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Degradation of silicon nitride glow plugs in electric field-experiments and modeling Karimi Sharif, Hamed 2011

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    DEGRADATION OF SILICON NITRIDE GLOW PLUGS IN ELECTRIC FIELD - EXPERIMENTS AND MODELING  by  Hamed Karimi Sharif  B.Sc., Iran University of Science and Technology, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate Studies (Materials Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   July 2011 © Hamed Karimi Sharif, 2011   ii Abstract Silicon nitride (Si3N4) based ceramic Glow Plugs (GP) are considered by the automotive industry as a reliable, long-term source of ignition for natural gas and hydrogen internal combustion engines. The commercial GPs investigated in this work comprised of an all-ceramic heater with two U-shaped tungsten carbide heating elements encased in an Yb2O3-doped silicon-nitride (Si3N4) insulating phase. Upon applying electric potentials of 10-14V, the temperature on the surface of ceramic heater rapidly raises to as high as 1500oC. This work looks into various modes of deterioration of GPs, particularly resulting from interaction of high operating temperature and the electric field within the GP heaters. An extensive scanning electron microscopy and energy dispersive x-ray spectroscopy investigation was performed to determine the degradation mechanisms of GPs in natural gas-burning rig, electric rig and engine. GP testing has shown that under the influence of constant electric load (DC) the sintering aid (Yb2O3) cations continuously migrate away from the high potential side of the heating elements following the electric field pattern. A 2D mathematical model was developed to simulate the redistribution of the sintering additive (Yb2O3) cations as a function of time, temperature, and electric field.  The damage pattern of the tested GPs suggests synergistic impact of temperature, voltage, and environment on GPs lifetime. For the GPs tested in the burner rig and in engine the internal joule heating, externally applied combustion heat, together with the corrosive nature of the combustion gases, synergistically contribute to the degradation of Si3N4-based heaters. The comparison of cross sections for aged GPs revealed an increase in Yb ions migration with increasing temperature, electric field, and test duration. This study confirms that the removal of just one of the failure stimuli may significantly improve the GP performance. For example, applying AC voltage provided a significant improvement of GP durability in electric rig, even without addressing any other damage phenomena.   iii Preface This research program was a collaborative R&D between Westport Innovations Inc. of Vancouver and the University of British Columbia. Westport has provided facilities such as the electric rig, natural gas-burning rig, and natural gas engine. The ceramic group (UBCeram) in the Materials Engineering Department of the University of British Columbia has focused on determining the degradation/failure mechanisms by analyzing the structural changes and on modeling. Given the long-term nature of this research project and the volume of work carried out over the past few years, many people have contributed to the project at various stages including Hamed Karimi Sharif, Carmen Oprea, Professor Tom Troczynski, Frankie Wong, Colin Blair, and Alan Welch.  GPs characterization: I was responsible for running the electric and burner rigs, data collection, sample preparation, and conducting SEM/EDX and XRD analysis.   A version of Chapter 5 has been submitted for publication: ― C. Oprea, F. Wong, Hamed Karimi Sharif, C. Blair, A. Welch and T. Troczynski, Degradation of Silicon Nitride Glow Plugs in Various Environments, Part 3: Engine, (2011). The manuscript was originally drafted by C. Oprea with input from all co-authors, and extensive modifications performed by me. Versions of Chapter 5 have been published in the following publications: ― C. Oprea, F. Wong, Hamed Karimi Sharif, C. Blair, A. Welch and T. Troczynski, Degradation of Silicon Nitride Glow Plugs in Various Environments, Part 2: Gas Burner Rig, International Journal of Applied Ceramic Technology (2011). The manuscript was originally drafted by C. Oprea with input from all co-authors, and extensive modifications performed by me.  iv ― C. Oprea, F. Wong, Hamed Karimi Sharif, C. Blair, A. Welch and T. Troczynski, Degradation of Silicon Nitride Glow Plugs in Various Environments, Part 1: DC Electric Field in Ambient Air, International Journal of Applied Ceramic Technology (2011). The manuscript was originally drafted by C. Oprea with input from all co-authors, and extensive modifications performed by me. The high-temperature XRD analysis presented in Chapter 5 was performed solely by me. The pyrometer analysis in Chapter 5 of the thesis was performed in collaboration with Colin Blair at Westport Innovation Inc.  Modeling: The modeling part of this project was conducted solely by me. Versions of Chapter 6 have been submitted for publications: ― Hamed Karimi Sharif, T. Troczynski, C. Oprea, C. Blair, A. Welch, Degradation of Si3N4 Glow Plugs in Air – Experiments and Modeling, (2011). The manuscript was originally drafted by me with subsequent editorial assistance from Professor Tom Troczynski.  ― Hamed Karimi Sharif, T. Troczynski, C. Oprea, C. Blair, A. Welch, Model for the DC Electric Field-Enhanced Degradation of Si3N4 – Based Ceramic Glow Plugs, (2011). The manuscript was originally drafted by me with subsequent editorial assistance from Professor Tom Troczynski. ― Hamed Karimi Sharif, T. Troczynski, C. Oprea, C. Blair, A. Welch, Model for the AC Electric Field-Enhanced Degradation of Si3N4 – Based Ceramic Glow Plugs, (2011). The manuscript was originally drafted by me with subsequent editorial assistance from Professor Tom Troczynski.   v Table of Contents Abstract ........................................................................................................................................... ii Preface............................................................................................................................................ iii Table of Contents............................................................................................................................ v List of Tables .................................................................................................................................. x List of Figures ............................................................................................................................... xii List of Symbols ........................................................................................................................... xxii Nomenclature............................................................................................................................. xxiii Acknowledgments...................................................................................................................... xxiv Dedication ................................................................................................................................... xxv 1 Introduction......................................................................................................................... 1 2 Literature Review................................................................................................................ 6 2.1 Ceramic glow plug (GP) technology ...................................................................... 6 2.1.1 The insulating ceramic........................................................................................ 7 2.1.2 Crystallization of grain boundary glass .............................................................. 7 2.1.3 Intergranular glassy phase................................................................................... 9 2.2 Oxidation of Si3N4 ................................................................................................ 10 2.2.1 Effects of corrosive combustion gases.............................................................. 15  vi 2.2.2 Effect of impurities in the combustion gases.................................................... 19 2.3 Electrical properties of silicon nitride ceramics.................................................... 20 2.3.1 Silicon nitride dielectrics .................................................................................. 20 2.3.2 Dielectric breakdown ........................................................................................ 21 2.3.3 Electrical conductivity ...................................................................................... 23 2.3.3.1 Effect of intergranular glassy phase on electrical conduction ............... 25 2.4 Nernst–Planck equation for ionic transport .......................................................... 28 3 Scope and Objectives........................................................................................................ 30 4 Experimental Procedures .................................................................................................. 34 4.1 Testing apparatus and materials............................................................................ 34 4.1.1 Engine testing of GPs........................................................................................ 34 4.1.2 Burner rig .......................................................................................................... 35 4.1.3 Electric rig characterization bench.................................................................... 36 4.1.3.1 DC mode ................................................................................................ 38 4.1.3.2 AC mode ................................................................................................ 38 4.2 Optical pyrometry measurements ......................................................................... 38 4.3 GP analysis methods and equipment .................................................................... 39 4.3.1 Scanning electron microscopy (SEM) .............................................................. 39 4.3.1.1 SEM sample preparation........................................................................ 40 4.3.2 High-temperature X-ray diffractometry............................................................ 41  vii 5 Experimental Results and Discussion............................................................................... 42 5.1 As-received GP ..................................................................................................... 42 5.1.1 High-temperature X-ray diffraction.................................................................. 42 5.2 GP characterization tests....................................................................................... 43 5.3 Degradation of silicon nitride GPs in engine........................................................ 52 5.3.1 Test conditions and sample description ............................................................ 52 5.3.2 SEM observations and EDX analysis ............................................................... 52 5.3.3 Summary........................................................................................................... 58 5.4 Degradation of silicon nitride GPs in gas burner rig ............................................ 61 5.4.1 Test conditions and sample description ............................................................ 61 5.4.2 SEM observations and EDX analysis ............................................................... 61 5.4.3 Summary........................................................................................................... 72 5.5 Degradation of silicon nitride GPs in DC electric field in air............................... 74 5.5.1 Test conditions and sample description ............................................................ 74 5.5.2 Characterization of GPs aged in electric rig ..................................................... 75 5.5.3 Summary........................................................................................................... 93 5.6 Degradation of Si3N4 GPs in AC electric field ..................................................... 95 5.6.1 Test conditions and sample description ............................................................ 95 5.6.2 SEM observations and EDX analysis ............................................................... 96 5.6.3 Summary......................................................................................................... 104 6 Degradation of GPs in Electric Rig—Modeling............................................................. 105  viii 6.1 Summary of GPs degradation observations........................................................ 105 6.2 A model for the electric field inside the Si3N4 heater......................................... 108 6.2.1 Electric potential along the WC-based heating element ................................ 108 6.2.2 Electric field distribution within the cross section of the Si3N4-based heater 110 6.2.3 Summary......................................................................................................... 116 6.3 Model for the electro-degradation of Si3N4–based GPs ..................................... 117 6.3.1 Heat transfer―3D  model............................................................................... 117 6.3.2 2D mass transfer model .................................................................................. 123 6.3.3 Summary......................................................................................................... 130 6.4 Degradation of Si3N4 GPs in AC electric field –modeling ................................. 132 6.4.1 2D mathematical model of Yb ions migration due to AC field...................... 132 6.4.2 Summary......................................................................................................... 136 7 Conclusions..................................................................................................................... 139 8 Future Work .................................................................................................................... 147 8.1 Further GP analysis............................................................................................. 147 8.2 Correlations between testing parameters and failure modes of GPs (Modeling) 147 8.3 Alternative sintering additives ............................................................................ 149 8.4 Surface modifications of Si3N4 ........................................................................... 149 8.5 Lower temperature operation.............................................................................. 150 References................................................................................................................................... 151  ixAppendices.................................................................................................................................. 170 A Thermodynamic Data.......................................................................................... 170 B XRD Spectrum of Ceramic Heater ..................................................................... 171 C Experimental Error in Analyzing the Elemental Yb Content ............................. 179 D Electrostatics Model............................................................................................ 180 D.1 Longitudinal cross-section of U-shaped conductor .................................. 180 D.2 Electric field distribution within the cross-section at the hot spot............ 185 E Heat Transfer Model ........................................................................................... 193 E.1 Assumptions .............................................................................................. 193 E.2 Boundary conditions.................................................................................. 194 E.3 Conductive Media DC............................................................................... 195 E.4 Mesh .......................................................................................................... 197 E.5 Heat transfer by conduction (ht) and conductive media DC ..................... 198 F Yb Ions Migration under DC Electric Field ....................................................... 200 F.1 Assumptions .............................................................................................. 200 F.2 Application mode: Nernst-Planck without Electroneutrality, Heat Transfer by Conduction, and Elctrostatics ........................................................................ 203 G Yb Ion Migration under an AC Electric Field .................................................... 205 G.1 Assumptions.............................................................................................. 205 G.2 Boundary conditions ................................................................................. 206  xList of Tables Table 4.1 : Specifications of three pyrometers used in this study. ............................................... 39 Table 5.1: GP testing parameters on the characterization bench (electric rig). ............................ 44 Table 5.2: GP testing parameters and summary of results in ETC (1635 rpm, 165 Nm)............. 52 Table 5.3: GP testing parameters and summary of results in steady state SS (2000 rpm, 450 Nm)........................................................................................................................................................ 53 Table 5.4: GP testing parameters on the burner rig. ..................................................................... 61 Table 5.5: Summary of analysis results of the GP heaters tested in Burner Rig. ......................... 64 Table 5.6: GP testing parameters on the DC electric rig. ............................................................. 74 Table 5.7: Summary of analysis results of the GP heaters (DC electric rig). ............................... 78 Table 5.8 : GP testing parameters on the AC electric rig. ............................................................ 96 Table  6.1: Pysical properties of Si3N4 and WC ceramics [28, 34]. ............................................ 119  Table  A.1: The standard Gibbs free energy of formation........................................................... 170 Table  A.2: The Gibbs free energy of formation. ........................................................................ 170 Table  A.3: The Gibbs free energy of formation. ........................................................................ 170 Table  D.1 : Mesh statistics.......................................................................................................... 180 Table  D.2: The parameters used in Conductive Media DC model. ............................................ 181 Table  D.3: 2D model settings. .................................................................................................... 183  xiTable  D.4: 2D model variables. .................................................................................................. 183 Table  D.5: 2D model solver settings........................................................................................... 184 Table  D.6: Parameters used in Electrostatics model................................................................... 189 Table  D.7: Grams in 1 mole of Yb2O3-doped Si3N4-based insulator based on the EDX measurement. .............................................................................................................................. 190 Table  D.8: Mesh statistics for the Electrostatics model.............................................................. 191 Table  D.9: Application mode properties and settings................................................................. 191 Table  D.10: Variables in the Electrostatics model...................................................................... 191 Table  D.11: Solver settings in the Electrostatics model. ............................................................ 192 Table  D.12: Parameters used in the Electrostatics model........................................................... 192 Table  E.1: Physical and thermal properties of Si3N4 and WC ceramics [ 29]. ............................ 195 Table  E.2: Mesh statistics in the Conductive Media DC model. ................................................ 197 Table  E.3: Application mode properties in the Conductive Media DC model. .......................... 198 Table  E.4: Variables in the Conductive Media DC model. ........................................................ 198 Table  E.5: Solver in the Conductive Media DC model. ............................................................. 198 Table  E.6: Property setting in the Conductive Media DC model. .............................................. 198 Table  E.7: Time stepping in the Conductive Media DC model.................................................. 199 Table  F.1: Parameters used in Nernst-Planck without Electroneutrality model. ........................ 204  xiiList of Figures Figure  2.1: Si3N4-based GP, a) photography of a glowing plug b) GP assembly showing two thin U-shaped heating elements; c) the cross-section of ceramic heater and microstructure schematic-not to scale; the two U-shaped heating elements appear as four white lines. ................................. 6 Figure  2.2: Phase relationship in the system Si3N4-SiO2-Yb2O3 at 1750 °C [53]. ......................... 8 Figure  2.3: Phase diagram of the binary system Yb2O3-SiO2 [56]. ................................................ 9 Figure  2.4: Schematic of pure silicon nitride oxidation in air [71]............................................... 11 Figure  2.5: Active to passive transition of Si3N4 as a function of temperature and oxygen partial pressure [34].................................................................................................................................. 12 Figure  2.6: Temperature dependence of the oxidation rate constants (Kp =parabolic constant) in Y2O3-doped Si3N4 [84]. ................................................................................................................ 15 Figure  2.7:  Temperature dependence of viscosity of 28Ln:56Si:16Al:82O:18N glasses (Ln: Eu, Ce, Sm, Dy, Ho, and Er;) [ 69]. ..................................................................................................... 26 Figure  2.8: Effects of RE cation field strength and nitrogen on viscosity of RE-Si-Al-O-N glasses [ 69]................................................................................................................................................ 27 Figure  2.9: Glass transition temperature, Tg, and softening temperature, Td, for Yb-Si-O-N glassy systems: (a) (Si3N4)x ((Yb2O3)0.3 (SiO2)0.7)100-x; (b) (Si3N4)8 (Yb2O3)92-y (SiO2)y)  [136]............. 28 Figure  4.1: Natural gas-burning rig. ............................................................................................. 36 Figure  4.2: Electric rig configuration, a) control panel; b) electric rig......................................... 37 Figure  5.1: Micrographs of cross-section through the ceramic pin of an unused GP: a-low magnification; b-insulator; c-WC heating element and surrounding insulator; d-WC heating element at high magnification....................................................................................................... 43  xiii Figure  5.2: XRD patterns of ceramic heater at different temperatures; SN: Si3N4, YS: Yb2Si2O7, C: cristobalite, S: SiO2, W: tungsten, Pt: platinum, WO: WO3, MS: MoSi2. ............................... 45 Figure  5.3: Warm-up profiles for different GPs loaded at 9.0V at 0.0h, in ambient air............... 46 Figure  5.4: Warm-up profiles for GP specimen “C1” at various voltages (8.0, 8.5, 9.0, 9.5, 10.0V) in ambient air. ................................................................................................................... 48 Figure  5.5: Steady-state temperature for GP specimen “C1” loaded at 9.0V measured by pyrometer in ambient air at different orientations (0o, 90o, 180o, 270o). ...................................... 48 Figure  5.6: Steady-state temperature distribution for new and engine-aged GPs; the temperature measurements were performed by optical pyrometer in ambient air............................................ 49 Figure  5.7: Change in GPs’ resistance (Ω) with temperature (oC). .............................................. 50 Figure  5.8: Variation in temperature-voltage profile of Si3N4-based GP in three warm-up cycles........................................................................................................................................................ 51 Figure  5.9: Micrographs of specimens ETC2 and ETC4; the (+) side is on the right. ................. 54 Figure  5.10:   Micrographs of specimens ETC2 and ETC4: Yb ions migration away from the side of the WC elements connected to the (+) pole. ............................................................................ 55 Figure  5.11: Variation of the mass loss with temperature. ........................................................... 56 Figure  5.12: Micrographs of samples tested at 1450°C in Steady State (SS): SS1 still working after 4.8 h; SS2 failed after 50.1 h. ............................................................................................... 56 Figure  5.13: Micrographs of the center and ends of the (+) side WC heating elements and surrounding Si3N4 of sampled tested at 1450°C in SS.................................................................. 57 Figure  5.14: Micrographs of samples failed in SS: SS5, after 4.8 h at 1500°C and SS8, after 8.9h........................................................................................................................................................ 57  xivFigure  5.15: Effect of the different voltages needed to reach the same temperature (1520-1525°C) in SS (top) versus ETC (bottom).................................................................................... 60 Figure  5.16: Photographs of the seven GPs tested on the burner rig. ........................................... 62 Figure  5.17: Micrographs of selected areas on the surface of failed GPs: top row - BR2 at 1425°C; middle row – BR5 at 1450°C; bottom row – BR7 at 1500°C; images at 1 mm back from the tip of the pin - left; at 5 mm - middle; at 7 mm – right; the white bar represents 20 µm for all images. .......................................................................................................................................... 63 Figure  5.18: Micrographs of cross-sections at 5mm back from the tip; BR0 is an as-received specimen; the white bars represent 2mm and the (+) side is on the right for all images. ............. 65 Figure  5.19: Micrographs of the WC heating element’s ends and the surrounding insulator at 5 mm, for the GPs tested for 10 h (BR1 at 1425 and BR6 at 1500°C); (0) denotes the grounded side of the WC filaments and (+) the side connected to the positive electrode; the bar is 50 µm for all images................................................................................................................................. 68 Figure  5.20 : Micrographs of the WC heating elements’ ends and the surrounding insulator at 5mm, for GPs tested to failure (BR2 at 1425 and BR7 at 1500°C); (0) denotes the grounded side of the WC filaments and (+) the side connected to the positive pole; the white bar is 50 µm for all images. ..................................................................................................................................... 69 Figure  5.21: Micrographs of the outer oxide scale on BR5: left - on the grounded side; right - on the positive side............................................................................................................................. 70 Figure  5.22: Variation of Yb concentration through the Si3N4 in cross-sections at 5mm back from tip: left - tested for 10 h at different temperatures; right - for different durations at 1450°C on the burner rig....................................................................................................................................... 71 Figure  5.23: Mass variation at the three testing temperatures, after 10 h and at failure............... 72 Figure  5.24: Yb2Si2O7 deposit on the surface of specimen DC1 compared to the heater surface of an unused GP (bottom). ................................................................................................................ 76  xvFigure  5.25: Yb2Si2O7deposit on the surface of specimen DC3: a - at the tip; b - at 3mm; c, d - at the hot spot (5mm); bar represents 10 µm for all images. ............................................................ 77 Figure  5.26: Elemental Yb variation (EDX results) on the surface of the ceramic pins for specimens DC1 and DC3 at two temperatures, compared to an unused specimen. ..................... 77 Figure  5.27: Micrograph of the cross-section through the ceramic pin of sample “DC1”, 5mm from tip (Yb wt% in Si3N4 by EDX is given). .............................................................................. 79 Figure  5.28: Marked areas 1-5 in the section through “DC1” (Figure 5.27), at different magnifications; area 2a – WC terminal in area 2 at higher magnification. .................................. 80 Figure  5.29: Micrographs of the cross-section at 5 mm through the ceramic pins of specimens tested at 1450°C: “DC2”-10 h, left; “DC3”-failed at 3366 h, right .............................................. 81 Figure  5.30: Micrographs of center and ends of the WC terminals at 5mm for specimens tested at 1450°C (“DC2”-10 h, “DC3”-failed at 3366 h): a-grounded side of “DC2”; b- grounded side of “DC3”; c-(+) side of “DC2”; d-(+) side of “DC3”. ...................................................................... 84 Figure  5.31: Micrographs of the marked areas 1-4 on section through specimen DC3 (Figure 5.29) at higher magnifications. ..................................................................................................... 85 Figure  5.32: Micrographs of the cross-sections at 5 mm through the ceramic pins of specimens tested at 1500°C: “DC4”-10 h, left; “DC5”-98 h, center; “DC6”-failed at 238.5 h, right............ 85 Figure  5.33: Specimen “DC4”- details of marked areas 1-6 in Figure 5.32 at higher magnifications; areas 2a, 3a and 5a are details in areas 2, 3 and 5, respectively.......................... 86 Figure  5.34: Specimen “DC5”- details of marked areas 7-11 in Figure 5.32 at higher magnifications; YS : Yb2Si2O7. .................................................................................................... 86 Figure  5.35: Specimen “DC5”- details of marked area 7 in Figure 5.34 at higher magnifications........................................................................................................................................................ 87  xviFigure  5.36: Specimen “DC6”- details of marked areas 12-17 in Figure 5.32 at higher magnifications............................................................................................................................... 