Thermodynamics and transport of ionic and electronic defects in crystalline oxides

Journal of the American Ceramic Society

Volumn 80, Issue 9, 1997, Pages 2175-2198

  Lankhorst, Martijn H R ^a   Bouwmeester, Henny J M ^a   Verweij, Henk ^a,b  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b AMERICAN CERAMIC SOCIETY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAND STRUCTURE; CURRENT DENSITY; DIFFUSION; ELECTRONIC DENSITY OF STATES; ELECTRONS; ENTROPY; FERMI LEVEL; IONS; POINT DEFECTS; THERMODYNAMICS;

ELECTRONIC DEFECT; IONIC DEFECT;

OXIDES;

EID: 0031236845     PISSN: 00027820     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1151-2916.1997.tb03107.x     Document Type: Article

References (85)

1. 7-x"; pp. 43-61 in Chemistry of Oxide Superconductors. Edited by C. N. R. Rao. Blackwell Scientific Publications, Oxford, U.K., 1988.
2. 3-δ" J. Solid State Chem., 29, 221-25 (1979).
3. P. J. L. Reijnen, "Nonstoichiometry and Sintering in Ionic Solids"; p. 219 in Problems of Nonstoichiometry. Edited by A. Rabenau. North-Holland, Amsterdam, The Netherlands, 1970.
4. S. B. Desu and D. A. Payne, "Interfacial Segregation in Perovskites: I, Theory," J. Am. Ceram. Soc., 73, 3391-97 (1990).
5. J. A. S. Ikeda and Y. Chiang, "Space Charge Segregation at Grain Boundaries in Titanium Dioxide: I, Relationship between Lattice Defect Chemistry and Space Charge Potential," J. Am. Ceram. Soc., 76, 2437-46 (1993).
6. M. F. Carolan, P. N. Dyer, J. M. LaBar Sr., and R. M. Thorogood, "Process for Recovering Oxygen from Gaseous Mixture Containing Water or Carbon Dioxide, Which Process Employs Ion Transport Membranes," U.S. Pat. No. 5 273 628, 1993.
7. H. J. M. Bouwmeester and A. J. Burggraaf, "Dense Ceramic Membranes for Oxygen Separation"; Ch. 14, pp. 481-553 in CRC Handbook of Solid State Electrochemistry: Edited by P. J. Gellings and H. J. M. Bouwmeester. CRC Boca Raton, FL, 1997.
8. E. A. Hazbun, "Ceramic Membrane and Use Thereof for Hydrocarbon Conversion," U.S. Pat. No. 4 827 071, 1989.
9. U. Balachandran, J. T. Dusek, S. M. Sweeney, R. B. Poeppel, R. L. Mieville, P. S. Maiya, M. S. Kleefisch, S. Pei, T. P. Kobylinsky, C. A. Udovich, and A. C. Bose, "Methane to Synthesis Gas via Ceramic Membranes," Am. Ceram. Soc. Bull., 74 [1] 71 (1995).
10. 2-Permeable Membrane Reactors," Ind. Eng. Chem. Res., 33, 3015, (1994).
11. R. J. H. Voorhoeve, "Perovskite-Related Oxides as Oxidation-Reduction Catalysts"; pp. 129-80 in Advanced Materials in Catalysis. Edited by J. J. Burton and R. L. Garten. Academic Press, New York, 1977.
12. (a) C. Wagner, "Beitrag zur Theorie des Anlaufsvorgangs," Z. Phys. Chem. B, 21, 25, (1933);
13. (b) ibid., "Beitrag zur Theories des Anlaufsvorgangs II," Z. Phys. Chem. B. 32, 447, (1936).
14. F. A. Kröger, The Chemistry of Imperfect Crystals; Ch. 9. North-Holland, Amsterdam, The Netherlands, 1964.
15. J. Maier, "Defect Chemistry: Composition, Transport, and Reactions in the Solid State: Part I: Thermodynamics," Angew. Chem. Int. Ed. Eng., 32, 313-35, (1993).
16. J. S. Anderson, "The Thermodynamics and Theory of Nonstoichiometric Compounds"; pp. 1-76 in Problems of Nonstoichiometry. Edited by A. Rabenau. North-Holland, Amsterdam, The Netherlands, 1970.
17. O. T. Sørensen, "Thermodynamics and Defect Structure of Nonstoichiometric Oxides"; pp. 1-59 in Nonstoichiometric Oxides. Edited by O. T. Sørensen. Academic Press, New York, 1981.
