在一濕式還原氣氛下燒結及隨後分別於乾、溼式氣氛中再氧化之受體(鈧或釔)摻雜鋯鈦酸鋇鈣陶瓷的介電性質與電阻衰退行為進行比較。在濕式氣氛中，發現氣氛中的水氣與鋯鈦酸鋇鈣陶瓷內部的氧空缺進行反應，在晶格中因氧原子脫離的空缺位置上，形成一氫氧根缺陷之帶正電離子。其中，帶正電荷之質子躍遷被認為會明顯提高離子導電度，進而連帶影響陶瓷體內部的晶粒的傳導。在居禮溫度點的最大相對介電常數變化，也因為氫氧根缺陷的存在所導致。另一方面，氣氛中含有水氣嚴重地影響電阻衰退行為，即電阻失效時間因氫氧根缺陷的存在而大幅縮短。至於陶瓷體內部的導電性研究，例如:晶粒導電性、晶界導電性、晶界能障高度以及空間電荷層厚度，則是利用交流阻抗分析儀 (IS) 來做進一步深入探討。除此之外，電子穿透式顯微鏡 (TEM) 搭配電子能量損失能譜分析儀 (EELS) 則是用來偵測陶瓷部內部微結構、微量化學以及氧化學計量改變。
關鍵字: BME 介電材料、交流阻抗分析儀、氫氧根缺陷、電阻衰退、電子能量損失能譜分析儀。

Dielectric property and degradation behavior of acceptor (Sc or Y)-doped (Ba,Ca)(Ti,Zr)O3 ceramics sintered in moist reducing atmosphere and subsequently re-oxidized in dry or wet atmospheres was contrasted. In moist firing atmosphere, water vapor was found to react with oxygen vacancies, forming positively charged hydroxyl defects on regular oxygen sites in the crystal lattice. Proton hopping is considered to raise the ionic conductivity significantly. Therefore, hydroxyl defects in turn influence the grain conduction. Hydroxyl defects are also considered to be responsible for alternations of the dielectric maximum at the Curie point. On the other hand, the degradation behavior critically depends on the water vapor incorporation, the time to degradation systematically decreased with the incorporation of hydroxyl defects. The electrical conductivity was investigated by means of impedance spectroscopy (IS) to determine properties, such as grain and grain boundary conductivity, grain boundary potential barrier height, and space charge layer thickness. Furthermore, transmission electron microscopy (TEM) and electron energy loss spectroscopy (EELS) were applied to consider microstructure, microchemistry, and oxygen stoichiometry changes.

[1] Seuter AMJH, “Defect Chemistry and Electrical Transport Properties of Barium Titanate,” Philips Res. Rpts.; Suppl., 3, 1-84 (1974).
[2] J. Daniels, “Defect Chemistry and Electrical Conductivity of Doped Barium Titanate: 2. Defect Equilibria in Acceptor-doped Barium Titanate,” Philips Res. Rpts., 31 [6] 505-15 (1976).
[3] J. M. Herbert, “High Permittivity Ceramics Sintered in Hydrogen,” Trans. Brit. Ceram. Soc., 62 [8] 645 (1963).
[4] R. Waser, T. Baiatu, and K.-H. Hardtl, “DC Electrical Degradation of Perovskite-Type Titanates: I, Ceramics,” J. Am. Ceram. Soc., 73 [6] 1645-1653 (1990).
[5] R. Waser, T. Baiatu, and K.-H. Hardtl, “dc Electrical Degradation of Perovskite-Type Titanates: II, Single Crystals,” J. Am. Ceram. Soc., 73 [6] 1654-1662 (1990).
[6] R. Waser, T. Baiatu, and K.-H. Hardtl, “dc Electrical Degradation of Perovskite-Type Titanates: III, A Model of the Mechanism,” J. Am. Ceram. Soc., 73 [6] 1663-1673 (1990).
[7] S. Rodewald, J. Fleig, and J. Maier, “Resistance Degradation of Iron-Doped Strontium Titanate Investigated by Spatially Resolved Conductivity Measurements,” J. Am. Ceram. Soc., 83 [8] 1969-1976 (2000).
[8] M. Vollmann and R. Waser, “Grain Boundary Defect Chemistry of Acceptor-Doped Titanates: High Field Effects,” J. Electroceram., 1 [1] 51-64 (1997).
