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Statistical Thermodynamics of Point Defects in Crystals

  • Chapter
Point Defects in Solids

Abstract

Point defects play an important part in determining the physical properties of most crystalline substances, most notably those controlling the transport of matter and the properties that stem from it. They also strongly influence the resistivity of metals by scattering conduction electrons, the low-temperature thermal conductivity of all crystalline solids by scattering phonons, the electronic conduction and related properties of semiconductors by acting as donors or acceptors, and the optical properties of ionic solids by introducing electron states with optical transitions, to name a few examples. They are the primary principal product in irradiation of crystals by energetic particles, and their subsequent behavior very much determines the nature of the damage suffered by the crystal during irradiation and the recovery processes that occur during subsequent annealing.

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References

  1. F. A. Kroger and H. J. Vink, in Solid State Physics, Vol. 3, Ed. by F. Seitz and D. Turnbull (Academic Press, New York, 1956), p. 307.

    Google Scholar 

  2. J. E. Mayer and M. G. Mayer, Statistical Mechanics (Wiley, New York, 1940), p. 219.

    MATH  Google Scholar 

  3. A. R. Allnatt and M. H. Cohen, J. Chem. Phys. 40, 1860 (1964).

    Article  ADS  Google Scholar 

  4. A. B. Lidiard, Phys. Rev. 94, 29 (1954).

    Article  ADS  Google Scholar 

  5. A. B. Lidiard, Phys. Rev. 112, 54 (1958).

    Article  ADS  Google Scholar 

  6. F. K. Fong, Phys. Rev. 187, 1099 (1969).

    Article  ADS  Google Scholar 

  7. R. E. Howard and A. B. Lidiard, Rept. Progr. Phys. 27, 161 (1964).

    Article  ADS  Google Scholar 

  8. F. A. Kroger, The Chemistry of Imperfect Crystals (North-Holland Publishing co., Amsterdam, 1964).

    Google Scholar 

  9. H. C. Abbink and D. S. Martin, J. Phys. Solids 27, 205 (1966).

    Article  ADS  Google Scholar 

  10. R. G. Fuller, M. H. Reilly, C. L. Marquardt, and J. C. Wells, Jr., Phys. Rev. Letters 20, 662 (1968).

    Article  ADS  Google Scholar 

  11. R. G. Fuller, C. L. Marquardt, M. H. Reilly, and J. C. Wells, Jr., Phys. Rev. 176, 1036 (1968).

    Article  ADS  Google Scholar 

  12. F. K. Fong, Phys. Rev. B 2 (Oct. 1) (1970).

    Google Scholar 

  13. M. P. Tosi and G. Airoldi, Nuovo Cimento 8, 584 (1958).

    Article  Google Scholar 

  14. A. B. Lidiard, private communication (1966); notes on lectures delivered at the University of Milan, March 1966.

    Google Scholar 

  15. J. S. Anderson, Proc. Roy. Soc. (London) A185, 69 (1946).

    ADS  Google Scholar 

  16. K. Hagemark, Kjeller Reports KR-48 and KR-67 (1964).

    Google Scholar 

  17. R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (University Press, Cambridge, 1939), Chapter 9.

    MATH  Google Scholar 

  18. L. M. Atlas, J. Phys. Chem. Solids 29, 91 (1968).

    Article  ADS  Google Scholar 

  19. L. M. Atlas, J. Phys. Chem. Solids 29, 1349 (1968).

    Article  ADS  Google Scholar 

  20. A. R. Allnatt and M. H. Cohen, J. Chem. Phys. 40, 1871 (1964).

    Article  ADS  Google Scholar 

  21. J. Frenkel, Kinetic Theory of Liquids (Clarendon Press, Oxford, 1946), p. 37.

    MATH  Google Scholar 

  22. K. Lehovec, J. Chem. Phys. 21, 1123 (1953).

    Article  ADS  Google Scholar 

  23. J. D. Eshelby, C. W. A. Newey, P. L. Pratt, and A. B. Lidiard, Phil. Mag. 3, 75 (1958).

    Article  ADS  Google Scholar 

  24. K. L. Kliewer and J. S. Koehler, Phys. Rev. 140, A1226 (1965).

    Article  ADS  Google Scholar 

  25. K. L. Kliewer, Phys. Rev. 140, A1241 (1965).

    Article  ADS  Google Scholar 

  26. G. Boato, Cryogenics 4, 65 (1964).

    Article  Google Scholar 

  27. G. L. Pollack, Rev. Mod. Phys. 36, 748 (1964).

    Article  ADS  Google Scholar 

  28. G. K. Horton, Am. J. Phys. 36, 93 (1968).

    Article  ADS  Google Scholar 

  29. R. M. J. Cotterill and M. Doyama, Phys. Letters 25A, 35 (1967).

    ADS  Google Scholar 

  30. R. O. Simmons and R. W. Balluffi, Phys. Rev. 117, 52 (1960).

    Article  ADS  Google Scholar 

  31. O. G. Peterson, D. N. Batchelder, and R. O. Simmons, Phil. Mag. 12, 1193 (1965).

    Article  ADS  Google Scholar 

  32. B. L. Smith and J. A. Chapman, Phil. Mag. 15, 739 (1967).

    Article  ADS  Google Scholar 

  33. W. van Witzenburg, Phys. Letters 25A, 293 (1967).

    ADS  Google Scholar 

  34. J. D. Eshelby, Acta Met. 3, 487 (1955).

    Article  Google Scholar 

  35. D. L. Losee and R. O. Simmons, Phys. Rev. Letters 18, 451 (1967); Phys. Rev. 172, 934 (1968).

    Article  ADS  Google Scholar 

  36. A. J. E. Foreman and A. B. Lidiard, Phil. Mag. 8, 97 (1963).

    Article  ADS  Google Scholar 