87 Figure  5.37: Specimen “DC8”, in working condition after 10 h at 1560°C: micrographs of the cross-section at 5mm..................................................................................................................... 89 Figure  5.38: Micrographs of the cross-sections at 5mm for specimens DC7, DC9 and 5.5mm for specimen DC10; marked areas 1 and 2 at higher magnifications. ................................................ 90 Figure  5.39: Variation of Yb concentration through the Si3N4 in cross-sections at 5 mm: tested for 10 hours at different temperatures (left) and for different times at 1500°C (right) ................ 91 Figure  5.40: Divergence between maximum and minimum Yb values calculated over the life in service (∆Yb) versus temperature when testing for 10 hours (left) and to failure (right) ............ 92 Figure  5.41 : The relationship between temperature and applied potential; the temperature was measured by a pyrometer at the hot spot on the surface of as-received GPs (i.e. at 0.0h service)........................................................................................................................................................ 97 Figure  5.42: Photos of the ceramic pins detached from GPs after the testing in AC electric rig (ambient air).................................................................................................................................. 97 Figure  5.43: Micrographs of the cross-section at 5 mm through the ceramic pin of specimen “AC1” tested at 1455°C in AC-electric field; running at 3366h; variation of Yb ions concentration is indicated in wt%. .............................................................................................. 100 Figure  5.44: Micrographs of the marked areas (1–4) on section through specimen AC1 (Figure 5.43); Yb2Si2O7 (YS) deposit on the surface at higher magnifications. ..................................... 101 Figure  5.45: Micrographs of center and ends of the WC terminal at 5mm for specimen AC1 tested at 1455°C in AC-electric rig; Marked areas 6-10 in the vicinity of WC heating terminal at higher magnifications.................................................................................................................. 102  xviiFigure  5.46: Micrographs of the cross-sections at 5 mm for specimens AC2, AC3, AC4, AC5, AC6. ............................................................................................................................................ 103 Figure  6.1: Micrograph of the section at 5mm through the GP DC4 - Yb ions depletion region is marked by the arrow. .................................................................................................................. 106 Figure  6.2: Micrograph of the cross-section at 5mm of GP DC10, showing extended Yb ions depletion field around the positive electrode of the heating elements........................................ 107 Figure  6.3: Schematics of the GP ceramic pin: a— passing of constant electric current in the heating elements results in joule-heating; b— axial and radial components of the electric field for constant electric current. ............................................................................................................. 108 Figure  6.4: The computed electric potential along the length of WC heating filaments for specimens “DC4” and “DC10”: a) specimen “DC4”; b) specimen “DC10”.............................. 110 Figure  6.5: Cross-section of ceramic GP pin with U-shaped element’s configuration: a—boundary conditions; b—Computed electric potential (V) through the cross-section of the GP (the arrows show the electric field vectors). ............................................................................... 112 Figure  6.6: SEM micrographs of Figure 6.1 and Figure 6.2 overlaid by the computed electric field (arrows) and electric potential (contours) for charge-free medium: a) specimen “DC4”; b) specimen “DC10”. ...................................................................................................................... 114 Figure  6.7: SEM micrographs of Figure 6.1 and Figure 6.2 overlaid by the computed electric field (arrows) and electric potential (contours) of charge-induced medium: a) specimen “DC4”; b) specimen “DC10”. .................................................................................................................. 115 Figure  6.8: Yb content (wt %) measured by EDX vs. computed electric field (PB) along the dashed line between high-potential WC terminal and centerline; initial Yb: 8.7 ± 0.4wt %. .... 115 Figure  6.9: GP geometry and computing domain: a- the image of glowing plug; b- Si3N4-based heater’s geometry; c- the computed temperature distribution on the surface of GP (the colormap shows the temperature in degree Celsius)................................................................................... 120  xviii Figure  6.10: The warm-up profile at the hot spot for the GP loaded at 9.0V: model vs. experiment................................................................................................................................... 121 Figure  6.11: The steady-state temperature distribution along the length of Si3N4-based rod of as-received (“0.0h”) GP loaded at 9.0V: model vs. experimental (measured by optical pyrometer)...................................................................................................................................................... 121 Figure  6.12: The computed steady-state temperature distributions within the cross-section of Si3N4-based heater of GP at hot spot. ......................................................................................... 123 Figure  6.13: The Yb ion redistribution under the influence of electric field and concentration gradient for the GP loaded at 12.1V (specimen DC4) for 10.0h, computed by 2D model for GP’s cross-section at the hot spot; gray map: concentration of Yb ions (%wt); arrows: electric field; contours: temperature.................................................................................................................. 126 Figure  6.14: The Yb ion redistribution under the influence of electric field and concentration gradient for the GP loaded at 14.0V (specimen DC10) for 2.7h, computed by 2D model of GP’s cross-section at hot spot; gray-map: concentration of Yb ions (%wt); arrows: electric field; contours: temperature.................................................................................................................. 127 Figure  6.15: SEM micrographs overlaid by the computed Yb ion concentration profile within the cross-section of Si3N4-based heater at the hot spot: a- GP aged at 12.0V (specimen DC4) in ambient air for 10.0h; b- GP aged at 14.0V (Specimen DC10) in ambient air for 2.7h; arrows: electric field; contours: temperature. .......................................................................................... 129 Figure  6.16: Yb ions content (wt %) measured by EDX  vs. computed Yb content (wt%) along the dashed line between the high-potential WC terminal and centerline; initial Yb for as received GP: 8.7 ± 0.4wt %....................................................................................................................... 130 Figure  6.17: Yb ion redistribution under the influence of AC-electric field and concentration gradient for the GP loaded at 13.0V (specimen AC1) for 3366h, computed by 2D model of the GP’s cross-section at the hot spot; gray-map: concentration of Yb ions (%wt) ; contours: temperature; arrows: electric field. ............................................................................................. 134  xixFigure  6.18: SEM micrographs overlaid by the computed Yb ion concentration profile within the cross-section of specimen AC1 in ambient air for 3366h; arrows: electric field vectors; contours: temperature. ................................................................................................................................ 135 Figure  6.19: SEM micrographs overlaid by the computed Yb ion concentration profile within the cross-section of  specimen AC2 in ambient air for 2881.5h....................................................... 137 Figure  6.20: Yb ion content (wt %) measured by EDX  vs. computed Yb content (wt%) along the dashed line between the high-potential WC terminal and low-potential WC terminal; initial Yb content for as received GP: 8.7 ± 0.4 wt %. ............................................................................... 138  Figure  B.1: XRD spectrum of ceramic heater after 2h at 20oC. ................................................. 171 Figure  B.2: XRD spectrum of ceramic heater after 2h at 200oC. ............................................... 172 Figure  B.3: XRD spectrum of ceramic heater after 2h at 400oC. ............................................... 172 Figure  B.4: XRD spectrum of ceramic heater after 2h at 600oC. ............................................... 173 Figure  B.5: XRD spectrum of ceramic heater after 2h at 700oC. ............................................... 173 Figure  B.6: XRD spectrum of ceramic heater after 2h at 800oC. ............................................... 174 Figure  B.7: XRD spectrum of ceramic heater after 2h at 900oC. ............................................... 174 Figure  B.8: XRD spectrum of ceramic heater after 2h at 1000oC. ............................................. 175 Figure  B.9: XRD spectrum of ceramic heater after 2h at 1100oC. ............................................. 175 Figure  B.10: XRD spectrum of ceramic heater after 2h at 1200oC. ........................................... 176 Figure  B.11: XRD spectrum of ceramic heater after 2h at 1300oC. ........................................... 176 Figure  B.12: XRD spectrum of ceramic heater after 2h at 1400oC. ........................................... 177  xxFigure  B.13: XRD spectrum of ceramic heater after 2h at 1500oC. ........................................... 177 Figure  B.14 : XRD spectrum of ceramic heater at1500oC at different times; SN: Si3N4, YS: Yb2Si2O7, C: cristobalite, Pt: platinum. ...................................................................................... 178 Figure  D.1: Geometry of U-shaped conductors and finite element mesh pattern. ..................... 181 Figure  D.2: Model navigator in COMSOL Multiphysics 3.3a. .................................................. 182 Figure  D.3: Subdomain settings-Conductive Media DC in COMSOL Multiphysics 3.3a......... 182 Figure  D.4: Boundary conditions imposed on the boundaries of U-shaped conductors (2D). ... 183 Figure  D.5: Computed electrical potentials at 5mm back from the front ends........................... 184 Figure  D.6: Boundary conditions imposed on the boundaries of the cross-section at the hot spot...................................................................................................................................................... 186 Figure  D.7: Subdomain settings-Electrostatics model in COMSOL Multiphysics 3.3a. ........... 187 Figure  E.1: Boundary conditions in heat transfer by conduction model. ................................... 194 Figure  E.2: Boundary condition at the outer surface of the ceramic heater in Conductive Media DC model. ................................................................................................................................... 195 Figure  E.3: Boundary condition at the surface of the U-shaped conductors in Conductive Media DC model. ................................................................................................................................... 195 Figure  E.4: Boundary condition at the grounded ends of the U-shaped conducting phase in Conductive Media DC model. .................................................................................................... 196 Figure  E.5: Boundary condition at the high potential ends of the U-shaped conducting phase in Conductive Media DC model. .................................................................................................... 196 Figure  E.6: Finite element mesh pattern in the Conductive Media DC model........................... 197  xxiFigure  E.7: Coupled Conductive Media DC-Heat Transfer by Conduction equations in Joule Heating model. ............................................................................................................................ 199 Figure  F.1: Boundary conditions for Nernst-Planck without Electroneutrality module............. 202 Figure  F.2: Coupled Electrostatics-Heat Transfer by Conduction-Nernst-Planck without Electroneutrality Modules........................................................................................................... 203 Figure  F.3:   Yb ion depletion layer in the ceramic heater aged at 1455oC. ............................... 204 Figure  G.1:   Boundary conditions for Poisson equation (AC model)........................................ 207                                xxiiList of Symbols D Diffusion coefficient µ  Mobility φ Electric potential E Electric field F Faraday’s constant η Viscosity c Concentration Ω Ohm ω Frequency ε Electric permittivity ∆G Gibbs free energy K Boltzmann constant T Temperature ∆E Activation energy R Gas constant J Mass flux              xxiii Nomenclature AC Alternating current BSE Back-scattered electrons DC Direct current DI Direct injection EDX Energy-dispersive X-ray spectroscopy ETC European transient cycle FEM Finite element method GP Glow plug IC Internal combustion  NP Nernst Planck NG Natural gas PB Poisson–Boltzmann PNP Poisson Nernst Planck RE Rare earth elements SEM Scanning electron microscopy SE Secondary electrons SN Silicon nitride YS Ytterbium disilicate     xxivAcknowledgments I would like to acknowledge my supervisor, Professor Tom Troczynski, for his patient guidance, immeasurable support, and encouragements throughout this process.   A big thank you goes to Westport Innovations Inc. without which this research would not have been possible.  Also, I would like to thank Alan Welch and Colin Blair, who shared with me their experience and personal insights and provided me with constant support. Special thanks go to Carmen Oprea for her assistance in bringing this project to completion.  I would also like to acknowledge my committee members: Dr. Daan Maijer, Dr. William G. Dunford, and Dr. Anthony Peirce who graciously agreed to serve on my committee. Also I want to extend my thanks to both of my families for their love and encouragement. I would especially like to thank my parents for allowing me to realize my own potential.          xxvDedication To my wife for her constant encouragement, endurance and moral support. I couldn’t have done this without you.            1  1 Introduction Natural gas (NG) internal combustion (IC) engines offer significantly lower harmful emissions of nitrogen oxides (NOx), particulate matter, and greenhouse gases than conventional diesel engines with similar performance [ 1– 3]. However, there are a number of technical, economical and regulatory challenges to be addressed before the larger acceptance of these engines. This research focuses on technical challenges related to NG ignition.  Due to its high autoignition temperature, natural gas will not ignite within the required time interval in a typical 17:1 compression ratio engine designed for diesel fuel. Ignition delays shorter than 2ms are critical for optimal engine performance and low emissions capabilities [ 4]. The studies have shown that temperatures > 927oC are required for natural gas to ignite within 2ms. A very high compression ratio (> 32:1) can be applied to raise the gas temperature up to 927oC, however high compression ratio may significantly limit the durability of the engine by subjecting it to very high mechanical and thermal stresses. Thus, a reliable high-temperature gas igniter is necessary in order to burn NG in the required ignition gap (<2 ms). Westport Innovations has recently developed a unique diesel fuel pilot injection technique in which a small quantity (5%) of diesel fuel will be injected first to raise the gas temperature to a level high enough for subsequent injection of natural gas (95%). The only disadvantage of this system is the need of two separate storage tanks on board.  Another method to ignite natural gas in IC engines is to use spark-plug ignition. However, timing the spark for the best running for different fuel-air mixtures and under various loads and speeds remain as a technical challenge [ 1,  5].    The development of new ignition technology is a critical factor in the success of a monofuel DI engine. The hot surface ignition (or Glow Plug, GP) technology appears most viable.  2 Unfortunately, the state-of-the art ceramic GPs fail prematurely in high-performance NG engines, usually after less than 1,000 h of operation, whereas at least 10,000 h (preferably 20,000 h) is sought by the industry. The primary goal of this research is to bring a more in-depth understanding of the performance and deterioration of GP ceramics under the harsh conditions of NG-IC engine.  Most of the currently used ceramic GPs consist of a conductive element embedded in a Si3N4-based insulator [ 6,  7]. Ytterbium oxide Yb2O3 is used as a sintering aid to lower the temperature/time requirements for proper sintering of silicon nitride (Si3N4) [ 8– 13]. In the sintering process, Yb2O3 combines with Si3N4 and pre-existing SiO2 to produce a liquid, out of which stable β-Si3N4 precipitates, leaving behind an amorphous matrix [ 14– 17]. A post-sintering heat treatment, just below the eutectic temperature, promotes the formation of high-temperature oxide phases including ytterbium silicon oxynitride Yb4Si2O7N2 and silicate phases (Yb2Si2O7 and Yb2SiO5) [ 18– 20]. However, complete crystallization of the grain boundary glass phase is nearly impossible, and even after long annealing times a residual, continuous glassy phase remains between the crystalline phases.  This can significantly affect the mechanical and physical properties of Si3N4 ceramics at high temperatures [ 21– 27].  The component of interest here is made of an insulating polyphased ceramic, mainly comprised of β-Si3N4, Yb2Si2O7, and an amorphous intergranular phase. RE2O3-doped (where RE is rare earth ion) Si3N4-based ceramics have gained interest over the past several decades due to their high fracture toughness (>6MPa√m) and strength (>700MPa), even at elevated temperatures [ 28– 33]. Furthermore, silicon nitride is a very good high-temperature electrical insulator with relatively high breakdown strength (>200 kV cm-1), as well as low dielectric loss and dielectric constant at a wide range of frequencies [ 34]. These materials are chemically resistant to reducing  3 environments; moreover, the formation of a protective silica film, even at low temperatures (e.g. as low as room temperature), makes them highly effective in oxidizing conditions as well [ 35– 49]. In a GP ceramic heater the temperature can rise up to about 1500oC by passing electrical current through two parallel U-shaped heating elements, based on conductive tungsten carbide (WC) particles embedded in an Yb2O3-doped Si3N4-based insulating phase [ 50].  However, the Si3N4-tipped GP operates typically at temperatures up to ~1400oC, achieved due to combined joule heating and combustion heating, with the desired lifetime in engine of up to 20,000 h [ 51,  52]. However, there are a number of phenomena that can cause GP failure in a much shorter time, such as thermal degradation due to the high operating temperature, chemical degradation due to the reaction of combustion gas with the Si3N4-based insulator and oxidation of the bulk ceramic, electrical degradation as a result of applied electric field, and mechanical degradation in the high-pressure/high-velocity gases engine [ 52]. In this work, particular attention is given to the internal degradation of the ceramic heater related to migration of Yb ions, under the influence of the electric field and the concentration gradient formed within the Si3N4-based insulator and across the section at the hot spot. The SEM-BSE images of aged GP showed that under the influence of the electric field Yb ions migrate away from the WC-based heating elements connected to the positive electrodes and towards the grounded sides.  Surface oxidation also occurred, due to the diffusion of Yb ions towards the surface of the silicon nitride body and to the inward diffusion of oxygen from the combustion environment or ambient air. The Yb ion migration process is quite rapid above 1400oC in a DC electric field, and it is also present (although to a much less extent) in the AC field. This causes considerable alterations of the internal structure of the ceramic heater and  4 degrades the mechanical and electrical properties of the GP. The progressive migration of the Yb ions leads to the formation of non-uniform intergranular phases, some with very high Yb ions content and others with very low, even zero, content.  We have observed that Yb ion migration under the influence of the electric field starts within the positive sides of the heating elements and this causes the “weakening” of Si3N4 structure, e.g. depleting it from the Yb2Si2O7 in the intergranular phase, and porosity increase.  Furthermore, the WC particles lose their interconnectivity in the electrically conducting phase; hence the resistance progressively increases, initially leading to local micro-hot-spots, and finally to the macroscopic collapse of the GP heater.  This research intends to identify the failure modes of the Yb2O3-fluxed Si3N4-based GP in the NG-IC engine. However, due to the cumulative and synergistic nature of the damage mechanisms, decoupling various degradation modes and studying them individually was desirable. Reference tests on a burner rig were performed to eliminate the effects of combustion, pressure and other variables affecting GP durability in the engine, whereas the tests on the electric rig in air focused on the electrical field effects and temperature only. The temperature on the surface of the GP ceramic heater was measured via pyrometry. A model was developed to simulate the migration/diffusion of Yb ions within the cross-section of GPs, driven by the combined effects of electric field and concentration gradient. The temperature dependence of the Yb ion diffusion coefficient and mobility is accounted for in the model. The model is verified qualitatively and semi-quantitatively by comparing the simulated Yb ions redistribution patterns and the SEM/EDX generated micrographs of the cross-section of the ceramic heaters. The model has confirmed the effects of temperature, power supply (for both AC and DC electricity), and GP geometry on GP lifetime.  The model may have implications beyond this work, predicting  5 elemental redistribution in components operating under high electric field conditions, such as actuators, catalytic converters, fuel cell electrodes, integrated circuit substrates or high-power transmission line conductors.               6 Si3N4 Si3N4 Intergranular  phase Ceramic Heater Si3N4+Yb2O3 Steel shield Heating elements WC + (Si3N4+Yb2O3) Tungsten wires a b c 2 Literature Review 2.1 Ceramic glow plug (GP) technology The state-of-the-art GP uses a DC-powered all-ceramic heater comprised of an electrically insulating silicon nitride (Si3N4) body and two parallel heating elements, whose conductive phase is made of tungsten carbide (WC) particles dispersed in a Yb2O3-doped Si3N4-based  matrix [ 6]. The U-shaped WC heating elements are connected to the high-melting point tungsten wires and embedded in the Si3N4-based insulator, Figure  2.1.       Figure  2.1: Si3N4-based GP, a) photography of a glowing plug b) GP assembly showing two thin U-shaped heating elements; c) the cross-section of ceramic heater and microstructure schematic-not to scale; the two U-shaped heating elements appear as four white lines.  Figure  2.1a shows a glowing 4.2mm diameter GP manufactured by Kyocera Inc. [ 7], where the high-temperature region appears brighter in the image. Figure  2.1b illustrates a schematic of the same GP with two heating loops embedded inside the Si3N4-based insulator. A rough schematic of Si3N4-based insulator’s microstructure is depicted in Figure  2.1c showing that the Si3N4 particles are bound together by an intergranular phase in the Yb2O3-Si3N4-SiO2 system.  7 These ceramic heaters exhibit quick heating (e.g. <20s to maximum operating temperature of about 1400oC), do not cause radio interference, ensure positive ignition and safety and have superior wear/corrosion resistance and durability. Such heaters have been widely used in the manufacture of GP for diesel internal combustion engines and igniters for gas heaters [ 6,  7].  2.1.1 The insulating ceramic   The ceramic heaters developed by Kyocera are made from high-purity silicon nitride (Si3N4) powder combined with Yb2O3 as a sintering aid. The heating source is a pair of U-shaped ceramic elements made by screen-printing a paste of WC particles (>80 weight (wt) %) mixed with Si3N4-Yb2O3 (<20 wt %) powders onto the insulator green body.  The ~0.25mm diameter tungsten wires, Figure  2.1, connect the WC heating elements to external power supply terminals.  The GP green body is then fired in nitrogen gas at 1600°–1800°C for up to 2 h. The structure is then heat-treated in nitrogen gas at 1400oC for 24 hours to promote the secondary crystalline phase formation within the grain boundary phase [ 6].  2.1.2 Crystallization of grain boundary glass The composition of the crystalline secondary grain boundary phases can be predicted by the phase diagram of the Si3N4-SiO2-Yb2O3 system, as shown in Figure  2.2, indicating only one ternary phase (Yb4Si2O7N2) and three binary phases (Yb2Si2O7, Yb2SiO5, and Si2N2O) [ 53]. The Si3N4 insulting ceramic of the GP belongs to the Si3N4-Si2N2O-Yb2Si2O7 compatibility triangle, Figure  2.2.    8          Figure  2.2: Phase relationship in the system Si3N4-SiO2-Yb2O3 at 1750 °C [ 53]. In the Yb-containing system both silicate phases (Yb2Si2O7 and Yb2SiO5) can be crystallized as a grain boundary phase in Si3N4-ceramics. The melting temperature of Yb4Si2O7N2 (1870oC) is slightly higher than that of the Yb2Si2O7 (1850°C) [ 54,  55].  The phase diagram of the binary system (Yb2O3-SiO2) in Figure  2.3 suggests a higher melting point for ytterbium monosilicate (Yb2O3.SiO2) compared to Yb2O3.2SiO2. Crystallization of high melting point crystals is highly desirable for the ultimate high temperature performance of silicon nitride ceramics. In the Si3N4-SiO2-Yb2O3 system, Yb2Si2O7 is the only phase that can coexist with SiO2 film within the grain boundaries [ 56].     9  Figure  2.3: Phase diagram of the binary system Yb2O3-SiO2 [ 56].  Depending on both the sintering aid composition and the processing parameters either amorphous or a combination of crystalline and amorphous secondary phases can form upon cooling [ 57,  58]. A post-sintering heat-treatment induces crystallization of the amorphous secondary phase in the triple-point pockets [ 11,  59,  60], which greatly reduces the volume fraction of residual glass.  2.1.3 Intergranular glassy phase The complete crystallization of the glass phase cannot be achieved, because thin intergranular films along the two-grain junctions almost always remain non crystalline. Such remnant intergranular films can range in width from 0.5 to 4 nm [ 23,  61– 63].   The residual glass phases, such as intergranular films, are generally assumed to consist mainly of SiO2 (from the surface of the Si3N4 grains) with dissolved sintering aids [ 64,  65]. However, the sintering additive (e.g. Yb2O3) is not uniformly dispersed within the intergranular glassy phase. The electron microscopy studies have shown that the sintering additives are less concentrated within the  10 intergranular film at the two grain junctions. Moreover, nitrogen might be dissolved in the intergranular glassy phase and hence change both the glass structure and the chemistry [ 66]. A higher N-volume fraction yields a higher density, viscosity, Young’s modulus, and glass transition temperature [ 67]. It has been reported that the oxynitride glasses are more resistant to chemical degradation mechanisms and possess much higher elastic modulus than the oxide glasses, likely because the Si-N bond is more covalent than the Si-O bond and also nitrogen may form more bridging bonds than oxygen [ 68]. Furthermore, many physical properties of the glass, such as diffusivity and electrical conductivity, that are primarily controlled by the viscosity of glass can be affected by dissolution of N atoms in the amorphous phase [ 69]. In the manufacturing of Si3N4 ceramics, MoSi2 is occasionally added to increase the long-term stability of Si3N4 ceramics by promoting the dissolution of nitrogen atoms in the intergranular glassy phase and hence reducing the redistribution of liquid phase in the Si3N4 material. MoSi2 is in equilibrium with Si3N4 up to 2000oC depending on the nitrogen pressure [ 6,  34,  70]. 2.2 Oxidation of Si3N4 Silicon nitride powder will oxidize when exposed to air or other oxidants, even at room temperature [ 71]. It is impossible to avoid the oxidation during manufacturing, milling and shaping of Si3N4 powders; it was shown that O/Si ratio can increase by 6%-8% after alcohol milling or dry pressing [ 72]. Furthermore, the oxides introduced as sintering aids have their contribution to the oxidation [ 73].  The detailed oxidation mechanisms of Si3N4 are not fully understood, because it is difficult to detect experimentally the sequence of oxidation; the parameters such as solubility, diffusivities, or the oxidation state of the product gases are not easily determined [ 34,  71]. Oxidation of Si3N4 is a complex phenomenon and involves a number of steps including the transport of O2 to oxide  11 surface, diffusion through the oxide film, reaction at the oxide/ceramic interface, transport of N2 gas through the oxide film, and transport of gases away from the surface (Figure  2.4). Many questions are still unanswered about these steps, such as which is the rate-controlling step, whether molecular or ionic oxygen is transported through the SiO2 scale, and what is the mechanism of transport of gases through the scale [ 71].  Figure  2.4: Schematic of pure silicon nitride oxidation in air [ 71]. Oxidation of pure Si3N4 in pure oxygen, resulting in a net weight gain, mainly occurs through the following reactions1: 4 Si3N4 + 3O2 → 6 Si2ON2 + 2 N2 (1.1) 2 Si2ON2+ 3O2 → 4 SiO2 + 2 N2 (1.2) However, there is also mass loss due to the gas evolution such as nitrous oxide (NOx). It is possible that gaseous SiO forms at high temperature, through one of the following reactions: Si3N4 + 1.5 O2 → 3 SiO +2 N2 (1.3) 2 SiO2 → 2 SiO + O2  (1.4) Si3N4 + 3 SiO2 → 6 SiO + 2 N2  (1.5)                                                  1 Thermodynamic data can be found in Appendix A.  12 In reactions (1.1) and (1.2) a weight gain takes place due to the formation of protective silica layer and this is called passive oxidation; during the active oxidation process described by the reactions (1.3), (1.4), and (1.5) the gaseous product (SiO) escapes from the system resulting in weight loss [ 34, 71]. The passive to active transition varies with oxygen partial pressures and temperature, Figure  2.5.   Figure  2.5: Active to passive transition of Si3N4 as a function of temperature and oxygen partial pressure [ 34]. In practice, depending on the surface quality and material imperfections such as cracks, bubbles, and lamination, the temperature and oxygen partial pressure for the active/passive transition equilibrium may be different than expected. For example, in gas turbines the active to passive transition and the resulting weight loss strongly correlates with the gas viscosity and velocity, and it depends on whether the flow is in the laminar or turbulent regime [ 38,  40]. In the presence of water vapour the protective silica film reacts with water to form volatile gaseous products such as Si(OH)4 or SiO(OH)2 [ 42– 45,  74]. This could be a serious problem in the natural gas and hydrogen direct injection IC engines.   