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External Vibrations in Complex Crystals

G. VENKATARAMAN and V. C. SAHNI

G. VENKATARAMAN and V. C. SAHNI

  • Nuclear Physics Division Bhabha Atomic Research Centre, Trombay, Bombay-85, India

Rev. Mod. Phys. 42, 409 – Published 1 October, 1970Erratum Rev. Mod. Phys. 43, 679 (1971)

DOI: https://doi.org/10.1103/RevModPhys.42.409

Abstract

The study of dispersion relations for external modes in molecular and complex ionic crystals is reviewed. The concept of external modes is introduced, so that the formal theory may be developed along the lines of standard Born-von Kármán formalism. The studies reported thus far in the literature are then surveyed against the background of the formal theory. The role of macroscopic electric fields in relation to external modes is next discussed, and the work of Kellermann is generalized to obtain Coulomb coefficients connected with external modes in complex ionic crystals. Finally, the group-theoretical aspects are considered, and the recent work of Maradudin and Vosko is extended to cover the external modes. A detailed illustrative example is also provided.

Erratum

Erratum: External Vibrations in Complex Crystals

G. VENKATARAMAN and V. C. SAHNI
Rev. Mod. Phys. 43, 679 (1971)

See Also

Lattice Vibrations in Deuterated Ammonium Chloride at 85°K. I. Experimental

H. C. Teh and B. N. Brockhouse
Phys. Rev. B 3, 2733 (1971)

References (137)

