 1450 1650Temperature (?C)3644526068768492100Relative density (%) NMKMKTOnset: ~1200?CTOnset: ~1000?C135   Moreover, due to the higher ratio of grain boundary in the nano composite in comparison to micron sized composites, higher grain boundary diffusion was expected between the nano grains. Both the densification and the grain growth occur by the diffusion process; therefore, a higher densification in the first two stages of sintering was expected for the NMK than for the MK composite. For the same reasons, a higher grain growth was also expected for NMK than for the MK composite during the final stages of sintering, where the grain growth mechanisms were active. The same phenomenon has been reported by Neves100, who compared the densification behavior of nano and micron size zinc oxide. He showed the densification rate and the grain growth rates of nano sized zinc oxide powder were both higher than the ones reported for the micron sized powder. Pietrzak et al.157 also reported that using nano alumina instead of micro alumina enhanced the densification of alumina ? Cr composites. They also attributed the results to the high surface area of the specimens prepared using nano alumina.   The results described above show that both MK and NMK composite experienced the three stages during the sintering schedule. However, despite the similarities in the sintering behavior of MK and NMK composites, the results show that reducing the particle size from ~1.2 ?m to 20 nm substantially enhanced the densification. The main drawback of reducing the particle size (neglecting the increased processing costs) was the increased grain growth. The grain size increased ~4 times from ~1.5 ?m to 7 ?m by sintering the MK composite at 1600?C; in contrast, the grain grew~400 times for the NMK composite, during the same sintering schedule.   It should be noted that in spite of the higher rate of the grain growth of the NMK composite, the final grain sizes were identical for both composites. It was also shown that there was a difference between the initial stage of sintering of MK and NMK. No significant density change was observed during the sintering of the MK composite, while the density increased 136  linearly during this stage for the NMK. In order to determine the mechanisms involved in the sintering and the reason for the difference in the sintering of MK and NMK composites, their sintering kinetics were compared.  6.3 Kinetics of sintering of MK and NMK composites  The main objective of this section is to determine the sintering mechanisms through studying the kinetics of sintering of the MK and NMK composites. The sintering practices in this study were performed isothermally, however owing to the high number of experiment runs, we were able to demonstrate the results in a non-isothermal pattern as well.  For this reason, the classic sintering model for the two spheres developed by Kingery and Berg5 was applied to the densification results to analyze and to estimate the sintering mechanism. According to this model, the kinetics of the initial stage sintering can be expressed by the following equation:      [    ]   6-3 where ??/? is the relative densification, H is a function of temperature and geometry, G is the grain size, t is the sintering time, m is a Herring scaling law exponent, and n is a parameter which depends on the sintering mechanism (Table ?6-4). The variation of ln(??/?) with ln(t) was plotted for different sintering temperatures resembling the initial stage of sintering. According to the following equation 5-12, the slope of this curve is the sintering exponent n, by which the sintering mechanism can be estimated. Table ?6-4 illustrates the correlation between the sintering mechanisms and the n values.   [   ]                   6-4 137   Figure ?6-27 shows the variation of ln(??/?) versus ln(t) for the MK composites sintered isothermally at 1000?C, 1100?C, and 1150?C. The sintering temperatures were selected based on the densification results presented in Figure ?6-18. It was shown that the sintering procedure for the MK composites can be divided into 3 sintering stages, i. e. the?initial?stage??950-1150?C?, the intermediate?stage??1200-1450?C?, and the final stage ?1475-1600?C?.? Table ?6-4. Exponent values reported for different sintering mechanisms4, 5   Mechanism n m Surface diffusion 0.286 4 Grain boundary diffusion 0.334 4 Lattice diffusion from surface 0.5 3 Lattice diffusion from grain boundary 0.4 3 Vapor transport 0.667 2 Viscous flow 1 1   As shown in Figure ?6-27, the sintering exponent for the densification data is slightly above 0.4, indicating that the lattice diffusion is responsible for the densification during the initial stage for the MK composite. In order to determine the activation energy of the densification during the initial stage of