13 Oxidation of RE2O3-fluxed silicon nitride is yet more complicated than for the pure Si3N4 [ 75– 81]. Although the protective silica layer makes a good barrier to the inward diffusion of oxygen, the silicate glasses are good solvents for the additive ions (e.g. Yb3+ and Al3+), oxygen and nitrogen, hence oxidation occurs mostly in the glassy phase of the oxidation layer and of the boundary phase [ 34, 82]. The SiO2 rich layer at the surface of the material creates a chemical gradient to the composition of the grain boundary phase in the bulk of the Si3N4. The need to relax this chemical gradient, along with the free energy of silicate formation, is the reason for the diffusion of additive ions [ 34]. The regions with concentrated grain boundary phase (rich in sintering additives) serve as paths for the increased inward oxygen diffusion [ 18]. In Yb2O3-doped Si3N4 ceramics, both Yb4Si2O7N2 and Yb2SiO5 undergo oxidation reaction in an oxidizing atmosphere. Yb4Si2O7N2 can react with oxygen to form Yb2SiO5 and then Yb2SiO5 react with SiO2, the product of Si3N4 oxidation, to form Yb2Si2O7 according to the following equations [ 55]:   2Yb4Si2O7N2(s) + 3O2 (g) = 4Yb2SiO5(s) + 2N2 (g)   (1.6) Si3N4(s) + 3O2 (g) = 3SiO2(s) + 2N2 (g)  (1.7) Yb2SiO5(s) + SiO2(s) = Yb2Si2O7 (s)  (1.8) Yb2Si2O7 is the only phase that can coexist with SiO2 in the Si3N4-SiO2-Yb2O3 ternary system; hence, a white scale layer of Yb2Si2O7 circumferentially forms on the surface of the Yb2O3-fluxed silicon nitride ceramic during oxidation [ 55,  56]. On the other hand, migration of sintering additive ions toward the surface and dissolution in the silica film reduces viscosity of the glassy silica and results in scale interruption and hence further diffusion of oxygen into the Si3N4 bulk. The presence of impurities in the fuel and oil in an engine has a strong influence on the surface morphology of the specimens after oxidation [ 51,  14  52]. It was reported that the crystals of disilicates are larger and have a more defined prismatic shape in the regions where calcium is detected [ 51]. A silicate phase containing calcium has a much lower melting point than SiO2 and a higher basicity [ 83], which causes increased dissolution of N2, which in turn contributes to formation and growth of the pits inside the bulk Si3N4 and that would weaken the whole structure, allowing more oxygen to diffuse into the bulk Si3N4. The long-term lifetime of Si3N4 ceramics at high temperatures may be significantly influenced by the oxidation damage [ 50–  52]. Literature data regarding the oxidation mechanisms of Si3N4-based materials are widely scattered and the results vary substantially as a function of the type and quantity of the secondary phases (usually silicates of yttrium or lanthanide oxides) present in the material.  However, the diffusion is most likely the prime mechanism of RE2O3-doped Si3N4-based materials oxidation. For example, in Y2O3-doped silicon nitride ceramics the oxidation is controlled by the diffusion of oxygen (with an activation energy of 110-140- kJ mol-1 [ 18,  84,  85]) at 1100-1350oC. At moderate temperatures (1350-1590oC) the diffusion of Y3+ (355 kJ mol-1) is the rate-limiting step. It was proposed that above 1600oC the diffusion of gaseous species (680 kJ mol-1) through the thick oxide scale is the controlling mechanism [ 84,  86,  87], (Figure  2.6).  15  Figure  2.6: Temperature dependence of the oxidation rate constants (Kp =parabolic constant) in Y2O3-doped Si3N4 [ 84]. Other oxidation mechanisms can be triggered at elevated temperatures, depending on the amount of sintering aids.  For the Si3N4-based ceramic containing 5wt% Y2O3 and 2.5 wt% Al2O3 the outward diffusion of cations (Al3+ and Y3+) was significantly restricted at temperatures around 1400oC due to the crystallization of the intergranular glassy phase and an increase in viscosity. The apparent activation energy for the oxidation of pressureless-sintered (5wt% Y2O3 and 2.5 wt% Al2O3)-fluxed Si3N4 ceramics is 800 (kJ mol-1) up to 1450oC and 440 (kJ mol-1) above 1450oC [ 84].  2.2.1 Effects of corrosive combustion gases Combustion environments contain N2, CO2 and H2O; fuel-lean contain additionally O2, whereas fuel-rich environments may additionally contain extra CO, H2 and complex hydrocarbons.  K-1  16 Hence the primary oxidant in the combustion environment is not always oxygen, but it can be H2O and CO2 (depending on the combustion cycle).  Water changes the oxidation behavior and alters the mass transport mechanism through the oxide scale [ 71]. It has been demonstrated that silicon oxidizes one order of magnitude faster in wet than in dry oxygen, due to the higher solubility of H2O, compared to O2, in SiO2 (~3.4×1019 molecules/cm3 vs. ~5.5×1016 molecules/cm3); the parabolic rate constant was directly proportional to the solubility of the oxidizing species [ 88]. Water also disrupts the SiO2 network, forming non-bridging SiOH groups, which permit faster H2O transport [ 88]. The wet oxidation (where rates are dependent on the partial pressure of water) of Si3N4 is attributed to the following reactions [ 89– 93]: Si3N4(s) + 6H2O(g) = 3SiO2(s) + 4NH3(g)  (1.9) 4NH3(g) + 5 O2(g) = 6 H2O(g) + 4NO(g)  (1.10) The formation of a SiO2 layer on Si-based ceramics usually follows linear (x = k × t), parabolic (x2 = 2kp × t) or mixed (x = C + klog × log(t)) growth laws, depending on the characteristics of the oxide layer; where x represents oxide thickness, t is time and k, kp, klog , and C are constant.  For a homogenous and continuous oxide layer with constant properties over time, the parabolic law is observed, while a constant change in properties of the layer (e.g. partial crystallization) will result in a logarithmic law [ 94]. In real applications often a model forcing data to yield parabolic rate constants is used to compare the performance of different materials.  The SiO2 volatility is an important factor in the oxidation of silicon nitride in combustion environments.  For example, at 1 bar oxygen pressure, the major vapor species above the SiO2 scale is SiO2(g) and the minor species is SiO(g) [ 71]. The recession rate of SiO2 (R) has been given by the following relation [ 95]:  17 R(m/s) = 10-6 J (mol (m2⋅s)-1) MW/ρ (1.11) where MW is SiO2 molecular weight; ρ is SiO2  density, and J is material flux. It was calculated that for desired lifetimes of silicon oxide components of over 10,000 h, the maximum acceptable total pressure of the vapor species above SiO2 should be 0.1 Pa [ 95]. To determine when SiO2 vaporization becomes a problem, the corresponding temperature was calculated. In a fuel-lean combustion environment, the pressure of SiO2 approaches 0.1 Pa only at temperatures close to the glass transition temperature of  amorphous SiO2-based phase (1423 ± 50oC) [ 71].  However, in a fuel-rich environment, there is a substantial pressure of SiO(g), hence vaporization might be an issue above 1497oC and the kinetics of the oxidation-vaporization couple might become paralinear. The active-passive oxidation boundary for silicon nitride in many gases is not known. In most combustion environments, active oxidation is generally not expected, but in the fuel-rich region with CO2, H2O and oxygen partial pressures as low as 10-4 Pa, the SiO2 scale might be actively reduced [ 71]. The combustion atmosphere for hydrocarbon/air systems contains up to ~10% water vapor, dependent of hydrocarbon type, fuel-to-air ratio and combustion cycle. Under such conditions, the simultaneous reactions of forming SiO2 and removing it as a volatile Si(OH)4 species are described by paralinear kinetics [ 96–  98]. A steady state, in which these reactions occur at the same rate, is eventually achieved and the oxide found on the surface has a constant thickness, with the recession of the underlying material occurring at a linear rate. The steady-state oxide thickness, the time to achieve steady state, and the steady-state recession rate can be described in terms of the rate constants for the oxidation and volatilization reactions. Accordingly, maps have been developed to show these steady-state conditions as a function of reaction rate constants, pressure, and gas velocity [ 99]. These maps can be used to predict the  18 behavior of SiO2 formers in the water-vapor-containing environments, such as combustion environments.  Different Si3N4 materials [ 99] exposed to dry oxygen flowing at 0.44 cm s-1 at temperatures between 1200 and 1400°C showed parabolic oxidation kinetics. When the same materials were exposed to a 50% H2O–50% O2 gas mixture flowing at 4.4 cm s-1, all exhibited paralinear kinetics. The material was oxidized by water vapor to form solid SiO2, which was in turn volatilized by water vapor to form primarily gaseous Si(OH)4.  Sintering additives such as the rare earth (RE) oxides provide, as silicates in the grain boundary phase of Si3N4, superior strength and oxidation resistance at high temperatures [ 38,  100,  101]. They also have a complex effect in the oxidation process: the RE oxides, initially found as silicate glass in the grain boundary phase, diffuse into the silica scale, forming silicates driven by the concentration gradient in the initially pure SiO2 and by the free energy of silicate formation [ 71]. The oxidation rates increase with the amount of additives and there are deviations from the parabolic rate law and some formulations will catastrophically oxidize, due to the volume expansion associated with the oxidation of the grain boundary phases [ 102]. Silica is selectively volatilized from the scale formed on additive-containing silicon nitrides exposed to combustion environments [ 99]. Rare-earth disilicate enrichment was observed on the surface of these exposed materials, even when there was a recession of Si3N4 by the corrosive gas [ 38], but not as a continuous layer. Thermal expansion coefficient mismatch and/or phase stability can cause the spallation of the surface rare-earth disilicate. A continuous RE disilicate layer would be very beneficial and understanding the factors that affect the formation of this protective layer would allow for the design of a rare-earth oxide/Si3N4 system with better durability in combustion environments [ 103].   19 Dense Si3N4 with different additives behave well under thermal cycling, showing similar weight gain as in isothermal conditions [ 95]. Experimental work comparing oxidation and corrosion behavior of Si3N4 materials with different sintering additives up to 1500ºC showed that even the best-performing one (with Lu2O3) exhibited mild corrosion in the moist air (13.4 wt% water). Only oxidation was observed in the dry air [ 104], as indicated by the mass change of the specimens. Silicon nitride is very resistant to thermal cycling in air [ 105– 107], as determined in comparative studies by quenching the specimens 100 times from 1200ºC into a fluidized bed with a heat transfer coefficient of  1,400 W (K.m2)-1. Compared to Al2O3/SiC composites, the thermal shock performance of Si3N4 was the best, as assessed by flexure strength measurements at room temperature; the tensile stress loss was minimal (57 MPa compared to 171-393 MPa for the other materials). Recent studies have shown improvements in vehicle performance by using different Si3N4 parts, such as reduced-weight valve systems, turbochargers, springs for gas turbines and glow-plugs [ 108,  109].   2.2.2 Effect of impurities in the combustion gases Even in small amounts, impurities such as SO2 and SO3, C, HCl, Na, vanadates, and transition metals, can have a deleterious effect on a silicon-based ceramic [ 95]. Pure SiO2 is resistant to attack by SO2 and SO3, but in the presence of hydrogen sulfide and at low oxygen pressures, the stable SiO2 surface scale might not form and SiS(g) and SiO(g) may lead to rapid degradation. SiO(g) also forms in predominantly CO environments. Actual combustion environments contain mixes of these impurities, in general with sufficient CO2 to be oxidizing [ 71]. Where hydrocarbons such as methane are present, a net transport of SiC has been observed; SiC is a product of the following reaction, involving SiO allowed to form by the low oxygen potential pressure:  20 SiO(g) + CH4(g) = SiC(s) + H2O(g) + H2(g) (1.12) Alkali metals (Na and K) are common impurities, which can deposit as sulfates on the material, or very small amounts can be incorporated in the growing scale of SiO2. Oxidation rates were 14 times higher probably due to a modification of the Si2N2O layer by sodium at 1100-1300oC[ 71]. Transition metals (V, Fe, Ni, Cr) can also be incorporated into the SiO2 scale, leading to more rapid oxidation [ 71,  95]. 2.3 Electrical properties of silicon nitride ceramics 2.3.1 Silicon nitride dielectrics Silicon nitride dielectrics have been widely investigated over the past four decades and have found many applications such as components of metal-insulator-metal (MIM) capacitors [ 110– 115], light emitting diodes [ 116], sensors [ 117,  118], and high-temperature resistant insulators in heaters and igniters [ 7]. The Si3N4-based dielectrics have a relatively high dielectric strength [ 119,  120], and low electrical permittivity [ 116– 119] and dielectric loss in a broad range of frequencies and temperatures [ 121,  122]. Si3N4-based insulating films have found new applications as diffusion masks [ 123] and passivation layers [ 124] for semiconductor devices. The electrical properties of Si3N4 ceramics are very sensitive to their stoichiometry, e.g. the electrical resistivity can vary between 1017 Ω-m for near stoichiometric silicon-to-nitrogen ratio (3/4) to as low as 105 Ω-m for Si-rich phases [ 125]. However, it should be noted that many of the outlined applications use pure silicon nitride ceramics, i.e. chemical vapor deposition (CVD) derived Si3N4, which is often non-stoichiometric and amorphous, hence very different to the β- Si3N4 materials used in the present study.  21 The electrical properties of Si3N4 with the residual intergranular phase vary from those of pure Si3N4. For example, the electrical resistivity of RE-doped Si3N4 -based materials extends from >1014 Ω-m at room temperature to as low as 106 Ω-m near the glass transition (Tg) temperature of the intergranular glassy phase [ 34]. The room temperature (RT) resistivity of RE-doped Si3N4 is 2-3 orders of magnitude lower than that of pure near-stoichiometric Si3N4. The dielectric breakdown strength of Yb-doped Si3N4 is about 1-1.5×105 (V cm-1), two orders of magnitude lower than that of pure Si3N4 [ 126,  127]. In the steady-state two conduction mechanisms were proposed to contribute to the total current density in Si3N4 -based insulators: (i) the electronic conduction dominating at moderate temperatures (25-1000oC) and (ii) the ionic conduction dominating above 1000oC. The activation energy for conduction varies from 1eV at temperatures below 800oC to 2.8-3eV, or higher, at temperatures above 1000oC [ 34,  128]. Although the steady-state and transient deterioration mechanisms of Si3N4 -based dielectrics have been studied, little is known about the failure modes of RE-doped Si3N4 dielectrics due to the complexity of microstructure and element redistribution [ 34,  125]. 2.3.2 Dielectric breakdown Silicon nitride is an excellent electrical insulator for a wide range of temperatures with a high electric break down strength (>200 kV cm-1) and low dielectric losses, tan δ, and dielectric constant, ε, (6-8.0 at 1MHz) [ 34]. Furthermore, owing to its effectiveness as a diffusion barrier, Si3N4 has been increasingly considered to replace SiO2 in microelectronic devices [ 29].   However, when a dielectric is subjected to an increasing electric field, at some point a short circuit develops across it. Dielectric breakdown is defined as the voltage gradient or electric field sufficient to cause the short circuit through the material, i.e. allowing charge carriers (electron and ions) to travel along a path without encountering electrical resistance [ 129]. This  22 phenomenon depends on many factors, such as sample thickness, temperature, electrode composition and shape, and porosity [ 128]. Dielectric breakdown in ceramics can be broadly split into two categories: intrinsic dielectric breakdown and thermal dielectric breakdown [ 28,  128]. The former occurs when electrons in the conduction band are accelerated to such a point that they start to ionize lattice ions and, as such, the number of free electron increases. A so-called “avalanche effect” is created as a result of this cumulative ionization (intrinsic breakdown). The latter occurs when the electrical conductivity of the insulator increases with increasing heat flux generated, whether through external source or through dielectric loss inside insulating materials (thermal breakdown). The heat generated under DC fields is given as [ 130]: 32 cmWEWdc σ=   (1.13) where E (V cm-1) is the DC electric field strength andσ  (S cm-1) is the electrical conductivity. Under AC field, the heat generated is [ 130]: 3122108.1tancmWfEW rac×=δε  (1.14) where ƒ is the frequency (Hz), δ is the loss angle, and εr is the dielectric constant. The breakdown occurs when Wdc or Wac exceeds the total heat dissipated from the system, raising the temperature inside the insulator.  The degradation mechanisms of RE-doped Si3N4-based electrical insulators are complex and synergistic [ 50– 52]. If the applied electric field does not exceed the dielectric break-down limit of the Si3N4 insulator, the failure mode mostly depends on the long term breakdown due to the aging of insulating materials.  Such “time-dependent dielectric breakdown” (TDDB) starts from  23 a small leakage current passing through the conducting path formed within the insulating medium and inception of partial discharge caused by gas trapped in the pores. The subsequent sparks across open and closed porosities lead to the chemical dissociation, electrical short-circuit and thus insulation failure. Unlike gases and liquids, once breakdown occurs the solid dielectrics are permanently damaged [ 28,  130]. TDDB is a progressive phenomenon mainly caused by the formation of weak spots within the RE-doped Si3N4 insulating medium. The weak spots may result from transformation/recrystallization and uneven growth/shrinkage of Si3N4 grains or grain boundaries, or as a result of re-distribution and migration of mobile RE ions within the grain boundaries. It was reported that when a dielectric such as Yb-doped Si3N4 -based ceramic is placed in an electric field, the thermally activated and mobile Yb ions migrate away from the high potential heating element/ insulator [ 50].  2.3.3 Electrical conductivity At room temperature the electrical resistivity of Si3N4 is very high (>1014 Ωcm), but at higher temperatures (1200 oC) the electrical resistivity drops to ~106  Ωcm [ 34]. Electrical behaviour is strongly affected by the chemical composition and microstructure of ceramics. For example for SiAlONs with the general formula of Si6-zAlzOzN8-z, where z represents the number of replaced Al and O ions, the electrical conductivity for z=1.5 at 700oC is 2 ×10-9 (Ω cm)-1 and 2×10-9 (Ω cm)-1 for z = 3.2 [ 34]. At elevated temperatures (>1000 oC) the electrical conduction of insulating ceramics is usually controlled by ionic transport which obeys the Arrhenius temperature dependence [ 128]: ( )RTEa−= exp0σσ  (1.15)  24 where 0σ  is a constant (usually between 10 and 103 Scm-1), and the activation energy, Ea, (typically >1eV) for ionic conduction in Si3N4 ceramics varies significantly with the composition and the type of mobile charge carriers [ 18].  Ionic transport can be described as the product of the ionic carrier concentration, c, (mol m-3), the mobility, µ , (m2 (V.s)-1) and the charge number, or Faraday’s constant (96,485 C mol-1) [ 131,  132].  σ+ = F µ+ c+ (1.16) The mobility can be calculated using the Nernst-Einstein relationship that relates self-diffusion coefficient to the mobility [ 28]. ++ = DRTzFµ  (1.17) where D+ is self-diffusion coefficient ( )RTHDD m∆−=+ exp0 of mobile ions [ 133], D0 is a pre-exponential term (approximately constant with temperature), R is the gas constant, T is temperature, and mH∆  is the motional activation energy (migration energy).  Given that at any instant of time only a fraction of carriers are mobile, the concentration of mobile charge carrier (c+) can be obtained [ 131]: ( )RTGCc f 2exp ∆−=+   (1.18) where C is the total ionic concentration, fG∆  is the free energy associated with the formation of a mobile charge carrier. Therefore the activation energy in equation (1.15) is comprised of two  25 elements: the dissociation energy of charge carriers fG∆ and the motional activation energy mH∆ .  The activation energy for ionic motion of positive Yb ions in Si3N4-based ceramics is relatively high (500-600 kJ mol-1) [ 18], so ionic conduction can only be dominant at high temperatures (>927oC). This allows relatively low dielectric constant, rε , (6.0-8.0) of Si3N4 ceramics [ 34]. 2.3.3.1 Effect of intergranular glassy phase on electrical conduction As discussed earlier, the Si3N4-based ceramics containing sintering additives produce a complex microstructure, wherein the glassy integranular phase serves as the fastest diffusion path. Yb ions diffusion/migration inside such a composite insulator is complex, but the net effect is the resulting macroscopic movement of matter from the high potential region to the low potential region [ 73]. At elevated temperatures (>1300 oC) the viscosity of the intergranular phase falls substantially and grain boundary diffusion becomes faster than the interfacial oxidation [ 34].   In the glass science literature it is assumed that the diffusion process occurs through a mechanism similar to viscous flow and, as such, there should be close relations between the ionic conduction and the viscous flow of the glassy phase, particularly at temperatures above the glass transition temperature. According to the Stokes-Einstein relationship, the diffusion coefficient, D, can be related to the viscosity of the glass η (Pa.s): piλη3kTD =  (1.19) [ 83] where λ is the molecular diameter [ 83].  The above equation suggests that in analogy to the diffusivity, viscous flow is also a thermally-activated process and follows the Arrhenius temperature dependence. The activation energy for viscous flow in Yb-Si-Mg-N-O glasses is  26 rather high (991 kJ mol-1) and hence flow can only be triggered at very high temperatures, Figure  2.7 [ 69,  134].  In addition, the viscosity of a glass is a strong function of the composition and type of network modifiers (e.g. Yb3+), and increases with increasing cationic field strength (CFS = Z/r2, where Z is the valence and r is the ionic radius of RE3+) of RE3+ modifiers and nitrogen content, Figure  2.8 [ 135].    Figure  2.7:  Temperature dependence of viscosity of 28Ln:56Si:16Al:82O:18N glasses (Ln: Eu, Ce, Sm, Dy, Ho, and Er;) [ 69].   27  Figure  2.8: Effects of RE cation field strength and nitrogen on viscosity of RE-Si-Al-O-N glasses [ 69].  Figure  2.9 illustrates the effect of composition on the glass transition temperature (Tg) and the glass softening temperature (Td), for bulk glasses in Yb-Si-N-O system. It is shown that the viscosity of Yb-Si-N-O glasses decreases with increasing Yb2O3 content which acts as a flux in the glass [ 136].   28  Figure  2.9: Glass transition temperature, Tg, and softening temperature, Td, for Yb-Si-O-N glassy systems: (a) (Si3N4)x ((Yb2O3)0.3 (SiO2)0.7)100-x; (b) (Si3N4)8 (Yb2O3)92-y (SiO2)y)  [ 136].  2.4 Nernst–Planck equation for ionic transport The migration and diffusion of Yb ions in the Si3N4-based insulating phase of the ceramic heater (GP) in air is driven by the combined effects of electric field and concentration gradient [ 50]. The Nernst-Planck (NP) equation is frequently used to describe the total flux of different ions under the simultaneous effects of electric field and a concentration gradient [ 137- 146].  The Nernst-Planck equation for transport by diffusion and migration reads: YbYbYbYbYb cDEcJ ∇−=r..µ   (1.20)  29 where JYb is the total flux (mol m-2 s-1) of Yb ions, cYb is the concentration of Yb ions (mol m-3), DYb is the diffusion coefficient (m2 s-1), µYb is the mobility (m2 s-1 V-1), and →E  is the electric field strength (V m-1).  When coupled with the Poisson equation, ερϕ −=∇2   (where φ and ρ are respectively the electrostatic potential and the charge density, and ε is the electric permittivity of the medium), to correlate the electric potential with charge density, the (Poisson-Nernst-Planck) PNP equations are widely used in a broad range of disciplines. In semiconductor physics (where it is also called the drift–diffusion model) [ 137] the mobile charge carriers are electrons and holes (positive charge).  In biological ion channels the physiological ions such as Na+, K+, Ca2+ and Cl– pass through ion-selective pores formed by the proteins embedded in the membrane [ 138– 140].  PNP equations can be also employed to model the fabrication of ion-exchange channel waveguides that are obtained by electric field-assisted diffusion of desired elements into the channel [ 140– 146].  In terms of model similarities, the glassy ion-exchange channel is the closest system to the Si3N4-based GP, where the Yb ions move along the lines of the electric force within an intergranular glassy medium [ 50]. However, dependent on the application, different assumption and simplifications may be made. In many studies it has been assumed that the diffusion coefficient and mobility are constant, and that the electric field is uniform for the blocking electrodes [ 146– 152]. However, for complex systems and geometries the diffusivity and mobility of the charged particles are a function of electric field and concentration, and also increase exponentially with temperature [ 128,  131– 133].     30 3 Scope and Objectives Silicon nitride structural ceramics have gained wide acceptance in a variety of industrial applications due to their attractive mechanical properties such as outstanding high-temperature strength, oxidation resistance, good chemical and physical stability at elevated temperatures, relatively high fracture toughness, very good electric break down strength, low dielectric constant, ε. and low dielectric loss, tan δ.  Due to this unique combination of structural and functional properties, silicon nitride is used in various fields in harsh conditions such as IC engines, gas turbines, cutting tools, etc.  This work focuses on silicon nitride - based hot surface ignition systems for natural gas (NG) direct injection (DI) engines, including GPs with all-ceramic heaters. The commercial GPs of interest were originally designed and manufactured for use in conventional diesel engines. These state of the art ceramic GPs fail prematurely in the high-performance natural gas engines of interest in this work, usually after less than 1,000 h of operation, whereas at least 10,000 hours durability is desirable. The component of particular interest here is the ceramic heater of a GP, which is an insulating rod of Si3N4 sintered with Yb2O3 additive.  The rod embeds two parallel U-shaped heating elements comprised of a tungsten carbide particle conductive phase, co-sintered with the Si3N4 /Yb2O3 binding phase. By controlling the passage of current through WC-based heating elements the GP temperature can be raised to as high as 1400oC in few seconds, as specified by automotive industry requirements for an effective combustion of lean NG/air mixtures. The nominal operating temperature of the state of the art commercial GPs is, however, <1200oC. We have found that at higher temperatures (up to 1450oC), and under the influence of applied electric field, the sintering additive (Yb2O3) cations migrate within the Si3N4-based insulator, progressively leading to the deterioration of its electrical and mechanical properties.   31 The present project explores GPs aged in engine, burner rig, and electric rig. The primary objective of this work is to develop an understanding of the degradation mechanisms of Si3N4-based GPs at high temperatures and under the simultaneous influence of electric field and concentration gradient of the sintering aid (Yb2O3) cations. The aim is to bring a better understanding of the causes of Si3N4-based ceramic deterioration in various working environments (IC engines, burner rigs, electric rigs), and to propose a quantitative model to predict the Si3N4-based dielectric degradation and sintering additive (Yb2O3) cation redistribution as a function of the electric field strength and GP temperature.  The specific objectives of this work are as follows: 1. Perform complete characterization of the ceramic constituents of the GPs.  2. Explore the degradation mechanisms of Si3N4-based GPs aged in NG-IC engines. 3. Improve the understanding of the GP failure modes by de-coupling the failure mechanisms and studying them individually on the burner rig (NG) and the electric rig (ambient air).  4. Investigate correlation between the Yb ions migration pattern and electric field strength (electrostatic model) and temperature (heat transfer model) distribution in GP.  5. Establish correlation between the electrical resistance of WC-based heating elements and the applied voltage and resulting joule-heating effect.  6. Determine the effects of using alternating current (AC) to power the GP compared to direct current (DC), on the GP damage pattern.  32 7. Model the Yb ion redistribution in DC and AC electric fields within the Si3N4-based heater of the GP.  The tasks undertaken to reach the above objectives can be detailed as follows: 1. Investigation of the microstructure and elemental composition of the Si3N4 body by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). Ceramographic analysis of the Si3N4-based insulating phase, as well as the WC-based conducting phase for the microstructure and any possible fabrication defects or imperfections such as pores or cracks.  2. SEM examination of the changes in the surface morphology as well as microstructural and compositional variations within the cross-section of degraded Si3N4 heaters.  3. Development of an electrostatic potential model using the finite element method (FEM) to predict the electric field distribution within the cross-section of GP at elevated temperatures. 4. Development of a heat transfer FEM model to predict the GP temperature profile in a transient mode; model verification through measurement of the surface temperature by pyrometry. 5. Development of a simulation model representing the electrical degradation of Si3N4-based heaters in ambient air by coupling the electrostatic and heat transfer models with the mass transfer model. Model verification performed using correlation of the predicted elemental redistribution within Si3N4 with SEM-EDX measurements.  33 It is anticipated that the models developed and verified for silicon nitride based GPs may have implications beyond this work, predicting elemental redistribution in other components operating under high electric field conditions, such as high temperature solid oxide fuel cells and integrated circuit substrates or high-power transmission line conductors.             