18. F. A. Kröger and H. J. Vink, "Relations between the Concentrations of Imperfections in Crystalline Solids"; p. 307 in Solid State Physics, Vol. 3. Edited by F. Seitz and D. Turnball. Academic Press, New York, 1956.
19. F. A. Kröger, F. H. Stieltjes, and H. J. Vink, "Thermodynamics and Formulation of Reactions Involving Imperfections in Solids," Philips Res. Rep., 14, 557 (1959).
20. W. Schottky, "Statistik und Thermodynamik der Unordnungs Zustände in Kristallen, Insbesondere bei Geringer Fehlordnung," Z. Elektrochem., 45, 33 (1939).
21. E. A. Guggenheim, Thermodynamics: An Advanced Treatment for Chemists and Physicists; Ch. 8. North-Holland, Amsterdam, The Netherlands, 1967.
22. H. B. Callen, Thermodynamics and an Introduction to Thermostatics; Ch. 17. Wiley, New York, 1980.
23. R. K. Pathria, Statistical Mechanics; Ch. 3. Pergamon Press, Oxford, U. K., 1972.
24. D. Adler, "The Imperfect Solid-Transport Properties"; pp. 237-32 in Treatise an Solid State Chemistry, Vol. 2, Defects in Solids. Edited by N. B. Hannay. Plenum Press, New York, 1975.
25. Commission on Thermodynamics, International Union of Pure and Applied Electrochemistry, International Thermodynamic Tables of the Fluid State - 9, Oxygen. Blackwell Scientific Publications, Oxford, U.K., 1987.
26. R. Fowler and E. A. Guggenheim, Statistical Thermodynamics; Ch. 9. University Press, Cambridge, U.K., 1960.
27. L. M. Atlas, "Spacing Statistics and the Distribution of Interacting Lattice Defects"; pp. 425-43 in The Chemistry of Extended Defects in Non-Metallic Solids, Proceedings of the Institute for Advanced Study on the Chemistry of Extended Effects in Non-Metallic Solids. Edited by L. Eyring and M. O'Keeffe. North-Holland, Amsterdam, The Netherlands, 1970.
28. L. Manes, "A New Method of Statistical Thermodynamics and its Application to Oxides of the Lanthanide and Actinide Series"; pp. 99-154 in Non-stoichiometric Oxides. Edited by O. T. Sørensen. Academic Press, New York, 1981.
29. S. Ling, "High-Concentration Point Defect Chemistry: Statistical Thermodynamic Approach Applied to Nonstoichiometric Cerium Dioxides," Phys. Rev. B: Condens. Matter, 49, 864, (1994).
30. S. Ling, "Statistical Thermodynamic Formulation of High-Concentration Point Defect Chemistry in Perovskite Crystalline Systems: Application to Strontium-Doped Lanthanum Chromite," J. Phys. Chem. Solids, 55, 1445-59 (1994).
31. R. J. Thorn and G. H. Winslow, "Nonstoichiometry in Uranium Dioxide," J. Chem. Phys., 44, 2632 (1966).
32. J. A. M. van Roosmalen and E. H. P. Cordfunke, "A New Defect Model to Describe the Oxygen Deficiency in Perovskite-type Oxides," J. Solid State Chem., 93, 212-19 (1991).
33. 3," Scand. J. Metall., 9, 3-11 (1980).
34. 3-δ," J. Solid State Chem., 80, 102-11 (1989).
35. 6+γ," Philips J. Res., 44, 99 (1989).
36. J. Zaanen, G. A. Sawatzky, and J. W. Allen, "Band Gaps and Electronic Structure of Transition-Metal Compounds," Phys. Rev. Lett., 55, 418 (1985).
37. J. B. Torrence and P. Lacorro, "Simple and Perovskite Oxides of Transition-Metals: Why Some are Metallic, while Most are Insulating," J. Solid State Chem., 90, 168-72 (1991).
38. J. Appel, "Polarons"; pp. 193-391 in Solid State Physics, Vol. 21. Edited by F. Seitz, D. Turnball, and H. Ehrenreich. Academic Press, New York, 1968.