sintering, the Semilogarithmic law25 was utilized:                 6-5 where ?0 is an initial density at time (t0), ? is a density at time (t) and K is a temperature dependent parameter, calculated from the following equation in which Q is an activation energy of densification, T is an absolute temperature and R is a gas constant:                 6-6  Based on the above equations, the relative density versus the natural logarithm of time was plotted for the selected temperatures. The slope of the curves in Figure ?6-28 (the K values) were used for the activation energy measurement. Figure ?6-29 shows the variation of ln(K) versus 138  (1/T). According to the equation ?6-6, the slope of the curve is the activation energy of sintering in the initial stage.  Based on the plot, the activation energy of sintering for the MK composite is about 317 kJ/mol*.   Figure ?6-27. Sintering kinetics of the initial stage of sintering of MK composite; the 95% confidence intervals for n values are ? 0.02 (2?)    In order to correlate this value with a sintering mechanism, the role of MgO on the densification has also been considered, since the microstructure of the MK composite consists of both MgO and spinel. A comparison between the activation energy of the diffusion of oxygen in MgO (261 kJ/mol)158 and the oxygen diffusion in the MgAl2O4 spinel (415 kJ/mol)159 shows that                                                              * Due to the lack of information about the initial stage sintering of MgCr2O4 and chromite in the literature; the similarities between the sintering of Cr2O3 and MgCr2O4 and also similarities between the structure of MgAl2O4 and MgCr2O4 all the kinetic data in this study was compared to the spinel and Cr2O3. 1 2 3 4 5 6 7ln(t) (minute)-4-3-2-1ln(????? n = 0.4441150?C1100?C1000?Cn = 0.423n = 0.427139  although MgO plays an important role in the densification of magnesia-chromite refractory composites, it is not a rate controlling species in the microstructure.  Furthermore, this value is very close to the activation energy of MgCr2O4 formation (323 kJ/mol)104, indicating the activation energy required for the cation movement in the closed packed array of oxygen in spinel structure. In addition, since Cr+3 is the rate controlling species,  this value indicates the activation energy of Cr+3 mobility in the MgCr2O4 structure.    Figure ?6-28. Variation of relative density versus the sintering time during the initial stage of sintering    Considering the above values, one can conclude that the volume diffusion of Cr+3 in the spinel phases is a rate controlling mechanism in the initial stage sintering of MK composite. This conclusion can be compared to the on drawn by Hagel et al.88, who reported that the oxygen diffusion was the rate controlling mechanism during the densification at this stage. Since the 1 2 3 4 5 6 7ln(t) (minute)444648505254565860Relarive density (%)K = 0.9511150?C1100?C1000?CK = 0.931K = 0.05140  oxygen ion is significantly larger than the chromium ion (rO2: 1.32 ? vs. rCr+3: 0.62 ?)109, its activation energy of diffusion (425 kJ/mol)88 is significantly higher than that of Cr+3 (255 kJ/mol), thus the former conclusion by Hagel is acceptable.    Considering the above discussion and the fact that the activation energy of diffusion from the grain boundaries is smaller than from the lattice, it is hypothesized that the initial stage sintering of the MK composite is governed by the oxygen diffusion from the grain boundaries. Hagel88 also mentioned that the same mechanism was observed during the sintering of pure Cr2O3.   Figure ?6-29. Calculation of activation energy of initial stage of sintering of MK composite using equations ?6-5 and ?6-6    Figure ?6-30 illustrates the variation of ln(??/?) versus ln(t) for the nano MK composite (NMK). The sintering exponent n = 0.35 is lower than the value obtained for the MK composite, indicating that contrary to the MK composite, where the volume diffusion was governing the 7 7.3 7.6 7.9104/T (K-1)-3.5-2.5-1.5-0.50.51.52.53.5ln(K)-Q/R = 38178 (K)Activation energy =  317.4 (kJ/mol)141  densification, the grain boundary diffusion is governing the densification of the NMK composite. Such a change in the densification mechanism can only be correlated to the dramatic increase in the grain boundary area in the nano MK powders in comparison to the micron MK powders.   The nano-MK (NMK) powders have a large fraction of atoms in the grain boundary, which provides a high concentration of short diffusion paths. Therefore, enhanced diffusivity compared to the micron MK powders was expected. As a result of the increased sinterability of the NMK composites, the sintering temperature of these powders was lower than for the MK composites.  Figure ?6-30.  