  37. L. S. Salter, Trans. Faraday Soc. 59, 657 (1963).

    Article  Google Scholar 

  38. R. H. Beaumont, H. Chihara, and J. A. Morrison, Proc. Phys. Soc. (London) 78, 1462 (1961).

    Article  ADS  Google Scholar 

  39. I. H. Hillier and J. Walkley, J. Chem. Phys. 43, 3713 (1965).

    Article  ADS  Google Scholar 

  40. P. Flubacher, A. J. Leadbetter, and J. A. Morrison, Proc. Phys. Soc. (London) 78, 1449 (1961).

    Article  ADS  Google Scholar 

  41. J. Kuebler and M. P. Tosi, Phys. Rev. 137, A1617 (1965).

    Article  ADS  Google Scholar 

  42. A. O. Urvas, D. L. Losee, and R. O. Simmons, J. Phys. Chem. Solids 28, 2269 (1967).

    Article  ADS  Google Scholar 

  43. D. L. Losee and R. O. Simmons, Phys. Rev. 172, 944 (1968).

    Article  ADS  Google Scholar 

  44. V. G. Manzhelii, V. G. Gavrilko, and V. I. Kuchner, Phys. Stat. Solidi 34, K55 (1969).

    Article  ADS  Google Scholar 

  45. A. C. Damask and G. J. Dienes, Point Defects in Metals (Gordon and Breach, New York, 1963).

    Google Scholar 

  46. L. A. Girifalco and D. O. Welch, Point Defects and Diffusion in Strained Metals (Gordon and Breach, New York, 1967).

    Google Scholar 

  47. M. W. Thompson, Defects and Radiation Damage in Metals (Cambridge University Press, Cambridge, 1969).

    Google Scholar 

  48. A. Seeger and D. Schumacher, in Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965), p. 15.

    Google Scholar 

  49. A. Seeger, in Theory of Crystal Defects, Ed. by B. Gruber (Academic Press, New York, 1966), p. 38.

    Google Scholar 

  50. A. Seeger, D. Schumacher, W. Schilling, and J. Diehl (eds.), Proc. Int. Conf. on Vacancies and Interstitials in Metals, Julich, 1968 (North-Holland Publishing Co., Amsterdam, 1970).

    Google Scholar 

  51. N. H. Nachtrieb, J. A. Weil, E. Catalano, and A. W. Lawson, J. Chem. Phys. 20, 1189 (1952).

    Article  ADS  Google Scholar 

  52. G. V. Kidson and R. Ross, in Proc. of the Conference on Radioisotopes in Scientific Research, Vol. I, Ed. by R. C. Extermann (Pergamon, New York, 1958), p. 185.

    Google Scholar 

  53. A. Seeger, G. Schottky, and D. Schumacher, Phys. Stat. Solidi 11, 363 (1965).

    Article  ADS  Google Scholar 

  54. A. Seeger and D. Schumacher, in Materials Science and Engineering, Vol. 2 (1967), p. 31.

    Article  Google Scholar 

  55. R. E. Howard, Phys. Rev. 144, 650 (1966); 154, 561 (1967).

    Article  ADS  Google Scholar 

  56. H. Mehrer and A. Seeger, Phys. Stat. Solidi 35, 313 (1969).

    Article  ADS  Google Scholar 

  57. H. Mehrer and A. Seeger, Phys. Stat. Solidi 39, 647 (1970).

    Article  ADS  Google Scholar 

  58. A. Seeger and H. Mehrer, Phys. Stat. Solidi 29, 231 (1968).

    Article  ADS  Google Scholar 

  59. D. Schumacher, A. Seeger, and O. Härlin, Phys. Stat. Solidi 25, 359 (1968).

    Article  ADS  Google Scholar 

  60. A. D. LeClaire, “Correlation Effects in Diffusion in Solids,” in Physical Chemistry, An Advanced Treatise, Vol. X, Ed. by W. Jost (Academic Press, New York, 1970), p. 261.

    Google Scholar 

  61. S. J. Rothman and N. L. Peterson, Phys. Stat. Solidi 35, 305 (1969).

    Article  ADS  Google Scholar 

  62. L. W. Barr and A. D. LeClaire, Proc. Brit. Ceram. Soc. 1, 109 (1964).

    Google Scholar 

  63. D. P. Gregory, Acta Met. 11, 623 (1963).

    Article  Google Scholar 

  64. A. C. Damask and G. J. Dienes, Phys. Rev. 120, 99 (1960).

    Article  ADS  Google Scholar 

  65. T. Mori, M. Meshii, and J. W. Kauffman, J. Appl. Phys. 33, 2776 (1962).

    Article  ADS  Google Scholar 

  66. C. P. Flynn, J. Bass, and D. Lazarus, Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965), p. 639.

    Google Scholar 

  67. R. O. Simmons, J. Phys. Soc. Japan 18 (Suppl. II), 172 (1963).

    Google Scholar 

  68. N. F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys (Clarendon Press, Oxford, 1936).

    Google Scholar 

  69. R. O. Simmons, and R. W. Balluffi, Phys. Rev. 119, 600 (1960).

    Article  ADS  Google Scholar 

  70. F. J. Bradshaw and S. Pearson, Proc. Phys. Soc. (London) 69B, 441 (1956).

    ADS  Google Scholar 

  71. K. Misek and J. Polák, J. Phys. Soc. Japan 18 (Suppl. II), 179 (1963).

    Google Scholar 

  72. Y. Fukai, Phil. Mag. 20, 1277 (1969).

    Article  ADS  Google Scholar 

  73. R. J. Berry and J. L. G. LaMarche, Phys. Letters 31A, 319 (1970).

    ADS  Google Scholar 

  74. R. R. Conte and J. Dural, Phys. Letters 27A, 368 (1968).

    ADS  Google Scholar 

  75. K. P. Chik, in International Conference on Vacancies and Interstitials in Metals, Julich Conference 2, Vols. I, II (obtainable from Zentralbibliothek der Kernforschungsanlage Julich GmbH, Julich, Germany); 1970, Vacancies and Interstitials in Metals, Ed. by A. Seeger, D. Schumacher, W. Schilling, and J. Diehl (North-Holland Publishing Co., Amsterdam, 1968), p. 183.