  1. Afaneseva, G. K., K. S. Aleksandrov, and A. I. Kitaigorodskii, 1967, Phys. Status Solidi 24, 161
  2. Amaros, J. L., and M. Amaros, 1968, Molecular Crystals: Their Transforms and Diffuse Scattering (Wiley, New York)
  3. Ancelme, A. I., and N. N. Porfireva, 1949, Zh. Eksp. Teor. Fiz. 19, 438
  4. Asano, S., and Y. Tomishima, 1957a J. Phys. Soc. Japan 12, 346
  5. Asano, S.Y. Tomishima, and Y. Tomishima, 1957b, J. Phys. Soc. Japan 12, 890
  6. Asano, S.Y. TomishimaY. Tomishima, and Y. Tomishima, 1957c, J. Phys. Soc. Japan 12, 900
  7. Bajorek, A., K. Parlinski, and T. Matchechina, 1965, in Inelastic Scattering of Neutrons (International Atomic Energy Agency, Vienna) Vol. 2, p. 355
  8. Barker, A. S., Jr., 1964, Phys. Rev. 135, A742
  9. Bellman, R. 1960, Introduction to Matrix Analysis (McGraw-Hill, New York), p. 56
  10. Bhagavantam, S., and T. Venkatarayudu, 1948, Theory of Groups and Its Applications to Physical Problems (Andhra U. P., Waltair, India)
  11. Biem, W., 1963, Phys. Status Solidi 3, 1927
  12. Blackman, M., 1955, in Handbuch der Physik, edited by S. Flügge (Springer, Berlin), Vol. 7/1
  13. Born, M., and T. von Kármán, 1912, Physik. Z. 13, 297
  14. Born, M.T. von Kármán, and K. Huang, 1954, Dynamical Theory of Crystal Lattices (Clarendon, Oxford)
  15. Bouckert, L. P., R. Smoluchowski, and E. P. Wigner, 1936, Phys. Rev. 50, 58
  16. Boutin, H., and S. Yip, 1968 Molecular Spectroscopy with Neutrons (M.I.T., Cambridge, Mass)
  17. Brockhouse, B. N., 1964, in Phonons and Phonon Interactions, edited by T. A. Bak (Benjamin, New York)
  18. Brockhouse, B. N., 1966, in Phonons in Perfect Lattices and Lattices with Point Imperfections, edited by R. H. W. Stevenson (Oliver and Boyd, Edinburgh)
  19. Brot, C., 1965, in Lattice Dynamics, edited by R. F. Wallis (Pergamon, New York), p. 217
  20. Burstein, E., 1965, in Lattice Dynamics, edited by R. F. Wallis (Pergamon, New York), p. 315
  21. Chang, S. S., and E. F. Westrum, 1960, J. Phys. Chem. 64, 1547
  22. Chen, S. H., and V. Dvorak, 1968, J. Chem. Phys. 48, 4060
  23. Cheutin, A., and J. P. Mathieu, 1956, J. Chim. Phys. 53, 106
  24. Choquet-Bruhat, Y., 1967, Problems and Solutions in Mathematical Physics (Holden-Day, San Francisco), p. 77
  25. Cochran, W., 1960, Advan. Phys. 9, 387
  26. Cochran, W., 1961, Advan. Phys. 10, 401
  27. Cochran, W., 1963, Rept. Progr. Phys. 26, 1
  28. Cochran, W., and G. S. Pawley, 1964, Proc. Roy. Soc. (London) A280, 1
  29. Cochran, W.G. S. Pawley, 1966, in Phonons in Perfect Lattices and Lattices with Point Imperfections, edited by R. H. W. Stevenson (Oliver and Boyd, Edinburgh)
  30. Cochran, W.G. S. Pawley, and R. A. Cowley, 1968, in Handbuch der Physik, edited by S. Flügge (Springer, Berlin), Vol. 25/2a
  31. Couture-Mathieu, L., J. P. Mathieu, J. Cremer, and H. Poulet, 1951, J. Chim. Phys. 48, 1
  32. Cowley, E. R., 1970, "Lattice Vibrations in Deuterated Ammonium Chloride at 85°K. II. Theoretical," Phys. Rev. (to be published)
  33. Cowley, E. R., and A. Okazaki, 1967, Proc. Roy. Soc. (London) A300, 45
  34. Cowley, R. A., W. Cochran, B. N. Brockhouse, and A. D. B. Woods, 1963, Phys. Rev. 131, 1030
  35. Craig, D. P., 1968, in Excitons, Magnons and Phonons in Molecular Crystals, edited by A. B. Zahlan (Cambridge U.P., Cambridge), p. 101
  36. Craig, D. P., and S. H. Walmsley, 1968, Excitons in Molecular Crystals (Benjamin, New York), p. 30
  37. Cruickshank, D. W. J., 1956a, Acta Cryst. 9, 754
  38. Cruickshank, D. W. J., 1956b, Acta Cryst. 9, 915
  39. Cruickshank, D. W. J., 1957a, Acta Cryst. 10, 470
  40. Cruickshank, D. W. J., 1957b, Acta Cryst. 10, 504
  41. Cruickshank, D. W. J., 1958, Rev. Mod. Phys. 30, 163
  42. Davydov, A. S., 1962, Theory of Molecular Excitons (McGraw-Hill, New York)