[9] J. B. McChesney, P. K. Gallagher and F. V. DiMarcello, “Stabilized Barium Titanate Ceramics for Capacitor Dielectrics,” J. Am. Ceram. Soc., 46 [5] 197-202 (1963).
[10] K. Okazaki and H. Igarashi, “Processing-property Relations in Ceramic Dielectric Capacitors,” Ferroelectrics, 27 [1] 263-268 (1980).
[11] R. Waser, “Solubility of Hydrogen Defects in Doped and Undoped BaTiO3,” J. Am. Ceram. Soc., 71 [1] 58-63 (1988).
[12] M. Vollman and R. Waser, “Grain Boundary Defect Chemistry of Acceptor-Doped Titanates: Space Charge Layer Width,” J. Am. Ceram. Soc., 77 [1] 235-243 (1994).
[13] S. Rodewald, J. Fleig and J. Maier, “Measurement of Conductivity Profiles in Acceptor-doped Strontium Titanate,” J. Eur. Ceram. Soc., 19 [6-7] 797-801 (1999).
[14] H. Saito, H. Chazono, H. Kishi and N. Yamaoka, “X7R Multilayer Ceramic Capacitors with Nickel Electrodes,” Jpn. J. Appl. Phys., 30, 2307-2310 (1991).
[15] H. Shizuno, S. Kusumi, H. Saito and H. Kishi, “Properties of Y5V Multilayer Ceramic Capacitors with Nickel Electrodes,” Jpn. J. Appl. Phys., 32, 4380-4383 (1993).
[16] K. Morita, Y. Mizuno, H. Chazono, H. Kishi, G.Y. Yang, W.E. Liu, E.C. Dicky, and C.A. Randall, “Electric Conduction of Thin-Layer Ni-Multilayer Ceramic Capacitors with Core–Shell Structure BaTiO3,” Jpn. J. Appl. Phys., 46, 2984-2990 (2007).
[17] X. W. Zhang, Y. H. Han, M. Lal, and D. M. Smyth, “Defect Chemistry of BaTiO3 with Additives of CaTiO3,” J. Am. Ceram. Soc., 70 [2] 100-103 (1987).
[18] Y. Sakabe, N. Wada, T. Hiramatsu, and T. Tonogaki, “Dielectric Properties of Fine-Grained BaTiO3 Ceramics Doped with CaO,” Jpn. J. Appl. Phys., 41, 6922-6925 (2002).
[19] Y. Sakabe and H. Takagi, “Nonreducible Mechanism of {(Ba1-xCax)O}mTiO2 (m>1) Ceramics,” Jpn. J. Appl. Phys., 41, 6461-6465 (2002).
[20] D. Hennings, A. Schnell, and G. Simon, “Diffuse Ferroelectric Phase Transitions in Ba(Ti1-yZry)O3 Ceramics,” J. Am. Ceram. Soc., 65 [11] 539-544 (1982).
[21] Q. Feng, C. J. McConville, and D. D. Edwards, “Dielectric Properties and Microstructures of Ba(Ti,Zr)O3 Multilayer Ceramic Capacitors with Ni Electrodes,” J. Am. Ceram. Soc., 88 [6] 1455–1460 (2005).
[22] S. Lee, W. H. Woodford, and C. A. Randall, “Crystal and Defect Chemistry Influences on Band Gap Trends in Alkaline Earth Perovskites,” Appl. Phys. Lett., 92 [20] 201909 (2008).
[23] K. Hurlbut, Manual of Mineralogy, 21st Ed. John Wiley and Sons, Inc., New York, 1993.
[24] A. J. Moulson and J. M. Herbert, Electroceramics, 2nd Ed. John Wiley and Sons, Inc., New York, 2003.
[25] K. C. Kao, Dielectric Phenomena in Solids: With Emphasis on Physical Concept of Electronic Process. Elsevier Academic Press, San Diego, 2004.
[26] H. D. Megaw, “Crystal Structure of Double Oxides of the Perovskite Type,” Proc. Phys. Soc., 58, 340 (1946).
[27] B. Jaffe, W. R. Cook, and H. Jaffe, Piezoelectric Ceramics. Academic Press, London, New York, 1971.
[28] V. M. Goldschmidt, Geochemisce Verterlungsgesetze der Elemente. Norske Videnskap, Oslo, 1927.