39. N. W. Ashcroft and N. D. Mermin, Solid State Physics; Ch. 28. Saunders College, Philadelphia, PA, and C. B. S. Publishing, Tokyo, Japan, 1976.
40. D. J. Sellmyer, "Electronic Structure of Metallic Compounds and Alloys: Experimental Aspects; pp. 83-248 in Solid State Physics, Vol. 33. Edited by H. Ehrenreich, F. Seitz, and D. Turnball. Academic Press, New York, 1978.
41. J. Rouxel, "The Electronic Transfer and the Formation of Cationic Intercalation Compounds," Mater. Res. Soc. Symp. Proc. 135, 431 (1989).
42. J. R. Dahn, J. N. Reimers, T. Tiedje, Y. Gao, A. K. Sleigh, W. R. McKinnon, and S. Cramm, "Correlation between X-ray Absorption and Chemical Potential Measurements in Lithium Intercalated Carbons," Phys. Rev. Lett., 68, 835 (1992).
43. 6-z," Phys. Rev. B: Condens. Matter, 35, 7275 (1987).
44. J. Friedel, "Electronic Structure of Primary Solid Solutions in Metals," Adv. Phys., 3, 446 (1954).
45. 3-δ," Phys. Rev. Lett, 77, 2989 (1996).
46. B. C. H. Steele, "Measurement of High-Temperature Thermodynamic Properties of Nonstoichiometric Oxides Using Solid-State EMF and Coulometric Techniques"; p. 165 in Mass Transport in Oxides. Edited by J. B. Wachtman and A. D. Franklin. Special Publication 296. U.S. National Bureau of Standards, Gaithursberg, MD, 1968.
47. R. D. Barnard. Thermoelectricity in Metals and Alloys; Ch. 2. Taylor & Francis, London, U.K., 1972.
48. 2-x, Determined by a Solid Electrochemical Method," J. Appl. Phys., 61, 4931-32 (1987).
49. 6+x and Application of Coulometric Titration," Solid State Ionics, 50, 209, (1992).
50. 3-x by Coulometric Titration," Solid State Ionics, 36, 121 (1989).
51. M. H. R. Lankhorst, H. J. M. Bouwmeester, B. A. Boukamp, and H. Verweij, "Oxygen Nonstoichiometry and Oxygen Diffusivity of Mixed Conducting Perovskites"; pp. 83-93 in Proceedings of the First International Symposium on Ceramic Membranes, Vol. 95-24. Edited by H. U. Anderson, A. C. Khandkar, and M. Liu. The Electrochemical Society, Pennington, NJ, 1997.
52. 3-δ," J. Electrochem. Soc., 136, 2082 (1989).
53. I. Barin, O. Knacke, and O. Kubaschewski, Thermochemical Properties of Inorganic Substances (with supplement). Springer Verlag, Berlin, Heidelberg, New York and Verlag Stahleisen, Dusseldorf, 1973 and 1977.
54. F. Seitz, The Modern Theory of Solids; p. 83. McGraw-Hill, New York, London, 1940.
55. C.J. Ballhausen, Introduction to Ligand Field Theory; p. 113. McGraw-Hill, New York, 1962.
56. L. Heyne, "Electrochemistry of Mixed Ionic-Electronic Conductors"; pp. 169-221 in Solid Electrolytes. Edited by S. Geller. Springer-Verlag, Berlin, Germany, 1977.
57. H. L. Tuller, "Mixed Conduction in Nonstoichiometric Oxides"; pp. 271-337 in Nonstoichiometric Oxides. Edited by O. T. Sørensen. Academic Press, New York, 1981.
58. J. Maier and G. Schwitzgebel, "Theoretical Treatment of the Diffusion Coupled with Reaction, Applied to the Example of a Binary Solid Compound MX," Phys. Status Solidi B, 113, 535 (1982).
59. J. Janek, M. Martin, and H.-I. Yoo, "Electrotransport in Ionic Crystals: I. Application of Liquid Electrolyte Theory," Ber. Bunsen-Ges. Phys. Chem., 98, 655 (1994).
60. J. Janek and M. Martin, "Electrotransport in Ionic Crystals: II. A Dynamical Model," Ber. Bunsen-Ges. Phys. Chem., 98, 665 (1994).