  43. Deprez, G., and R. Fouret, 1964, Compt. Rend. 259, 3491
  44. Deprez, G.R. Fouret, and R. Fouret, 1966, J. Phys. (Paris) 27, 147
  45. Dolling, G., 1968, in Molecular Dynamics and Structure of Solids, edited by J. J. Rush and R. S. Carter (National Bureau of Standards, Washington D.C.,) p. 289
  46. Dolling, G., 1970, "Dynamics of Molecular Crystals and Intermolecular Interactions," Transactions of the American Crystallographic Association (to be published)
  47. Dolling, G., and B. M. Powell, 1970, "Intermolecular Dynamics of Hexamethylenetetramine," Proc. Roy. Soc. (London) (to be published)
  48. Dolling, G.B. M. Powell, and A. D. B. Woods, 1965, in Thermal Neutron Scattering, edited by P. A. Egelstaff (Academic, New York)
  49. Ewald, P. P., 1917, Ann. Physik, 54, 519, 557
  50. Ewald, P. P., 1921, Ann. Physik 64, 253
  51. Frenkel, J., 1935, Acta Physiochim. U.R.S.S. 3, 23
  52. Frenkel, J., 1946, Kinetic Theory of Liquids (Clarendon, Oxford), p. 84
  53. Garland, C. W., and R. Renard, 1966, J. Chem. Phys. 44, 1130
  54. Gilat, G., and G. Dolling, 1964, Phys. Letters 8, 304
  55. Gilat, G.G. Dolling, and L. J. Raubenheimer, 1966, Phys. Rev. 144, 390
  56. Gliss, B., and H. Bilz, 1968, Phys. Rev. Letters 21, 884
  57. Goldstein, H., 1953, Classical Mechanics (Addison-Wesley, Cambridge, Mass)
  58. Hahn, H., and W. Biem, 1963, Phys. Status Solidi 3, 1911
  59. Halford, R. S., 1946, J. Chem. Phys. 14, 8
  60. Haussühl, S., 1958, Acta Cryst. 11, 58
  61. Heine, V., 1960, Group Theory in Quantum Mechanics (Pergamon, London)
  62. Henry, C. H., and J. J. Hopfield, 1965, Phys. Rev. Letters 15, 964
  63. Herzberg, G., 1945, Infrared and Raman Spectra (Nostrand, Princeton, N.J.)
  64. Hirschfelder, J. O., C. F. Curtiss, and R. B. Bird, 1954, Molecular Theory of Gases and Liquids (Wiley, New York), p. 22
  65. Huntington, H. B., S. G. Gangoli, and J. L. Mills, 1969, J. Chem. Phys. 50, 3844
  66. Janik, J. A., 1968, in The Theory of Condensed Matter (International Atomic Energy Agency, Vienna)
  67. Joshi, S. K., and A. K. Rajagopal, 1969, in Solid State Physics, edited by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic, New York), Vol. 22
  68. Kay, M. I., B. C. Frazer, and I. Almodovar, 1964, J. Chem. Phys. 40, 504
  69. Kellermann, E. W., 1940, Phil. Trans. Roy. Soc. (London) A238, 513
  70. King, J. S. and D. Steinman, 1969 (private communication)
  71. Kitaigorodskii, A. I., 1966, J. Chim. Phys. 63, 6
  72. Kitte., C., 1966, Introduction to Solid State Physics (Wiley, New York), 3rd ed
  73. Korn, G. A., and T. M. Korn, 1968, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York), p. 463
  74. Kovalev, O. V., 1964, Irreducible Representations of Space Groups (English Transl: Gordon and Beach Science Publishers, New York; Russian original: Academy of Sciences of the Ukranian SSSR, Kiev, 1961)
  75. Krishnan, R. S., 1947, Proc. Indian Acad. Sci. A26, 432
  76. Lax, M., 1965, in Lattice Dynamics, edited by R. F. Wallis (Pergamon, New York), p. 583
  77. Leibfried, G., 1955, in Handbuch der Physik, edited by S. Flügge (Springer, Berlin), Vol. 7/1
  78. Lonsdale, K., 1952, International Tables of X-ray Crystallography (Kynoch, Birmingham, England), Vol. 1
  79. Loudon, R., 1964, Advan. Phys. 13, 423
  80. Ludwig, W., 1967, Springer Tracts in Modern Physics, edited by G. Hohler (Springer, Berlin), Vol. 43
  81. Lutz, U. A., and W. Halg, 1970, Solid State Commun. 8, 165
  82. Maradudin, A. A., E. W. Montroll, and G. H. Weiss, 1963, Theory of Lattice Dynamics in the Harmonic Approximation (Academic, New York)
  83. Maradudin, A. A.E. W. MontrollG. H. Weiss, and S. H. Vosko, 1968, Rev. Mod. Phys. 40, 1
  84. Margenau, H., and G. M. Murphy, 1956, The Mathematics of Physics and Chemistry (Nostrand, New York), p. 313