[29] R. D. Shannon, “Revised Effective Ionic Radii and Systematic Studies of Inter-atomic Distances in Halides and Chalcogenides,” Acta Crystallogr., A32, 751-767 (1976).
[30] D. Hennings, “Barium Titanate Based Ceramic Materials for Dielectric Use,” Int. J. High Tech. Ceram., 3 [2] 91–111 (1987).
[31] J. C. Slater, “The Lorentz Correction in Barium Titanate,” Phys. Rev., 78 [6] 748-761 (1950).
[32] N.-H. Chan, R. K. Sharma, and D. M. Smyth, “Nonstoichiometry in Undoped BaTiO3,” J. Am. Ceram. Soc., 64 [9] 556–562 (1981).
[33] W. Heywang, “Resistivity Anomaly in Doped Barium Titanate,” J. Am. Ceram. Soc., 47 [10] 484–490 (1964).
[34] G. Arlt, D. Hennings, and G. de With, “Dielectric Properties of Fine‐Grained Barium Titanate Ceramics,” J. Appl. Phys., 58 [4] 1619 (1985).
[35] F. A. Kröger and H. J. Vink, Relations Between the Concentration of Imperfections in Crystalline Solids, in Solid State Physics 3, ed. By F. Seitz and D. Turnbull, Academic Press, New York, USA, 1956.
[36] G. V. Lewis and C. R. A. Catlow, “PTCR Effect in BaTiO3,” J. Am. Ceram. Soc., 68 [10] 555-558 (1985).
[37] G. M. Choi, H. Tuller and D. Goldschmidt, “Electronic Transport Behavior of Single Crystalline Ba0.03Sr0.97TiO3,” Phys Rev B Condens Matter., 34 [10] 6972-6979 (1986).
[38] J. Nowotny and M. Rekas, “Defect Structure, Electrical Properties and Transport in Barium Titanate. II. Consistency Requirements Between Defect Models and Crystal Properties,” Ceram. Int., 20 [4] 217-224 (1994).
[39] J. Daniels and R. Wernicke, “Part I. Electrical Conductivity at High Temperature of Donor-Doped BariumTitanate Ceramics,” Philips Res. Rpts., 31 [6] 516 (1976).
[40] R. Waser, T. Baiatu and K. H. Härdtl, “dc Electrical Degradation of Perovskite-Type Titanates: I, Ceramics,” J. Am. Ceram. Soc., 73 [6] 1645–1653 (1990).
[41] R. Waser, T. Baiatu, and K.-H. Hardtl, “dc Electrical Degradation of Perovskite-Type Titanates: III, A Model of the Mechanism,” J. Am. Ceram. Soc., 73 [6] 1663-1673 (1990).
[42] D. M. Smyth, The Defect Chemistry of Metal Oxides, Oxford University Press, 2000.
[43] R. Waser, T. Baiatu, and K.-H. Hardtl, “dc Electrical Degradation of Perovskite-Type Titanates: II, Single Crystals,” J. Am. Ceram. Soc., 73 [6] 1654-1662 (1990).
[44] M. Vollmann and R. Waser, “Grain Boundary Defect Chemistry of Acceptor-Doped Titanates: High Field Effects,” J. Electroceram., 1 [1] 51-64 (1997).
[45] G. Y. Yang, E. C. Dickey, C. A. Randall, M. S. Randall, and L. A. Mann, “Modulated and Ordered Defect Structures in Electrically Degraded Ni/BaTiO3 Multilayer Ceramic Capacitors,” J. Appl. Phys., 94 [9] 5990–5996 (2003).
[46] G. Y. Yang, G. D. Lian, E. C. Dickey, C. A. Randall, D. E. Barber, P. Pinceloup, M. A. Henderson, R. A. Hill, J. J. Beeson, and D. J. Skamser, “Oxygen Nonstoichiometry and Dielectric Evolution of BaTiO3. Part II—Insulation Resistance Degradation Under Applied dc Bias,” J. Appl. Phys., 96 [12] 7500–7508 (2004).
[47] J. B. McChesney, P. K. Gallagher, and F. V. DiMarcello, “Stabilized Barium Titanate Ceramics for Capacitor Dielectrics,” J. Am. Ceram. Soc., 46 [5] 197-202 (1963).
[48] K. Okazaki and H. Igarashi, “Processing-property Relations in Ceramic Dielectric Capacitors,” Ferroelectrics, 27 [1] 263-268 (1980).
