研究生: |
朱永如 Chu, Yung Ju |
---|---|
論文名稱: |
低溫共燒多晶介電陶瓷Bi2(Zn1/3Nb2/3)2O7的束縛燒結及其電容失效機制之研究 Constrained Sintering and Failure Analysis of a Low-Fire, Polycrystalline Bi2(Zn1/3Nb2/3)2O7 Dielectric |
指導教授: |
簡朝和
Jean, Jau Ho |
口試委員: |
曾俊元
王錫福 許志雄 林樹均 |
學位類別: |
博士 Doctor |
系所名稱: |
工學院 - 材料科學工程學系 Materials Science and Engineering |
論文出版年: | 2015 |
畢業學年度: | 103 |
語文別: | 中文 |
論文頁數: | 170 |
中文關鍵詞: | 束縛燒結 、失效機制 、低溫共燒陶瓷 |
外文關鍵詞: | Constrained Sintering, Failure Analysis, LTCC |
相關次數: | 點閱:4 下載:0 |
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本論文主要研究多晶陶瓷材料於束縛燒結時的緻密行為與顯微結構發展,並探討於束縛燒結時其緻密行為延緩的原因,以及分析其積層陶瓷電容之失效機制。首先在第一章中簡介低溫共燒陶瓷製程技術與材料選擇,以及積層共燒材料間的匹配度問題,束縛燒結技術與其所面臨的問題。近年來新興的無玻璃陶瓷具本質低溫燒結特性,因不需添加助燒結劑且於燒結後即為單一純相,此可降低燒結體與電極材料間交互作用的可能性,有利於元件後續製程,將更適合低溫共燒陶瓷的應用,因此本研究選用無玻璃陶瓷Bi2(Zn1/3Nb2/3)2O7 (BZN)為研究對象,採用無應力協助之束縛燒結(Pressureless-assisted sintering, PLAS)技術,以氧化鋁生胚層作為束縛層,在第二章中探討BZN於束縛燒結時的緻密行為與顯微結構發展,以及造成多晶材料於束縛燒結下緻密行為延遲的原因(包含平面張應力、燒結機制、異向性等)。在850oC持溫兩小時BZN於自由燒結下可達緻密(相對燒結密度達95%),在相同的燒結條件下BZN於束縛燒結時僅只有相對燒結密度78.7%,延長燒結時間至五小時,對於燒結密度的提升有限(83.3%),但將燒結溫度提高至900oC持溫兩小時,束縛燒結下的BZN可達緻密化。BZN於束縛燒結下無顯著異向性顯微結構發展且具有與自由燒結時相似的晶粒尺寸,因此可利用等向性構成方程式分析BZN於束縛燒結時的緻密行為與應力變化。
在材料於自由燒結可緻密化的燒結條件(溫度與時間)下,於PLAS時材料的緻密行為發生延緩,具有較低的緻密度與較慢的緻密速率,為了解決此問題,於PLAS技術中輔以外加單軸向壓應力的方式來達到緻密化的需求,因此在第三章中探討外加應力對BZN於PLAS時的影響,包含緻密行為與顯微結構,BZN於束縛燒結下之緻密度隨外加應力增加而增加,達緻密化的時間隨應力增加而縮短,顯微結構不因外加應力而有特殊發展趨勢,接著利用構成方程式推導之理論公式,計算使BZN於PLAS時具有與自由燒結時相同之緻密速率所需施加的單軸向壓應力為50-600 kPa,與實驗量測結果相符,表示材料於束縛燒結時的多孔體黏度之量測正確性以及構成方程式的適用性。在第三章最後總結BZN與各多晶材料系統於束縛燒結時之緻密行為與顯微結構等性質的相關性,以束縛和自由燒結溫度之比值,表示多晶材料於束縛燒結時緻密行為的延遲程度與顯微結構的異向性程度,以及燒結機制改變的可能性。
在第四章中探討以BZN為介電層,選擇不需氣氛控制且高導電率的銀為內電極材料所組成之積層陶瓷電容(Multilayer ceramic capacitance, MLCC)於高溫和高壓時的失效機制,以及BZN與銀之間的化學穩定性。內電極材料銀與BZN之間無化學反應,兩者共燒後可得具良好緻密度且無脫層等缺陷的積層陶瓷電容。由加速生命試驗的結果表示元件失效時間隨溫度或電壓的增加而縮短。分析失效前後元件的銀濃度變化,顯示在高電場下使內電極銀發生遷移。由阻抗頻譜量測,驗證MLCC-BZN絕緣電阻的下降來自共燒時銀離子擴散與氧空缺的生成,而加速介電崩潰的發生。失效後元件外部產生破裂,內部則有孔洞與裂縫並有銀顆粒的填充,表示元件的失效機制主要為熱崩潰主導。
[1] Y. G. Wang, G. N. Zhang, and J. S. Ma, “Research of LTCC/Cu, Ag Multilayer Substrate in Microelectronic Packaging,” Mater. Sci. Eng. B-Solid., 94 [1] 48-53 (2002).