34 4 Experimental Procedures 4.1 Testing apparatus and materials 4.1.1 Engine testing of GPs Twelve commercially available GPs manufactured by Kyocera Corporation (Kyoto, Japan), with a 4.2 mm diameter ceramic heater, were tested at Westport Innovation Inc. in a diesel engine with 18:1 compression, using stoichiometric mixes of natural gas and air.  Four GPs (samples coded ETC1–4; please refer to Table  5.2 for coding and description of the GP samples tested ‘in engine’) were tested in the Transient Driving Cycle similar to the ETC, European Transient Cycle, which are light duty drive cycles, with low engine speed and load (i.e. average 1635 rpm and 165 Nm, respectively).  Due to time constrains, 8 more GPs (SS1-8, Table  5.3) were tested under Steady State (SS) engine cycles, at an average engine speed of 2000 rpm and average load of 450 Nm; the variable parameters were the applied voltage and duration of testing. The SS is an accelerated testing mode, which ran the GPs at higher temperatures and considerably higher engine load and speed.  The GP voltage and currents were recorded using the data-logging feature of the GP control unit. The surface temperature was estimated from the voltage values assigned through the GP control unit and the characterization of the GPs before and after testing (section  4.1.3), where electrical properties, diameter, mass and surface temperature were determined. For the characterization, the GP surface temperature was read with 1-color Ircon and Rayteck SX-HT optical pyrometers, which average the temperature read over the entire spot and it was used to scan the pin and find the hottest location; its maximum reading error was ± %1. The GPs were either removed while  35 they still performed normally, or were tested until failure. In the engine, failure means the inability to further maintain ignition of the fuel, regardless of the degree of internal degradation in the ceramic heater.  4.1.2 Burner rig The burner rig was built in-house at Westport Innovations Inc. (Vancouver, Canada), and it was comprised of 2 Xantrex XHR 20-50 power supplies controlled through a Labview Data Acquisition (DAQ) using a direct feedback to monitor the GP voltage and a Wiedmuller current transducer for the GP current, controlled by a Labview DAQ data acquisition system. A Fisher Blast Burner was used, with air and fuel mixed at the base of the burner to ensure pre-mixed combustion (Figure  4.1). Pressure regulators and rotameter flow meters controlled the air/fuel mixtures. To ensure a uniform combustion environment, and not introduce supplemental variables, all of the experiments on the burner rig were conducted with stoichiometric mixtures of natural gas and air, with volume flow rates of 0.0472 (m3 s-1) [100 (ft3 min-1)] at 0.8 Pa [11.6 (psi)] for air and 0.00387 (m3 s-1) [8.2 (ft3 min-1)] at 0.455 Pa [6.6 (psi)] for natural gas. The burner rig assembly also contained a flame arrestor on the burner to prevent flash-backs and a thermocouple mounted in the flame for safety (if the flame goes out, a Programmable Logic Controller shuts off the gas). The DAQ collected the hourly average voltage and current data, as well as their standard deviation; when the standard deviation exceeded a trigger value, the data was collected for the last hour at 10 Hz and stored in a separate file, to allow for tracing of rapid changes, usually towards the end of the GP lifetime. Seven commercially available GPs manufactured by Kyocera Corporation (Kyoto, Japan), coded BR1–7 (Table  5.4), with a 4.2 mm diameter of ceramic heater (as shown in Figure  2.1), were tested on a burner rig with a stoichiometric flame (λ = 1) under constant (DC) electrical load, at different temperatures for  36 different durations. Some GPs were run until failure, and for others the test stopped while the GP still performed normally.        Figure  4.1: Natural gas-burning rig. 4.1.3 Electric rig characterization bench Twenty eight commercially available GPs manufactured by Kyocera Corporation (Kyoto, Japan), with a 4.2 mm diameter ceramic heater (Figure  2.1), were tested at Westport Innovations Inc. in an electrical rig to characterize and test the GPs under DC and AC electrical power under ambient conditions (Figure  4.2). The data acquisition system was set to collect the data (average voltage and current data, as well as the standard deviation) every hour in the steady state, and accelerate to 10 Hz when the standard deviation exceeded a trigger value (i.e. heralding near-failure of GP). The GP temperature data was collected throughout each test using a Rayteck SX-HT optical pyrometer. For all GPs tested in the electric rig, the voltage and currents were recorded using the data-logging feature of the control unit before and after testing. Twelve GPs Top view Side view  37 (C1-12, Table  5.1) were used for characterization studies only, i.e. they were loaded for short times (a few minutes) only to carry out the measurements.              Figure  4.2: Electric rig configuration, a) control panel; b) electric rig. a b Electric rig Pyrometer  38 4.1.3.1 DC mode Ten GPs (DC1–10, Table  5.6) were tested on an electrical rig under constant DC voltage, at different temperatures for different durations, some up to failure, which was determined as the drop of current passed through GP by at least 50%, indicating failure of at least one heating element.  4.1.3.2 AC mode A total of six GPs (AC1-6, Table  5.8) were tested in an AC electric rig in ambient air. GP temperature, resistance, voltage, current and test time were monitored during the experiment. A solid state H-bridge circuit was developed in-house at Westport Innovation Inc. to generate a square-wave AC signal by switching the polarity of the voltage applied to the GP with pre-determined frequency.  The peak-to-peak AC voltage of the output waveform was the same as the DC voltage supplied to the circuit. The operating frequency had been set to an arbitrary value of 468 Hz for the purpose of this work, but can be modified to the maximum operating frequency of up to 50 kHz.  4.2 Optical pyrometry measurements Three different optical pyrometers (Raytek SX-HT, Ircon UX-20P, Mikron MI-SQ5) were evaluated with varying operating temperature ranges and focal spot sizes (Table  4.1). The Ircon and Raytek pyrometers average the temperature over the entire spot size.     39 Table  4.1 : Specifications of three pyrometers used in this study. Pyrometer Type Temperature range (oC) Spot size (mm) Comments Ircon UX-20P 1-colour 500-3000 2 average the temperature over the entire spot size Raytek SX-HT 1-colour 500-2000 1.8 average the temperature over the entire spot size Mikron MI-SQ5 2-colour 800-3000 1.5 must fill 5% of spot size The Ircon UX-20P (1-colour) works over the broader temperature range (500-3000 oC), however the spot size is wider (2mm) than that of Raytek and for proper operation 100% of spot size should be filled. Mikron MI-SQ5 (2-colour, 800-3000oC) has a smaller spot size (1.5 mm) and only must fill 5% of spot size, which makes it the most suitable for high-temperature spot reading. Raytek SX-HT has a smaller spot size (1.8 mm) compared to the Ircon UX-20P (2mm) and can detect lower temperatures (>500oC) than the Mikron MI-SQ5 (>800oC). The standard deviation between measurements (GP loaded at 6V) was found to average 3.5oC for the Ircon, 1.1 oC for the Raytek and 1.5oC for the Mikron. The Raytek temperature sensor accuracy was quoted by the manufacturer as ± 1% of the measured values with ± 0.1ºC resolution. 4.3 GP analysis methods and equipment  4.3.1 Scanning electron microscopy (SEM) The investigation of the ceramic heaters of the GPs was done by Scanning Electron Microscopy (SEM) on a Hitachi S 3000-N Scanning Electron Microscope with an Energy Dispersive X-Ray Spectroscopy (EDX) detector. The specimens were studied in the secondary electron (SE) and back-scattered electron (BSE) modes of SEM, at 5kV or 20 kV, to obtain higher magnification and greater depth of focus as well as local X-ray microanalysis for localization of details. The GPs studied in the SE mode of SEM were carbon-coated or gold-sputtered after polishing.  40 BSE imaging in the SEM was used to obtain material contrast, based on the atomic number Z. Elements of high atomic number, (such as Mo, Yb and W)  appeared bright relative to the elements of low atomic number (e.g. C, N, O and Si). Their compounds were also well contrasted, owing to the significant differences between their average atomic numbers, so areas with different chemical compositions are easily observed in the BSE images.  SEM/EDX analyses  in High Vacuum as well as in Low Vacuum - Variable Pressure modes were performed on the surface of the detached ceramic heaters, as well as on cross-sections (surface are analyzed < 10µm). The Low Vacuum - Variable Pressure mode allows working with the non-conducting phases without applying any coating. The semi-quantitative SEM/EDX analysis was performed to obtain the level of elemental concentration as weight percentage. Values for the porosity were estimated by means of image analysis of the micrographs of the cross-sections. 4.3.1.1 SEM sample preparation ― Analysis of the GP surface For each of the analyzed specimens, the Si3N4-based ceramic heater (pin or rod) was detached from the body of the GP at the base of the metallic shell that surrounds the metallic sleeve. Given the fragility of the oxidation layer deposited on the surface of the ceramic heater, the specimens were gently rinsed in alcohol, dried and positioned on the SEM sample holders without any other processing. ― Analysis of the cross-sections  41 After the GPs had been aged, their Si3N4–based pins were detached from the body of GP at the base of the metallic shell that surrounds the metallic sleeve. The ceramic pins were then mounted in a low- shrinkage resin and cut through, the hot spot, of the heater by a low speed saw LECO VC-50 saw. The samples were then polished on the rotating polishing wheels with 600 and 1200 grit sandpaper, followed by alumina powders (1µm and 0.06µm) on the wheel pad and cleaned with alcohol in an ultrasonic bath in a typical metallographic sample preparation manner. The microstructure evaluation of the Si3N4-based insulators was performed on the cross-section of the ceramic pins by Scanning Electron Microscopy (SEM-EDX). 4.3.2 High-temperature X-ray diffractometry  For phase analyses, X-Ray diffractometry (XRD) was performed on the as-received ceramic heater for various temperatures and duration. The Si3N4 heater of GP was converted to powder by grinding in a small mortar and pestle until an amount sufficient for the X-ray specimen was gained. The phase analyses were performed by X-ray diffractometry with a Bruker D8 Advance machine operated at 40 kV and 100 mA from room temperature to 1500oC in a platinum sample holder. XRD spectra were collected at 2 o/min over a diffraction angle range of 10o  -  90o and were analyzed using the Jade 5.0 software.      42 5 Experimental Results and Discussion  5.1 As-received GP Micrographs of the cross-section through the ceramic pin of an as-received GP are presented in Figure  5.1. The EDX characterization confirmed that the heating elements consist of WC-based conductive filament embedded in an Si3N4-based insulator, with Yb-Si-O-N containing intergranular phase (Figure  5.1a.). The porosity (as estimated by image analysis) of the two heating loops terminals is ~0.70% (Figure  5.1b.). The insulating substrate consists of β-Si3N4 with a mix of Yb2Si2O7 crystals and oxynitride silicate glass as the grain boundary phase (analyzed by XRD in combination with EDX). The amount of ytterbium throughout the cross-section of ceramic insulator varies between 8.8 and 9.2 wt%.  A higher magnification of ceramic pin is illustrated in Figure  5.1c. The average Yb ions content was detected to be ~9.0 wt%. Figure  5.1d illustrates a higher magnification image of the WC filaments: the lighter granular matrix shows the WC particles mixed with a Si3N4-Yb2O3 binder. 5.1.1 High-temperature X-ray diffraction  The XRD patterns were analyzed in Jade 5 software to reveal the phase transformations of the different ceramic heater components (Si3N4 insulator, WC heating elements, and W connecting wire) with time and temperature. Figure  5.2 shows the XRD patterns of the as-received ceramic heater ground into powder in a small mortar and pestle, at different temperatures. Large well defined peaks confirm the predominant phase to be beta-silicon nitride (β-Si3N4) for nearly all temperatures. Tungsten oxide (WO3) was detected above 700oC, and predominantly at temperatures 800-1000oC, and disappeared above 1100oC. At higher temperatures (>1000oC) SiO2 was detected as cristobalite. It likely formed through further oxidation of Si3N4 and  43 crystallization of residual crystalline and amorphous silica. As the powder was mounted in a sample holder of platinum, the X-ray diffraction pattern of Pt at temperatures above 1000oC2 was identified. MoSi2 is occasionally added to Si3N4-based insulator to improve the high- temperature properties (such the oxidation resistance and thermal shock resistant) [ 6].  Figure  5.1: Micrographs of cross-section through the ceramic pin of an unused GP: a-low magnification; b-insulator; c-WC heating element and surrounding insulator; d-WC heating element at high magnification. 5.2 GP characterization tests A batch of GPs was tested and characterized on the electric rig to determine the transient and steady-state temperature profile. Owing to the long-term nature of this research, GPs were chosen from different batches and as such some GPs had different electrical resistance, rooted in the slight geometry difference of the U-shaped heating elements. All GPs were initially                                                  2 Additional XRD patterns of ceramic heater can be found in Appendix B.  44 characterized in a short span of time (0.01-5 min) indicating that the standard deviation of temperature in the repeated tests was lower than 2oC and the results showed no significant variation in the electrical and thermal properties of Si3N4 insulator. Table  5.1 reviews the testing parameters of GPs and their conditions after the test.  Table  5.1: GP testing parameters on the characterization bench (electric rig).                   *Read with the optical pyrometer at the hottest spot near GP tip. †At the end of the testing period the GPs (C1-C12) still worked normally. Figure  5.3 shows the warm-up profiles for specimens (coded C1–C12; refer to Table  5.1) measured by infrared optical camera (Raytek SX-HT pyrometer) at the hot spot. To prevent the internal degradation of WC heating elements and an accelerated oxidation of the Si3N4 insulator at the surface, the GP was powered such that the temperature at the hot spot only rose to a maximum 1350oC (i.e. 100oC above nominal operating temperature).  Code† Voltage (V) Current (A) Power (W) Temperature (0C)* Life (h) C1 10.0 8.7 87.0 1284 0 C2 9.9 8.4 83.8 1315 0 C3 9.9 8.8 87.2 1326 0 C4 9.9 8.6 85.8 1313 0 C5 9.9 8.5 84.3 1306 0 C6 9.9 8.5 84.9 1320 0 C7 10.0 8.4 84.0 1288 0 C8 10.0 8.7 87.0 1324 0 C9 10.0 8.2 82.0 1194 0 C10 10.0 8.3 83.0 1304 0 C11 10.0 8.4 84.0 1295 0 C12 10.0 8.1 81.0 1198 0  45  Figure  5.2: XRD patterns of ceramic heater at different temperatures; SN: Si3N4, YS: Yb2Si2O7, C: cristobalite, S: SiO2, W: tungsten, Pt: platinum, WO: WO3, MS: MoSi2.   46 The temperature data scatter is higher in the beginning of the test and then decreases with increasing time up to the first 30s and then remained approximately constant in the steady-state regime.  This can be partially attributed to the Raytek SX-HT optical pyrometer accuracy, i.e. the pyrometer’s readings are less precise near the operating range extremes (500 and 2000oC). In addition, measurements made for areas smaller than the spot size (1.8 mm) using the Raytek pyrometer are likely to be misleading as the pyrometer averages the temperature of the entire focal spot size [ 153].                    Figure  5.3: Warm-up profiles for different GPs loaded at 9.0V at 0.0h, in ambient air. Specimen “C1” was used to evaluate the warm-up profiles of a GP under various voltages (V = 8.0, 8.5, 9.0, 9.5, 10.0V), Figure  5.4. Previous studies [ 50] showed that after aging the GPs in ambient air, ytterbium-based compound formed on the surface of ceramic heater, which affected  47 the pyrometric temperature readings (i.e. measured values were lower by about 20.0oC) in the regions where this coating was most dense (hot spot).  Figure  5.5 shows the temperature distributions at different orientations of the infrared optical camera vs. GP axis (0o, 90o, 180o, 270o) for the specimen “C1”. There are some variations in temperature determined around the circumference of the GP, likely due to the non-uniform geometry of the WC conducting filaments inside the Si3N4 heater. Figure  5.6 presents the steady-state temperature distributions measured by pyrometer along the length of the Si3N4 -based rod. For each temperature reading the GP was held for 2 minutes to assure that the steady-state condition was reached. In all heating rods, the hot spot lies within a region 3-5 mm back from the front end, with a minimum temperature of less than 400oC at the base (steel sheath, measured by type K thermocouple reader). A relatively sharp change in temperature at 14-15mm from the tip (600oC) is due to the design of ceramic heater, i.e. 14mm long WC heating elements are embedded within the insulating silicon nitride ceramic’s body (Figure  2.1).   48  Figure  5.4: Warm-up profiles for GP specimen “C1” at various voltages (8.0, 8.5, 9.0, 9.5, 10.0V) in ambient air.  Figure  5.5: Steady-state temperature for GP specimen “C1” loaded at 9.0V measured by pyrometer in ambient air at different orientations (0o, 90o, 180o, 270o).   49  Figure  5.6: Steady-state temperature distribution for new and engine-aged GPs; the temperature measurements were performed by optical pyrometer in ambient air. Figure  5.7 shows the increase in GPs resistance with temperature. Given that the position of the cross-section and the length of the WC filaments remained unchanged during the test, it can be concluded that the resistivity (or inversely, conductivity) of WC heating elements increases nearly linearly with temperature.    50  Figure  5.7: Change in GPs’ resistance (Ω) with temperature (oC). Figure  5.8 shows the temperature vs. voltage plot for the as-received GP (C1) loaded under the static electric field. For every temperature measurement enough time (>40 sec.) was given to the surface of the glowing tip to reach the steady-state condition. The temperature was recorded for the hottest spot at ~5mm from the front end.  The GP was energized to reach temperatures as high as 1500oC and then it was left to cool in ambient air to the room temperature; the test was repeated two more times. The temperature increased linearly with voltage and showed very little hysteresis with applied bias. The maximum standard deviation of temperature at the hottest spot was ~11oC for GP at 6V. At higher voltages the standard deviation drops to ~0.6oC. The scatter in the results reflects the variability in the pyrometer readings at lower temperatures.    51  Figure  5.8: Variation in temperature-voltage profile of Si3N4-based GP in three warm-up cycles.               52 5.3 Degradation of silicon nitride GPs in engine3 5.3.1 Test conditions and sample description The testing parameters and a summary of the results in ETC and SS engine conditions are presented in Table  5.2 and Table  5.3 respectively.  Table  5.2: GP testing parameters and summary of results in ETC (1635 rpm, 165 Nm). Specimen Voltage, V Surface temperature, a °C Test duration, h Failed or Running b Min Yb, c wt%  Max Yb, c wt%  Mass Loss Rate, d  mg/h ETC1 9.50 1270 847.4 R 1.88 9.35 0.171 ETC2 9.50 1300 992.4 R 1.83 9.65 0.191 ETC3 9.50 1315 911.0 R 2.19 9.81 0.221 ETC4 11.00 1520 64.0 R 2.15 10.16 0.250 a – estimated from characterization values and applied voltage; b - at the end of the testing period; c - elemental Yb content determined by EDX through Si3N4 insulator cross-sections at the hot spot; d -  calculated from the weights of the entire GPs before and after testing. 5.3.2 SEM observations and EDX analysis At the conclusion of the engine tests, there were surface deposits on the first ~10-12mm from the front end of all ceramic pins, i.e. the effective heating zone with the highest resistivity of the U-shaped WC heating elements. The surface deposit was ytterbium disilicate precipitated on the layer of silica formed as a result of the silicon nitride oxidation. In this case, the silicate deposit was less protective towards the silicon nitride, due to the cyclic presence of reducing conditions, which would reduce the SiO2 to the volatile SiO. The specimens tested in this study were manufactured on an industrial scale and, as such, there are small but inherent variations in their                                                  3 A version of this section has been submitted for publication. C. Oprea, F. Wong, H. Karimi Sharif, C. Blair, A. Welch and T. Troczynski, Degradation of Silicon Nitride Glow Plugs in Various Environments, Part 3: Engine, (2011).  53 properties; for example, the 9.5V applied to three of the GPs tested in the ETC cycle yielded temperatures between 1270 and 1315°C, due to variation in the geometry and resistivity of the heating elements.  Table  5.3: GP testing parameters and summary of results in steady state SS (2000 rpm, 450 Nm). Specimen Voltage, V Surface temperature, a °C Test duration, h Failed or Running b Min Yb, c wt%  Max Yb, c wt%  Mass Loss Rate, d  mg/h SS1 12.9 1450 4.8 R 1.8 11.7 -3.083 SS2 12.9 1450 50.1 F 0.79 16.8 0.952 SS3 12.8 1450 50.1 F 0.75 14.0 1.07 SS4 13.3 1475 29.7 F 1.76 14.8 0.892 SS5 13.7 1500 8.90 F 1.09 12.1 0.551 SS6 14.3 1525 4.80 F 0.91 10.0 0.063 SS7 14.3 1550 8.90 F 0.00 22.8 0.337 SS8 14.3 1550 8.90 F 0.00 24.4 1.135 a – estimated from characterization values and applied voltage; b - at the end of the testing period; c - elemental Yb by EDX through Si3N4 insulator in cross-sections at the hot spot; d - as calculated from the weights of the entire GPs before and after testing. In the light-duty cycle testing, three specimens (ETC1-3) were removed from the engine after 847.4–992.4 hours, when they were still fully functional, meaning that they still provided ignition of the fuel. At these temperatures, normal for this type of engine, the internal structure of the ceramic pin was not found to be much degraded during this set of experiments. Low magnification SEM micrographs of the cross-sections at the hot spots through the Si3N4 pins of the GPs tested for different durations in ETC are shown in Figure  5.9. The loss of uniformity of the sintering additive (Yb2O3) cations and its redistribution in the intergranular phase of Si3N4 is apparent in all images by the darker-contrast areas, with a lower concentration of Yb, and the lighter-contrast areas, with higher concentration of Yb ions (Figure  5.10). The insulator phase in the as-received GPs contains ~9 wt% Yb, while in these specimens, Yb content varied between  54 1.83 and 10.16 wt% (Table  5.2). The variation of the sintering additive (Yb2O3) cations through the intergranular phase of the Si3N4 insulator was determined by the concentration (wt%) of elemental ytterbium as detected by EDX on the cross-sections. The standard deviation values were 1.42–2.03 and the maximum error for the calculated Yb was ±2.64 wt%. All the micrographs presented are of the cross-section through the ceramic pins at the hot-spot4.                   Figure  5.9: Micrographs of specimens ETC2 and ETC4; the (+) side is on the right. The overall mass balance at the conclusion of testing was negative, even though the silicate deposit of Yb2Si2O7 has formed on the surface of the ceramic pins and there should have been a mass gain due to the ingress of oxygen from the environment; the average mass loss for these GPs was 0.171-0.250 mg/h (Table  5.2, Figure  5.11). Material was lost on the surface of the pins, which is due to factors related to both the erosion by the hot high velocity gases and to complex chemical reactions.  The GPs placed in the engine's cylinders were surrounded by perforated metal shields and there was visible loss of material corresponding to the positions of the holes in                                                  4 The procedure for determining the experimental error in analyzing the elemental Yb concentration by EDX was detailed in Appendix C. 2 mm 2 mm JE2 JE4 TC2 TC4  55 the shields.  A computational fluid dynamic (CFD) analysis conducted by Westport Innovations indicated that peak velocities of ~ 150 m/s can occur near the inlet holes and velocities in the 10 m/s range can occur elsewhere inside the shield.  The GPs tested under the Steady State (SS) conditions were subjected to much higher voltage as well as much harsher engine conditions (higher speed and load), as an accelerated test,  due to time constrain (Table  5.3). The GPs were tested 4 at a time, in the 4 cylinders of the engine, which created some inconsistencies in the results, as different cylinders have different air flow, fuel flow, injector, etc., which in turn would create significant differences in the wear rates of the GPs.   Figure  5.10:   Micrographs of specimens ETC2 and ETC4: Yb ions migration away from the side of the WC elements connected to the (+) pole.  Micrographs of cross-sections of representative specimens are shown in Figure  5.12, Figure  5.13, and Figure  5.14. SS1 was removed from the engine after 4.8h, when it was still functional, while all the other samples were tested in SS to failure. Due to the higher applied voltage and higher temperatures, the degradation of the internal structure occurred much sooner and to a higher JE2-1300°C-992 h 200 µm JE4-1520°C-64 h ETC4-1520oC-64TC2-13 0oC-99 h  56 degree than in the ETC test. Elemental ytterbium values ranged between minimum 1.8/maximum 11.7 wt% for SS1 and minimum 0/maximum 24.4 wt% for SS8.   Figure  5.11: Variation of the mass loss with temperature.          Figure  5.12: Micrographs of samples tested at 1450°C in Steady State (SS): SS1 still working after 4.8 h; SS2 failed after 50.1 h.  SS1 SS2 2 mm (SS) (ETC)  57         Figure  5.13: Micrographs of the center and ends of the (+) side WC heating elements and surrounding Si3N4 of sampled tested at 1450°C in SS.        Figure  5.14: Micrographs of samples failed in SS: SS5, after 4.8 h at 1500°C and SS8, after 8.9h. Figure  5.13 depicts the microstructure of the (+) side of WC heating loops at the hot spot for the samples tested at 1450 °C. The GP that was tested for only 4.8h, and was still functional, showed very little degradation of either the WC terminals or the surrounding Si3N4 insulator. The WC heating filaments of the failed GP were also in good condition (judging by the central portion left SS5 SS8 2 mm SS1 50 µm SS2 100 µm 50µm  58 in place), but the Si3N4 had lost its intergranular phase in the vicinity of the heating element terminals, so part of the WC conducting material became dislodged during sample preparation. The significant mass loss in the ceramic heaters of the GPs failed under SS (Table  5.3, Figure 5.11) indicates that the erosion by the hot gases is the dominant cause of the degradation and failure of the Si3N4-based GPs in the engine. The material loss increases with the duration of exposure. The maximum mass loss rate of the ceramic material in SS was 4.5 times higher than the maximum in ETC (1.135 mg/h for SS8 compared to 0.250 mg/h for ETC4).  The influence of the engine cycle parameters on the internal degradation of the GPs is shown in Figure  5.15. In ETC the voltage applied to reach 1520°C was 11.0V, while in SS, to reach a similar temperature (1525°C), 14.3V had to be applied. The higher electrical field in SS led to stronger migration of the Yb ions away from the (+) side of the WC heating terminals and through the bulk of the Si3N4 insulator. The sample SS6 failed to maintain the ignition after only 4.8h, while sample ETC4 was still running at the end of the experiment, after 64h. Higher voltage is necessary in SS to ensure ignition because of the much higher gas flow that removes heat from the surface of the GP at a much higher rate than in ETC. 5.3.3 Summary  Some aspects of the Si3N4-based GP degradation in natural gas with direct injection engines are presented. The testing of the GPs was conducted both in the ETC and  SS cycles, the latter for accelerated runs. The higher speed and load in the SS resulted in much faster failure of the GPs. The engine is a very complex and dynamic environment with four modes of degradation (i-iv) which contribute synergistically to the failure of the GPs.   59 It appears that (i) the chemical degradation occurs through the following routes: oxidation of Si3N4 to SiO2, reduction of the protective SiO2, migration of the sintering additive ions towards the surface (which degrades the mechanical and electrical properties of the ceramic heater), reactions with the impurities in combustion gases (which form soft silicates, easy to remove).  The mechanical degradation (ii) is triggered by erosion by the high-pressure combustion gases, leading to mass loss in the ceramic heater. Cracking, due to thermal cycling and the associated thermal stress due to differences in the thermal expansion coefficients between the surface oxides and the base material, also contribute to the degradation. The thermal degradation (iii) results from increased temperature, which increases the rate of chemical reactions at an exponential rate and is accelerated by the electrical degradation of the conductive phase.  The electrical degradation (iv) is caused by the sintering additive ions migrating under the electrical field, leading to dielectric breakdown of Si3N4 across the WC heating loops; higher applied voltages accelerate this process.           60                Figure  5.15: Effect of the different voltages needed to reach the same temperature (1520-1525°C) in SS (top) versus ETC (bottom).      JE4-11.0 V 2 mm SS6-14.3 V ETC4- 1.0  V  61 5.4 Degradation of silicon nitride GPs in gas burner rig5 5.4.1 Test conditions and sample description A summary of the testing parameters for the seven GPs (coded BR1 to BR7) and their status at the end of testing (if failed or still in working condition) is presented in Table  5.4. The temperatures employed in this accelerated testing program were higher than the maximum 1250°C specified by the manufacturer; as a result, the degradation occurred faster and it is not indicative of the real performance in the conditions for which the GPs were designed. Table  5.4: GP testing parameters on the burner rig. Specimen Voltage, V Current, A Surface temperature a, °C Test duration, hours Condition b BR1 9.14 6.60 1425 10 working BR2 8.72 7.01 1425 406.5 failed BR3 9.32 7.06 1450 10 working BR4 9.93 7.22 1450 100.0 working BR5 9.96 6.85 1450 119.5 failed BR6 11.40 7.37 1500 10 working BR7 11.60 7.45 1500 27.9 failed a - read with the optical pyrometer at the hottest spot near GP tip; b - at the end of the testing period. 5.4.2 SEM observations and EDX analysis At the conclusion of burner rig testing, all Si3N4-based ceramic heaters showed a surface deposit on the first ~10 mm back from the front end (tip of Si3N4 heater); this is the effective heating zone with the highest resistivity of the U-shaped WC-containing heating elements.  The surface                                                  5 A version of this section was published online. C. Oprea, F. Wong, H. Karimi Sharif, C. Blair, A. Welch and T. Troczynski, Degradation of Silicon Nitride Glow Plugs in Various Environments, Part 2: Gas Burner Rig, International Journal of Applied Ceramic Technology (2011).  