Kinetics study on the initial stage sintering of NMK composite according to the two sphere model (Kingery et al.5, 16)   The effect of particle size on the densification of WC-Co composites wasinvestigated by Porat et al.160. They showed that the reduction in particle size to the nano range not only enhanced the densification, but also changed the sintering mechanism of WC-Co from liquid phase sintering to solid state mechanism. He et al.161 showed the same phenomenon studying the 1 2 3 4 5 6 7ln(t)-3-2.5-2-1.5-1-0.5ln(????? n = 0.3521150?C1100?C1000?Cn = 0.342n = 0.354142  sintering of nano and micron size Al2O3. Neves et al.100 studied the initial stage sintering of ZnO and? showed? that? the? activation? energy?of? nano?ZnO? (202?kJ/mol)?was? significantly? below? the?values reported for the micron size ZnO (270?320 kJ/mol).    In order to calculate the activation energy of sintering during the initial stage for the NMK composite, the same approach was used to analyze the data ; however, the data did not fit the Kingery two-sphere model24. This model could also not be used for the analysis of densification results for the intermediate and final stage of sintering.   Several investigations addressed the densification models for analyzing the densification data during the final stage of sintering. Coble30developed a model assuming a tetrakaidecahedra distribution of pore channels along the edges. According to this geometrical model, the densification rate is a function of grain boundary and lattice diffusion, which are expressed in equations  2-3  and  2-4. It is impossible to solve the equations since the relationship between G and??? is still unknown. Several explanations and models were developed based on the Kingery and?Coble?s?models; however, none of them were solvable mathematically162, 162, 163.   Lately, a new model has been proposed by Su and Johnson23 - Master Sintering Curve (MSC). The MSC predicts the sintering behavior and the activation energy of sintering of a given powder with specific particle size and green density, regardless of the sintering profile. The MSC model have been successfully used to sintering systems such as YSZ164, MgAl2O4165, TiO2166.    In this model, the grain growth was assumed to be only a function of density. The model was constructed based on the combined stage sintering model by Hansen167, in which the immediate densification rate of a given compact was related to the volume, grain boundary diffusion coefficients, microstructure parameters and surface tensions, as follow: 143           ?  (?      ?      )  6-7 where ? is a surface energy, ? is an atomic volume, ? is a grain boundary width, ?b and Db are microstructure scaling factor for the grain boundary and the grain boundary diffusion coefficient respectively, ?v and Dv are microstructure scaling factor for the lattice and the lattice  diffusion coefficient respectively. Based on MSC theory, the sintering rate, microstructure and temperature parameters can be separated into two equations, as follows:??(?) demonstrates all the microstructure evolution during sintering (6-8), and ?(?) shows the sintering parameters depending on the thermal history (6-9):         ?  ?         ?          6-8           ?                6-9 where ?(?) incorporates G(?), scaling parameters ?(?) ,and Q is an activation energy of sintering. Since the latter equations are equal, the MSC that demonstrates the relation between density and ??(?) can be constructed from the experimental results by knowing or estimating the activation energy of sintering and plotting the curve of density versus the ?(?) function.  In order to estimate the apparent activation energy of sintering MK and NMK composites, the MSC theory was applied to analyze the densification data. MK and NMK compacts were isothermally sintered at temperatures ranging from 1150?C to 1500?C and quenched to room temperature after different sintering durations. The density was then measured and used to construct the master sintering curve, as shown in Figure ?6-31 for the MK composite.  Since no information about the activation energy of MgCr2O4 or MgO-chromite ceramics was available, the value was estimated based on the activation energy values reported for 144  sintering of MgO, MgAl2O4 and MgCr2O4102,103. In this regard, a few Q values ranging from 250 kJ/mol to 650 kJ/mol were used in a primary estimation. As mentioned earlier, the heating profile does not affect the MSC, which only depends on the powder type, grain size and green density of compacts. Therefore, if the right activation energy is estimated, all sintering data should converge to a single curve.    