[2] M. R. Gongora-Rubio, P. Espinoza-Vallejos, L. Sola-Laguna, and J. J. Santiago-Aviles, “Overview of Low Temperature Co-Fired Ceramics Tape Technology for Meso-System Technology (MsST),” Sens. Actuator A-Phys., 89 [3] 222-41 (2001).
[3] C. Q. Scrantom and J. C. Lawson, “LTCC Technology: Where We are and Where We're Going . II,” IEEE MTT-S., 193-200 (1999).
[4] S. Yano, H. Yamaguchi, and T Hirai, “Distributed Constant Circuit Board Using Ceramic Substrate Material,” US patent No. 5,232,765, 1993.
[5] R. R. Tummala, “Ceramic and Glass-Ceramic Packaging in the 1990s,” J. Am. Ceram. Soc., 74 [5] 895-908 (1991).
[6] S. H. Knickerbocker, A. H. Kumar, and L. W. Herron, “Cordierite Glass-Ceramics for Multilayer Ceramic Packaging,” Am. Ceram. Soc. Bull., 72 [1] 90-95 (1993).
[7] C. R. Chang and J. H. Jean, “Crystallization Kinetics and Mechanism of Low-Dielectric, Low-Temperature, Cofirable CaO-B2O3-SiO2 Glass-Ceramics,” J. Am. Ceram. Soc., 82 [7] 1725-32 (1999).
[8] J. H. Jean, Y. C. Fang, S. X. Dai, and D. L. Wilcox, “Devitrification Kinetics and Mechanism of K2O-CaO-SrO-BaO-B2O3-SiO2 Glass-Ceramic,” J. Am. Ceram. Soc., 84 [6] 1354-60 (2001).
[9] N. Kamehara, K. Kurihara and K. Niwa, “Method for Producing Multilayered Glass-Ceramic Structure with Copper-Based Conductors Therein,” US patent No. 4,504,339, 1985.
[10] J. H. Jean and S. C. Lin, “Effects of Borosilicate Glass on Densification and Properties of Borosilicate Glass Plus TiO2 Ceramics,” J. Mater. Res., 14 [4] 1359-63 (1999).
[11] J. H. Jean and T. K. Gupta, “Liquid-Phase Sintering in the Glass-Cordierite System,” J. Mater. Sci., 27 [6] 1575-84 (1992).
[12] J. H. Jean and T. K. Gupta, “Liquid-Phase Sintering in the Glass-Cordierite System: Particle Size Effect,” J. Mater. Sci., 27 [18] 4967-73 (1992).
[13] J. H. Jean, Y. C. Fang, S. X. Dai, and D. L. Wilcox, “Effects of Alumina on Devitrification Kinetics and Mechanism of K2O-CaO-SrO-BaO-B2O3-SiO2 Glass,” Jpn. J. Appl. Phys. 1, 42 [7A] 4438-43 (2003).
[14] J. H. Jean, Y. C. Fang, S. X. Dai, and D. L. Wilcox, “Sintering of a Crystallizable K2O-CaO-SrO-BaO-B2O3-SiO2 Glass with Titania Present,” J. Mater. Res., 17 [7] 1772-78 (2002).
[15] M. T. Sebastian and H. Jantunen, “Low Loss Dielectric Materials for LTCC Applications: A Review,” Int. Mater. Rev., 53 [2] 57-90 (2008).
[16] J. H. Jean and T. K. Gupta, “Densification Kinetics and Modeling of Glass-Filled Alumina Composite,” J. Mater. Res., 9 [3] 771-80 (1994).
[17] J. H. Jean, T. H. Kuan, and C. R. Chang, “Low-Temperature-Fired, Low-Dielectric-Constant Silica Glass Composite for Substrate Application," Mater. Chem. Phys., 41 [2] 123-27 (1995).
[18] M. Udovic, M. Valant, and D. Suvorov, “Dielectric Characterisation of Ceramics from the TiO2-TeO2 System,” J. Eur. Ceram. Soc., 21 [10-11] 1735-38 (2001).