62 deposit consisted of ytterbium disilicate (Yb2Si2O7) precipitated from the layer of cristobalite covering the silicon nitride insulator [ 34].  The specimens tested for 10h at 1425 and 1450°C showed thin surface deposits (< 10µm), slightly more concentrated 5 mm back from the tip only on the pin region facing the flame (BR1 and BR3 in Figure  5.16  and Table  5.5). For this type of GP, the highest temperature of the ceramic pin is designed (through composition and dimension) to occur at ~5 mm back from the front end, at the center of the high-resistivity zone of the WC heating elements. These positions are easily identified on the pin surface, as the silicate deposit is the thickest and most disturbed (i.e. cracked and porous) there, and were also documented by X-ray images of failed specimens.  Additionally, at that level, the temperature on the circumference of the pin is ~50 °C higher in the two regions where the WC terminals are the closest to the surface, as verified by experimental readings and modeling results. After a 10h test at 1500°C (BR6 in Figure  5.16), the deposit was thicker on both areas where the WC heating element’s terminals are closer to the surface of the ceramic heater, as measured by SEM-BSE.  In contrast, the scale on the GPs tested to failure (BR2, BR5 and BR7 in Figure  5.16) was much thicker (up to 65 µm) and it was very disturbed at the hot spot, as shown by the micrographs of the ceramic pin surface depicted in Figure  5.17. The cristobalite layer was very cracked, (see dark grey contrast phase in Figure  5.17), thus likely without any protective qualities towards the substrate.   Figure  5.16: Photographs of the seven GPs tested on the burner rig.  63   Figure  5.17: Micrographs of selected areas on the surface of failed GPs: top row - BR2 at 1425°C; middle row – BR5 at 1450°C; bottom row – BR7 at 1500°C; images at 1 mm back from the tip of the pin - left; at 5 mm - middle; at 7 mm – right; the white bar represents 20 µm for all images. The thickness of the surface deposit formed under different conditions was measured using the SEM, and the results relating to the cross-sections at the hot spot are shown in Table  5.5. The cross-sections of the ceramic pins were analyzed by SEM/EDX; wt% Yb values determined in 20 positions on a set pattern and in other positions through the Si3N4 insulator are also presented in Table  5.5.   64  Table  5.5: Summary of analysis results of the GP heaters tested in Burner Rig. Specimen Minimum Yb, wt%c Maximum Yb, wt% c Mass variation, mg/h d W present on surface e W present in Si3N4 bulk e Scale thickness, µmf BR1 2.9 10.5 0.59 no no 1-4 BR2 0.0 34.5 0.54 yes yes 0-15 BR3 2.5 12.6 0.63 no no 1-7 BR4 0.0 38.7 0.48 no no 15-45 BR5 0.0 48.2 0.39 yes yes 14-65 BR6 0.6 16.4 0.70 no no 2-24 BR7 0.0 47.6 0.27 no no 6-38 c - elemental Yb by EDX through Si3N4 insulator in cross-sections at the hot spot; d - as calculated from the weights of the entire GPs before and after testing; e - elemental W by EDX on the cross-sections at the hot spot; f - SEM measurements on the cross-sections at the hot spot Low-magnification SEM micrographs of the cross-section at 5 mm through the ceramic pins of the tested GPs, along with an as-received GP (BR0) are presented in Figure  5.18. Throughout the bulk of the Si3N4 insulator, the lighter contrast areas contain higher levels of Yb than the darker ones. The side of WC heating elements connected to the positive terminal of the GPs is for all instances on the right side of the images and a higher structural alteration in these regions is evident, due to the Yb ion migration from the positive side towards the grounded side, with lower potential. The wt% of elemental ytterbium, as detected by EDX, was used to determine the ytterbium variation through the intergranular phase (composed of complex glass and crystalline Yb2Si2O7). The standard deviation values were 0.51-1.13 wt%, and the maximum error for the calculated Yb wt% was in this case ±1.52 wt%.  65   Figure  5.18: Micrographs of cross-sections at 5mm back from the tip; BR0 is an as-received specimen; the white bars represent 2mm and the (+) side is on the right for all images.  66 As seen in Figure  5.18, there is no lower Yb band just below the surface for GP BR1, as seen for BR6 at 1500°C. The scale on BR6 is thicker (2-24µm) and is not uniform around the perimeter; it is 2-24 µm thick on the side of the grounded WC filaments and only 2-11 µm on the side of the positive connector (+). This could be explained by the larger availability of Yb in this area, as the positive ions were pushed away from the (+) side and this is characteristic to all samples with extended test duration. Figure  5.19 shows the ends of the WC heating elements and the surrounding Si3N4 insulator in two GPs tested for 10 h, at higher magnifications; the grounded sides of BR1 and BR6 are marked (0) and the positive sides are marked (+). There was not a large variation of the Yb ion concentration in the region adjacent to the grounded side at 1425°C (8.2-10.5 wt% Yb, compared to the 9 wt% in an unused GP).  At the highest testing temperature of 1500°C, the region around the (0) side WC filaments showed a higher than initial concentration of Yb (10.3-16.4 wt%) and the right narrow end of the WC terminal, facing the centre of the section, was surrounded by a very thin but compact band of Yb2Si2O7. In contrast, for both temperatures, the (+) side showed lower Yb ion concentrations, decreasing with increasing temperature; 2.9-3.8 wt% in BR1 and only 0.6-0.7 wt% in BR6, on a much larger area. For BR6, the ‘wave-like’ patterns of higher Yb are well developed, as the higher potential of the (+) side drives away the Yb ions.  The internal structure of the WC heating elements was not altered, even at 1500°C.  For the same temperatures, micrographs of the WC filaments in the ceramic pins of GPs tested to failure (BR2 and BR7) are presented in Figure  5.20. At both temperatures, there was significant accumulation of Yb2Si2O7 in the form of a band around the ends facing the (+) side; the Yb ions were pushed away from the (+) side and towards the lower potential ground (0) side. Also, the insulator area surrounding the low potential WC terminals (0) contained much less Yb on the  67 side closest to the surface of the section, as the combustion atmosphere induced the outward concentration-driven diffusion of Yb ions and the oxide scale was thicker (0-15 µm for BR2 and 6-38 µm for BR7).  The general pattern of degradation and failure incurred due to the redistribution of the sintering additive (Yb2O3) cations under the influence of the electric field appears to be synergistically supplemented on the burner rig by the chemical (combustion) component of the system. On the burner rig the measured value is a function of both the flame temperature and the electrical load on the GP.  After 10h on the burner rig, the maximum Yb value throughout the bulk of the Si3N4 insulator was 12.6 wt% and the thickness of the oxide scale was 1-7 µm. At failure, these values were much higher: 48.2 wt% Yb on burner rig and the thickness of the scale was 14-65 µm on the burner rig. Also, the Si3N4 decomposition on the burner rig was much more extensive on the (0) side, with evidence of significant degassing and W from the heating elements found as WO3 in the scale, as seen in Figure  5.21.   68  Figure  5.19: Micrographs of the WC heating element’s ends and the surrounding insulator at 5 mm, for the GPs tested for 10 h (BR1 at 1425 and BR6 at 1500°C); (0) denotes the grounded side of the WC filaments and (+) the side connected to the positive electrode; the bar is 50 µm for all images.  69  Figure  5.20 : Micrographs of the WC heating elements’ ends and the surrounding insulator at 5mm, for GPs tested to failure (BR2 at 1425 and BR7 at 1500°C); (0) denotes the grounded side of the WC filaments and (+) the side connected to the positive pole; the white bar is 50 µm for all images.   70  Figure  5.21: Micrographs of the outer oxide scale on BR5: left - on the grounded side; right - on the positive side. The failure on the burner rig occurred at the hot spots, which are at 5 mm back from the front end (tip) of the ceramic pin, and see the highest temperatures. Failure means the physical destruction of one of the WC heating loops. Failure originates inside the WC heating loops; gradual degradation of the internal structure begins inside the WC elements, with the migration of the additive (Yb2O3) cations from the positive side, when voltage is applied. In time, as Si3N4 loses its intergranular phase, the WC particles lose their interconnectivity, which may cause localized arcing and very high temperatures inside the WC heating elements, leading to thermal decomposition. With an increase in temperature and duration of exposure, the divergence between the minimum and maximum values of Yb concentration in the bulk of the Si3N4 insulation increases, to higher maximums and lower minimums (Figure  5.22). The maximum Yb concentration rises quickly and approaches a value near 40 wt% at failure.  The minimum Yb concentration typically approaches 0% at failure but low Yb concentration values have been also detected in functional GPs. The ytterbium concentration at the center of the cross section does not provide a reliable failure determination, as waves of ytterbium can travel through the center and no definitive / reproducible value has yet been identified.  71  Figure  5.22: Variation of Yb concentration through the Si3N4 in cross-sections at 5mm back from tip: left - tested for 10 h at different temperatures; right - for different durations at 1450°C on the burner rig. The GPs were weighed before and after testing on the burner rig and it was considered that any mass variation would be only due to corrosion/erosion of the ceramic heater (the remaining GP body does not reach temperatures higher than 650ºC).  The resulting average weight variation over the testing duration (mg/h) is presented in Table  5.5 and in Figure  5.23. For the 10h tests, there was mass increase in the range 0.6-0.7 (mg/h), indicative of more significant oxidation of the Si3N4 surface with temperature. For the longer testing durations (and up to GP failure), some mass loss occured by the decomposition of the superficial layer of Si3N4 and its corrosion products; this loss increased with temperature, thus reducing the mass increase rate.  72  Figure  5.23: Mass variation at the three testing temperatures, after 10 h and at failure.  5.4.3 Summary Experimental results of accelerated degradation tests of all-ceramic Si3N4-based GPs on a burner rig are presented. Even though not statistically reliable due to the relatively small number of samples, this study identified some consistent trends of GP degradation and failure in the natural gas burner rig, where the combustion atmosphere containing reducing agents combined with applied bias creates the deterioration mechanism. It appears that the degradation mechanism of the ceramic heater has two synergistic components: (1) redistribution of the sintering additives in the Si3N4/Yb2O3 system under the influence of a DC electric field and temperature and (2) chemical interaction with the combustion gases.  In a typical test campaign only one of the two GP heating elements had completely failed (this refers to each of the three failed GPs). The ytterbium migration levels were reasonably consistent: the minimum Yb concentration was 0.0 wt% for all three GPs and the maximum Yb concentration was a strong function of temperature, increasing from ~35 wt% at 1425°C to ~48 wt% at 1450°C.  The  73 maximum Yb concentration was roughly linear with the test duration and approached ~ 48 wt% at failure; this may prove useful in estimating GP life when analyzing functional GPs from the engine tests.  The minimum Yb concentration typically approached 0.0 wt% at failure but the very low values detected in functional GPs make this measure difficult to use.   The measured mass increase due to the inward migration of oxygen and the formation / erosion of the ytterbium disilicate on the surface of the SiO2 is indicative of significant oxidation of the Si3N4 surface with temperature. For the longer testing durations, there was some mass loss, which likely included the decomposition of the superficial layer of Si3N4 caused by locally reducing combustion gases; this loss increased with temperature, thus reducing the mass increase rate.          74 5.5 Degradation of silicon nitride GPs in DC electric field in air6 5.5.1 Test conditions and sample description The testing parameters of the ten GPs (coded DC1 to DC10), as well as their condition at the end of testing (if failed or still in working condition) are presented in Table  5.6. As this was a long-term study, the specimens required for testing could not be secured all at the same time, i.e. they originated from different lots, with the inherent slight variations in their properties. For example, specimen "DC3" had an excessively high resistance, so the voltage required to reach the same temperature (1450°C) as specimen "DC2" was higher (13.5 V compared to 11.2V).    Table  5.6: GP testing parameters on the DC electric rig. Specimen Voltage, V Current, A Surface temperature a, °C Test duration, hours Condition b DC1 11.37 8.80 1370 5289 working DC2 11.16 8.48 1450 10 working DC3c 13.48 9.03 1450 3366 failed DC4 12.14 8.96 1500 10 working DC5 12.07 8.68 1500 98 working DC6 12.00 9.10 1500 238.5 failed DC7 13.01 8.92 1520 36.5 failed DC8 12.56 9.06 1560 10 working DC9 13.50 9.27 1590 3.2 failed DC10 14.02 8.62 1610 2.7 failed a - read with the optical pyrometer at the hottest spot near GP tip; b - at the end of the testing period; c - this specimen had an excessively high resistance, so a much higher voltage had to be applied to reach the same temperature as “DC2”                                                   6 A version of this section was published. C. Oprea, F. Wong, H. Karimi Sharif, C. Blair, A. Welch and T. Troczynski, Degradation of Silicon Nitride Glow Plugs in Various Environments, Part 1: DC Electric Field in Ambient Air, International Journal of Applied Ceramic Technology (2011).   75 Although the temperatures employed in this accelerated testing program were much higher than those specified by the manufacturer as the maximum (1250°C) for this type of GPs, hence degradation incurred much faster,  the electric rig testing still captured many important degradation modes (such as redistribution of Yb ions). 5.5.2 Characterization of GPs aged in electric rig At the conclusion of electric rig testing, all ceramic pins  of the GPs showed a surface deposit, that consisted of ytterbium disilicate (Yb2Si2O7) crystallized on top of a layer of cristobalite, on the first ~10 mm  from the front end, which is the effective heating zone with the highest resistivity of the U-shaped WC-containing heating filaments. Micrographs of the surface deposit on select specimens are presented in Figure  5.24 and Figure  5.25. For specimen DC1, tested for the longest time (5,289 h) at the lowest temperature of 1370°C, the highest concentration of elemental Yb (63.8 wt%) was found at 5 mm back from the tip (Figure  5.24) and it was very close to the stoichiometric value in Yb2Si2O7, indicating a very compact, possibly single-phase, surface deposit. The morphology was also very different from the areas with less compact deposits, such as at the tip, where the Yb2Si2O7 crystals were acicular and the elemental Yb was detected at 36.1 wt%. For specimen DC3, tested to failure at 1450°C, the silicate deposit was more compact and covered a larger area of the ceramic pin, as seen in Figure  5.26.  The crystals were better developed than at the corresponding locations in specimen DC1 (Figure  5.25) and the concentration of elemental Yb found at the tip was higher (46.3 wt%). However, at the hot spot, where the failure of the WC heating loops occurred, (Figure  5.25c, d) the silicate deposit was very thick, with numerous cracks (possibly induced by the strong degassing at that level, due to the high temperature decomposition of Si3N4) and concentrated in a small region on top of a very thick and heavily cracked cristobalite layer. The surface deposit formed under  76 different conditions was measured and the results in the hot spot cross-sections are shown in Table  5.7.  The cross-sections of GPs at different levels were analyzed by SEM/EDX and wt% Yb values determined in 20 positions on a set pattern, as well as in other locations of interest throughout the bulk of the Si3N4 insulator, are also presented in Table  5.7.    Figure  5.24: Yb2Si2O7 deposit on the surface of specimen DC1 compared to the heater surface of an unused GP (bottom).  77  Figure  5.25: Yb2Si2O7deposit on the surface of specimen DC3: a - at the tip; b - at 3mm; c, d - at the hot spot (5mm); bar represents 10 µm for all images.            Figure  5.26: Elemental Yb variation (EDX results) on the surface of the ceramic pins for specimens DC1 and DC3 at two temperatures, compared to an unused specimen. Unused “DC1” 1370oC “DC3” 1450oC  78 Table  5.7: Summary of analysis results of the GP heaters (DC electric rig). Specimen minimum Yb, wt%d maximum Yb, wt% d mass variation, mg/hr e W present on surface f W present in Si3N4 bulk f scale thickness, µm g DC1 2.34 13.52 - no no 15-20 DC2 5.84 9.11 0.160 no no 1-5 DC3 0.00 20.16 - no no 10-40 DC4 1.86 20.43 0.210 no no 5-7 DC5 1.05 40.86 0.043 no no 5-15 DC6 1.48 45.17 0.008 yes yes 23-47 DC7 0.00 55.12 0.002 no no 17-40 DC8 0.00 48.42 0.151 no no 3-14 DC9 0.50 23.64 -0.281 yes yes 12-48h DC10 0.62 25.91 -2.148 no yes 0-3i d-elemental Yb by EDX through Si3N4 insulator in cross-sections at the hot spot; e-as calculated from the weights of the entire GPs before and after testing; f-elemental W by EDX on the cross-sections at the hot spot; g-SEM measurements on the cross-sections at the hot spot;   h - very disturbed surface deposit, with significant degassing; i - very thin and spotty deposit  A low-magnification SEM micrograph of the cross-section (at 5mm back from the tip, where the highest temperature was read) through specimen DC1 (aged for 5,289 h at 1370°C and still working at test termination) is presented in Figure  5.27. The side of the two WC heating loops connected to the positive electrode on the GP (marked “+”) appears to have incurred much more structural disruption (both inside and in the adjacent insulator) than the side connected to the ground. There is a significant variation of the amount of Yb2Si2O7 in the intergranular phase of Si3N4; the slightly darker contrast regions of the Si3N4 contain less Yb than the lighter regions. In the immediate vicinity of the (+) side there is much less Yb (~2.3 wt% compared to ~9.0 wt% in the cross-section of a new ceramic heater, indicating a lower concentration of Yb2Si2O7), followed by a band of higher concentration (11.9 wt% Yb) as well as agglomeration of Yb around the grounded side. It appears that the higher electric potential of the (+) side drives away  79 the positive ions Yb into the insulator bulk. Cracks and delamination of the structure, both in the WC elements and in the Si3N4 near the WC terminals, can also be observed.   Figure  5.27: Micrograph of the cross-section through the ceramic pin of sample “DC1”, 5mm from tip (Yb wt% in Si3N4 by EDX is given).  The higher magnification micrographs presented in Figure  5.28 show modifications of the internal GP structure. The Si3N4 just below the Yb2Si2O7 surface scale (diffusion layer, shown in “area 1”) contains much less Yb than originally present in the sintered Si3N4; local spots of a few microns with even zero concentration of Yb have also been found. The surface silicate scale was quite porous, with a columnar structure and the maximum thickness of ~20µm. Images depicting “area 2” and “area 3” show the loss of Yb in the insulator in the vicinity of the (+) electrode of the heating elements. A compact band of Yb2Si2O7 with high ytterbium content (54 wt%) is seen in “area 5” as formed on the grounded electrode.  It appears that Yb ions were pushed away from the (+) side of the WC heating element towards this lower potential region. The damage of the sintered structure inside the WC heating elements on the (+) side can clearly be observed in “area 2a” (area 2 at higher magnification) compared to the regular structure of the grounded electrode,  80 seen in “area 4”. EDX analysis showed 0.5 wt% Yb in the structure of the low potential WC heating terminal, but no Yb inside the (+) WC filament structure, indicating that Yb ion migration had started from inside the (+) side of the WC terminals (there is 0.5-0.7 wt% Yb in the WC terminals of an unused GP).   Figure  5.28: Marked areas 1-5 in the section through “DC1” (Figure  5.27), at different magnifications; area 2a – WC terminal in area 2 at higher magnification.  81            Figure  5.29: Micrographs of the cross-section at 5 mm through the ceramic pins of specimens tested at 1450°C: “DC2”-10 h, left; “DC3”-failed at 3366 h, right Low-magnification images of the cross-sections through specimens DC2 and DC3, aged at 1450°C for 10 h and to failure for 3,366 h (Figure  5.29) , respectively show the development of Yb ion migration from the (+) side to the low potential side of the WC heating element ends, with time; in “DC2”, the Yb content throughout the section varied between 5.8 wt% and 9.1 wt% (in the centre) and the surface deposit was very thin (2-5 µm), while in “DC3”, the Yb content range was 0–20.2 wt% and the scale was 10-50 µm thick. Images of the WC terminals (centre and ends) at higher magnifications are shown in Figure  5.30. The structures of both the WC filaments and the insulator do not change after 10 hours in service and there is little migration of the Yb through the bulk of the insulator (Figure  5.30a, c); at the tapered ends of the WC filaments (i.e. at the brightest contras area), there is no Si3N4 mixed with WC, so the electrical conductivity in this region would be increased. By contrast, Figure  5.30b,d, as well as Figure  5.31, show dramatic modifications of the internal structure of the insulator and both sides of the DC2 DC3  82 WC heating elements, albeit much less for the grounded side. Decomposition of Si3N4, areas of high Yb2Si2O7 concentration in the insulator, large voids surrounding the WC heating filaments, and Si3N4 regions with high porosity have been observed. The progressive diffusion of the Yb ions leads to the loss of uniformity in the intergranular phase and formation of different regions, some with very high additive ion content and others that are very low, even zero. This likely causes the weakening of the insulator structure, as the Si3N4 grains are not supported by the intergranular phase. The structure of the WC heating loops also collapses, the WC particles loose their interconnectivity and the resistance increases, perhaps leading to local regions of high current flux, arcing and micro hot-spots. This effect may be cumulative, eventually leading to microscopic short-circuits generating very high temperatures inside the WC heating elements, leading to WC and silicon nitride thermal decomposition, which would explain the voids surrounding the positive side of the WC terminals. This proposed mechanism of the WC heating elements failure is supported by the results obtained from the heat transfer model which indicate that the temperature on the surface points closest to the WC heating element ends can be ~50-100°C higher (dependent on the applied bias)  than on the rest of the circumference. The breakdown occurs exponentially faster at higher temperatures, and the higher applied voltage also accelerates the diffusion of Yb, independently of temperature. It is most likely that a short circuit occurs as a consequence of the intrinsic dielectric breakdown, leading to a rapid local increase in temperature, which will accelerate the diffusion rate of the mobile Yb ions. Moreover, this will also cause the decomposition of the WC element. Images of the cross-section at the hot spot for the specimens tested at 1500°C (specimens DC4, DC5 and DC6) are presented in Figure  5.32−Figure  5.37. The surface scale on specimen “DC4” after 10 hours is slightly thicker than for “DC2”, (5-7 µm), shown in Figure  5.29, and the elemental Yb in the bulk of the insulator is in the range 1.9 - 20.4 wt%. There is a substantial  83 band of ytterbium disilicate surrounding the side of the grounded WC heating elements that faces the centre of the section (Figure  5.33, area 3a). For sample “DC5”, tested for 98 hours, there are thin but sharp lines of Yb2Si2O7, including large particles of Yb2Si2O7 (Figure  5.34-area 9). The higher Yb concentration (up to 41 wt%) waves move clearly away from the positive electrode and towards the grounded side, but there is not much Yb variation between the two U-shaped heating elements. The compact Yb2Si2O7 band around the grounded sides extends to ~1/4 of the WC heating elements width (Figure  5.34, area 7). Figure  5.35 shows the higher magnification of area 7 on the grounded side in GP “DC5”. The accumulation of Yb ions at the insulator/WC element interface is visible and WC particles are loosely bound by the intergranular glassy and Yb2Si2O7 phase.  The elemental Yb concentration is 1.1-40.9 wt%, or 1.5-61 wt% Yb2Si2O7 and the surface silicate deposit is thicker (5-15 µm). For the failed specimen DC6, the divergence of the minimum and maximum Yb values is even higher (1.5-45.5 wt%) and the Yb2Si2O7 oxide scale deposit is very thick (23-47 µm). It is to be noted that tungsten based complex was found on the surface, as part of the scale (Figure  5.36, area 16), as well as throughout the Si3N4 bulk, as very small particles. This section shows much more significant high-concentration Yb lines, moving in parallel waves away from the positive electrodes of the heating elements. The accumulation of space charge through the bulk of the insulator, causing variations in the electric field, would determine the locations of the Yb ions agglomerations. Areas of loose particles of Si3N4 around the low potential sides of the WC terminals (Figure  5.36, area 15), as well as numerous areas of porous Si3N4 (Figure  5.36, area 12) are visible.    84  Figure  5.30: Micrographs of center and ends of the WC terminals at 5mm for specimens tested at 1450°C (“DC2”-10 h, “DC3”-failed at 3366 h): a-grounded side of “DC2”; b- grounded side of “DC3”; c-(+) side of “DC2”; d-(+) side of “DC3”.   85  Figure  5.31: Micrographs of the marked areas 1-4 on section through specimen DC3 (Figure  5.29) at higher magnifications.   Figure  5.32: Micrographs of the cross-sections at 5 mm through the ceramic pins of specimens tested at 1500°C: “DC4”-10 h, left; “DC5”-98 h, center; “DC6”-failed at 238.5 h, right.  86  Figure  5.33: Specimen “DC4”- details of marked areas 1-6 in Figure  5.32 at higher magnifications; areas 2a, 3a and 5a are details in areas 2, 3 and 5, respectively.   Figure  5.34: Specimen “DC5”- details of marked areas 7-11 in Figure  5.32 at higher magnifications; YS : Yb2Si2O7.         87                      Figure  5.35: Specimen “DC5”- details of marked area 7 in Figure  5.34 at higher magnifications.    Figure  5.36: Specimen “DC6”- details of marked areas 12-17 in Figure  5.32 at higher magnifications.   5µm Yb-containing phase WC  88 Specimen DC8 was tested at 1560°C for 10 hours and it was still in working condition, albeit with degraded performance at test termination (Figure  5.37). There were areas with zero Yb concentration (marked area 1), at darker contrast spots, as the insulator contains no Yb2Si2O7   and the structure is very porous.  The maximum Yb content found on the cross-section at 5 mm back from the tip was 48.4 wt%. There were areas with zero Yb around the WC filaments, so there was significant damage to the structure; at the least, some of the WC particles lost their binding phase, becoming weakoned. Thus the missing heating element matter was probably lost during the sample preparation, e.g. when cutting or polishing. Specimens DC7, DC9 and DC10 were tested to failure at 1520°C (lifetime of 36.5 hours), 1590°C (lifetime of 3.2 hours) and 1610°C (lifetime of 2.7 hours), respectively. They showed rapid degradation leading to failure at these temperatures, with massive destruction of the internal structure. Micrographs of the cross-sections at the hot spot are presented in Figure  5.38. For specimens DC9 and DC10, the maximum Yb concentration in the bulk of the insulator is about half that of “DC7”, even though the temperature was higher.  This is likely due to the very short lifetime of these specimens.  The high applied voltage (13.5 and 14.0 V respectively) caused the rapid destruction of the WC heating filaments, not allowing for the development of well-defined Yb migration lines, such as in “DC7”. There is noticeable mass loss for “DC9”, but especially for “DC10” (~10 times higher than for “DC9”), most of it from matter lost on the surface of the ceramic pin, especially in the planes of the heating loops, where the temperature is ~50°C higher than on the rest of the circumference. At the moment of GP failure, the temperature was probably high enough to vaporize the intergranular phase of the insulator. Also, tungsten was detected as WO3 on the surface and in the bulk of Si3N4 (Figure  5.38) for “DC9”, but only inside for “DC10”, indicating that the insulator structure was very cracked and porous, allowing the oxidation of WC to form the volatile WO3 oxide. Except for specimen “DC2”,  89 tested for only 10h at 1450°C, the compact band of Yb2Si2O7 around the grounded side of the heating loops was observed in all sections at 5mm back from the tip (Figure  5.28, Figure  5.30, Figure  5.33, Figure  5.34, Figure  5.36).     Figure  5.37: Specimen “DC8”, in working condition after 10 h at 1560°C: micrographs of the cross-section at 5mm.          90                              Figure  5.38: Micrographs of the cross-sections at 5mm for specimens DC7, DC9 and 5.5mm for specimen DC10; marked areas 1 and 2 at higher magnifications. GPs that were tested for the same duration (10.0h) show increased degradation of the performance at higher temperatures, as expected. The variation in ytterbium concentration for these GPs is shown in Figure  5.39 (left). The maximum of Yb values increases with temperature and the difference between minimum and maximum values also increases with temperature. The degradation is higher for longer testing times, as seen in Figure  5.39 for the specimens subjected to 1500°C.   DC7 DC9 DC10  91 The effect of test duration at the same temperature (1500°C) is shown in Figure  5.39 (right), showing the noticeable trend of increasing ytterbium migration away from the (+) side of the heater; the maximum Yb values in the cross-sections at the hot spot increase with testing time. After 10 hours, there is a minimal variation of the Yb concentration, while after 98.0 hours more migration is evident and at 238.0 hours, the SEM micrographs show very noticeable migration around all four elements; also, the range of Yb wt% values found in the bulk of the Si3N4 is much larger. The difference between the maximum and minimum values of Yb per hour of testing of these GPs was calculated as ∆Yb/life = (maxYb-minYb)/h and presented in Figure  5.40. The divergence between the minimum and maximum Yb values increases dramatically at temperatures higher than 1500°C.  