[49] H. Chazono and H. Kishi, “dc-Electrical Degradation of the BT-Based Material for Multilayer Ceramic Capacitor with Ni internal Electrode: Impedance Analysis and Microstructure,” Jpn. J. Appl. Phys., 40, 5624–5629 (2001).
[50] G. Y. Yang, E. C. Dickey, C. A. Randall, E. Barber, R. Pinceloup, M. A. Herderson, R. A. Hill, J. J. Beeson, and D. J. Skamser, “Oxygen Nonstoichiometry and Dielectric Evolution of BaTiO3. Part I – Improvement of Insulation Resistance with Re-oxidation,” J. Appl. Phys., 96 [12] 7492-7499 (2004).
[51] M. Vollman and R. Waser, “Grain Boundary Defect Chemistry of Acceptor-doped Titanates: Space Charge Layer Width,” J. Am. Ceram. Soc., 77 [1] 235-243 (1994).
[52] K. Hayashi, T. Yamamoto, Y. Ikuhara, and T. Sakuma, “Formation of Potential Barrier Related to Grain-Boundary Character in Semiconducting Barium Titanate,” J. Am. Ceram. Soc., 83 [11] 2684–2688 (2000).
[53] N. Szydlo and R. Poirer, “I‐V and C‐V Characteristics of Au/TiO2 Schottky Diodes,” J. Appl. Phys., 51 [6] 3310-3312 (1980).
[54] D. P. Cann and C. A. Randall, “Electrode Effects in Positive Temperature Coefficient and Negative Temperature Coefficient Devices Measured by Complex‐plane Impedance Analysis,” J. Appl. Phys., 80 [3] 1628-1632 (1996).
[55] E. H. Rhoderick and R. H. Williams, Metal-semiconductor Contact, 2nd ed., Clarendon Press, Oxford, 1988.
[56] S. M. Sze, Physics of Semiconductor Devices, 2nd ed., Wiley, New York, 1981.
[57] K. Kaneda, S. Lee, N. J. Donnelly, W. Qu, C. A. Randall, and Y. Mizuno, “Kinetics of Oxygen Diffusion into Multilayer Ceramic Capacitors During the Re-oxidation Process and its Implications on Dielectric Properties,” J. Am. Ceram. Soc., 94 [11] 3934-3940 (2011).
[58] D. C. Joy, A. D. Romig, and J. I. Goldstein, Principles of Analytical Electron Microscopy, Plenum, New York, 1986.
[59] P. Hansen, D. Hennings, and H. Schreinemacher, “Dielectric Properties of Acceptor-Doped (Ba,Ca)(Ti,Zr)O3 Ceramics,” J. Electroceram., 2 [2] 85-94 (1998).
[60] H. Dederichs and G. Arlt, “Aging of Fe-Doped PZT Ceramics and the Domain Wall Contribution to the Dielectric Constant,” Ferroelectrics, 68 [1] 281-292 (1986).
[61] U. Robels and G. Arlt, “Domain Wall Clamping in Ferroelectrics by Orientation of Defects,” J. Appl. Phys., 73 [7] 3454-3460 (1993).
[62] P. Coufová, J. Novák, and N. Hlasivcová, “Hydroxyl as a Defect of the Perovskite BaTiO3 Lattice,” J. Chem. Phys., 45 [9] 3171-3174 (1966).
[63] S. Stotz, and C. Wagner, “The Solubility of Water Vapor and Hydrogen in Solid Oxides,” Ber. Bunsen. Phys. Chem., 70 [8] 781-788 (1966).
[64] D. F. Hennings, and B. S. Schreinemacher, “Characterization of Hydrothermal Barium Titanate,” J. Eur. Ceram. Soc., 9 [1] 41-46 (1992).
[65] R. Waser, “Solubility of Hydrogen Defects in Doped and Undoped BaTiO3,” J. Am. Ceram. Soc., 71 [1] 58–63 (1988).
[66] N. Bonanos, “Transport Properties and Conduction Mechanism in High-Temperature Protonic Conductors,” Solid State Ionics, 53-56, 967-974 (1992).
[67] T. Norby, “Solid-state Protonic Conductors: Principles, Properties, Progress and Prospects,” Solid State Ionics, 125 [1-4] 1–11 (1999).
[68] K. D. Kreuer, “Proton Conductivity:  Materials and Applications,” Chem. Mater., 8 [3] 610–641 (1996).