[19] J. J. Bian, D. W. Kim, and K. S. Hong, “Glass-Free LTCC Microwave Dielectric Ceramics,” Mater. Res. Bull., 40 [12] 2120-29 (2005).
[20] D. K. Kwon, M. T. Lanagan, and T. R. Shrout, “Microwave Dielectric Properties of BaO-TeO2 Binary Compounds,” Mater. Lett., 61 [8-9] 1827-31 (2007).
[21] D. Zhou, C. A. Randall, H. Wang, L. X. Pang, and X. Yao, “Ultra-Low Firing High-k Scheelite Structures Based on [(Li0.5Bi0.5)xBi1-x][MoxV1-x ]O4 Microwave Dielectric Ceramics,” J. Am. Ceram. Soc., 93 [8] 2147-50 (2010).
[22] D. Zhou, C. A. Randall, L. X. Pang, H. Wang, X. G. Wu, J. Guo, G. Q. Zhang, L. Shui, and X. Yao, “Microwave Dielectric Properties of Li2(M2+)2Mo3O12 and Li3(M3+)Mo3O12 (M=Zn, Ca, Al, and In) Lyonsite-Related-Type Ceramics with Ultra-Low Sintering Temperatures,” J. Am. Ceram. Soc., 94 [3] 802-05 (2011).
[23] D. Zhou, C. A. Randall, H. Wang, L. X. Pang, and X. Yao, “Microwave Dielectric Ceramics in Li2O-Bi2O3-MoO3 System with Ultra-Low Sintering Temperatures,” J. Am. Ceram. Soc., 93 [4] 1096-100 (2010).
[24] K.Niwa, N. Kamehara, K. Yokouchi, and Y. Imanaka, “Multilayer Ceramic Circuit Boards with Copper Conductors,” Adv. Ceram. Mater., 2 [4] 832-35 (1987).
[25] T. Motoki, M. Naito, H. Sano, T. Konoike, and K. Tomono, “Effect of Microstructure on Reliability of Ca(TiZr)O3-Based Multilayer Ceramic Capacitors,” Jpn. J. Appl. Phys., 39 [9B] 5565-68 (2000).
[26] R. J. Weachock, and D. Liu, “Failure Analysis of Dielectric Breakdowns in Base-Metal Electrode Multilayer Ceramic Capacitors.” presented at the Capacitors and Resistors Technology Symposium International, Houston, TX, 2013.
[27] J. Yamamatsu, N. Kawano, T. Arashi, A. Sato, Y. Nakano, and T. Nomura, “Reliability of Multilayer Ceramic Capacitors with Nickel Electrodes,” J. Power Sources, 60 [2] 199-203 (1996).
[28] Y. T. Shih, J. H. Jean, and S. C. Lin, “Failure Mechanism of a Low-Temperature-Cofired Ceramic Capacitor with an Inner Ag Electrode,” J. Am. Ceram. Soc., 93 [10] 3278-83 (2010).
[29] N. J. Donnelly and C. A. Randall, “Refined Model of Electromigration of Ag/Pd Electrodes in Multilayer PZT Ceramics Under Extreme Humidity,” J. Am. Ceram. Soc., 92 [2] 405-10 (2009).
[30] J. C. Lin and J. Y. Chan, “On the Resistance of Silver Migration in Ag-Pd Conductive Thick Films Under Humid Environment and Applied DC Field,” Mater. Chem. Phys., 43 [3] 256-65 (1996).
[31] R. Z. Zuo, L. T. Li, and Z. L. Gui, “Influence of Silver Migration on Dielectric Properties and Reliability of Relaxer Based MLCCs,” Ceram. Int., 26 [6] 673-76 (2000).
[32] M. Valant and D. Suvorov, “New Generation of LTCC Materials,” Bol. Soc. Esp. Ceram. V., 43 [3] 634-39 (2004)
[33] N. X. Wu and J. J. Bian, “Glass-Free Low-Temperature Co-Fired Ceramics Microwave Ceramic AW1-xTexO4 (A=Ca, Sr, Zn),” Int. J. Appl. Ceram. Technol., 8 [6] 1494-500 (2011).
[34] M. Valant and D. Suvorov, “Glass-Free Low-Temperature Cofired Ceramics: Calcium Germanates, Silicates and Tellurates,” J. Eur. Ceram. Soc., 24 [6] 1715-19 (2004).