Figure  5.39: Variation of Yb concentration through the Si3N4 in cross-sections at 5 mm: tested for 10 hours at different temperatures (left) and for different times at 1500°C (right)    92  Figure  5.40: Divergence between maximum and minimum Yb values calculated over the life in service (∆Yb) versus temperature when testing for 10 hours (left) and to failure (right) The GPs were weighed before and after the aging on the electric rig; the average rate of mass variation is shown in Table  5.7. For a short duration of testing (10.0h), there was a mass gain of 0.15-0.21 mg/hr, most likely due to the formation of the silicate deposits on the surface. At longer testing times there is also mass loss in the Si3N4 bulk, which reduces the overall mass variation rate; for more drastic conditions such as for the failed specimens DC6, DC9 and DC10, relatively fast mass loss was observed (up to -2.15 mg/hr). In short, it is determined that the degradation process of the ceramic heater begins in the WC loops (including the conductive WC powder embedded into insulating Si3N4 sintered with Yb2O3 additive), with progressive migration of the Yb ions under the influence of the applied voltage, away from the positively biased arm of the heating loops. Under the applied electric voltage, the Yb ions diffuse through the intergranular silicate phase, expectedly following the lines of the electric field. The progressive diffusion of the Yb ions leads to the loss of uniformity / integrity in the intergranular phases, some including very high Yb content and others with very low, even zero, Yb content. This likely causes the weakening of the Si3N4 structure, as the Si3N4 particles are ultimately left without the intergranular bonding phase, as seen in the most drastic cases. Consequently, as the structure of the WC filaments collapses, the WC particles lose their  93 interconnectivity, which may lead to localized arcing, generating very high temperature inside the WC heating elements.  Ultimately, both the Si3N4 insulator and the heating filament melt or decompose in the region surrounding the WC elements; W also migrates towards the surface, depositing as WO3, interspersed with the ytterbium disilicate.  The thickness of the surface silicate scale and the maximum concentration of Yb in the Si3N4 bulk increased parabolically with the exposure time, which is typical of the oxidation trends of Si3N4 in dry air. At 10 h exposure time, the maximum thickness of the scale and the maximum concentration of Yb in the Si3N4 bulk increased parabolically with the heater's temperature. With an increased voltage (hence increased test temperature), the surface silicate scale is less compact and becomes relatively thin and non-continuous. At higher test voltages, there is significantly less Yb diffusion observed towards the surface, indicating that the failure occurred too fast for significant oxidation and surface silicate formation to take place. The failure in tests above 1500oC is relatively fast (just a few hours at ~1600oC), not allowing sufficient time for the ion migration to occur. Much higher GP mass loss rates are also observed at these temperatures, including WC lost as a volatile oxide, likely due to electric arcing.  As a result of Yb redistribution due to the applied voltage, the maximum Yb concentration value in GP regions close to the grounded electrode rises quickly with test temperature and appears to approach a value of about 45 wt% at failure.   5.5.3 Summary Experimental results of accelerated degradation tests of all-ceramic Si3N4-based GPs in air, using an electric rig, are presented. This study identified some consistent trends of GP failure while not providing for a statistically reliable / reproducible sample.  The degradation  94 mechanism of the ceramic heater has been linked primarily to the redistribution of the sintering additives in the Si3N4/Yb2O3 system under the influence of a DC electric field and temperatures in excess of 1350°C, as commonly experienced by GPs in-service with natural gas direct injection engines. Under these conditions Yb ions migrate away from the positive electrodes, continuously changing the composition of the intergranular phase, thus leading to gradual performance degradation and eventual failure.           95 5.6 Degradation of Si3N4 GPs in AC electric field7  5.6.1 Test conditions and sample description The purpose of this test was to examine the durability of conventional GPs under AC electrical load and to compare the resulting damage pattern, mostly in terms of Yb ion redistribution, with results obtained previously in the DC electric rig [ 50,  51,  153,  154]. Initially, two GPs (Specimen DC3 and AC1) were tested continuously on such an H-bridge electric rig; GP “DC3” was powered by DC while the GP “AC1” was powered through the H-bridge.  Both GPs were tested at the same steady-state temperatures on the surface of the GPs, at the hot spot (1455°C), to determine whether or not the AC square wave showed any potential for increasing the GP durability. The remaining five GPs (AC2- AC6), Table  5.8, were aged at different temperatures and for different lengths of time to map the degradation of the GPs as a function of temperature and applied potential. Table  5.8 summarizes the aging parameters for the GPs tested in the AC-electric rigs. The specimens “DC3” and “AC1” were tested at the same temperature (1455oC) but under different electrical loading patterns; the specimen “DC3” was aged in a DC electric field and failed after 3,366h while specimen “AC1” was aged in an AC electric rig and was still running at the end of the test (i.e. at 3,366h).  To further investigate the effect of using a square wave signal to power the GPs, another 5 GPs (specimens AC2- AC6) were tested under AC power and run to failure to map the degradation of the GPs due to the AC-electric field. Characterization of the GPs was made before and after testing to determine the deterioration patterns.                                                   7 A version of this section has been submitted for publication. H. Karimi Sharif, T. Troczynski, C. Oprea, C. Blair, A. Welch, Model for the AC Electric Field-Enhanced Degradation of Si3N4 – Based Ceramic Glow Plugs, (2011).  96 Table  5.8 : GP testing parameters on the AC electric rig. Code Aging Condition Voltage (V) Current (A) Power (W) Temperature (oC)* Condition† Life (h) AC1 HB 13.0 9.9 128.7 1455 Running 3366 AC2 HB 13.4 9.8 131.3 1500 Failed 2881.5 AC3 HB 14.3 9.9 141.6 1533 Failed 287.5 AC4 HB 14.4 10.0 144.0 1535 Failed 371.9 AC5 HB 14.3 10.1 144.4 1543 Failed 327.5 AC6 HB 15.0 10.0 150.0 1577 Failed 4.6 *Read with the optical pyrometer at the hottest spot near GP tip. †At the end of the testing period. Figure  5.41 shows the variation of temperature with voltage and confirms that the temperature increased nearly linearly with an increase in H-bridge applied voltage. Photos of the ceramic pins DC3 and AC1-AC6 after the testing are shown in Figure  5.42. The oxidation is more advanced within 3-5 mm from the tip, referred to as the “hot spot” [ 50– 52,  153,  154]. This is in agreement with the pyrometry studies [ 153] in that the temperature is not uniform all over the outer surface at the hot spot (Figure  5.42).  5.6.2 SEM observations and EDX analysis Figure  5.29 (Specimen “DC3”) shows the 3,366 hour micrographs of GP tested in DC electric rig (refer to Table  5.6 and Table  5.8 for the test parameters settings), in parallel with the specimen “AC1”. It is evident that the ends of the two U-shaped heating elements where the voltage is applied are completely destroyed and there is extensive migration of Yb ions from the intergranular phase away from the high-potential WC terminals [ 154], leading to increased porosity throughout the bulk of the insulating Si3N4 substrate.   97  Figure  5.41 : The relationship between temperature and applied potential; the temperature was measured by a pyrometer at the hot spot on the surface of as-received GPs (i.e. at 0.0h service).              Figure  5.42: Photos of the ceramic pins detached from GPs after the testing in AC electric rig (ambient air). DC3 AC1 AC2 AC3 AC4 AC5 AC6  98 When the specimen “DC3” failed (signified by an electric power decrease by a factor of two), the specimen “AC1” was also removed from the AC test rig so that it would have experienced the same amount of aging time in the test rig under the same steady-state temperature of 1455oC. While the specimen “DC3” has completely failed, the specimen “AC1” has experienced a performance degradation of about 4%, i.e. the temperature at the hot spot dropped by about 50oC.  Figure  5.43 illustrates the SEM/EDX micrograph of specimen “AC1” at the hot spot. While the DC-powered GP (“DC3”) showed  typical damage of two heating filament terminals and Yb ion migration patterns for the failed high potential WC terminals [ 50– 52,  153,  154], the specimen “AC1” tested in the AC electric rig showed considerably different, notably symmetrical, Yb ion migration patterns around all the WC heating element terminals, and minimal WC heating element damage. The SEM/EDX analysis of Yb ion concentration for the regions presented in Figure  5.43 shows that the Yb ion concentration decreased significantly in the immediate vicinity of all WC heating element ends on the cross section of “AC1”, resulting in the formation of four symmetrical Yb-depleted regions. The Yb-depleted regions had a “leaf” shape, with the thinner tip towards the surface. The concentration of Yb ions slightly increased in the center, between the heating elements, as well as at the outer tips of heating filaments. In addition, owing to the migration of Yb ion under the effect of concentration gradient, a band of low Yb ion concentration was formed at the circumference of the Si3N4 –based, body beneath the silica enriched layer, and showed evidence of preferential diffusion paths for the Yb ions.  Figure  5.44 presents the micrographs of the marked areas (1–4) on the cross section of specimen “AC1” in Figure  5.43, showing oxide deposits and the band of Yb ion depletion at higher magnification. The bright, thin surface oxide deposit had the same composition on the circumference of the ceramic heater, indicating that crystals of Yb2Si2O7 developed on top of the SiO2 film covering the Si3N4 surface. Furthermore, Figure  5.44 demonstrates that rounded  99 crystals developed in a compact scale on the surface of specimen “AC1” at the hot spot. Previous studies showed that the morphology of the silicate deposit mainly depends on the temperature, i.e. discrete acicular crystals were present in areas of lower temperature [ 50– 52,  153,  154]. The average width of the depletion layer was calculated to be ~ 100µm, based on the SEM images presented in Figure  5.44.   Figure  5.45 shows the micrographs of the center and ends of the upper-left WC terminal on the cross-section of GP “AC1”, shown in Figure  5.43, at higher magnification.  The Si3N4 insulator in the vicinity of the WC terminal was more affected, causing void formation around the centre of the WC heating elements’ ends. In the same position, the inside structure of the WC heating element is also damaged, with loss of the Si3N4(Yb)-based binder between WC particles.  100            Figure  5.43: Micrographs of the cross-section at 5 mm through the ceramic pin of specimen “AC1” tested at 1455°C in AC-electric field; running at 3366h; variation of Yb ions concentration is indicated in wt%.    8.85 9.06 9.15 8.86 11.17 11.14 10.95 10.76 6.84 10.14 8.81 9.60 9.50 1 2 3 4 1mm  101                          Figure  5.44: Micrographs of the marked areas (1–4) on section through specimen AC1 (Figure  5.43); Yb2Si2O7 (YS) deposit on the surface at higher magnifications. The remaining five GPs (specimens AC2-AC6) were all tested to failure using the AC-electric field at temperatures between 1500 oC and 1577oC to determine the declining longevity with temperature.  Figure  5.46 illustrates the micrographs of the Si3N4 -based heater cross-sections at the hot spot, in the order of increasing temperature.  The first four cross-sections show similar damage to all four heating filaments and Yb ion migration patterns, while the fifth cross-section shows considerable damage to the top two WC heating loops and virtually no Yb ion migration pattern.  This suggests that there is a change in the failure mechanism of the GPs tested between 1543oC and 1577oC.  The cross-section of failed specimens (AC2-AC5) shows that both heating 3 2 1 4 1.37wt% Yb 6.55wt% Yb SiO2+ Yb2Si2O7 1.33wt% Yb 7.77wt% Yb SiO2 1.46 wt% Yb 8.03wt% Yb 0.90wt% Yb 50um 6.20wt% Yb 1 2 3 4  102 loops had typically failed during the AC tests compared to typically only one heating loop in the DC tests [ 50].         Figure  5.45: Micrographs of center and ends of the WC terminal at 5mm for specimen AC1 tested at 1455°C in AC-electric rig; Marked areas 6-10 in the vicinity of WC heating terminal at higher magnifications.  6 8 7 1.05 wt% Yb 1.10wt% Yb 9 10 20um 10 20um 6 20um 7 20um 8 20um 9 500um  103               Figure  5.46: Micrographs of the cross-sections at 5 mm for specimens AC2, AC3, AC4, AC5, AC6. AC2 AC3 AC4 AC5 AC6  104 5.6.3 Summary This section is a continuation of the previous reports on the GPs operating under DC field.   We have determined that operating the GPs using AC electric power offered a better resistance to the internal degradation of Si3N4 insulator, related to the migration of sintering additive cations, as compared to the DC field. The Yb ion migration patterns and the WC heating element’s damage differed considerably between the DC powered GP and the AC powered GPs.  In the case of DC powered GPs, typically the Yb ions migrate away from only the side of two heating elements, with higher electric potential, and damage to only one side of the  heating filaments is observed.  The AC powered GPs exhibited Yb ion migration away from both sides of the heating elements (based on WC) on the cross-section of Si3N4 insulator.  The migration was to a much lesser extent (compared to the DC field), and in a uniform symmetric manner, causing only slight damage to the Si3N4 insulator near all the WC terminals.  However, GPs aged in AC electric field showed a relatively strong increase in Yb ion migration with increasing test temperature. In addition, the oxidation pattern on the surface of Si3N4 heater was more severe.                    105 6 Degradation of GPs in Electric Rig—Modeling 6.1 Summary of GPs degradation observations An extensive SEM/EDX analysis of several GPs tested in the electric rig was presented in the previous chapter. It was shown that migration of Yb ions, within the intergranular glassy phase of Si3N4, in an electric field is the primary cause of GP degradation and failure. It was also indicated that a slight to severe increase in porosity may occur due to the Yb migration from the surroundings of the WC heating elements on their positive side. At higher voltages, Yb ions may also migrate from within the volume of the WC heating elements, causing the conducting WC particles to loose their connectivity, thus increasing the heating element’s electrical resistivity, which consequently raises the temperature and accelerates the deterioration process of the ceramic insulator.  It was also shown that the Yb ions “piled up” in the vicinity of the WC filament-insulator interface on the ground side of the WC heating elements, which may eventually change the electric field characteristics in that region (Figure  5.35).  At high temperatures just before the electrical breakdown of the GP, possibly involving local arcing and plasma gas formation, tungsten also migrated from the inside of the conducting phase and oxidized to tungsten oxide (WO3).  At ~1000oC WO3 becomes a volatile gas [ 155] that may enhance the mass loss of the WC-based conducting phase of the GP. The previous SEM/EDX analysis showed that the degradation of the GP’s performance involves (i) the internal degradation of the Si3N4-based insulator body and the resulting dielectric breakdown of the Si3N4 ceramic and (ii) the destruction of the WC heating elements themselves that resulted in either (1) gradual aging and decrease of heat generation due to the reduction in electric current passing through the WC heating elements or (2) rapid generation of very high temperatures as a result of arcing and sparks. The latter is a transient process resulting in a catastrophic failure of the  106 conductive elements.  It is anticipated that the catastrophic GP failure model (2) could be triggered by pre-existing (e.g. manufacturing) defects in the plug, whereas the gradual ageing (1) takes place through the homogenous deterioration of the conducting path within the plug, e.g. is due to the progressing migration of Yb ions.    Figure  6.1 and Figure  6.2 show the cross-sections of GPs (DC4 and DC10) aged on the electrical rig with the two U-shaped heating elements appearing as the four white lines. The change of concentration of the Yb ions due to migration is clearly seen around the positive terminals of the heating loops.  The darker grey areas around the positive terminals indicate that the majority of the Yb ions have migrated away from this region (this process has been quantified previously in the electric rig study (Chapter 5) through detailed EDX measurements).             Figure  6.1: Micrograph of the section at 5mm through the GP DC4 - Yb ions depletion region is marked by the arrow.   +  107                    Figure  6.2: Micrograph of the cross-section at 5mm of GP DC10, showing extended Yb ions depletion field around the positive electrode of the heating elements. The darker contrast depletion region results from the Yb ion migration under the influence of the electric field generated by the heating elements in the GP (Figure  6.3a). Therefore, the principal thrust of the proposed model is the prediction of electric field distribution in the cross-section of the GP’s ceramic heater, loaded under constant electric potential, and its correlation with the depletion profiles determined through SEM. However, as discussed earlier, there are different synergistic degradation mechanisms activated by temperature and bias voltage, which resulted in the GP’s failure. In order to isolate extraneous influences such as the degradation and detachment of the WC heating elements and insulator, as well as the significant compositional variations both inside the insulator and the WC heating filaments, the specimens (GPs “DC4” and “DC10”) were selected in such a way that the Yb redistribution pattern in the cross-section at the hot spot only reflects the electric field intensity and direction. +  108  Figure  6.3: Schematics of the GP ceramic pin: a— passing of constant electric current in the heating elements results in joule-heating; b— axial and radial components of the electric field for constant electric current. 6.2 A model for the electric field inside the Si3N4 heater8 6.2.1 Electric potential along the WC-based heating element 9 To model the electric field distribution within the cross section of the Si3N4-based heater, the current-carrying wire analogy is used [ 156,  157]. Electric current passing through the conducting filament disturbs the perfect electrostatic screening of positive ions by the free electrons. Therefore, there will be a continuous gradient of surface charges distributed along the length of the heating elements, more positive towards the positive terminal of the power supply, decreasing in magnitude until reaching zero in the ground terminal, as schematically illustrated in Figure  6.3b [ 157]. This model is of significant importance to explore the electric field outside current-carrying WC-based conducting medium, as perceived in this work by the redistribution of Yb ions. Figure  6.3b shows schematically the resulting radial and axial components of electric field outside the U-shaped heating elements of the Si3N4-based GP. The WC heating filaments, however, possess a relatively low electrical resistivity (~2.2×10-5 Ωcm at the temperatures of interest), so the axial electric field is small (<10 V cm-1) compared to the electric breakdown of                                                  8 A version of this section has been submitted for publication. H. Karimi Sharif, T. Troczynski, C. Oprea, C. Blair, A. Welch, Degradation of Si3N4 Glow Plugs in Air – Experiments and Modeling, (2011). 9 A detailed description of the model implementation in COMSOL Multiphysics 3.3a can be found in Appendix D.  109 Si3N4 ceramics (>105 V cm-1). Hence the axial component of electric field at the surface is also relatively small. Therefore the total electric field outside the WC filaments must be nearly perpendicular and follows the geometry of the U-shaped elements. At the tip of the GP, where the WC filament is bent, the electric field changes its direction accordingly. The magnetic field generated by the flow of electrons in the conductors can be assumed to be insignificant and therefore the resulting radial Hall Effect is negligible [ 158]. Thus, the electric field inside the WC conducting phase that drives the current is constant along the conducting phase, and the potential and surface charge distribution is a linear function of distance between two terminals of the U-shaped heating elements [ 156– 158].  Figure  6.4 illustrates the computed electric potential for every point along the length of the conducting phase in the 2D longitudinal model of U-shaped elements, according to the above assumptions. The model was implemented in the Conductive Media DC module of COMSOL Multiphysics 3.3a [ 159]. The model confirms that for a constant electrical conductivity of the U-shaped conducting elements, the electric potential is a linear function of distance all the way from the positive to the ground electrode. The dashed line in Figure  6.4 marks the cross-section of the Si3N4-based insulator at the hot spot (~5mm back from the tip) where the electric potential was evaluated by the 2D longitudinal model. The computed electric potentials at the terminals of the WC heating elements on the cross-section of the GP were imposed as the internal boundary conditions to solve for Poisson’s equation within the cross-section of Si3N4-based rod.   110  Figure  6.4: The computed electric potential along the length of WC heating filaments for specimens “DC4” and “DC10”: a) specimen “DC4”; b) specimen “DC10”. 6.2.2 Electric field distribution within the cross section of the Si3N4-based heater Poisson’s equation ερϕ −=∇2   (where φ and ρ are, respectively, the electrostatic potential and charge density, and ε is electric permittivity of medium) was solved over the 2D domain of the ceramic cross-section at the hot spot to determine the electric potential distribution within the cross-section of the Si3N4-based rod. For the sake of simplicity we assumed that the characteristic parameters change abruptly at the interface between the ceramic insulator and the surroundings (i.e. air).  Furthermore, it is assumed that the interface carries no charge, i.e. the normal component of the electric displacement field is continuous across the interface: (Dinsulator - Dair).n = 0 (6.1) Dn insulator - Dn air = 0 (6.2) where D (C m-2) is the electric displacement field (Dn: the normal component of displacement field) and is related to electric field by the displacement law [ 156]   111 D = ε0 ε E (6.3) in which ε0 is the permittivity of vacuum, (ε0 = 8.854×10-12 (F m-1)) and ε is the dimensionless relative permittivity, (ε = 6-8 for different intergranular compositions involving silicon nitride) [ 156].  Inside the Si3N4 insulating body, because the tangential component of electric field is continuous across a heating element, the terminal’s dielectric interface at the surface of WC filaments, E, satisfies the relation: EWC outside = EWC inside   (6.4) On the other hand, as shown schematically in Figure  6.3b, the boundary conditions require that at the surface of the WC heating elements: Dn outside – Dn inside = σ (6.5) where σ is the surface charge density on the WC conducting terminals. Since En is zero inside the WC filaments, at the WC-insulator interface, the normal component of the electric field outside the WC heating elements (Figure  6.3b) is proportional to the surface charge density of the WC conducting phase, therefore combining equations (6.3) and (6.5) yields: εεσ0=nE  (6.6) Also, the equation (6.4) implies the continuity of the electric potential across the interface between WC and insulator:   insideoutside φφ =  (6.7)  112 Figure  6.5a illustrates the boundary conditions imposed in order to solve Poisson’s equation over the cross-section domain of the Si3N4-based rod of the GP. In the present work, the calculation of the electrical quantities was performed using a finite element software, COMSOL MULTIPHYSICS 3.3a [ 159]. Typical results are shown in Figure  6.5b, wherein the arrows indicate the magnitude and the direction of the electric field. It was assumed that there is no interaction between the electric field and the positive Yb ions at this stage, i.e. the charge distribution, ρ, on the right side of Poisson’s equation is zero (i.e. resulting in Laplace’s equation).   Figure  6.5: Cross-section of ceramic GP pin with U-shaped element’s configuration: a—boundary conditions; b—Computed electric potential (V) through the cross-section of the GP (the arrows show the electric field vectors). The computed electric field profile, overlaid with SEM/BSE micrographs of specimens “DC4” and “DC10” cross-sections at the hottest point, shown in Figure  6.6, suggests that the Yb ion redistribution pattern follows the electric force lines. However, the SEM micrographs suggest a depletion layer that is essentially symmetric and elliptical in shape. As there is no detachment or delamination at the WC element-insulator interface for these two GPs (DC4 and DC10), the Yb  113 depletion pattern should follow the electric force. However, the depleted region resulting from the migration of Yb ions on the high potential side of WC filaments does not exactly follow the electric field lines.  In previous chapters, it was reported that there were regions with near-zero Yb concentration at the GP hot spot; although the Si3N4 insulator became porous in these regions, the Si3N4 grains maintained their connectivity. It can be therefore speculated that only Yb ions were mobile and silicon, oxygen and nitrogen can be assumed to be immobile, at least relative to Yb. Therefore upon migration of Yb ions the depleted region became negatively charged with respect to the bulk. Thus, the free-charged domain (Laplace’s equation) may not be the best assumption in this case and the interaction between the electric field and Yb ions that appeared as Yb ions migration should be accounted for in order to develop a better model for the electric field distribution within the cross-section of the Si3N4 insulating phase. The higher the electric field applied, the more Yb ions migrated resulting in a much larger depleted volume (Figure  6.6).  To better illustrate the double layer effects and the interaction of the electric field with the ytterbium ions, the SEM micrographs of the Si3N4-insulator were superimposed with the 2D-electric field model, where the electric field force lines and potential contours are marked on the image. The resulting Figure  6.7 suggests that the electric field magnitude and direction are affected by the amount of the applied electric potential. This could explain why the Yb ion distribution is more symmetrical for the Si3N4-insulator tested at higher voltage, Figure  6.7b. However, because the Yb ion migration comprises other factors including the ion’s diffusivity, mobility, hopping barrier energy, and also the effect of the transient change in the Si3N4 ceramic composition due to the migration of Yb ions, it may not be appropriate to prejudge electric field distribution solely based on the migration of Yb ions, albeit there is a logical correlation between  114 the ions migration pattern and the electric field distribution. A more extensively developed model to include this correlation is proposed in the following chapter.   Figure  6.8 confirms that the Yb concentration is much lower across the area where the electric field is the highest. However, EDX-measurement of the Yb ions concentration in the immediate vicinity of the WC element-insulator interface is nearly impossible due to the strong interference of EDX signals from WC particles inside the WC filaments and the Yb-containing phase within the grain boundaries in the Si3N4-based insulating phase.      Figure  6.6: SEM micrographs of Figure  6.1 and Figure  6.2 overlaid by the computed electric field (arrows) and electric potential (contours) for charge-free medium: a) specimen “DC4”; b) specimen “DC10”.    115  Figure  6.7: SEM micrographs of Figure  6.1 and Figure  6.2 overlaid by the computed electric field (arrows) and electric potential (contours) of charge-induced medium: a) specimen “DC4”; b) specimen “DC10”.   Figure  6.8: Yb content (wt %) measured by EDX vs. computed electric field (PB) along the dashed line between high-potential WC terminal and centerline; initial Yb: 8.7 ± 0.4wt %.  116 6.2.3 Summary A two-dimensional model for the electric field distribution within the cross-section of ytterbium oxide doped silicon nitride insulator of GPs is proposed.  The model is verified based on the SEM/EDX observations of the redistribution of Yb ions as a result of undergoing electric force imposed by the WC-based heating elements within the GP body. The general shape of Yb-depletion layer is predicted well through the model. As the test temperature increases, the depletion layer becomes more elliptical in shape around the positive terminal of the heating elements.  However, at higher temperatures, the depletion layer also appeared wider at the vicinity of the positive WC filament’s ends. This can be attributed to the increase in the mobility of Yb ions with temperature. The model suggests that the electric field significantly increases at higher voltages, which increases mobility of Yb ions and hence could lead to the formation of long-range polarization and double layer under the influence of the applied electric load.  A more sophisticated model that takes into account the effect of temperature on the ionic mobility and diffusivity of Yb ions in the Yb-doped Si3N4-based insulator is explained in Section  6.3.2. The model solves the Poisson-Boltzmann’s equation for electrostatic analysis of the heater within its cross section, coupled with the time-dependent Nernst-Planck equation for diffusion/migration analysis of sintering additive (Yb2O3) cations within the ceramic heater.         117 6.3 Model for the electro-degradation of Si3N4–based GPs10 6.3.1 Heat transfer―3D  model A 3D heat transfer model for the GP operating in ambient air was developed using COMSOL Multiphysics 3.3a as the software development tool.  The predictions from the simulation models were compared to the GPs warm-up performance and steady state longitudinal temperature profiles. In COMSOL, the Electro-Thermal Interaction module was used for transient and steady-state analysis of the GP’s temperature distribution11.  The first law of thermodynamics is used to determine the temperature variation on the surface and inside the Si3N4-based heater. In this study, the relevant equation consists of heat transfer by convection and radiation from the surface, outE& , energy generation due to Ohmic heating within the WC heating elements, and a change in thermal energy storage, stE& , stoutg EEE &&& =−   (6.8) where gE&  is energy generation due to the electric resistance heating; for a control volume of length L: LRIE eg2=& (6.9)                                                  10 A version of this section has been submitted for publication. H. Karimi Sharif, T. Troczynski, C. Oprea, C. Blair, A. Welch, Model for the Electric Field-Enhanced Degradation of Si3N4 – Based Ceramic Glow Plugs, (2011). 