    Google Scholar 

  76. C. J. Meechan and J. A. Brinkman, Phys. Rev. 103, 1193 (1956).

    Article  ADS  Google Scholar 

  77. H. B. Huntington and F. Seitz, Phys. Rev. 61, 315 (1942).

    Article  ADS  Google Scholar 

  78. R. O. Simmons and R. W. Balluffi, Phys. Rev. 125, 862 (1962).

    Article  ADS  Google Scholar 

  79. B. Okkerse, Phys. Rev. 103, 1246 (1956).

    Article  ADS  Google Scholar 

  80. S. M. Makin, A. H. Rowe, and A. D. LeClaire, Proc. Phys. Soc. (London) B70, 545 (1957).

    ADS  Google Scholar 

  81. D. Duhl, K.-I. Hirano, and M. Cohen, Acta Met. 11, 1 (1963).

    Article  Google Scholar 

  82. H. M. Gilder and D. Lazarus, J. Phys. Chem. Solids 26, 2081 (1965).

    Article  ADS  Google Scholar 

  83. A. Gianotti and L. Zecchina, Nuovo Cimento 40B, 295 (1965).

    ADS  Google Scholar 

  84. U. Ermert, W. Rupp, and R. Sizmann, in International Conference on Vacancies and Interstitials in Metals, Julich Conference 2, Vols. I, II (obtainable from Zentralbibliothek der Kernforschungsanlage Julich GmbH, Julich, Germany, 1968), p. 30.

    Google Scholar 

  85. W. De Sorbo, Phys. Rev. 117, 444 (1960).

    Article  ADS  Google Scholar 

  86. D. Jeannotte, and E. S. Machlin, Phil. Mag. 8, 1835 (1963).

    Article  ADS  Google Scholar 

  87. J. A. Ytterhus and R. W. Balluffi, Phil. Mag. 11, 707 (1965).

    Article  ADS  Google Scholar 

  88. F. J. Kedves and P. deChatel, Phys. Stat. Solidi 4, 55 (1964).

    Article  ADS  Google Scholar 

  89. T. Kino and J. S. Koehler, Phys. Rev. 162, 632 (1967).

    Article  ADS  Google Scholar 

  90. J. Burton and D. Lazarus, Phys. Rev. B2, 787 (1970).

    ADS  Google Scholar 

  91. C. Lee and J. S. Koehler, Phys. Rev. 176, 813 (1968).

    Article  ADS  Google Scholar 

  92. A. Camanzi, N. A. Mancini, E. Rimini, and G. Schianchi, in International Conference on Vacancies and Interstitials in Metals, Julich Conference 2, Vols. I, II (obtainable from Zentralbibliothek der Kernforschungsanlage Julich GmbH, Julich, Germany, 1968), p. 154.

    Google Scholar 

  93. R. P. Heubener and C. G. Homan, Phys. Rev. 129, 1162 (1963).

    Article  ADS  Google Scholar 

  94. J.-I. Takamura, in Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965), p. 521.

    Google Scholar 

  95. S. D. Gertsricken and N. N. Novikov, Phys. Metals Metallogr. 9(2), 54 (1960).

    Google Scholar 

  96. Y. Quéré, Compt. Rend. 252, 2399 (1961).

    Google Scholar 

  97. M. Doyama and J. S. Koehler, Phys. Rev. 127, 21 (1962).

    Article  ADS  Google Scholar 

  98. F. Ramsteiner, W. Schule, and A. Seeger, Phys. Stat. Solidi 2, 1005 (1962).

    Article  ADS  Google Scholar 

  99. C. T. Tomizuka and E. Sonder, Phys. Rev. 103, 1182 (1956).

    Article  ADS  Google Scholar 

  100. S. J. Rothman, N. L. Peterson, and J. T. Robinson, Phys. Stat. Solidi 39, 635.

    Google Scholar 

  101. M. Beyeler and Y. Adda, in Physics of Solids at High Pressures, Ed. by C. T. Tomizuka and R. M. Emrick (Academic Press, New York, 1965), p. 349.

    Google Scholar 

  102. R. H. Dickerson, R. C. Lowell, and C. T. Tomizuka, Phys. Rev. 137, A613 (1965).

    Article  ADS  Google Scholar 

  103. C. T. Tomizuka, in Progress in Very High Pressure Research (Proc. Intern. Conf., Bolton Landing), Ed. by F. B. Bundy, W. R. Hibbard, Jr., and H. M. Strong (Wiley and Sons, New York, 1961), p. 266.