[69] K. D. Kreuer, “Proton-Conducting Oxides,” Annu. Rev. Mater. Res., 33, 333–359 (2003).
[70] C. R. I. Chisholm, “Superprotonic Phase Transitions in Solid Acids: Parameters Affecting the Presence and Stability of Superprotonic Transitions in the MHnXO4 Family of Compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs),” Ph. D. thesis, California Institute of Technology, 2003.
[71] M. S. Islam, “Ionic Transport in ABO3 Perovskite Oxides: A Computer Modelling Tour,” J. Mater. Chem., 10 [4] 1027-1038 (2000).
[72] K. D. Kreuer, “On the Complexity of Proton Conduction Phenomena,” Solid State Ionics, 136-137, 149-160 (2000).
[73] R. Glöckner, M. S. Islam, and T. Norby, “Protons and Other Defects in BaCeO3: A Computational Study,” Solid State Ionics, 122 [1-4] 145-156 (1999).
[74] R. A. Davies, M. S. Islam, and J. D. Gale, “Dopant and Proton Incorporation in Perovskite-Type Zirconates,” Solid State Ionics, 126 [3-4] 323–335 (1999).
[75] M. S Islam and M Cherry, “Protons in LaMO3: Atomistic Modelling and ab Initio Studies,” Solid State Ionics, 97 [1-4] 33–37 (1997).
[76] R. A Davies, M. S Islam, A. V Chadwick, and G. E Rush, “Cation Dopant Sites in the CaZrO3 Proton Conductor: A Combined EXAFS and Computer Simulation Study,” Solid State Ionics, 130 [1-2] 115-122 (2000).
[77] J. M. Herbert, “High Permittivity Ceramics Sintered in Hydrogen,” Trans. Brit. Ceram. Soc., 62 [8] 645-653 (1963).
[78] I. Burn and G. H. Maher, “High Resistivity BaTiO3 Ceramics Sintered in CO-CO2 Atmospheres,” J. Mater. Sci., 10 [4] 633-640 (1975).
[79] H. J. Hagemann and H. Ihrig, “Valence Change and Phase Stability of 3d-Doped BaTiO3 Annealed in Oxygen and Hydrogen,” Phys. Rev. B, 20 [9] 3871-3878 (1979).
[80] Y. Sakabe, N. Wada, T. Hiramatsu, and T. Tonogaki, “Dielectric Properties of Fine-Grained BaTiO3 Ceramics Doped with CaO,” Jpn. J. Appl. Phys., 41, 6922-6925 (2002).
[81] L. Zhang, O. P. Thakur, A. Feteira, G. M. Keith, A. G. Mould, D. C. Sinclair, and A. R. West, “Comment on the Use of Calcium as a Dopant in X8R BaTiO3-Based Ceramics,” Appl. Phys. Lett., 90, 142914 (2007).
[82] Z. Q. Zhuang, M. P. Harmer, D. M. Smyth, and R. E. Newnham, “The Effect of Octahedrally-Coordinated Calcium on the Ferroelectric Transition of BaTiO3,” Mater. Res. Bull., 22 [10] 1329-1335 (1987).
[83] N. Mas´o, M. Prades, H. Beltr´an, E. Cordoncillo, D. C. Sinclair, and A. R. West, “Field Enhanced Bulk Conductivity of Acceptor-doped BaTi1−xCaxO3−x Ceramics,” Appl. Phys. Lett., 97, 062907 (2010).
[84] Y. Sakabe, “Calcium-Doped Barium Titanate Ceramics for Nickel Electrode Multilayer Capacitors,” Ph. D. thesis, Kyoto University, 2002.
[85] S. Lee and C. A. Randall, “A Modified Vegard's Law for Multisite Occupancy of Ca in BaTiO3–CaTiO3 Solid Solutions,” Appl. Phys. Lett., 92 [11] 111904 (2008).
[86] Y. Sakabe and H. Takagi, “Nonreducible Mechanism of {(Ba1-xCax)O}mTiO2 (m>1) Ceramics,” Jpn. J. Appl. Phys., 41, 6461-6465 (2002).
[87] T. N. Verbitskaia, G. S. Zhdanov, I. N. Venevtsev, and S. P. Soloviev, “Electrical and X-Ray Diffraction Studies of the BaTiO3-BaZrO3 System,” Sov. Phys. -Cryst., 3 [2] 182-92 (1958).