Figure ?6-31. MSC of isothermally sintered MK composite      A polynomial curve (fitted to all data points and the sum of the residual squares of the points with respect to the fitted curve) was used to quantify the measure of the convergence. Figure ?6-32 shows the variation of the mean residual squares for the estimated activation energies. The minimum mean residual square occurs at about 444 kJ/mol, indicating that the apparent activation energy of sintering for the MK composite is 444 kJ/mol. Several studies have been performed on pressureless sintering of spinel79,81. Bratton77,81 investigated the initial and the 145  intermediate stages sintering of a MgAl2O4 powder, and showed that the rate controlling mechanism was the lattice diffusion of oxygen in the MgAl2O4 lattice.   Ting et.al.79 also determined the sintering mechanisms for magnesia and alumina rich spinels, and showed that the oxygen lattice diffusion was responsible for the densification of MgAl2O4 spinel. Several activation energies for the diffusion of oxygen in spinel have been reported. Reddy159 reported that the oxygen self-diffusion? coefficient? in? spinel? is? about? 440?kJ/mol, which is higher than the value reported for the self-diffusion of Al+3 (250 kJ/mol)168 and Mg+2 (360 kJ/mol)168 in spinel. Nassira et al.165 reported the activation energy of grain boundary diffusion of oxygen in MgAl2O4 spinel at ~265 kJ/mol, which was smaller than the activation energy of lattice diffusion. Comparing the measured activation energy for the MK composite to the values reported for MgAl2O4, it is hypothesized that the lattice diffusion of oxygen is the rate determining species during the sintering of MgCr2O4.         Figure ?6-32. The variation of mean residual squares for estimated activation energies; the minimum was obtained at ~444 kJ/mol    250 350 450 550 650Activation energy (kJ/mol)0.010.040.070.10.130.160.19Mean residual squaresActivation energy =  443.7 (kJ/mol)146     Figure ?6-33 and Figure ?6-34 show the MSC curve and the variation of the mean residual squares for the estimated activation energies for NMK composite. All curves converged when the activation energy of 302 kJ/mol was used for the data analysis. This value is considerably lower than the reported value for the MK composite, indicating that different mechanisms are responsible for its densification. It was already explained that reducing the particle size to the range of nano size increases the volume of grain boundaries in comparison to the micro size powder. As a result, the grain boundary would react as a short circuit for diffusion and results in the faster densification. As shown in Figure ?6-26, the onset sintering temperature of NMK composite was about 200?C lower than that of MK composite, which verifies the above explanation.  Figure ?6-33. MSC of isothermally sintered NMK composite   In addition, the activation energy obtained for the NMK composite (303 kJ/mol) was close to the value reported for the self-diffusion of cations in the spinel structure and also for the self-147  diffusion of cations in the parent oxide. The activation energy of diffusion of Mg and Cr in MgO and Cr2O3 is 261 and 255 kJ/mol11,17,88 respectively. Comparing the values to the activation energy of the NMK composite and considering the fact that oxygen diffusion in an oxide structure is lower than cations diffusion, it is expected that the oxygen diffusion is still the slowest species during the sintering of NMK composite.   Grain boundary is a sink for the lattice imperfections, which are short paths for diffusion; therefore, a lower activation energy for the densification of ions is expected at grain boundaries4,5. As a result, the lower activation energy for the sintering of the NMK composite in comparison to the MK composite is attributed to the oxygen diffusion through the grain boundaries of the NMK composite.   Figure ?6-34. The variation of mean residual squares for estimated activation energies; the minimum was obtained at ~303 kJ/mol     250 350 450 550Activation energy (kJ/mol)0.020.060.10.140.180.220.260.30.340.38Mean residual squaresActivation energy =  302.6 (kJ/mol)148  Chapter 7. Conclusions and future work  7.1 The influence of spinel forming oxides (Fe2O3 and Al2O3) on sintering of MgCr2O4  The kinetics of MgCr2O4 formation in the presence of Al and Fe was studied using the simultaneous thermal analysis (DSC/TGA) method. Based on the obtained results, the activation energy of spinel formation and the Avrami constant were calculated. It was shown that the addition of Al2O3 reduces the activation energy of MgCr2O4 spinel formation from 329?7 kJ/mol to 206?3 kJ/mol. In contrast, Fe2O3 was less effective in reducing the formation activation energy of MgCr2O4 spinel, lowering it to 298?11 kJ/mol. These activation energies correlate well with the results of previous studies.   