    Google Scholar 

  104. R. O. Simmons and R. W. Balluffi, Phys. Rev. 129, 1533 (1963).

    Article  ADS  Google Scholar 

  105. J. Bass, Phil. Mag. 15, 717 (1967).

    Article  ADS  Google Scholar 

  106. R. O. Simmons and R. W. Balluffi, Phys. Rev. 117, 62 (1960).

    Article  ADS  Google Scholar 

  107. R. R. Bourassa, D. Lazarus, and D. A. Blackburn, Phys. Rev. 165, 853 (1968).

    Article  ADS  Google Scholar 

  108. T. S. Lundy and J. F. Murdoch, J. Appl. Phys. 33, 1671 (1962).

    Article  ADS  Google Scholar 

  109. J. J. Spokas and C. P. Slichter, Phys. Rev. 113, 1462 (1959).

    Article  ADS  Google Scholar 

  110. B. M. Butcher, H. Hutto, and A. L. Ruoff, Appl. Phys. Letters 7, 34 (1965).

    Article  ADS  Google Scholar 

  111. M. Doyama and J. S. Koehler, Phys. Rev. 134, A522 (1964).

    Article  ADS  Google Scholar 

  112. Ya. A. Kraftmakher and P. G. Strelkov, Soviet Phys.—Solid State 8, 460 (1966).

    Google Scholar 

  113. A. Ascoli, M. Asdente, E. Germagnoli, and A. Manara, J. Phys. Chem. Solids 6, 59 (1958).

    Article  ADS  Google Scholar 

  114. G. L. Bacchella, E. Germagnoli, and S. Granata, J. Appl. Phys. 30, 748 (1959).

    Article  ADS  Google Scholar 

  115. J. J. Jackson, Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965).

    Google Scholar 

  116. F. Cattaneo, E. Germagnoli, and F. Grasso, Phil. Mag. 7, 1373 (1962).

    Article  ADS  Google Scholar 

  117. V. S. Kopan and M. J. Skorochod, Isledovanie nesovershenstv kristallicheskovo stroeniya (Naukovaya dumka, Kiev, 1965), p. 99.

    Google Scholar 

  118. J. Polák, Phys. Stat. Solidi 21, 581 (1967).

    Article  ADS  Google Scholar 

  119. J. Polák, Phys. Letters 24A, 649 (1967).

    ADS  Google Scholar 

  120. R. Feder and A. S. Nowick, Phil. Mag. 15, 805 (1967).

    Article  ADS  Google Scholar 

  121. F. M. d’Heurle, R. Feder, and A. S. Nowick, J. Phys. Soc. Japan 18 (Suppl. II), 184 (1963).

    Google Scholar 

  122. J. B. Hudson and R. E. Hoffman, Trans. AIME 221, 761 (1961).

    Google Scholar 

  123. N. H. Nachtrieb, H. A. Resing, and S. A. Rice, J. Chem. Phys. 31, 135 (1959).

    Article  ADS  Google Scholar 

  124. H. Mehrer, H. Kronmüller, and A. Seeger, Phys. Stat. Solidi 10, 725 (1965).

    Article  ADS  Google Scholar 

  125. R. C. Brown, J. Worster, N. H. March, R. C. Perrin, and R. Bullough, Diffusion Processes (Proc. Thomas Graham Mem. Symp., Univ. Strathclyde) (Gordon and Breach, New York, 1970)

    Google Scholar 

  126. R. E. Hoffman, W. Pikus, and R. E. Ward, Trans. AIME 206, 483 (1956).

    Google Scholar 

  127. D. L. Martin, J. Phys. Chem. Solids, Supplement 1, Lattice Dynamics, Proc. of an International Conference, Copenhagen, Ed. by R. F. Wallis (Pergamon Press, Oxford, 1963), p. 255.

    Google Scholar 

  128. A. Lodding, J. N. Mundy, and A. Ott, Phys. Stat. Solidi 38, 559 (1970).

    Article  ADS  Google Scholar 

  129. J. N. Mundy, L. W. Barr, and F. A. Smith, Phil. Mag. 14, 785 (1966).

    Article  ADS  Google Scholar 

  130. R. Feder and H. P. Charbnau, Phys. Rev. 149, 464 (1966).

    Article  ADS  Google Scholar 

  131. R. Feder, Phys. Rev. B2, 828 (1970).

    ADS  Google Scholar 

  132. D. K. C. MacDonald, J. Chem. Phys. 21, 177 (1953).

    Article  ADS  Google Scholar 

  133. R. A. Hultsch and R. G. Barnes, Phys. Rev. 125, 1832 (1962).

    Article  ADS  Google Scholar 

  134. C. R. Kohler and A. L. Ruoff, J. Appl. Phys. 36, 2444 (1965).

    Article  ADS  Google Scholar 

  135. I. M. Torrens and M. Gerl, Phys. Rev. 187, 912 (1969).

    Article  ADS  Google Scholar 

  136. R. C. Brown, J. Worster, N. H. March, R. C. Perrin, and R. Bullough, to be published.

    Google Scholar 

  137. A. Ott, A. Lodding, and D. Lazarus, Phys. Rev. 188, 1088 (1969).

    Article  ADS  Google Scholar 

  138. D. Jeannotte and J. M. Galligan, Phys. Rev. Letters 19, 232 (1967).

    Article  ADS  Google Scholar 

  139. H. Schultz, Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965), p. 761.

    Google Scholar 

  140. R. L. Andelin, J. D. Knight, and M. Kahn, Trans. AIME 233, 19 (1965).

    Google Scholar 

  141. A. S. Nowick, Comments on Solid State Physics 2, 30 (1969).

    Google Scholar 

  142. C. J. Beevers, Acta Met. 11, 1029 (1963).

    Article  Google Scholar 

  143. C. Mairy, J. Hillairet, and D. Schumacher, Acta Met. 15, 1258 (1967).

    Article  Google Scholar 

  144. C. Janot, G. Bianchi, and B. George, Compt. Rend. 267B, 336 (1968).

    Google Scholar 

  145. P. G. Shewmon, J. Metals 8, 918 (1956).

    Google Scholar 

  146. A. Seeger and K.-P. Chik, Phys. Stat. Solidi 29, 455 (1968).

    Article  ADS  Google Scholar 

  147. A. Seeger, Comments on Solid State Physics 1, 157; 2, 55 (1969).

    ADS  Google Scholar 

  148. A. Seeger and M. L. Swanson, Lattice Defects in Semiconductors, Ed. by R. R. Hasiguti (University of Tokyo Press, 1968).