[88] D. Hennings, A. Schnell, and G. Simon, “Diffuse Ferroelectric Phase Transitions in Ba(Ti1-yZry)O3 Ceramics,” J. Am. Ceram. Soc., 65 [11] 539-544 (1982).
[89] G. Smolensky, “Ferroelectrics with Diffuse Phase Transition,” Ferroelectrics, 53 [1] 129-135 (1984).
[90] S. Lee, W. H. Woodford, and C. A. Randall, “Crystal and Defect Chemistry Influences on Band Gap Trends in Alkaline Earth Perovskites,” Appl. Phys. Lett., 92 [20] 201909 (2008).
[91] R. D. Levi, “Solid Solution Trends that Impact Electrical Design of Submicron Layers in Dielectric Capacitors,” Ph. D. thesis, The Pennsylvania State University, University Park, PA, 2009.
[92] A. R. West, D.C. Sinclair, and N. Hirose, “Characterization of Electrical Materials, Especially Ferroelectrics, by Impedance Spectroscopy,” J. Electroceramics, 1 [1] 65-71 (1997).
[93] B,-Y. Chang and S.-M. Park, “Electrochemical Impedance Spectroscopy,” Annual Annu. Rev. Anal. Chem., 3, 207-229 (2010).
[94] N. M. Beekmans and L. Heyne, “Correlation Between Impedance, Microstructure and Composition of Calcia-Stabilized Zirconia,” Electrochim. Acta., 21 [4] 303-310 (1976).
[95] T. van Dijk and A. J. Burggraaf, “Grain Boundary Effects on Ionic Conductivity in Ceramic GdxZr1-xO2-(x/2) Solid Solutions,” phys. stat. sol. (a), 63 [14] 229-240 (1981).
[96] M. J. Verkerk, B. J. Middelhuis, and A. J. Burggraaf, “Effect of Grain Boundaries on the Conductivity of High-Purity ZrO2-Y2O3 Ceramics,” Solid State Ionics, 6 [2] 159-170 (1982).
[97] E. Barsoukov and J. R. Macdonald, Impedance Spectroscopy: Theory, Experiment, and Applications 2nd Edition, Wiley-Interscience, Hoboken, USA, 2005.
[98] D. C. Sinclair and A. R. West, “Impedance and Modulus Spectroscopy of Semiconducting BaTiO3 Showing Positive Temperature Coefficient of Resistance,” J. Appl. Phys., 66 [8] 3850-3856 (1989).
[99] I. M. Hodge, M. D. Ingram, and A. R. West, “Impedance and Modulus Spectroscopy of Polycrystalline Solid Electrolytes,” J. Electroanal. Chem., 74 [2] 125-143 (1976).
[100] M. H. Frey, Z. Xu, P. Han and D. A. Payne, “The Role of Interfaces on an Apparent Grain Size Effect on the Dielectric Properties for Ferroelectric Barium Titanate Ceramics,” Ferroelectrics, 206 [1] 337-353 (1998).
[101] Z. Zhao, V. Buscaglia, M. Viviani, M. T. Buscaglia, L. Mitoseriu, A. Testino, M. Nygren, M. Johnson and P. Nanni, “Grain-Size Effects on the Ferroelectric Behavior of Dense Nanocrystalline BaTiO3 Ceramics,” Phys. Rev. B, 70 [2] 024107 (2004).
[102] G. Spinolo, G. Chiodelli, A. Magistris and U. A. Tamburini, “Data Processing for Electrochemical Measurements with Frequency Response Analyzer,” J. Electrochem. Soc., 135 [6] 1419-1424 (1988).
[103] Seuter AMJH, “Defect Chemistry and Electrical Transport Properties of Barium Titanate,” Philips Res. Rpts.; Suppl. 3, 1-84 (1974).
[104] J. Daniels, “Defect Chemistry and Electrical Conductivity of Doped Barium Titanate: 2.Defect Equilibria in Acceptor-doped Barium Titanate,” Philips Res. Rpts., 31 [6] 505-15 (1976).
[105] R. Waser, “Electrochemical Boundary Conditions for Resistance Degradation of Doped Alkaline-Earth Titanates,” J. Am. Ceram. Soc., 72 [12] 2234-40 (1989).