Based on the comparison between the measured activation energies of spinel formation and the activation energies of the diffusion of cations in their parent oxides, it is concluded that the diffusion of Cr+3 is the rate controlling mechanism during spinel formation in all compositions. However, the early formation of MgAl2O4 retards the spinel formation and increases the quantity of the unreacted oxides at the calcination temperature (850?C). It is proposed that faster MgAl2O4 spinel formation could be attributed to the smaller cation radii of Al+3 (0.54 ?), in comparison to that of Fe+3 (0.67 ?) and Cr+3 (0.62 ?).   The sintering behavior of Mg[Cr1-xMex]2O4 (Me: Al, Fe, and Sn; 0?x?0.2) compositions was investigated by comparing the relative density for the different sintering temperatures of 1200?C to 1500?C, for 300 min soak. The results showed that Al2O3, Fe2O3, and SnO2 enhanced the densification of MgCr2O4. The increase in the density in presence of Al2O3 and Fe2O3 was attributed to the solid solution formation in the presence of the sintering additives. Due to the 149  size mismatch between the cations and also to their inherent location preference in a spinel structure, it is proposed that the solid solution formation of MgCr2O4 lattice might have been distorted, and consequently changed the diffusion coefficient of the cations in favor of densification.   Extensive XRD analyses were performed on the specimens that were quenched from the sintering temperatures. For the first time, the cation distribution in a spinel structure (expressed through the ?inversion?parameter?)?was calculated from the XRD data for the Mg[Cr1-xMex]2O4 system. The results showed that for Mg[Cr0.8Fe0.2]2O4 the inversion parameter increased from 0.16 at 750?C to 0.24 at 1475?C. For Mg[Cr0.8Al0.2]2O4 the inversion parameter was 0.11 and 0.17 at 750?C and 1475?C respectively. This indicates that in both cases the inversion increased with the sintering temperature.   The correlation between the inversion parameter and the densification results revealed that the increase in the inversion parameter enhanced the densification. The addition of Al2O3 and Fe2O3 increased the inversion parameter and densification rate; however, the inversion parameter of Mg[Cr0.8Al0.2]2O4 was less than that of Mg[Cr0.8Fe0.2]2O4. It is hypothesized that the high degree of inversion resulted in enhancement of the sintering driving force as a result of cation interchange between the octahedral and the tetrahedral sites.    To understand the contribution of solid solution formation and proposed inversion phenomenon on the densification behavior of MgCr2O4, the effects of SnO2 as a sintering additive were also studied. The SnO2 was selected for this purpose because it forms Mg2SnO4, which is a normal spinel in a wide temperature range. The results showed the addition of 0.2 mol% SnO2 increased the lattice parameter of MgCr2O4 from 8.3351?0.002 ? to 8.4015?0.002 ?, and increased the density of MgCr2O4 from 51% to 59% via the solid solution formation 150  mechanism. The comparison between the densification results of MgCr2O4 in the presence of SnO2 and Fe2O3 reveals that the inversion phenomenon could be responsible for the better performance of Fe2O3 in comparison to SnO2 in increasing the density, since on one hand for both compositions same green density were recorded, and on the other hand they both have unlimited solid solubility with MgCr2O4.  In order to quantify the effects of solid solution formation and of the inversion phenomenon on the densification of MgCr2O4, the effect of Fe2O3 and SnO2 on the densification of Cr2O3 was also studied, and the results were compared to the densification data obtained from sintering of MgCr2O4 in the presence of SnO2 and Fe2O3.  There is unlimited solid solubility in MgCr2O4-Mg2SnO4, MgCr2O4-MgFe2O4, and Cr2O3-Fe2O3 systems. In contrast, it was shown that the maximum solid solubility of SnO2 in Cr2O3 is ~0.5 mol% at 1475?C in air. Therefore, for the Cr2O3-vSnO2 compositions, an increase in SnO2 up to 0.5 mol% raised the final density from 51 to 59%.  However, the increase in SnO2 content beyond the solid solubility limit of SnO2 in Cr2O3 decreased the density. In contrast, for MgCr2O4-Mg2SnO4 compositions, the increase in SnO2 continuously increased the density up to 64%, since there is no solid solubility limit in the MgCr2O4-Mg2SnO4 system. This shows that the formation of the solid solution is responsible for the enhanced densification of MgCr2O4 and Cr2O3.  A comparison between the density of MgCr2O4-NAMgFe2O4 and Cr2O3-vFe2O3 compositions, quenched from 1475?C after 300 minutes sintering, showed that the addition of Fe2O3 increased the density of both MgCr2O4 and Cr2O3. However, the extent of densification for the MgCr2O4-NAMgFe2O4 compositions was higher than for Cr2O3-vFe2O3. For instance, 10 mol% Fe2O3 concentrations resulted in 68% density of MgCr2O4, and 56% density of Cr2O3. 