    Google Scholar 

  149. G. D. Watkins, J. Phys. Soc. Japan 18(Suppl. II), 33 (1963).

    Google Scholar 

  150. G. D. Watkins, Radiation Damage in Semiconductors, Ed. by P. Baruch (Dunod, Paris, 1965).

    Google Scholar 

  151. G. D. Watkins, Radiation Effects in Semiconductors, Ed. by F. L. Vook (Plenum Press, New York), 1968.

    Google Scholar 

  152. R. E. Whan, Appl. Phys. Letters 6, 221 (1965).

    Article  ADS  Google Scholar 

  153. R. E. Whan, Phys. Rev. 140, A690 (1965).

    Article  ADS  Google Scholar 

  154. A. Scholz and A. Seeger, Radiation Damage in Semiconductors, Ed. by P. Baruch (Dunod, Paris, 1965), p. 315.

    Google Scholar 

  155. M. M. Valenta and C. Ramasastry, Phys. Rev. 106, 73 (1957).

    Article  ADS  Google Scholar 

  156. P. A. Thrower, Chemistry and Physics of Carbon, Ed. by P. L. Walker, Jr. (Marcel Dekker, New York, 1967), p. 217.

    Google Scholar 

  157. G. R. Hennig, J. Chem. Phys. 40, 2877 (1964).

    Article  ADS  Google Scholar 

  158. G. R. Hennig, J. Appl. Phys. 36, 1482 (1965).

    Article  ADS  Google Scholar 

  159. J. H. W. Simmons, Radiation Damage in Graphite (Pergamon Press, New York, 1965), p. 133.

    Google Scholar 

  160. L. Bochirol and E. Bonjour, Carbon 6, 661 (1968).

    Article  Google Scholar 

  161. R. W. Henson and W. N. Reynolds, Carbon 3, 277 (1965).

    Article  Google Scholar 

  162. N. S. Rasor and J. D. McClelland, J. Phys. Chem. Solids 15, 17 (1960).

    Article  ADS  Google Scholar 

  163. R. J. Thorn and G. H. Winslow, J. Chem. Phys. 26, 186 (1957).

    Article  ADS  Google Scholar 

  164. P. R. Goggin and W. N. Reynolds, Phil. Mag. 8, 265 (1963).

    Article  ADS  Google Scholar 

  165. J. A. Turnbull and M. S. Stagg, Phil. Mag. 14, 1049 (1966).

    Article  ADS  Google Scholar 

  166. J. Friedel, Les Dislocations (Gauthier Villiers, Paris, 1956).

    Google Scholar 

  167. C. Baker and A. Kelly, Nature 193, 235 (1962).

    Article  ADS  Google Scholar 

  168. P. A. Thrower, Phil. Mag. 18, 697 (1969).

    Article  ADS  Google Scholar 

  169. P. A. Thrower, Carbon 6, 687 (1968).

    Article  Google Scholar 

  170. G. R. Hennig, Second Conference on Industrial Carbon and Graphite (Society of Chemical Industry, London, 1966), p. 109.

    Google Scholar 

  171. M. Kanter, Phys. Rev. 107, 655 (1957).

    Article  ADS  Google Scholar 

  172. M. Kanter, Kinetics of High Temperature Processes, Ed. by W. D. Kingery, Jr. (Technology Press, MIT, Cambridge, Mass., 1959), p. 61.

    Google Scholar 

  173. R. B. Evans, L. D. Love, and E. H. Kobisk, J. Appl. Phys. 40, 3058 (1969).

    Article  ADS  Google Scholar 

  174. F. S. Feates, J. Nucl. Materials 27, 325 (1968).

    Article  ADS  Google Scholar 

  175. L. W. Barr and A. B. Lidiard, “Defects in Ionic Solids,” in Vol. 10, Physical Chemistry—An Advanced Treatise (Academic Press, New York, 1970).