[106] H. J. Hagemann, and D. F. Hennings, “Reversible Weight Change of Acceptor Doped Barium Titanate,” J. Am. Ceram. Soc., 64 [10] 590-4 (1981).
[107] M. R. Opitz, K. Albertsen, J. J. Beeson, D. F. Hennings, J. L. Routbort, and C. A. Randall, “Kinetic Process of Base Metal Technology BaTiO3-Based Multilayer Capacitors,” J. Am. Ceram. Soc., 86 [11] 1879-84 (2003).
[108] D. F. Hennings, and H. Schreinemacher, “Ca-Acceptors in Dielectric Ceramics, Sintered in Reducing Atmosphere,” J. Eur. Ceram. Soc., 15 [8] 795-800 (1995).
[109] R. Waser, “Solubility of Hydrogen Defects in Doped and Undoped BaTiO3,” J. Am. Ceram. Soc., 71 [1] 58-63 (1988)
[110] C. Y. Su, C. Pithan, D. F. Hennings, and R. Waser, “Proton Defects in BaTiO3: New Aspects Regarding the Re-oxidation of Dielectric Materials Fired in Reducing Atmospheres,” J. Eur. Ceram. Soc., 33 [15-16] 3007-3013 (2013).
[111] J. T. S. Irvine, D C. Sinclair, and A. R. West, “Electroceramics: Characterization by Impedance Spectroscopy,” Adv. Mat., 2 [3] 132-8 (1990).
[112] J. Jamnik and J. Maier, “Treatment of the Impedance of Mixed Conductors Equivalent Circuit Model and Explicit Approximate Solutions,” J. Electrochem. Soc., 146 [11] 4183 – 8 (1999).
[113] J. P. Heath, J. S. Dean, J. H. Harding, and D. C. Sinclair, “Simulation of Impedance Spectra for Core-Shell Grain Structures Using Finite Element Modeling,” J. Am. Ceram. Soc., 98 [6] 1925-1931 (2015).
[114] X. Guo and J. Maier, ‘‘Grain Boundary Blocking Effect in Zirconia: A Schottky Barrier Analysis,’’ J. Electrochem. Soc., 148 [3] E121–6 (2001).
[115] J. R. Macdonald and W. R. Kenan, Impedance Spectroscopy: Emphasizing Solid Materials and Systems; pp. 1–20. John Wiley & Sons, Inc., New York, 1987.
[116] J. Fleig, S. Rodwald, and J. Maier, ‘‘Microcontact Impedance Measurements of Individual Highly Resistive Grain Boundaries: General Aspects and Application to Acceptor-Doped SrTiO3,’’ J. Appl. Phys., 87 [5] 2372–81 (2000).
[117] N. Hirose and A. R. West, “Impedance Spectroscopy of Undoped BaTiO3 Ceramics,” J. Am. Ceram. Soc., 79 [6] 1633-41 (1996).
[118] S. M. H Rahman, I. Ahmed, R. Haugsrud, S. G. Eriksson, and C. S. Knee, “Characterisation of Structure and Conductivity of BaTi0.5Sc0.5O3−δ,” Solid State Ionics, 255, 140-146 (2014).
[119] R. Hagenbeck and R. Waser, “Influence of Temperature and Interface charge on the Grain-boundary Conductivity in Acceptor-doped SrTiO3 Ceramics,” J. Appl. Phys., 83 [4] 2083-2092 (1998).
[120] R. Waser and M. Klee, “Theory of Conduction and Breakdown in Perovskite Thin Films,” Integr. Ferroelectr., 2 [1-4] 23-40 (1992).
[121] A. Yu. Emelyanov, N. A. Pertsev, S. Hoffmann-Eifert, U. Bottger, and R. Waser, “Grain-Boundary Effect on the Curie-Weiss Law of Ferroelectric Ceramics and Polycrystalline Thin Films: Calculation by the Method of Effective Medium,” J. Electrochem. Soc., 9 [1] 5-16 (2002).
[122] O. Kienzle and F. Ernst, “Effect of Shear Stress on the Atomistic Structure of a Grain Boundary in Strontium Titanate,” J. Am. Ceram. Soc., 80 [7] 1639–1644 (1997).
[123] J. Tanaka, J. F. Baumard, and P. Abelard, “Nonlinear Electrical Properties of Grain Boundaries in an Oxygen-Ion Conductor (CeO2•Y2O3),” J. Am. Ceram. Soc., 70 [9] 637–643 (1987).