11 A detailed description of the model implementation in COMSOL Multiphysics 3.3a can be found in Appendix E.  118 where I is electric current passing through the WC elements and Re is the Ohmic resistance of WC U-shaped elements. The energy outflow is due to convection and radiation from the surface: ( ) ( )44 surout TTATThAE −+−= ∞ εσ&  (6.10) where h is the convection heat transfer coefficient, A is the area of heat exchange, T is the surface temperature, ∞T is the fluid temperature, ε  is the emissivity of the surface, σ  is the Stefan-Boltzmann constant, and surT  is the temperature of the surroundings. The change in energy storage is due to the temperature change, ( )VcTdtddtdUE tst ρ==&    (6.11) The energy storage is the rate of change in the internal thermal energy, tU , of the Si3N4-based heater, where ρ  and c are respectively the mass density and the specific heat of the different components of Si3N4-based heater (i.e. Si3N4 insulator and WC heating elements), and V is the volume of the Si3N4-based heater. A free-convection heat transfer coefficient was assumed on the surface of the ceramic heater suspended in still air (15.0 W m-2 K-1). The heat flux passing across the WC filament/insulator interfacial contact was assumed to be constant. For the sake of simplicity only the thermal conductivity of the Yb2O3-doped Si3N4-based insulator was assumed to be a linear function of temperature [ 29].   119 All other coefficients and terms remained constant in this research and are listed in Table 6.1. These simplifications may affect the transient evaluation of temperature profile at the hot spot but considerably decrease the cost of modeling, in terms of computer memory and processing time.  Table  6.1: Pysical properties of Si3N4 and WC ceramics [ 28,  34]. Figure  6.9a shows a glowing plug and the temperature at the hot spot is indicated with a black dot. For the sake of simplicity, only the resisting part made of the WC-based elements was imported into the GP’s geometry, Figure  6.9b, i.e. the effects of tungsten wires were neglected. Pyrometry confirmed that the tungsten wires did not contribute significantly to the temperature rise of the heating ceramic. Figure  6.9c shows the temperature distribution on the surface of the Si3N4-based heater computed by the above model and compares it qualitatively with the photographed glowing heater (Figure  6.9a). Figure  6.10 illustrates the warm-up profile computed by the above heat transfer model (line) for GP loaded at 9.0V, verified against pyrometer readings (symbols) for samples C1–C12. The computed warm-up profile matches reasonably the experimental data in the steady-state for t > 30s; the discrepancy between the model and the pyrometric measurements during the dynamic warm-up period ~2 < t < 30s (T data are not available below 500oC at t < 2s) can be attributed to the differences in the GP’s characteristics and the conducting phase’s geometry, as evident from Figure  5.3. Furthermore, as mentioned earlier, the simplifying assumptions (constant parameters) used in the numerical model mainly affect the transient part of the warm-up profile. Figure  6.11 presents a comparison between the steady-state part of the solution (t > 30s) and the experimental data. The computed temperatures are in a good agreement with the measured temperature distribution along the length of the Material Density  (kg m-3) Electrical resistivity (Ω cm) Thermal conductivity (W m-1 K-1) Specific heat capacity (J kg-1 K-1) Emissivity Si3N4 3170 1014 0.0134 T + 34.443 [ 34] 670 0.9 WC 15630 2.2× 10-5 63 203 N/A  120 Si3N4-based heater. The steady-state condition is of more interest in this research owing to the fact that because of the long-term nature of the study, the GPs had enough time to reach the steady-state temperatures.   Figure  6.9: GP geometry and computing domain: a- the image of glowing plug; b- Si3N4-based heater’s geometry; c- the computed temperature distribution on the surface of GP (the colormap shows the temperature in degree Celsius).  121                      Figure  6.10: The warm-up profile at the hot spot for the GP loaded at 9.0V: model vs. experiment.           Figure  6.11: The steady-state temperature distribution along the length of Si3N4-based rod of as-received (“0.0h”) GP loaded at 9.0V: model vs. experimental (measured by optical pyrometer).  122 Now that the model showed a good fit between the computed and the measured temperatures at steady state conditions, we can use the model to predict the temperature variations inside the Si3N4 heater, in order to later model the temperature effect on Yb redistribution. The temperature distribution within the cross-section of the GP at the hot spot (i.e. the highest temperature) was of interest as temperature plays an important role in both the oxidation of Si3N4 at the surface and the diffusion/migration of Yb ions inside the heater [ 17,  18,  39,  41]. Figure  6.12 shows the computed steady-state temperature distributions within the cross-section of the GP at the hot spot predicted by the 3D model. According to the model the temperature difference between the core of the Si3N4 insulating body and the outer surface for the GP loaded at 9.0V is over 55oC, which may result in significant variation in the diffusivity and mobility of Yb ions.  Based on further analysis of the model, it was determined that the temperature variations from the core of Si3N4-based insulator to the surface within the cross-section of the GP loaded at 12.0V could be as high as 100oC.    The primary goal of this study is to model Yb ion migration (due to electric field) and diffusion (due to concentration gradient) on the cross-section at the hot spot. Many physical properties of ceramics are dependent on temperature, such as the diffusivity and mobility of Yb ions. Hence, without having a good estimate of the temperature gradient inside the Si3N4-based insulator, the diffusion-migration model is not well-posed. On the other hand, the temperature dependence of mass transfer and heat transfer coefficients make the model highly non-linear and expensive in terms of computer time and memory usage. Therefore, owing to the fact that the GP’s failure mainly originated at the hot spot (i.e. 3-5 mm back from tip) [ 50] it has been assumed that the 2D model is sufficient to study the migration and diffusion of Yb ions inside Si3N4. The validity of this assumption is ultimately verified comparing the results of modeling and SEM tracing of Yb redistribution.  The boundary conditions gained from the 3D heat transfer model were imposed  123 in the Electro-Thermal Interaction module (Joule Heating) of COMSOL Multiphysics 3.3a for the 2D geometry of the cross-section of ceramic heater to get the same temperature distribution as obtained by the 3D model within the cross-section12.     Figure  6.12: The computed steady-state temperature distributions within the cross-section of Si3N4-based heater of GP at hot spot. 6.3.2 2D mass transfer model In order to explore the Yb ion diffusion due to the concentration gradient and Yb ion migration under the influence of electric field, the Chemical Engineering Module of COMSOL Multiphysics 3.3a was used to solve the Nernst-Planck (NP) equation (equation 1.20) over a 2D cross-section domain; NP without electroneutrality was employed because the Yb ion                                                  12 A detailed description of the model implementation in COMSOL Multiphysics 3.3a can be found in Appendix F.  124 concentration does not fulfill the electroneutrality condition independently from the oxygen and nitrogen anions within the grain boundaries of the Si3N4-based insulator; so there is no constraint for the net charge to be zero at a given volume.  The exact diffusivity of Yb ions in the intergranular glassy phase is not known, however it is considered that the activation energy for the diffusion of Yb ions in the grain boundary glass phase is similar to the activation energy for oxidation in these ceramics, i.e. 416-600 KJ mol-1 [ 18].  It was reported that in the Yb2O3-fluxed Si3N4 ceramics the oxidation rate was controlled by the rate of outward diffusion of Yb ions [ 18,  160,  161]. In this study, it was assumed that the diffusion of Yb ions was the rate controlling step and the diffusion coefficient obeyed the Arrhenius-type relationship. The activation energy for Yb ions diffusion in the intergranular glassy phase was estimated to be 460 kJ mol-1 [ 55], and their mobility was calculated by using the Nernst-Einstein relationship (equation 1.17) [ 28]. The diffusion coefficient and mobility are both changing with temperature, in particular close to 1570oC, which is the eutectic temperature for the Si3N4-Yb2O3-SiO2 system. However, the glass transition temperature of the intergranular oxynitride glassy phase, at which the diffusivity and mobility values drop rapidly by orders of magnitudes, is not well-defined [ 136]. The WC filament terminals on the cross-section of Si3N4 heater were assumed to be quasi-blocking electrodes where there is no ion penetration from the insulator to the WC terminals and Yb ions cannot be directly neutralized at the WC terminals [ 162].  As presented before [ 18,  50], the oxidation of Si3N4 at the GP surface and the formation of a silica layer provides a concentration gradient driving force for Yb ions to diffuse into the silica film, leading to the formation of Yb-containing crystalline phase (Yb2Si2O7) on the top of the silica film. Further oxidation depends on the concentration of Yb ions at the interface between  125 the silica film and Si3N4 body. Therefore a concentration-dependent flux of Yb ions at the circumference of the Si3N4 body was imposed for the boundary conditions at the outer surface of the Si3N4-based heater.    The potential distribution was obtained by solving the Poisson equation at the 2D cross-section domain of the hot spot [ 154]. The boundary conditions for Poisson’s equation were fully imposed and explained in section  6.2.2. The WC heating element terminals on the GP cross-section at the hot spot hold different electric potential, which was computed and shown in Figure  6.4, and is used for the coupled Poisson-Nernst-Planck (PNP) model presented in this section. The resulting Yb ion concentration distribution for the specimens “DC4” and “DC10” are presented in Figure  6.13 and Figure  6.14 (refer to Table  5.6 and Table  6.1 for test parameters). The arrows show the electric field distribution and magnitude and the contours illustrate the temperature variations within the cross section of the Si3N4 heater. The computed images of Yb ion redistribution were overlaid with the SEM micrographs of the same GPs to provide a common ground for qualitative comparison, in Figure  6.15.   126  Figure  6.13: The Yb ion redistribution under the influence of electric field and concentration gradient for the GP loaded at 12.1V (specimen DC4) for 10.0h, computed by 2D model for GP’s cross-section at the hot spot; gray map: concentration of Yb ions (%wt); arrows: electric field; contours: temperature. In both specimens the predicted Yb ion concentration patterns match the experimentally determined depletion layer close to the high-potential side, and Yb ions “pile-up” near the low-potential WC terminals. As the model suggests, the temperatures are also higher in the vicinity of the WC terminals, which accelerates Yb ion migration. Based on the observations of Yb concentration with time and temperature, at elevated temperatures (>1570oC), the minimum Yb ion concentration in the cross section drops rapidly to ~2% even after only a few hours and was often found to be near 0.0% at failure (refer to Chapter 5).  The center of the GP cross section appears to experience an increase in Yb concentration from its initial value of about ~8.7 ± 0.4 wt% to around ~15 wt% as Yb ions migrate through the center and to the surface, and then the concentration drops down to nearly 2 wt% at failure.    127   Figure  6.14: The Yb ion redistribution under the influence of electric field and concentration gradient for the GP loaded at 14.0V (specimen DC10) for 2.7h, computed by 2D model of GP’s cross-section at hot spot; gray-map: concentration of Yb ions (%wt); arrows: electric field; contours: temperature. The maximum Yb ion concentration value rises quickly and appears to asymptotically reach a value of about 45 wt% at failure. The above samples were chosen in such a way as to be representative of migration-diffusion of Yb ions on the cross-section of the ceramic heater at the hot spot. Other failure mechanisms have been described previously, such as WC terminal/insulator detachment, delamination and crack formation in the Si3N4 insulator, oxidation of tungsten in the WC heating elements, widening of grain boundaries as a result of oxygen diffusion inside and further oxidation of Si3N4 grains, and a few other atomistic and microscopic parameters that may change the electric field distribution and the resultant Yb ion redistribution [ 50].  128 Yb ion migration is believed to occur through a chain of reactions including dissolution and precipitation of Yb ions inside the intergranular glassy phase.  The formation of Yb-containing crystalline phases within the grain boundary phases [ 62,  67,  73,  163] may locally hinder further migration of Yb ions [ 18].  Figure  6.16 shows the variation of computed Yb ion concentration along the dashed line verified semi-quantitatively against X-ray spectrometry (SEM-EDX) analysis of Yb ion concentration. It is known that high atomic number elements such as Yb scatter electrons more strongly than light elements with low atomic number (i.e. Si, O, N), and thus appear brighter in the image. Si3N4 grains, on the other hand, might be coated with a thin layer of Yb- containing intergranular glassy phase [ 8,  26,  62] thus may appear brighter in the image. Therefore, although the SEM micrograph may show qualitative contrast between the area of high-Yb concentration and low-Yb concentration, it is not the best method of judging the presence or absence of Yb ions or their volume percentage within the cross-section of the Si3N4 insulator. On the other hand, in the EDX analysis the X-rays are produced in the bulk, i.e. 500-5000 nm below the surface. Hence, the Yb ion concentration detected by EDX reflects the concentration level of Yb ions at the subsurface regions.    129   Figure  6.15: SEM micrographs overlaid by the computed Yb ion concentration profile within the cross-section of Si3N4-based heater at the hot spot: a- GP aged at 12.0V (specimen DC4) in ambient air for 10.0h; b- GP aged at 14.0V (Specimen DC10) in ambient air for 2.7h; arrows: electric field; contours: temperature.  130   Figure  6.16: Yb ions content (wt %) measured by EDX  vs. computed Yb content (wt%) along the dashed line between the high-potential WC terminal and centerline; initial Yb for as received GP: 8.7 ± 0.4wt %. 6.3.3 Summary The silicon nitride based GP current and surface temperatures were measured with an infrared pyrometer for a series of GPs at different voltages in ambient air along the length of the silicon nitride (Si3N4)-based insulator rod of the GP.  The 3D heat transfer model has been developed and verified against the steady-state GP temperatures. The 3D model showed a good quantitative match with the experiments in the steady state regime (>30s) of the warm-up profile. The computed steady-state temperature along the length of Si3N4-based rod was in good agreement with the experimental data.  The model was also used to find the temperature distribution inside the GP within the cross-section of the hottest spot. The model predicts temperature gradients inside the Si3N4-based body of up to 100oC depending on the applied voltage, which can  131 significantly influence the rate of Yb ion migration, particularly above the glass transition temperature of the intergranular glassy phase.  The 2D diffusion-migration model gives a good estimation of the Yb ion migration and redistribution over the cross-section of the Si3N4-based heater, under the influence of the electric field within GP. The formation of Yb-depletion regions (appearing as a darker-contrast areas in the vicinity of higher-potential WC terminals) and the formation of higher Yb-concentration regions in the vicinity of lower-potential WC terminals are well predicted by the model, based on the influence of electric field and temperature gradients. The model, as well as the experimental results, confirm the transient migration and diffusion of Yb ions within the cross section of the Si3N4 heater until all Yb ions are gone from the vicinity of the high-potential WC terminals (i.e. steady-state is reached).  It is anticipated that the loss of Yb from these regions leads to microporosity and then loss of integrity of the ceramic. This in turn may trigger localized microarcing, and thus runaway conditions of increasing temperature finally leading to GP destruction. It is therefore of paramount importance to redesign the GP geometry and its operating parameters, in order to avoid such a chain of events leading to the premature failure of  the GP.  SEM micrographs and SEM-EDX analysis of GP cross-section at the hottest point both confirm the results obtained from the model for different GPs in a qualitative and semi-quantitative manner.         132 6.4 Degradation of Si3N4 GPs in AC electric field –modeling13  6.4.1 2D mathematical model of Yb ions migration due to AC field In order to model the Yb ion redistribution pattern, due to the concentration gradient and Yb ion migration under the influence of electric field, the coupled Nernst-Planck (NP) equation (refer to Chapter 2, equation 1.20) without electroneutrality, the Poisson equation (refer to Section  2.4), and the Joule Heating equation (refer to Section  6.3) were solved simultaneously, using the Chemical Engineering Module, Electromagnetics, and Electro-Thermal Interaction modules of COMSOL Multiphysics 3.3a, respectively14. The transient boundary condition at four WC-based conducting terminals on the cross section of the ceramic heater was implemented by using a simple sine function at the internal boundaries (WC element terminals) so that the electric potential, ( )tϕ , is oscillating around some positive mean value.  (φ (t)/ φ0) = ½ + (4/π) sin (ωt )  (6.12) where the frequency can be conveniently controlled by angular frequency (ω), t is time (second), φ0 is the maximum potential. Figure  6.17 presents the resulting Yb ion concentration distribution generated by the coupled transient Poisson and Nenrst-Planck equations for the specimen “AC1”. The arrows show the                                                  13 A version of this section has been submitted for publication. H. Karimi Sharif, T. Troczynski, C. Oprea, C. Blair, A. Welch, Model for the AC Electric Field-Enhanced Degradation of Si3N4 – Based Ceramic Glow Plugs,(2011). 14 A detailed description of the model implementation in COMSOL Multiphysics 3.3a can be found in Appendices F and G.  133 electric field vectors in the plane; the contours illustrate the temperature variation within the cross section of the Si3N4-based heater. The computed image of the Yb ion redistribution was overlaid with the SEM micrographs of the same GP in order to visually observe the correlations between model and experiment, Figure  6.18. The oxidation reaction on the surface of the Si3N4-based body is assumed to be directly proportional to the driving force, i.e. the first order chemical reaction. Hence, the model also predicts the formation of a band of Yb- depleted region close to the surface and beneath the silica layer inside the Si3N4 insulator. However, to better address the formation of the depletion layer beneath the silica scale, a number of factors should be accounted for, such as existing oxide layers (i.e. Yb2Si2O7, SiO2, Si2N2O) and the interface at which the reaction takes place. Therefore, a slight discrepancy between the computed depletion layer and the SEM micrographs can be attributed to the fact that several effects were not treated in this work.  The predicted Yb ion concentration profile on the cross-section of specimen “AC1” at the hot spot shows a good fit with the SEM image, i.e. a net migration of Yb ions away from the heating elements, regardless of the polarity of the voltage applied. As discussed in section  6.2.2, modeling the effects of a DC field on Yb migration [ 154], even a very limited interaction of external electric field and mobile Yb ions resulted in non-uniform electric field distribution within the cross section of the ceramic heater close to the WC terminals. Therefore, once the Yb ions are pushed forward by the electric field, they cannot return to the initial position by solely reversing the electric field polarity because, upon switching the polarity, Yb ions closer to the lower-potential electrode ends undergo lower electric driving force. At an atomic scale, it may be speculated that the migration of Yb ions causes local rearrangement of other neighbouring ions resulting in local composition variations within the intergranular glassy phase. Once a mobile Yb ion is pushed forward by the electric field, the physical and chemical properties of the  134 surrounding medium are affected.  Therefore changing the polarity of the electric field will force the Yb ion to move back into the now chemically and compositionally different material. We also believe that this reorganization of the ionic atmosphere results in long range migration of Yb ions under the AC electric field, as reported elsewhere [ 132].   Figure  6.17: Yb ion redistribution under the influence of AC-electric field and concentration gradient for the GP loaded at 13.0V (specimen AC1) for 3366h, computed by 2D model of the GP’s cross-section at the hot spot; gray-map: concentration of Yb ions (%wt) ; contours: temperature; arrows: electric field.    135  Figure  6.18: SEM micrographs overlaid by the computed Yb ion concentration profile within the cross-section of specimen AC1 in ambient air for 3366h; arrows: electric field vectors; contours: temperature. Another interesting phenomenon observed was the leaf-like symmetric pattern of Yb ion redistribution. Our model predicts formation of such a pattern, i.e. the base of the leaf. This can be explained by the temperature variations within the cross-section of the Si3N4-based insulator. The contours in Figure  6.18 suggest that the temperature is much higher in the center of the section and decreases gradually toward the surface of the Si3N4 insulating body. Even within the core of the ceramic insulator the temperature is still higher from the heating element tips to the centre.    136 Figure  6.19 shows a predicted distribution of mobile Yb ions for specimen “AC2”. The GP “AC2” was aged in the AC-electric rig and the applied bias for GP “AC2” (13.4 V), comparing to that of specimen “AC1” (13.0 V), was only slightly higher, but resulted in 50oC higher temperature at the hot spot compared to the specimen “AC1”. The 50oC higher temperature on the surface translates to much larger temperature variations inside the ceramic heater [ 153].  It is known that the viscosity of the intergranular glassy phase dramatically drops around 1600oC [ 8,  32,  55, and  62]. In specimen “AC2”, an increase in temperature and consequently decrease in viscosity of the grain boundary glass accelerated the migration of Yb ions and resulted in a shorter lifetime with more pronounced Yb ion migration patterns.  It should be noted, however, that other failure mechanisms such as detachment, delamination and crack formation in the Si3N4 insulator and WC heating elements are neglected at this point. Furthermore, it was assumed that Yb ions only migrate within the fastest diffusing path (i.e. within the intergranular glassy phase), whereas the diffusion and migration mechanisms of Yb ion in Si3N4-based materials are much more complex [ 18,  84].  Figure  6.20 shows the variation of computed Yb ion concentration along the dashed line, verified quantitatively against SEM-EDX analysis of Yb ion concentration. The model is quantitatively in a good agreement with the EDX measurements.  6.4.2 Summary This part of the work reports evaluation and damage modeling of the all-ceramic silicon nitride based GP, powered with an AC electric field.  The mathematical model showed that for the GP loaded with 13.0V in an AC electric field the temperature in the center of the cross-section is nearly 100oC higher than the temperature on the surface.  The model also suggests that the temperature is higher near the WC terminal tips, toward the center, resulting in a formation of “leaf” pattern of Yb ion migration.  Even though the model did not use an exact square wave pattern in the electrostatics module, the sinusoidal variation of potential can still simulate the  137 effect of AC load on the migration of Yb ions effectively.  It is modeled and confirmed experimentally that the Yb migration was effectively restricted in the AC field, resulting in longer lifetime of the GPs. In agreement with the SEM analysis, the model evidences the migration of Yb ions away from both sides of the WC heating elements (the four white lines in images), on the cross-section of the silicon nitride ceramic insulator. The model was verified quantitatively against the EDX analysis of Yb ions within the cross-section of the Si3N4 insulator and showed a good fit. Additional test should be carried out to explore the effect of the AC field frequency on longevity and the degradation mechanisms of the Si3N4-based heaters.  Figure  6.19: SEM micrographs overlaid by the computed Yb ion concentration profile within the cross-section of  specimen AC2 in ambient air for 2881.5h.  138  Figure  6.20: Yb ion content (wt %) measured by EDX  vs. computed Yb content (wt%) along the dashed line between the high-potential WC terminal and low-potential WC terminal; initial Yb content for as received GP: 8.7 ± 0.4 wt %.         139 7 Conclusions The following major conclusions are drawn from this study:  1. Different aspects of the Yb2O3-doped, Si3N4-based ceramic GP degradation mechanisms were studied for GPs exposed to the complex and dynamic environment of direct injection natural gas internal combustion engines. The tests were conducted both in the ETC (“European Testing Cycle”) mode and in the accelerated SS (“Steady State”) conditions for higher engine speed and load. Four modes of deterioration were observed to contribute synergistically to the failure of the GPs: a. Chemical degradation occurring through the following routes:  — The oxidation of Si3N4 to SiO2 and further formation of Yb2Si2O7 due to the migration of the sintering additive (Yb2O3) cations towards the surface and the resulting creation of a depletion region beneath the silicate scale. Although not explicitly tested, it is anticipated that the mechanical properties of the ceramic heater were significantly affected by the resulting increase of porosity in the Si3N4 bulk, resulting from this process. — The reduction of the oxide film contributing to GP mass reduction after testing.  b. Physical degradation:   — The loss of mass occurred at the surface through the erosion of the surface Yb-silicates deposits by the rapidly moving, hot combustion gases.   140 — Surface and subsurface cracking was observed due to thermal stresses that arise because of the differences in thermal expansion coefficients between the surface oxides and the base material. c. Thermal degradation:  — Aging the GPs at higher temperatures (1450 to 1550oC) induced more damage to the structure of the ceramic heaters and increased exponentially the kinetics of chemical reactions, as well as the diffusion rate. As a combined net effect of these, the GPs tested under various conditions showed an exponential decrease of their lifetime with temperature.  — Accelerated rate of heat generation inside the ceramic heaters due to the electrical degradation of the WC heating elements. d. Electrical degradation: the sintering additive (Yb2O3) cations migrate away from the high-potential heating elements towards the low-potential heating elements and GP surface. Porosity increases in the areas with Yb-deficient intergranular phase, which finally leads to dielectric breakdown; higher applied voltages accelerate this process. 2. The degradation mechanism of the ceramic heater on the natural gas burning rig has two synergistic effects:  a. Mass variation with time and temperature: — The measured mass increase due to the inward diffusion of oxygen and the  141 formation of the Yb2Si2O7 on the top of the silica film, a product of oxidation of the Si3N4 base ceramic. — The reducing conditions on the burner rig cause the decomposition of silicate sub-scale layer. Outgassing of the products of reaction disrupts the continuity of the oxide deposits, exposing new Si3N4 to the combustion environment. As a result, the GPs tested on the natural gas-burning rig underwent drastic compositional and structural alterations. The applied external heat, together with the corrosive behaviour of the combustion gases, contributed significantly to the alteration of the structure of the Si3N4–based ceramic heaters.  However, testing in the burner rig removed certain deteriorating effects present in the engine (such as vibration and rapid thermal cycling).   b. Redistribution of the sintering aid cations in Yb2O3-fluxed Si3N4 system under the influence of DC electric field, causing more severe internal degradation at higher temperatures.  The resulting local minimum Yb content (wt%) was 0.0 for all three GPs and the local maximum Yb wt% increased with increasing temperature, from ~35 wt% at 1425°C to ~48 wt% at 1450°C. The maximum ytterbium concentration nearly linearly increased with the test duration and locally approached ~ 48 wt% at GP failure.  3. Experimental results of accelerated electric rig tests of Yb2O3-doped Si3N4-based GPs in air showed that the aged GPs exhibited Yb ion migration away from the high-potential heating elements under the influence of a DC electric field at relatively high temperatures (>1350°C).  However the amount of migration and related damage did not always correlate  142 with temperature or applied voltage. Upon migration of Yb ions away from the high-potential heating elements, a Yb-deficient intergranular phase (i.e. a mix of Yb2Si2O7 crystals and intergranular glassy phase) was formed, followed by creation of pores and cracks and likely softer grain boundary phase, leading to gradual performance degradation and GP failure.   4. The extensive GP analyses performed using the scanning electron microscope (SEM) provided consistent images of the migration of Yb ion. The Yb ions distribution pattern, resulting from the Yb ion migration, resembles the electric field pattern generated by the WC-based heating elements within the GP.  To further investigate the link between the migration pattern and an electric field, a two-dimensional mathematical model was developed to predict the electric field generated by the WC heating elements within the GP.  The model predicts well the general trend of the Yb ion distribution pattern, confirming that the Yb ions migrate away from the high-potential heating elements.  The Yb-depletion region in the vicinity of the high-potential heating elements becomes more elliptical in shape with increasing temperature, suggesting an increased interaction between the ionic species in the insulating silicon nitride bulk. The model also suggests that the electric field significantly increases with increase in the applied voltage and, as such, enhances the mobility of Yb ions, and therefore it could lead to the formation of long-range polarization within the GP at elevated temperatures. 