    Google Scholar 

  176. A. B. Lidiard, Proc. Brit. Ceram. Soc. 1967 (9), 1.

    ADS  Google Scholar 

  177. A. B. Lidiard, Handbuch der Physik, Vol. 20 (Springer-Verlag, Berlin, 1957), p. 246.

    Google Scholar 

  178. P. Süptitz and J. Teltow, Phys. Stat. Solidi 23, 9 (1967).

    Article  ADS  Google Scholar 

  179. Y. Adda and J. Philibert, La Diffusion dans les Solides (Presses Universitaires de France, 1966).

    Google Scholar 

  180. R. J. Friauf, J. Appl. Phys. 33, 494 (1962).

    Article  ADS  Google Scholar 

  181. M. Eisenstadt and A. G. Redfield, Phys. Rev. 132, 635 (1963).

    Article  ADS  Google Scholar 

  182. D. L. Kirk and P. L. Pratt, Proc. Brit. Ceram. Soc. 1967 (9), 215.

    Google Scholar 

  183. A. R. Allnatt and P. W. M. Jacobs, Trans. Faraday Soc. 58, 116 (1962).

    Article  Google Scholar 

  184. J. Rolfe, Can. J. Phys. 42, 2195 (1964).

    Article  ADS  Google Scholar 

  185. S. C. Jain and S. L. Dahake, Indian J. Pure Appl. Phys. 2, 71 (1964).

    Google Scholar 

  186. J. B. Beaumont and P. W. M. Jacobs, J. Chem. Phys. 45, 1496 (1966).

    Article  ADS  Google Scholar 

  187. D. K. Dawson, and L. W. Barr, Phys. Rev. Letters 19, 844 (1967).

    Article  ADS  Google Scholar 

  188. S. Chandra and J. Rolfe, Can. J. Phys. 48, 397 (1970).

    Article  ADS  Google Scholar 

  189. S. Chandra and J. Rolfe, Can. J. Phys. 48, 412 (1970).

    Article  ADS  Google Scholar 

  190. S. C. Jain and D. C. Parashar, J. Phys. C (Solid State Phys.) Ser. 2, 2, 167 (1969).

    Article  ADS  Google Scholar 

  191. T. G. Stoebe and P. L. Pratt, Proc. Brit. Ceram. Soc., 1967(9), 181.

    Google Scholar 

  192. K. Tharmalingam and A. B. Lidiard, Phil. Mag. 6, 1157 (1961).

    Article  ADS  Google Scholar 

  193. L. W. Barr, J. A. Morrison, and P. A. Schroeder, J. Appl. Phys. 36, 624 (1965).

    Article  ADS  Google Scholar 

  194. S. Mandel’, Soviet Phys.—Solid State 10, 2530 (1969).

    Google Scholar 

  195. O. S. Spencer and C. A. Plint, J. Appl. Phys. 40, 168 (1969).

    Article  ADS  Google Scholar 

  196. K. L. Kliewer and J. S. Koehler, Phys. Rev. 157, 685 (1967).

    Article  ADS  Google Scholar 

  197. R. W. Davidge, Phys. Stat. Solidi 3, 1851 (1963).

    Article  ADS  Google Scholar 

  198. C. A. Plint and M. L. Breig, J. Appl. Phys. 35, 2745 (1964).

    Article  ADS  Google Scholar 

  199. R. Strumane and R. DeBatist, Phys. Stat. Solidi 6, 817 (1964).

    Article  ADS  Google Scholar 

  200. R. D. Fouchaux and R. O. Simmons, Phys. Rev. 136, A1664 (1964).

    Article  ADS  Google Scholar 

  201. C. Tubandt, Z. Anorg. allgem. Chem. 115, 113 (1920).

    Google Scholar 

  202. J. E. Hove, Phys. Rev. 102, 915 (1956).

    Article  ADS  Google Scholar 

  203. M. D. Weber and R. J. Friauf, J. Phys. Chem. Solids 30, 407 (1969).

    Article  ADS  Google Scholar 

  204. H. Layer, M. G. Miller, and L. Slifkin, J. Appl. Phys. 33, 478 (1962).

    Article  ADS  Google Scholar 

  205. A. E. Abey and C. T. Tomizuka, J. Phys. Chem. Solids 27, 1149 (1966).

    Article  ADS  Google Scholar 

  206. K. L. Kliewer, J. Phys. Chem. Solids 27, 705 (1966).

    Article  ADS  Google Scholar 

  207. H. Wakabayasi, J. Phys. Soc. Japan 15, 2000 (1960).

    Article  ADS  Google Scholar 

  208. B. B. Snavely, Ph. D. Thesis, Cornell University, Ithaca, New York (1962).

    Google Scholar 

  209. L. Slifkin, W. McGowan, A. Fukai, and J.-S. Kim, Phot. Sci. and Eng. 11, 79 (1967).

    Google Scholar 

  210. E. Zintl and A. Udgard, Z. Anorg. allgem. Chem. 240, 150 (1939).

    Article  Google Scholar 

  211. C. Tubandt, H. Reinhold, and G. Liebold, A. Anorg. allgem. Chem. 197, 225 (1931).

    Article  Google Scholar 

  212. R. W. Ure, Jr., J. Chem. Phys. 26, 1363 (1957).

    Article  ADS  Google Scholar 

  213. V. H. J. Matzke and R. Lindner, Z. Naturforsch. 19A, 1178 (1964).

    ADS  Google Scholar 

  214. J. Short and R. Roy, J. Phys. Chem. 68, 3077 (1964).

    Article  Google Scholar 

  215. E. Barsis and A. Taylor, J. Chem. Phys. 48, 4362 (1968).

    Article  ADS  Google Scholar 

  216. E. Barsis and A. Taylor, J. Chem. Phys. 48, 4357 (1968).

    Article  ADS  Google Scholar 

  217. D. C. Stockbarger, J. Opt. Soc. Am. 39, 731 (1949).

    Article  ADS  Google Scholar 

  218. W. Bontinck, Physica 24, 650 (1958).

    Article  ADS  Google Scholar 

  219. K. Muto and K. Awazu, J. Phys. Chem. Solids 29, 1269 (1968).

    Article  ADS  Google Scholar 

  220. J. A. Champion, Brit. J. Appl. Phys. 16, 805 (1965).

    Article  ADS  Google Scholar 

  221. B. R. Rossing, D. Sc. Thesis, MIT (1966).

    Google Scholar 

  222. A. D. Franklin, S. Marzullo, and J. B. Wachtman, Jr., J. Res. Nat. Bur. Std. 71A, 355 (1967).

    Article  Google Scholar 

  223. H. B. Johnson, G. R. Miller, and I. B. Cutler, J. Am. Ceram. Soc. 50, 526 (1967).

    Article  Google Scholar 

  224. M. J. Weber and R. W. Bierig, Phys. Rev. 134, A1492 (1964).

    Article  ADS  Google Scholar 

  225. F. K. Fong, Progr. Solid State Chem. 3, 135 (1966).

    Article  Google Scholar 

  226. J. M. Baker, E. R. Davies, and J. P. Hurrell, Phys. Letters 26A, 352 (1968); Proc. Roy. Soc. (London) A308, 403 (1968).