151  This difference in the densification of MgCr2O4-NAMgFe2O4 and Cr2O3-vFe2O3 is attributed to the inversion phenomenon, which is responsible for the better densification.  7.2 The effects of spinel forming oxides on the sintering of magnesia- chromite composites  The effects of Cr2O3, Al2O3 and Fe2O3 on the densification of magnesia-chromite refractory composites (MgO-Mg[Cr1-xMex]2O4; Me: Al, Fe) were investigated. The densification behavior of twelve compositions (MK1-MK12) at different sintering temperatures was compared. Also, the effect of sintering additives on the dihedral angels was studied. The results showed that for the compositions with the high chromium content (Cr2O3 ? 6.9 mol%) the relative density would not increase above 80% even at 1600?C for 300 minutes. In contrast, the compositions with 2.7 mol% Fe2O3 and 4.9 mol% Al2O3 densify to 96% at 1475?C after 300 minutes. In addition, Fe2O3 was also shown to be more effective than Al2O3 in increasing the densification of the magnesia-chromite composites.   The dihedral angles of the composites with different concentrations of the sintering additives were measured and correlated to the densification results. It was shown that the increase in Cr2O3 content from 4.9 to 8.9 mol% increased the average dihedral angle from 80 to 128 degrees. The increase in Al2O3 (4.9-8.9 mol%) decreased the dihedral angle from 124 to 75 degrees. The increase in Fe2O3 content from 0.9 to 4.9 mol% also decreased the dihedral angle from 120 to 75 degrees. It is concluded that the enhanced densification at the higher concentration of Fe2O3 can be attributed to the smaller dihedral angle; however, there is an optimum composition at which the maximum density of 96% could be achieved at 1475?C. The optimum composite contained 6.9 mol% Al2O3, 6.9 mol% Cr2O3, 2.7 mol% Fe2O3 and MgO. The sintering behavior of this optimized composition [MgO-6.9Al2O3-2.7Fe2O3-6.9Cr2O3] (called 152  MK), was further investigated by sintering samples isothermally for different durations and temperatures. The results show the optimum sintering temperature of 1475?C for 70 minutes.   In order to study the effect of the particle size on the densification behavior of MK composites, the nano particles of the optimized magnesia-chromite refractory composite with the particle size of 20 nm was? synthesized? via? Pechini?s? method and called NMK. The NMK composite powders were further processed in the same way as the MK composites. The results showed that the decreasing of the particle size of magnesia chromite composites from 1.2 ?m to 20 nm reduced the onset sintering temperature by about 200?C. The onset sintering temperature for the MK composite was ~1200?C and for the NMK composite was ~1000?C. When sintered at 1475?C for 300 minutes, the density for NMK was ~99%, while for MK it was 95%. For NMK the 95% density was achieved at ~1300?C, while the same density was achieved for MK at 1475?C. In addition, the minimum time that was required to reach to 95% density at 1475?C for MK and NMK was ~70 and ~20 minutes respectively. This indicated that the densification rate of NMK is higher than of MK. In other words, reducing the particle size of the optimized magnesia-chromite composite to the range of 20 nm increased the densification rate ~3.5 times. The drawback of using nano particles was however the extensive grain growth. During the sintering at 1600?C the average grain size of NMK composites increased dramatically from ~40 nm to ~8000 nm, while for the same sintering condition, the grain size of the MK composite increased from 1.2 ?m to 7 ?m.   For the first time, the sintering kinetics parameters were measured in this work for magnesia-chromite composites, based on the master sintering curve theory. The results showed that the activation energy of sintering of the composites with micron-size grains was 443.7 kJ/mol, whereas the activation energy of the nano-sized composite is reported to be 302.6 153  kJ/mol. A comparison between these data and the activation energy of diffusion of ions in spinel revealed that in both cases the diffusion of oxygen was the rate controlling mechanism of sintering for the MK and NMK composites. However, the lower activation energy of nano-sized composite was attributed to the diffusion of oxygen through grain boundaries, in contrast to the higher activation energy in micron sized composite, which was attributed to the lattice diffusion of oxygen.   In this study we showed that the solid solution formation could enhance the densification of MgCr2O4.  It was found that the effect of sintering additives on the densification is controlled by the solid solubility of the additives in the host spinel structure, by the rate of solid solution formation and how it affects the cation distribution, and by the unit cell dimensions of the host structure. We introduced a hypothesis based on which the inversion phenomenon contributes to the densification of magnesia-chromite spinel.   