[35] D. Zhou, H. Wang, X. Yao, and L. X. Pang, “Microwave Dielectric Properties of Low Temperature Firing Bi2Mo2O9 Ceramic,” J. Am. Ceram. Soc., 91 [10] 3419-22 (2008).
[36] D. Zhou, C. A. Randall, L. X. Pang, H. Wang, J. Guo, G. Q. Zhang, Y. Wu, K. T. Guo, L. Shui, and X. Yao, “Microwave Dielectric Properties of (ABi)1/2MoO4 (A = Li, Na, K, Rb, Ag) Type Ceramics with Ultra-Low Firing Temperatures,” Mater. Chem. Phys., 129 [3] 688-92 (2011).
[37] M. J. Chiang, J. H. Jean, and S. C. Lin, “Effects of Green Density Difference on Camber Development During the Cofiring of a Bi-Layer Glass-Based Dielectric Laminate,” Mater. Chem. Phys., 128 [3] 413-17 (2011).
[38] J. C. Chang and J. H. Jean, “Camber Development During the Cofiring of Bi-Layer Glass-Based Dielectric Laminate,” J. Am. Ceram. Soc., 88 [5] 1165-70 (2005).
[39] J. B. Ollagnier, O. Guillon, and J. Rodel, “Constrained Sintering of a Glass Ceramic Composite: I. Asymmetric Laminate,” J. Am. Ceram. Soc., 93 [1] 74-81 (2010).
[40] D. J. Green, O. Guillon, and J. Rodel, “Constrained Sintering: A Delicate Balance of Scales,” J. Eur. Ceram. Soc., 28 [7] 1451-66 (2008).
[41] P. Z. Cai, D. J. Green, and G. L. Messing, “Constrained Densification of Alumina/Zirconia Hybrid Laminates, I: Experimental Observations of Processing Defects,” J. Am. Ceram. Soc., 80 [8] 1929-39 (1997).
[42] G. Q. Lu, R. C. Sutterlin, and T. K. Gupta, “Effect of Mismatched Sintering Kinetics on Camber in a Low-Temperature Cofired Ceramic Package,” J. Am. Ceram. Soc., 76 [8] 1907-14 (1993).
[43] R. K. Bordia and G.W. Scherer, “On Constrained Sintering – II, Comparison of Constitutive Models,” Acta. Metall., 36 [9] 2399-409 (1988).
[44] P. Z. Cai, G. L. Messing and D. J. Green, “Determination of the Mechanical Response of Sintering Compacts by Cyclic Loading Dilatometry,” J. Am. Ceram. Soc., 80 [2] 445-52 (1997).
[45] A. Mohanram, G. L. Messing and D. J. Green, “Measurement of Viscosity of Densifying Glass-Based Systems by Isothermal Cyclic Loading Dilatometry,” J. Am. Ceram. Soc., 87 [2] 192-96 (2004).
[46] Y. L. Tung, T. M. Peng, J. H. Jean, and S. C. Lin, “Stress Development During the Co-firing of Integrated Ferrite/Dielectric Laminates,” J. Am. Ceram. Soc., 95 [3] 946-50 (2012).
[47] Y. L. Tung, J. H. Jean, and Y. H. Cheng, “Effects of a Non-Magnetic CuZn Ferrite Layer on Cofiring and Electrical Properties of a Low-Fire, Multilayer NiCuZn Ferrite Inductor,” Ceram. Int., 39 [7] 7583-87 (2013)
[48] R. T. Hsu and J. H. Jean, “Key Factors Controlling Camber Behavior During the Cofiring of Bi-Layer Ceramic Dielectric Laminates,” J. Am. Ceram. Soc., 88 [9] 2429-34 (2005).
[49] R. K. Bordia and G.W. Scherer, “On Constrained Sintering – I, Constitutive Model for a Sintering Body,” Acta. Metall., 36 [9] 2393-97 (1988).
[50] F. Lautzenhiser and E. Amaya, “Self-Constrained LTCC Tape,” Am. Ceram. Soc. Bull., 81 [10] 27-32 (2002).
[51] W. A. Vitrio and R. L. Brown, “Process for Fabricating Dimensionally Stable Interconnect Boards,” US patent No. 4,656,552, 1987.
[52] C. D. Lei and J. H. Jean, “Effect of Crystallization on the Stress Required for Constrained Sintering of CaO-B2O3-SiO2 Glass-Ceramics,” J. Am. Ceram. Soc., 88 [3] 599-603 (2005).
[53] C. C. Huang and J. H. Jean, “Stress Required for Constrained Sintering of a Ceramic-Filled Glass Composite,” J. Am. Ceram. Soc., 87 [8] 1454-58 (2004).