61. H. J. M. Bouwmeester, H. Kruidhof, and A. J. Burggraaf, "Importance of the Surface Exchange Kinetics as Rate-Limiting Step in Oxygen Permeation through Mixed Conducting Oxides," Solid State Ionics, 72, 185 (1994).
62. N. W. Ashcroft and N. D. Mermin, Solid State Physics; Ch. 16. Saunders College, Philadelphia, PA, and C. B. S. Publishing, Tokyo, Japan, 1976.
63. I. G. Austin and N. F. Mott, "Polarons in Crystalline and Noncrystalline Materials," Adv. Phys., 18, 41 (1969).
64. H. Rickert, Electrochemistry of Solids, An Introduction; Ch. 6. Springer-Verlag, Berlin, Germany, 1982.
65. A. T. Fromhold Jr., "Space Charge Effects and Transport in Oxide Films"; pp. 37-50 in High-Temperature Corrosion, International Corrosion Conference Series, National Association of Corrosion Engineers. Edited by R. A. Rapp. Houston, TX, 1983.
66. J. B. Goodenough, "Fast Ionic Conduction in Solids," Proc. R. Soc. London A, 393, 215 (1984).
67. 6+x," Solid State Ionics, 66, 61 (1993).
68. R. Dieckmann, "Cobaltous Oxide Point Defect Structure and Nonstoichiometry, Electrical conductivity, Cobalt Tracer Diffusion," Z. Phys. Chem. Neue Folge, 107, 189 (1977).
69. 1-δO under Usual Oxygen Partial Pressures. A Monte Carlo Study," J. Phys. Chem. Solids, 55, 617 (1994).
70. 1-δO," J. Phys. Chem. Solids, 57, 65 (1996).
71. 1-δO," Solid State Ionics, 80, 5 (1995).
72. J. Maier, "Mass Transport in the Presence of Internal Defect Reactions, Concept of Conservative Ensembles: I, Chemical Diffusion in Pure Compounds," J. Am. Ceram. Soc., 76, 1212 (1993).
73. (a) L. Onsager, "Reciprocal Relations in Irreversible Processes. I," Phys. Rev., 37, 405 (1931);
74. (b) ibid., "Reciprocal Relations in Irreversible Processes. II," Phys. Rev., 38, 2265 (1931).
75. H.-D. Wiemhöfer, "Coupling between Electron and Ion Transport in Mixed Conductors," Solid State Ionics, 40/41, 530 (1990).
76. (a) J. O'M. Bockris and A. K. N. Reddy, Modern Electrochemistry, Vol. 1; p. 180. Plenum Press, New York, 1970;
77. (b) P. Debye and E. Hückel, "Lowering of Freezing Point and Related Phenomena," Z. Phys., 24, 185 (1923);
78. (c) L. Onsager and R. M. Fuoss, "Diffusion, Conductance, and Viscous Flow in Arbitrary Mixtures of Strong Electrolytes," J. Phys. Chem., 36, 2689 (1932).
79. M. Martin, "Transport in Oxides in an Oxygen Potential Gradient," Solid State Phenom., 21 & 22, 1 (1992).
80. G. J. Dudley and C. H. Steele, "Theory and Practice of a Powerful Technique for Electrochemical Investigation of Solid Solution Electrode Materials," J. Solid State Chem., 31, 233 (1980).
81. M. H. R. Lankhorst, H. J. M. Bouwmeester, and H. Verwey, "Theory of Oxygen Transport in Mixed Conducting Perovskites; pp. 697-702 in Electroceramics IV, Proceedings of the 4th International Conference on Electroceramics and Applications, Vol. II. Edited by R. Waser, S. Hoffman, D. Bonnenberg, and Ch. Hoffmann. Verlag der Augustinus Buchhandlung, Aachen, Germany, 1994.
82. S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics; p. 39. North-Holland, Amsterdam, The Netherlands, 1962.
83. 3-δ," J. Solid State Chem., 58, 257(1985).
84. 3-δ, Part I: Permeation in Air-He Gradients," Solid State Ionics, 81, 97 (1995).
85. C. Wagner, "Equations for Transport in Solid Oxides and Sullides of Transition Metals," Prog. Solid State Chem., 10, 3 (1975).