Further work should be done in addition to these observations to develop a quantitative relationship between the inversion parameter and the densification. Such analysis for other spinel structures could develop a model which might facilitate better selection of sintering additives for spinel structures. This could be important for sintering of electronic ceramics with spinel structure, where the concentration and type of additives change their performance significantly. It is recommended to use normal spinels with low sintering temperature (T<1100?C) as host structures, because high sintering temperatures may induce inversion in the host structure.    In order to calculate the inversion parameter several assumptions were made to simplify the calculation of the XRD intensity. In addition, the procedure that was introduced by Porta3 and used by us was based on assumptions which might affect the results. According to this method, the intensity was measured for each peak separately. To solve the intensity equations, the 154  estimated value for the inversion parameter was changed with 0.01 intervals, which is not very accurate for inversion parameter measurements. In fact, in the previous studies the inversion parameter was reported with three significant figures.  Had we been able to perform the Rietveld analysis, the desired accuracy might have been achieved, since with this technique, all the peaks would be analyzed in the same time. Therefore, it is recommend that the cation distribution in the spinel structures is calculated based on more accurate analysis techniques such as the Rietveld analysis.  We have successfully applied the master sintering curve theory to analyze the densification results of magnesia-chromite refractories with the optimum composition (MK) and to calculate the sintering activation energy. We have determined that the dominant sintering mechanism in the MK composite was the diffusion of oxygen through either lattice or grain boundary.  However, the isothermal sintering data may introduce an additional source of error in the calculation of the sintering activation energy. Therefore, it is recommended that the results of these experiments are verified with dilatometric studies by recording the dimensions of one specimen over the course of sintering. This would reduce the errors introduced in the isothermal studies due to the variation of the initial conditions for each specimen.   The master sintering curve theory assumes that the initial conditions of specimens i.e. green density, porosity, particle size, particle shape and chemical composition, are similar. In our isothermal studies, the chemical compositions of the particles, the particle size and particle shape were similar for all specimens, as they were prepared from one batch of synthesized composite. However, the green density of specimens varied in the 0.5-1.0 % range, which might induce some error in the activation energy calculations. 155   In this regard, the application of dilatometry to calculate the activation energies of the studied compositions is recommended.      In this study we showed that it is possible to sinter a magnesium-chromite refractory composite to nearly full density (~98%) in air at temperatures as low as 1475?C, which is about 300?C below the current sintering temperatures. The key component in reducing the sintering temperature was the addition of Fe2O3, as it formed an inverse solid solution with MgCr2O4. In addition, we found that reducing the particle size of the magnesia-chromite composite with the optimum composition to ~20 nm reduced the sintering temperature to 1350?C, which is 425?C below the sintering temperature that is currently used for these composites. Based on these results it is recommended that the performance of a mag-chrome brick with MK composite as the binding system is investigated in-field, and compared with the performance of industrially available mag-chrome bricks. In another study, which is not reported here, we sintered a mag-chrome brick, with the MK binding system, at 1475?C for 5 hours.   We showed that the physical properties of our brick, including strength, density and porosity, were comparable to the industrially available refractories. For this reasons, a similar in-field performance is expected for our brick. Since our brick is sintered at 1475?C and the industrially available brick is sintered at 1700?C, the comparable performance of the two bricks opens the opportunities to prepare mag-chrome bricks with lower sintering temperatures.     156  References 1. MN. Rahaman, Ceramic Processing and Sintering, Marcel Dekker, United state of America, 1995.   2. M. A. Alper, High temperature oxides. 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