[54] K. R. Mikeska and R. H. Jensen, “Pressure-Assisted Sintering of Multilayer Packages,” Ceram. Trans., 15 629-50 (1990).
[55] K. R. Mikeska and D.T. Schaefer, “Method for Reducing Shrinkage During Firing of Ceramic Bodies,” US patent 5,454,741, 1994.
[56] Y. C. Lin and J. H. Jean, “Constrained Densification Kinetics of Alumina/Borosilicate Glass+Alumina/Alumina Sandwich Structure,” J. Am. Ceram. Soc., 85 [1] 150-54 (2002).
[57] S. Y. Tzeng and J. H. Jean, “Stress Development During Constrained Sinetring of Alumina/Glass/Alumina Sandwich Structure,” J. Am. Ceram. Soc., 85 [2] 335-40 (2002).
[58] T. J. Garino and H. K. Bowen, “Deposition and Sintering of Particle Films on a Rigid Substrate,” J. Am. Ceram. Soc., 70 [11] C315-17 (1987).
[59] T. J. Garino and H. K. Bowen, “Kinetics of Constrained-Film Sintering,” J. Am. Ceram. Soc., 73 [2] 251-57 (1990).
[60] G. W. Scherer and T. Garino, “Viscous Sintering on a Rigid Substrate,” J. Am. Ceram. Soc., 68 [4] 216-20 (1985).
[61] B. Geller, B. Thaler, A. Fathy, M. J. Liberatore, H. D. Chen, G. Ayers, V. Pendrick and Y. Narayan, “LTCC-M: An Enabling Technology for High Performance Multilayer RF Systems,” J. Microwave, 42 [7] 64-72 (1999).
[62] J. C. Chang and J. H. Jean, “Self-Constrained Sintering of Mixed Low-Temperature-Cofired Ceramic Laminate,” J. Am. Ceram. Soc., 89 [3] 829-35 (2006).
[63] C. H. Liao, J. H. Jean, and Y. Y. Hung, “Self-Constrained Sintering of a Multilayer Low-Temperature-Cofired Glass-Ceramics/Alumina Laminate,” J. Am. Ceram. Soc., 91 [2] 648-51 (2008).
[64] R. K. Bordia, R. ZuO, O. Guillon, S. M. Salamone, and J. Rodel, “Anisotropic Constitutive Laws of Sintering Bodies,” Acta Mater., 54 [1] 111-18 (2006).
[65] L. Amaral, C. Jamin, A. M. R. Senos, P. M. Vilarinho, and O. Guillon, “Effect of the Substrate on the Constrained Sintering of BaLa4Ti4O15 Thick Films,” J. Am. Ceram. Soc., 95 [12] 3781-87 (2012).
[66] J. B. Ollagnier, D. J. Green, O. Guillon, and J. Rodel, “Constrained Sintering of a Glass Ceramic Composite: II. Symmetric Laminate,” J. Am. Ceram. Soc., 92 [12] 2900-06 (2009).
[67] O. Guillon, E. Aulbach, J. Rodel, and R. K. Bordia, “Constrained Sintering of Alumina Thin Films: Comparison Between Experiment and Modeling,” J. Am. Ceram. Soc., 90 [6] 1733-37 (2007).
[68] R. Z. Zuo, E. Aulbach, and J. Rodel, “Viscous Poisson's Coefficient Determined by Discontinuous Hot Forging,” J. Mater. Res., 18 [9] 2170-76 (2003).
[69] S. M. Salamone, L. C. Stearns, R. K. Bordia, and M. P. Harmer, “Effect of Rigid Inclusions on the Densification and Constitutive Parameters of Liquid-Phase-Sintered YBa2Cu3O6+x Powder Compacts,” J. Am. Ceram. Soc., 86 [6] 883-92 (2003).
[70] F. Li, J. Z. Pan, O. Guillon, and A. Cocks, “Predicting Sintering Deformation of Ceramic Film Constrained by Rigid Substrate Using Anisotropic Constitutive Law,” Acta Mater., 58 [18] 5980-88 (2010).
[71] X. Wang and A. Atkinson, “Microstructure Evolution in Thin Zirconia Films: Experimental Observation and Modelling,” Acta Mater., 59 [6] 2514-25 (2011).
[72] J. W. Choe, J. N. Calata, and G. Q. Lu, “Constrained-Film Sintering of a Gold Circuit Paste,” J. Mater. Res., 10 [4] 986–94 (1995).