    ADS  Google Scholar 

  227. A. D. Franklin, Proc. Brit. Ceram. Soc., 1967 (9), 15.

    Google Scholar 

  228. A. D. Franklin, J. Phys. Chem. Solids 29, 823 (1968).

    Article  ADS  Google Scholar 

  229. Hj. Matzke, J. Materials Science 5, 831 (1920).

    Article  ADS  Google Scholar 

  230. A. D. Franklin and S. M. Marzullo, in Proc. Brit. Ceram. Soc., Conference on Mass Transport in Non-Metallic Solids, Dec. 17 and 18, 1969.

    Google Scholar 

  231. W. D. Copeland and R. A. Swalin, J. Phys. Chem. Solids 29, 313 (1968).

    Article  ADS  Google Scholar 

  232. I. E. Leksina and S. I. Novikova, Soviet Phys.—Solid State 5, 798 (1963).

    Google Scholar 

  233. R. M. Emrick, Phys. Rev. 122, 1720 (1961).

    Article  ADS  Google Scholar 

  234. H. H. Grimes, J. Phys. Chem. Solids 26, 509 (1965).

    Article  ADS  Google Scholar 

  235. M. Doyama and J. S. Koehler, Phys. Rev. 119, 939 (1960).

    Article  ADS  Google Scholar 

  236. Y. Quéré, Compt. Rend. 251, 367 (1960).

    Google Scholar 

  237. O. N. Ovcharenko, Phys. Metals Metallogr. 11, 3, 78 (1961).

    Google Scholar 

  238. L. J. Cuddy and E. S. Machlin, Phil. Mag. 7, 745 (1962).

    Article  ADS  Google Scholar 

  239. R. R. Hasiguti, Y. Nakao, and H. Kimura, J. Phys. Soc. Japan 20, 553 (1965).

    Article  ADS  Google Scholar 

  240. Ya. A. Kraftmakher, Soviet Phys.—Solid State 9, 1458 (1967).

    Google Scholar 

  241. W. de Sorbo and D. Turnbull, Acta Met. 7, 83 (1959).

    Article  Google Scholar 

  242. W. de Sorbo and D. Turnbull, Phys. Rev. 115, 560 (1959).

    Article  ADS  Google Scholar 

  243. K. Detert and I. Ständer, Z. Metallic. 52, 677 (1961).

    Google Scholar 

  244. D. Locati and T. Federighi, reported by T. Federighi, Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965), p. 217.

    Google Scholar 

  245. G. Bianchi, D. Mallejac, C. Janot, and G. Champier, Compt. Rend. 263B, 1404 (1966).

    Google Scholar 

  246. A. D. King, A. J. Cornish, and J. Burke, J. Appl. Phys. 37, 4717 (1966).

    Article  ADS  Google Scholar 

  247. T. Federighi, in Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965), p. 217.

    Google Scholar 

  248. Y. N. Lwin, M. Doyama, and J. S. Koehler, Phys. Rev. 165, 787 (1968).

    Article  ADS  Google Scholar 

  249. Ya. A. Kraftmakher and F. B. Lanina, Soviet Phys.—Solid State 7, 92 (1965).

    Google Scholar 

  250. G. R. Piercy, Phil. Mag. 5, 201 (1960).

    Article  ADS  Google Scholar 

  251. W. Bauer and A. Sosin, Phys. Rev. 147, 482 (1966).

    Article  ADS  Google Scholar 

  252. G. A. Sullivan and J. W. Weymouth, Phys. Rev. 136, A1141 (1964).

    Article  ADS  Google Scholar 

  253. J. D. Filby and D. L. Martin, Proc. Roy. Soc. (London) 284, 83 (1965).

    Article  ADS  Google Scholar 

  254. D. F. Holcomb and R. E. Norberg, Phys. Rev. 98, 1074 (1955).

    Article  ADS  Google Scholar 

  255. A. N. Naumov and G. Ya. Ryskin, Zh. Tekhn. Fiz. 29, 189 (1959).

    Google Scholar 

  256. D. C. Ailion and C. P. Slichter, Phys. Rev. 137, A235 (1965).

    Article  ADS  Google Scholar 

  257. A. Ott, J. N. Mundy, L. Löwenberg, and A. Lodding, Z. Naturforsch. 23A, 771 (1968).

    Google Scholar 

  258. N. H. Nachtrieb, E. Catalano, and J. A. Weil, J. Chem. Phys. 20, 1185 (1952).

    Article  ADS  Google Scholar 

  259. J. N. Mundy, L. W. Barr, and F. A. Smith, Phil. Mag. 15, 411 (1967).

    Article  ADS  Google Scholar 

  260. Ya. A. Kraftmakher, Soviet Phys.’Solid State 5, 696 (1963).

    Google Scholar 

  261. Ya. A. Kraftmakher, Soviet Phys.—Solid State 6, 396 (1964).

    Google Scholar 

  262. J. D. Meakin, A. Lawley, and R. C. Koo, Lattice Defects in Quenched Metals, Ed. by R. M. J. Cotterill, M. Doyama, J. J. Jackson, and M. Meshii (Academic Press, New York, 1965), p. 767.