5. GP temperature data were collected with an infrared pyrometer at different voltages in ambient air along the Si3N4-based tip (“ceramic rod”) of the GP. A 3D heat transfer model was developed and verified against the steady-state temperature profile measured along the length of ceramic rod, as well as transient temperature distribution at the hot spot (about  143 5mm back from the front end). The 3D model showed a good quantitative fit with the steady state regime (time >30s) of the GP warm-up profile, obtained experimentally by pyrometry. The simulated steady-state temperature along the length of the Si3N4-based rod shows a reasonable fit with the experimentally determined data.  Since there are no practical means to measure the temperature variations within the cross-section of the ceramic heater in the GP, the model was then employed to predict the temperature gradients within the cross-section of Si3N4-based ceramic rod at the hot spot. The model suggests a temperature difference of up to 100oC between the core and the surface of the ceramic heater at the hot spot. The temperature difference is a strong function of the applied voltage.  6. A more sophisticated model was proposed to address the diffusion and migration of Yb ions within the cross section of the GP at the hot spot. The 2D diffusion-migration model provides a good prediction of Yb ions redistribution over the cross-section of the Si3N4-based heater. The model incorporates the heat transfer and mass transfer kinetics associated with Yb ion diffusion and migration under the simultaneous effects of the concentration gradient and the electric field. The fine details of Yb redistribution, such as the creation of a Yb-deficient area in the vicinity of the high-potential heating elements, and the formation of a Yb-concentrated layer in the immediate vicinity of the low-potential heating elements, are well predicted by the model. The model, as well as the experimental results, confirm the transient migration and diffusion of Yb ions within the cross section of the ceramic heater until all Yb ions within the section are completely removed (i.e. steady-state is reached).  The loss of Yb2O3-based binding phase from Si3N4 leads to progressively increasing microporosity and thus loss of integrity of the ceramic. This in turn may trigger localized microarcing, and thus runaway conditions of increasing temperature finally  144 leading to GP destruction. It is therefore of paramount importance to redesign the GP geometry and its operating parameters, in order to avoid such a chain of events leading to the premature failure of the GPs.  Both SEM-BSE micrographs and SEM-EDX analysis of the GP cross-section at the hottest point confirm the results obtained from the model for different GPs in a qualitative and semi-quantitative manner. 7. Operating the GPs using an AC wave pattern (compared to the typical DC pattern) offered a significantly better resistance to Yb cation redistribution inside the Si3N4 insulating body. The following specific conclusions are drawn from this part of the research: a. The electric degradation pattern in the AC-powered GP is notably different from that of the DC-powered GP.  In the case of DC powered GPs,  Yb ions migrate away from the high-potential heating elements resulting in greater damage only to that side of the WC heating elements, and their surrounding Si3N4 insulator. In the AC powered GP, the Yb ions migrate away from both sides of WC heating elements within the Si3N4 insulator.  However, the extent of the Yb ion migration was smaller in AC-loaded GPs as compared to the DC-powered GPs, and in a uniform symmetric manner, causing only slight damage (i.e. limited to formation of pores and detachment of the WC filaments/Si3N4 body) to the Yb2O3-doped silicon nitride insulator near the all WC heating elements. The migration of Yb ions was a strong function of the AC electric field and showed an increase in Yb ion diffusion and migration with increasing test temperature, and a more severe oxidation pattern on the cross section of Si3N4 heater. Furthermore, more severe internal degradation occurred at higher temperatures.  The resulting local minimum Yb content (wt%) was 0.0 for the GPs tested at 1535, and 1543oC and the local maximum Yb wt%  145 increased with increasing temperature, from ~11.2 wt% at 1455°C to ~56.7 wt% at 1543°C.  b. The 2D mathematical model proposed for the DC-powered GPs was modified to allow for the incorporation of transient boundary conditions related to the AC electric field. The model showed that for the GP loaded with 13.0V in an AC electric field, the temperature in the center of its cross-section is nearly 100oC higher than the temperature on the surface, in agreement with the results obtained in the DC-powered ceramic heater.  The model also suggests that the temperature is higher near the WC element tips toward the center, resulting in the formation of “leaf” pattern of Yb ion migration.  The model used sine wave at the fundamental frequency in the Fourier series of the ideal square wave. This significantly improved computational efficiency while not significantly affecting the model outcome.  c. It is modeled and confirmed experimentally that Yb ion migration was limited in the AC field, resulting in a longer life of GP. The model confirmed the change in the distribution pattern of Yb ions with increasing applied AC voltage, hence temperature. The durability of the ceramic heater was increased by a factor of about ten for the GP tested at 1455oC compared to the one tested at 1543oC (temperature at the surface of the hot spot). This can be attributed to the increase in the diffusivity of Yb ions at higher temperatures. In agreement with the SEM micrographs, the AC model suggests the migration of Yb ions away from all four WC terminals, on the cross-section of the silicon nitride ceramic insulator. The  146 model was verified semi-quantitatively against the EDX analysis of Yb ion concentration within the cross-section of Si3N4 insulator and showed a good fit.                      147 8 Future Work Test methodologies and accelerated testing rigs (Electric and burner rigs) have all been evaluated during this series of tests and the level of confidence in the Si3N4-based GP’s ability to pass these tests has been greatly increased. The data obtained during this work has been a catalyst to encourage more detailed testing to further understand GP deterioration with the aim of improving ignition durability and performance. Additional studies concerning gaining on understanding of the mechanism of degradation of the state of the art Si3N4-based ceramic heaters (GPs) under the working conditions in the NG high-pressure DI engines, based on the findings revealed in this research project, are suggested as follows: 8.1 Further GP analysis Our initial test methods on the electric and burner rigs are simplistic and not all factors, that affect lifetime, are included. In our first attempts to understand how the GP life varied, we only related life to peak GP surface temperature. It is likely, as verified by engine testing, that the practical GP life is also sensitive to the in-cylinder flame temperature history, chemistry (air-fuel ratio), thermal cycling due to start-up/shut down and cool intake air/fuel injection and engine vibration.  8.2 Correlations between testing parameters and failure modes of GPs (Modeling) A detailed list of variables, which likely have some effect on GP durability, is included below:  148 • Thermal gradients due to localized heat production, convection, conduction, and radiation. • Thermal cycling due to cool intake air/ fuel injection / combustion process / hot exhaust flow. • Thermal transients due to engine start-up and shutdown cycles. • Flame chemistry (air/fuel ratio) and surface oxidation. • Combustion deposits (from fuel and lubricating oil – alkali elements in particular). • GP voltage effects  o (AC vs. DC – alternating current reduced ion migration) o Pulse width modulation for temperature control vs. voltage in AC mode (Additional tests should be carried out to explore the effect of H-bridge frequency on longevity and degradation mechanisms of Si3N4-based heaters (this is an on-going test, to be reported in the future) • Engine vibration Some of these variables can be simulated and controlled (such as voltage effect, number of thermal cycles during a test), on a test rig, while others are secondary effects such as thermal gradients inside ceramic heater and are more difficult to control and may only be understood through mathematical modeling techniques. Future studies should discuss these other effects and develop a more sophisticated model to address extraneous variables such as engine vibration.  149 Furthermore, the burner rig can be modified to accurately reflect actual engine conditions, e.g. engine vibration; this is particularly helpful for later model validations. In addition, improvements to the burner rig such as providing a cyclic reducing environment may provide a better comparison to the engine operation. 8.3 Alternative sintering additives  High-temperature silicates forming an intergranular phase with a high crystalline content were obtained by using rare earth oxides as sintering additives. It is known that the cationic field strength of the rare earths increases with decreasing ionic radii, e.g. La>Sm>Er>Yb>Lu. Lu2O3-fluxed silicon nitride ceramics have shown superior creep resistance over the Yb2O3-fluxed Si3N4 ceramics studied in this work. It was reported that using Lu2O3 as a sintering additive reduces the thickness of the grain boundary phase and facilitates the complete crystallization of the grain boundary phases [ 32]. 8.4 Surface modifications of Si3N4 It is also common to observe a white powdery coating on the outside of the GP.  It is known that Si3N4 combines with O2 to form the SiO2. However, further SEM/EDX analysis in this study evidenced the existence of a sintering additive (Yb2O3) depletion layer beneath the silica film, which formed due to the outward diffusion of Yb ions. The resulting Yb2Si2O7   deposited on the surface was cracked and porous, exposing the Si3N4 surface to further oxidation.  In another work conducted by Frankie Wong at the ceramic group (UBCeram) of the University of British Columbia, it was shown that mullite-mullite environmental barrier coatings (~3µm thick) significantly reduce the oxidation of Si3N4 in ambient air. 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Wickleder, “ChemInform Abstract: Inorganic Lanthanoid Compounds with Complex Anions”,33[34], 2011-87 (2002)      170 Appendices A Thermodynamic Data  Table  A.1: The standard Gibbs free energy of formation Reaction [ 174] oH∆− (J mol-1) oS∆−  (J mol-1 K-1) Range Si(s) + O2(g) = SiO2 (s) 907,091 175.728 298-1685 Si(s)+1/2O2(g) = SiO(g) 104,182 -82.508 298-1685 3Si(s)+2N2(g) = Si3N4(s) 723,832 315.055 298-1685 2Y(s)+3/2O2(s) = Y2O3(s) 1,897,862 281.960 298-1799 W(s)+3/2O2(g) = WO3(s) 833,453 245.433 298-1745   Table  A.2: The Gibbs free energy of formation. G(T)=A+BT+CTlnT+DT2+ET3+F/T [ 175] Species A×10-5 B×10-2 C×10-1 D×103 E×107 F×10-5 Si(OH)4 -13.7229 5.06064 -12.5752 -15.9765 6.52809 -13.3145 SiO -1.153070 0.3988578 -3.664745 -0.301647 0.09317488 7.200307 SiO(OH)2 -9.32119 3.32737 -9.10899 -9.53907 3.31410 -3.14321 SiO(OH) -5.23173 1.79359 -6.53519 -6.02243 1.67320 0.627915 SiO(OH)2 -8.39113 3.32935 -9.10899 -9.53907 3.31410 -3.14321 SiO(OH) -3.44378 1.88591 -6.53519 -6.02243 1.67320 0.627915  Table  A.3: The Gibbs free energy of formation. G(T)=a+bT+cTlnT+dT2+e/T +f/T2 Species a b c d e f Si2N2O[ 176] -966,832 731.008 -111.723 0.00587 -2,185,000 0          171 B XRD Spectrum of Ceramic Heater Figure  B.1-Figure  B.13 illustrate the XRD spectra of the ceramic heater at different temperatures and testing durations.  Figure  B.1: XRD spectrum of ceramic heater after 2h at 20oC.   172  Figure  B.2: XRD spectrum of ceramic heater after 2h at 200oC.  Figure  B.3: XRD spectrum of ceramic heater after 2h at 400oC.  173  Figure  B.4: XRD spectrum of ceramic heater after 2h at 600oC.  Figure  B.5: XRD spectrum of ceramic heater after 2h at 700oC.  174  Figure  B.6: XRD spectrum of ceramic heater after 2h at 800oC.  Figure  B.7: XRD spectrum of ceramic heater after 2h at 900oC.   175  Figure  B.8: XRD spectrum of ceramic heater after 2h at 1000oC.  Figure  B.9: XRD spectrum of ceramic heater after 2h at 1100oC.  176  Figure  B.10: XRD spectrum of ceramic heater after 2h at 1200oC.  Figure  B.11: XRD spectrum of ceramic heater after 2h at 1300oC.  177  Figure  B.12: XRD spectrum of ceramic heater after 2h at 1400oC.  Figure  B.13: XRD spectrum of ceramic heater after 2h at 1500oC.  178  Figure  B.14 : XRD spectrum of ceramic heater at1500oC at different times; SN: Si3N4, YS: Yb2Si2O7, C: cristobalite, Pt: platinum.   179 C Experimental Error in Analyzing the Elemental Yb Content The experimental error in analyzing the elemental Yb concentration by EDX was calculated as follows:  1) Three spectra were collected from the same area in 10 regions throughout a cross-section. 2) For these 10 sets, the Standard Deviation values were determined.  3) Also, for all the spectra collected, ZAF factor values were calculated by the post-analysis calculations provided by the X-One software in the Quantify Tab (the calculated matrix correction) and 2 Sigma (measure of uncertainty).  4) The values of the product (ZAF × 2 Sigma) were determined and correlated to the corresponding errors for the calculated Yb wt%.         180 D Electrostatics Model D.1 Longitudinal cross-section of U-shaped conductor  D.1.1 Assumptions 1. Current-carrying wire analogy is made. 2. Yb2O3-doped Si3N4-bound WC-based conducting phase is a continuum.  3. Electrical conductivity of U-shaped conductors is constant. 4. Hall constant is negligible (WC: -21.8e-4 cm3/A.s). Figure  D.1 shows the geometry of U-shaped conductors and finite element mesh pattern. Figure  D.2-Figure  D.4 demonstrate the model implementation procedures and boundary conditions. Figure  D.5 presents the computed electrical potential within the longitudinal cross-section of U-shaped conductors. D.1.2 Mesh Table  D.1 : Mesh statistics. Mesh Statistics Number of degrees of freedom 1702 Number of mesh points 477 Number of elements 750 Triangular 750 Number of boundary elements 208 Number of vertex elements 20 Minimum element quality 0.706 Element area ratio 0.003      181                        Figure  D.1: Geometry of U-shaped conductors and finite element mesh pattern.  Table  D.2: The parameters used in Conductive Media DC model. Description Variable Value Unit Permittivity of vacuum epsilon0_dc 8.854187817×10-12 F/m Electrical Conductivity sigma 4.55 ×106 S/m                  182 D.1.3 Application Mode Properties    Application Mode: Conductive Media DC (dc)        Figure  D.2: Model navigator in COMSOL Multiphysics 3.3a.            Figure  D.3: Subdomain settings-Conductive Media DC in COMSOL Multiphysics 3.3a.  Equation that is solved in this study  183                    Figure  D.4: Boundary conditions imposed on the boundaries of U-shaped conductors (2D).   Table  D.3: 2D model settings. Property Value Default element type Lagrange - Quadratic Weak constraints Off Constraint type Ideal  D.1.4 Variables Table  D.4: 2D model variables. Property Value Dependent variables V Shape functions shlag(2,'V') Interior boundaries active           184 D.1.5 Solver settings Table  D.5: 2D model solver settings. Property Value Solve using a script off Auto select solver On Solver Stationary Solution form  Automatic Symmetric auto Adaption Off Optimization Off Solver type Linear system solver (UMPACK)                          Figure  D.5: Computed electrical potentials at 5mm back from the front ends.           185 D.2 Electric field distribution within the cross-section at the hot spot D.2.1 Assumptions 1. Yb2O3-doped Si3N4-based insulating phase is a continuum.  2. Electrical resistivity of Yb2O3-doped Si3N4-based insulator is constant (1×1014 Ω m). 3. Oxygen and nitrogen ions are immobile. 4. Ytterbium ions are mobile, i.e. (the driving force is such as to induce the Yb ions to migrate away from the conductors). 5. Blocking electrodes: Yb ions cannot penetrate from insulator to conductors and cannot be directly neutralized at the conductors. 6. Two Si-O tetrahedrons (pyrosilicate group) are assumed as a large anion with an effective (-1) charge distributed over the entire anion. The associated Yb cation can be located anywhere in the immediate vicinity of this anion so that the effective charge on the cation can be assumed to be (+1). The boundary conditions (Figure  D.6) for the electric field model on the cross-section of ceramic heater at the hot spot were obtained from the earlier model (Figure  D.5). The asymmetry in the force at the interface between WC-based conductor and Yb2O3-doped Si3N4-based insulator (due to the applied bias) in turn induces the Yb ions to migrate away from the high-potential side. For the sake of simplicity, it is assumed that the O and N ions are immobile and that the driving force is such as to induce the Yb ions to migrate away from the surface, so the surface surrounding will now be negatively charged with respect to the bulk, i.e. the vacancies of Yb ions are  186 diffusely distributed in the bulk of the ceramic insulator. Figure  D.6 and Figure  D.7 demonstrate the model boundary conditions and implementation procedures.                    Figure  D.6: Boundary conditions imposed on the boundaries of the cross-section at the hot spot.        187         Figure  D.7: Subdomain settings-Electrostatics model in COMSOL Multiphysics 3.3a.   The Poisson-Boltzmann (PB) equation reads:  ( ) +∆−×=∇∇−RTVFzGMFzatV dissYbr...exp...100/%0βρεε  ( D-1) V: electric potential (V m-1) 0ε : Permittivity of vacuum (F m-1) rε : relative permittivity of silicon nitride (~8) at%: atom percent ρ  : density (kg m-3) Poisson-Boltzmann Equation is solved in this study  188 z : charge number F: Faraday constant (96,485.34 C mol-1) M: atomic weight (kg) dissG∆ : energy barrier for formation of defect  R: gas constant (8.3145 J (mol.K)-1) T: Temperature (K) β : transfer coefficient ( β = 0.5, in this study, verified against BSE-SEM micrographs) [ 177– 180]. In the structure of Yb2Si2O7, each Yb ion is coordinated by six oxygen atoms and the single bond strength of Yb-O is 375kJ/mol [ 181,  182,  183]. Therefore, the activation energy to break two bonds is about 750 KJ/mol, which is comparable with the activation energy for the viscous flow of intergranular amorphous film in the Yb2O3-doped Si3N4-based ceramics. As the Yb-O bond strength is high, the breakage of all six bonds does not seem to be realistic. The bonds, however, have different lengths; therefore it is feasible that only a fraction of bonds can break at high temperatures (primarily due to the slight difference in the interatomic distances). The behaviour of the grain boundary phase is complex, nonetheless, one might visualize each two Si-O tetrahedra as a large anion with an effective (-1) charge distributed over the entire anion. The associated Yb cation can be located anywhere in the immediate vicinity of this anion so that the effective charge on the cation can be assumed to be (+1); this assumption follows the procedure described elsewhere [ 184, 185].  189     Table  D.6: Parameters used in Electrostatics model. Electrostatics model 0ε : Permittivity of vacuum (F/m) 8.854187817×10-12 rε : relative permittivity of silicon nitride (~8) 8 at%: atom percent 1.13027† ρ  : density (kg/m3) 3170 z : charge number +1 F: Faraday constant (C/mol) 96,485.34 M: atomic weight (kg) 21.95056 ×10-3† dissG∆ : energy barrier for formation of defect (KJ/mol) 750 R: gas constant (J/mol.K) 8.3145 †the data can be found in Table D.7.   190     Table  D.7: Grams in 1 mole of Yb2O3-doped Si3N4-based insulator based on the EDX measurement.                Element     Grams in 100g sample Measured by EDX   for as-received GP Moles in 100g sample     Moles in 1 mole of Yb2O3-doped  Si3N4-based insulator Atom percent (at%)  Molar Mass     Grams in 1 mole of Yb2O3-doped  Si3N4-based insulator    Weight percent (wt%)      Yb 8.91000 0.05149 0.01130 1.13027 173.02000 1.95559 Si 50.94000 1.81372 0.39812 39.81247 28.08600 11.18173 O 6.08000 0.38002 0.08342 8.34182 15.99900 1.33461 N 32.07000 2.28957 0.50258 50.25785 14.00700 7.03962 Mo 2.00000 0.02085 0.00458 0.45759 95.94000 0.43902              Total 100.00000 4.55565 1.00000    21.95056  191 D.2.2 Mesh Table  D.8: Mesh statistics for the Electrostatics model. Mesh Statistics Number of degrees of freedom 17329 Number of mesh points 4409 Number of elements 8508 Triangular 8508 Number of boundary elements 316 Number of vertex elements 20 Minimum element quality 0.675 Element area ratio 0.0   D.2.3 Application mode: Electrostatics (es) Application mode properties  Table  D.9: Application mode properties and settings. Property Value Default element type Lagrange - Quadratic Input property Forced voltage Weak constraints Off Constraint type Ideal  Variables Table  D.10: Variables in the Electrostatics model. Property Value Dependent variables V Shape functions shlag(2,'V') Interior boundaries active          192 Solver settings Table  D.11: Solver settings in the Electrostatics model.  Property Value Solve using a script off Auto select solver On Solver Stationary Solution form  Automatic Symmetric auto Adaption Off Solver type Linear system solver (UMPACK)    Table  D.12: Parameters used in the Electrostatics model. Description Variable Value Unit Permittivity of vacuum epsilon0_dc 8.854187817e-12 F/m            193 E Heat Transfer Model E.1 Assumptions 1. The Yb2O3-Si3N4-bound WC-based conducting phase is a continuum.  2. Electrical conductivity of the U-shaped conductors is constant. 3. Thermal conductivity of the WC-based conductors is constant. 4. Density of the WC-based conductors is constant. 5. Heat capacity of the WC-based conductors is constant. 6. The Yb2O3-doped Si3N4-based insulating phase is a continuum.  7. Electrical conductivity of the Si3N4-based insulator is constant. 8. Thermal conductivity of the Si3N4-based insulator is a linear function of temperature. 9. Density of the Si3N4-based insulator is constant. 10. Heat capacity of the Si3N4-based insulator is constant. 11. A free-convection heat transfer coefficient was assumed on the surface of the ceramic heater suspended in still air (15.0 W m-2 K-1) 12. Emissivity of the Si3N4-based insulator is constant (0.9).  194 E.2 Boundary conditions Heat transfer by conduction All the interior boundaries are assumed to be a continuity of the heat flux, i.e. an interface between the U-shaped conductors and the ceramic insulator. Figure  E.1-Figure  E.6 show the geometry of the ceramic heater and demonstrate the model implementation procedures, boundary conditions, and the finite element mesh pattern.                               Figure  E.1: Boundary conditions in heat transfer by conduction model.     Boundary Condition 1 2 4 3 Boundary Condition Continuity  195 Table  E.1: Physical and thermal properties of Si3N4 and WC ceramics [ 29].  E.3 Conductive Media DC               Figure  E.2: Boundary condition at the outer surface of the ceramic heater in Conductive Media DC model.                Figure  E.3: Boundary condition at the surface of the U-shaped conductors in Conductive Media DC model.   Material Density  (kg m-3) Electrical resistivity (Ω cm) Thermal conductivity (W m-1 K-1) Specific heat capacity (J kg-1 K-1) Emissivity Si3N4 3170 1014 0.0134.T + 34.443 670 0.9 WC 15630 2.2 × 10-5 63 203 N/A  196                    Figure  E.4: Boundary condition at the grounded ends of the U-shaped conducting phase in Conductive Media DC model.                     Figure  E.5: Boundary condition at the high potential ends of the U-shaped conducting phase in Conductive Media DC model.    197 E.4 Mesh  Table  E.2: Mesh statistics in the Conductive Media DC model. Mesh Statistics Number of degrees of freedom 44050 Number of mesh points 22025 Number of elements 128685 Tetrahedral 128685 Prism 0 Hexahedral 0 Number of boundary elements 13600 Triangular 13600 Number of vertex elements 76 Minimum element quality 0.184               Figure  E.6: Finite element mesh pattern in the Conductive Media DC model.      198 E.5 Heat transfer by conduction (ht) and conductive media DC   Application mode properties Table  E.3: Application mode properties in the Conductive Media DC model. Property Value Default element type Lagrange - Quadratic Analysis type Transient Weak constraints Off Constraint type Ideal  Variables Table  E.4: Variables in the Conductive Media DC model. Property Value Dependent variables T Shape functions shlag(1,'V') Interior boundaries continuity  GMRES solver Table  E.5: Solver in the Conductive Media DC model. Property Value Solver type Linear system solver Relative tolerance 1.0e-6 Factor in error estimate 400.0 Maximum number of iterations 20,000 Number of iterations before restart 50 Preconditioning Left Incomplete LU  Table  E.6: Property setting in the Conductive Media DC model. Property Value Solver type Preconditioner Pivot threshold 1.0 Respect pattern on Number of iterations 1 Relaxation factor (omega) 1.0 Drop tolerance 0.01  199 Time stepping Table  E.7: Time stepping in the Conductive Media DC model. Property Value Times 0:1:40 Relative tolerance 0.01 Absolute tolerance 0.0010 Times to be stored in output Specified times Time steps taken by solver Free Manual tuning of step size off Initial time step 0.0010 Maximum time step 1.0 Initialization Backward Euler Constraint handling method  Elimination           Figure  E.7: Coupled Conductive Media DC-Heat Transfer by Conduction equations in Joule Heating model. Heat transfer by conduction Poisson’s equation for conductive media Heat generated by joule heating  200 F Yb Ions Migration under DC Electric Field F.1 Assumptions 1. Yb2O3-doped Si3N4-based insulating phase is a continuum.  2. Electrical conductivity of the Si3N4-based insulator is constant. 3. Thermal conductivity of the Si3N4-based insulator is a linear function of temperature. 4. Density of the Si3N4-based insulator is constant. 5. Heat capacity of the Si3N4-based insulator is constant. 6. A free-convection heat transfer coefficient was assumed on the surface of the ceramic heater suspended in still air (15.0 W m-2 K-1) 7. Emissivity of the Si3N4-based insulator is constant (0.9). 8. The diffusion coefficient of Yb ions obeys the Arrhenius relation with the constant activation energy of 453 KJ/mol. 9. Oxygen and nitrogen anions are immobile. 10. Charge neutrality is maintained throughout the system; therefore the Nenrst-Planck equation without electroneutrality is used.  201 11. Blocking electrode: Yb ions cannot penetrate into the WC-based conductor ends and cannot be neutralized at the interface (no reaction occurs at the conductor/insulator interface). 12. Two Si-O tetrahedra (pyrosilicate group) are assumed as a large anion with an effective (-1) charge distributed over the entire anion. The associated Yb cation can be located anywhere in the immediate vicinity of this anion so that the “effective” charge on the cation can be assumed to be (+1).  Figure  F.1 shows the model implementation procedures and boundary conditions in Nernst-Planck without Electroneutrality module.          202               Figure  F.1: Boundary conditions for Nernst-Planck without Electroneutrality module.      YbYb ckJ .= , i.e. the rate of change of the concentration of Yb ion at the surface is proportional to the Yb ions concentration present [ 71] Boundary condition: “Blocking electrodes”  203    F.2 Application mode: Nernst-Planck without Electroneutrality, Heat Transfer by Conduction, and Elctrostatics Figure  F.2 illustrates the implementation process for the  Nernst-Planck without Electroneutrality model coupled with Heat Transfer by Conduction and Electrostatics models.                     Figure  F.2: Coupled Electrostatics-Heat Transfer by Conduction-Nernst-Planck without Electroneutrality Modules.  204 Table  F.1: Parameters used in Nernst-Planck without Electroneutrality model. The RE ions transport rate within the Si3N4-based ceramics would be substantially increased at temperatures over 1300°C where the liquid (or low viscosity phase) is formed. If the formation temperature of the liquid phase varies from sample to sample, this could also explain the large scatter in oxidation rates observed at 1300°C. The activation energy for diffusion of RE ions varies between 134KJ/mol and 870KJ/mol and as such the diffusion coefficient of Yb is not well determined. For this study the activation energy is taken to be 453kJ/mol and pre-exponential was determined to be ~6.4×105 based on this work (Figure  F.3) and reference [ 18,  65].  −×=RTmolKJDYb/453exp104.6 5   ( F-1)            Figure  F.3:   Yb ion depletion layer in the ceramic heater aged at 1455oC.   Material Density  (kg m-3) Electrical resistivity (Ω cm) Thermal conductivity (W m-1 K-1) Specific heat capacity (J kg-1 K-1) Emissivity Si3N4 3170 1014 0.0134.T + 34.443 670 0.9 50µm 100µm  3366h 1455oC   205 G Yb Ion Migration under an AC Electric Field G.1 Assumptions 1. The Yb2O3-doped Si3N4-based insulating phase is a continuum.  2. Electrical conductivity of the Si3N4-based insulator is constant. 3. Thermal conductivity of the Si3N4-based insulator is a linear function of temperature. 4. Density of the Si3N4-based insulator is constant. 5. Heat capacity of the Si3N4-based insulator is constant. 6. A free-convection heat transfer coefficient was assumed on the surface of the ceramic heater suspended in still air (15.0 W m-2 K-1) 7. Emissivity of the Si3N4-based insulator is constant (0.9). 8. The diffusion coefficient of Yb ions obeys an Arrhenius relation with the constant activation energy of 453 KJ/mol. 9. Oxygen and nitrogen anions are immobile. 10. Charge neutrality is maintained throughout the system; therefore the Nenrst-Planck equation without electroneutrality is to be used.  206 11. Blocking electrode: Yb ions cannot penetrate into the WC-based conductors’ ends and cannot be neutralized at the interface (no reaction occurs at the conductor/insulator interface). 12. Two Si-O tetrahedra (pyrosilicate group) are assumed as a large anion with an effective (-1) charge distributed over the entire anion. The associated Yb cation can be located anywhere in the immediate vicinity of this anion so that the effective charge on the cation can be assumed to be (+1). 13. Dielectric loss of the Yb2O3-doped Si3N4-based insulator is negligible (Loss tangent: 0.0006 @35GHz) 14. The square wave is approximated by a Fourier series.  G.2 Boundary conditions ( ( )+= ∑∞= ,...5,3,100 sin421.)(ntnnVtV ωpi), using only first harmonic.  ( )∑∞=+=,...5,3,10sin421)(nn xnnxS ωpi     The one term representation of the square wave signal is given:  207 ( )+= tVtV 00 sin421.)( ωpi  ( G.1) The error in power in the first harmonic approximation is 18.9%. The power is manually set in the model so as to get the same temperature distribution within the cross-section of ceramic heater while not changing the signal amplitude. Figure  G.1 shows the boundary conditions for Poisson equation (AC model).                 Figure  G.1:   Boundary conditions for Poisson equation (AC model). ( )+= tVtV 00 sin421.)( ωpi ( )+= tVtV 00 sin421.)( ωpi Zero charge/symmetry 

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