[73] R. T. Hsu, J. H. Jean, and Y. Y. Hung, “Stress Required to Densify a Low-Fire NiCuZn Ferrite Under Constrained Sintering,” J. Am. Ceram. Soc., 91 [6] 2051-54 (2008).
[74] Y. C. Lin and J. H. Jean, “Constrained Sintering of Silver Circuit Paste,” J. Am. Ceram. Soc., 87 [2] 187-91 (2004).
[75] C. L. Fan and M. N. Rahaman, “Factors Controlling the Sintering of Ceramic Particulate Composites: I, Conventional Processing,” J. Am. Ceram. Soc., 75 [8] 2056-65 (1992).
[76] R. K. Bordia and R. Raj, “Sintering Behavior of Ceramic Films Constrained by a Rigid Substrate,” J. Am. Ceram. Soc., 68 [6] 287-92 (1985)
[77] J. Bang and G. Q. Lu, “Densification Kinetics of Glass Films Constrained on Rigid Substrates,” J. Mater. Res., 10 [5] 1321-26 (1995).
[78] L. Amaral, C. Jamin, A. M. R. Senos, P. M. Vilarinho, and O. Guillon, “Constrained Sintering of BaLa4Ti4O15 Thick Films: Pore and Grain Anisotropy,” J. Eur. Ceram. Soc., 33 [10] 1801-08 (2013).
[79] D. Bernard, O. Guillon, N. Combaret, and E. Plougonven, “Constrained Sintering of Glass Films: Microstructure Evolution Assessed through Synchrotron Computed Microtomography,” Acta Mater., 59 [16] 6228-38 (2011).
[80] O. Guillon, L. Weiler, and J. Rodel, “Anisotropic Microstructural Development During the Constrained Sintering of Dip-Coated Alumina Thin Films,” J. Am. Ceram. Soc., 90 [5] 1394-400 (2007).
[81] J. B. Ollagnier, O. Guillon and J. Rodel, “Effect of Anisotropic Microstructure on the Viscous Properties of an LTCC Material,” J. Am. Ceram. Soc., 90 [12] 3846-51 (2007).
[82] C. L. Martin and R. K. Bordia, “The Effect of a Substrate on the Sintering of Constrained Films,” Acta Mater., 57 [2] 549-58 (2009).
[83] R. Z. Zuo, E. Aulbach, R. K. Bordia, and J. Rodel, “Critical Evaluation of Hot Forging Experiments: Case Study in Alumina,” J. Am. Ceram. Soc., 86 [7] 1099-105 (2003).
[84] J. B. Ollagnier, O. Guillon and J. Rodel, “Viscosity of LTCC Determined by Discontinuous Sinter-Forging,” Int. J. Appl. Ceram. Tec., 3 [6] 437-41 (2006).
[85] J. C. Chang, J. H. Jean, and Y. Y. Hung, “The Effect of Applied Stress on the Densification of a Low-Temperature Cofired Ceramic-Filled Glass System Under Constrained Sintering,” J. Am. Ceram. Soc., 92 [9] 1946-50 (2009).
[86] B. Henrich, A. Wonisch, T. Kraft, M. Moseler, and H. Riedel, “Simulations of the Influence of Rearrangement During Sintering,” Acta Mater., 55 [2] 753-62 (2007).
[87] O. Guillon, S. Krauss, and J. Rodel, “Influence of Thickness on the Constrained Sintering of Alumina Films,” J. Eur. Ceram. Soc., 27 [7] 2623-27 (2007).
[88] D. R. Carroll and M. N. Rahaman, “ An Initial Stage Model for the Sintering of Constrained Polycrystalline Thin Films,” J. Eur. Ceram. Soc., 14 [5] 473-79 (1994).
[89] X. Wang, J. S. Kim, and A. Atkinson, “Constrained Sintering of 8 mol% Y2O3 Stabilised Zirconia Films,” J. Eur. Ceram. Soc., 32 [16] 4121-28 (2012).
[90] H. Zheng, D. I. Woodward, L. Gillie, and I. M. Reaney, “Structure and Microwave Dielectric Properties of BaLa4Ti4O15,” J. Phys.-Condes. Mat., 18 [31] 7051-62 (2006).
[91] D. Zhou, H. Wang, X. Yao, and L. X. Pang, “Sintering Behavior and Microwave Dielectric Properties of Bi2O3-ZnO-Nb2O5-Based Ceramics Sintered Under Air and N2 Atmosphere,” Ceram. Int., 34 [4] 901-04 (2008).