    Google Scholar 

  263. V. Ya. Chekhovskoy, and V. A. Petrov, International Conference on Vacancies and Interstitials in Metals, Julich Conference 2, Vols. I, II (obtainable from Zentralbibliothek der Kernforschungsanlage Julich GmbH, Julich, Germany, 1968), p. 6.

    Google Scholar 

  264. W. Glaeser and H. Wever, Phys. Stat. Solidi 35, 367 (1969).

    Article  ADS  Google Scholar 

  265. M. L. Swanson, G. R. Piercy, G. V. Kidson, and A. F. Quenneville, J. Nucl. Materials 34, 340 (1970).

    Article  ADS  Google Scholar 

  266. D. Lazarus, Diffusion in Body-Centered Metals, Ed. by J. A. Wheeler, Jr., and F. R. Winslow (Am. Soc. for Metals, Metals Park, Ohio, 1965), p. 155.

    Google Scholar 

  267. C. Janot, D. Mallejac, and B. George, Compt. Rend. 270B, 404 (1970).

    Google Scholar 

  268. H. Letaw, L. Slifkin, and W. M. Portnoy, Phys. Rev. 102, 636 (1956).

    Article  ADS  Google Scholar 

  269. R. F. Peart, Phys. Stat. Solidi 15, K119 (1966).

    Article  ADS  Google Scholar 

  270. E. Barsis, E. Lilley, and A. Taylor, Proc. Brit. Ceram. Soc. 1967, (9), 203 (1967).

    Google Scholar 

  271. C. F. Bauer and D. H. Whitmore, Phys. Stat. Solidi 37, 585 (1970).

    Article  ADS  Google Scholar 

  272. L. W. Barr, in Proc. Brit. Ceram. Soc., Conference on Mass Transport in Non-Metallic Solids, Dec. 17 and 18, 1969.

    Google Scholar 

  273. R. W. Dreyfus and A. S. Nowick, J. Appl. Phys. 33, 473 (1962).

    Article  ADS  Google Scholar 

  274. A. R. Allnatt and P. Pantelis, Solid State Comm. 6, 309 (1968).

    Article  ADS  Google Scholar 

  275. V. Trnovcova, Czech. J. Phys. B19, 663 (1969).

    Article  ADS  Google Scholar 

  276. E. Rzepka and J.-P. Chapelle, Compt. Rend. 268B, 1770 (1969).

    Google Scholar 

  277. V. K. Jain, Indian J. Pure Appl. Phys. 7, 330 (1969).

    Google Scholar 

  278. R. G. Fuller, Bull. Am. Phys. Soc. 15, 384 (1970).

    Google Scholar 

  279. A. V. Chadwick, B. D. McNicol, and A. R. Allnatt, Phys. Stat. Solidi 33, 301 (1969).

    Article  ADS  Google Scholar 

  280. P. J. Harvey and I. M. Hoodless, Phil. Mag. 16, 543 (1967).

    Article  ADS  Google Scholar 

  281. J. N. Maycock, V. R. Pai Verneker, and C. S. Gorzynski, Jr., Phys. Stat. Solidi 37, 857 (1970).

    Article  ADS  Google Scholar 

  282. F. Bénière and M. Chemla, Compt. Rend. 266C, 660 (1968).

    Google Scholar 

  283. R. G. Fuller, Phys. Rev. 142, 524 (1966).

    Article  ADS  Google Scholar 

  284. M. Eisenstadt, Phys. Rev. 132, 630 (1963).

    Article  ADS  Google Scholar 

  285. T. G. Stoebe and R. A. Huggins, J. Mat. Sci. 1, 117 (1966).

    Article  ADS  Google Scholar 

  286. J. Itoh, M. Satoh, and A. Hiraki, J. Phys. Soc. Japan 16, 343 (1960).

    ADS  Google Scholar 

  287. M. Eisenstadt, Phys. Rev. 133, A191 (1964).

    Article  ADS  Google Scholar 

  288. M. Satoh, J. Phys. Soc. Japan 20, 1008 (1965).

    Article  ADS  Google Scholar 

  289. G. Pellegrini and J. Pelsmaekers, J. Chem. Phys. 51, 5190 (1969).

    Article  ADS  Google Scholar 

  290. J. Pelsmaekers, G. Pellegrini, and S. Amelinckx, Solid State Comm. 1, 92 (1963).

    Article  ADS  Google Scholar 

  291. B. von Guerard, H. Peisl, and W. Waidelich, Phys. Stat. Solidi 29, K59 (1968).

    Article  ADS  Google Scholar 

  292. J. S. Koehler, D. Langreth, and B. von Turkovich, Phys. Rev. 128, 573 (1962).

    Article  ADS  Google Scholar 

  293. H. Kanzaki, K. Kido, and T. Ninomiya, J. Appl. Phys. 33, 482 (1962).

    Article  ADS  Google Scholar 

  294. P. Muller, Phys. Stat. Solidi 12, 775 (1965).

    Article  ADS  Google Scholar 

  295. E. Barsis and A. Taylor, J. Chem. Phys. 45, 1154 (1966).

    Article  ADS  Google Scholar 

  296. M. Baker and A. Taylor, J. Phys. Chem. Solids 30, 1003 (1969).

    Article  ADS  Google Scholar 

  297. R. J. Lysiak and P. P. Mahendroo, J. Chem. Phys. 44, 4025 (1966).

    Article  ADS  Google Scholar 

  298. J. R. Miller and P. P. Mahendroo, Phys. Rev. 174, 369 (1968).

    Article  ADS  Google Scholar 

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Franklin, A.D. (1972). Statistical Thermodynamics of Point Defects in Crystals. In: Crawford, J.H., Slifkin, L.M. (eds) Point Defects in Solids. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2970-1_1

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