  85. Martin, R. M., 1968, Phys. Rev. Letters 21, 536
  86. Martin, R. M., 1969, Phys. Rev. 186, 871
  87. Mathieu, J. P., and L. Couture-Mathieu, 1952, J. Phys. Radium 13, 271
  88. McMurry, H. L., A. W. Solbrig, Jr., J. K. Boyter, and C. Noble, 1967, J. Phys. Chem. Solids 28, 2359
  89. Musgrave, M. J. P., and J. A. Pople, 1962, Proc. Roy. Soc. (London) A268, 474
  90. Parlinski, K., 1968, Acta Phys. Polonica 34, 1019
  91. Parlinski, K., 1969, Acta Phys. Polonica 35, 223
  92. Pawley, G. S., 1967, Phys. Status Solidi 20, 347
  93. Pawley, G. S., and S. J. Cyvin, 1970, J. Chem. Phys. 52, 4073
  94. Pawley, G. S.S. J. Cyvin, and E. A. Yeats, 1969, Solid State Commun. 7, 385
  95. Phillips, J. C., 1956, Phys. Rev. 104, 1263
  96. Pick, R. M., 1970, Advan. Phys. 19, 269
  97. Porto, S. P. S., B. Tell, and T. C. Damen, 1966, Phys. Rev. Letters 16, 450
  98. Porto, S. P. S.B. TellT. C. Damen, and J. F. Scott, 1967, Phys. Rev. 157, 716
  99. Powell, B. M., 1968, in Neutron Inelastic Scattering (International Atomic Energy Agency, Vienna), Vol. 2, p. 185
  100. Powell, B. M., and E. Sandor, 1970, "The Thermal Diffuse Scattering of X-Rays and Molecular Dynamics of Hexamethylenetetramine," J. Phys. C (to be published)
  101. Rafizadeh, H. A., and S. Yit, 1970 "Lattice Dynamics of Hexamine—A Rigid-Molecule Approximation" (to be published)
  102. Ramachandran, G. N., and W. A. Wooster, 1951, Acta Cryst. 4, 431
  103. Raskin, Sh. Sh., A. V. Sechkarev, and F. I. Skripov, 1949, Dokl. Akad. Nauk SSSR 66, 837
  104. Raubenheimer, L. J., and G. Gilat, 1967, Phys. Rev. 157, 586
  105. Rousset, A., 1947, La Diffusion de la Lumiere par les Molecules Rigides (Gauthier-Villars, Paris)
  106. Russel, J. P., and R. Loudon, 1965, Proc. Phys. Soc. (London) 85, 1029
  107. Sahni, V. C., and G. Venkataraman, 1970, Phys. Kondensierten Materie 11, 199, 212
  108. Sakurai, J., R. A. Cowley, and G. Dolling, 1967, Bull. Am. Phys. Soc. 12, 282
  109. Sakurai, J., R. A. Cowley, and G. Dolling, 1970, J. Phys. Soc. Japan 28, 1426
  110. Sandor, E., 1962, Acta Cryst. 15, 463
  111. Seitz, F., 1940, Modern Theory of Solids (McGraw-Hill, New York)
  112. Skripov, F. I., 1949, Dokl. Akad. Nauk SSSR 66, 1075
  113. Smith, T., 1966, in Phonons in Perfect Lattices and Lattices with Point Imperfections, edited by R. H. W. Stevenson (Oliver and Boyd, Edinburgh)
  114. Smith, H. G., J. G. Traylor, and W. Reichardt, 1969, Phys. Rev. 181, 1218
  115. Smith, H. G.J. G. TraylorW. Reichardt1949, Proc. Inst. Radio Engrs. 37, 1378
  116. Stockmeyer, R., and H. Stiller, 1968, Phys. Status Solidi 27, 269
  117. Suzuki, M., T. Yokoyama, and M. Ito, 1968, Spectrochim. Acta 24A, 1091
  118. Tasumi, M., and T. Shimanouchi, 1965, J. Chem. Phys. 43, 1245
  119. Teh, H. C., and B. N. Brockhouse, 1970, Phys. Rev. (to be published)
  120. Teh, H. C.B. N. Brockhouse, B. N. Brockhouse, and G. A. Dewit, 1969, Phys. Letters 29A, 694
  121. Toya, T., 1958, J. Res. Inst. Catalysis, Hokkaido Univ. 6, 183
  122. Tramer, A., 1959, Compt. Rend. 248, 3546 ibid.249, 2531
  123. Trevino, S., H. Prask, T. Wall, and S. Yip, 1968, in Neutron Inelastic Scattering (International Atomic Energy Agency, Vienna), Vol. 1, p. 362
  124. van Hove, L., 1953, Phys. Rev. 89, 1189
  125. van Kranendonk, J. and V. F. Sears, 1966, Can. J. Phys. 44, 313
  126. Venkataraman, G., K. Usha Deniz, P. K. Iyengar, A. P. Roy, and P. R. Vijayaraghavan, 1966, J. Phys. Chem. Solids 27, 1103
  127. Wagner, E. L., and D. F. Hornig, 1950, J. Chem. Phys. 18, 296
  128. Walmsley, S. H., 1968, in Excitons, Magnons and Phonons in Molecular Crystals, edited by A. B. Zahlan (Cambridge U. P., Cambridge)
  129. Warren, J. L., 1968, Rev. Mod. Phys. 40, 38
  130. Wilson, E. B., Jr., J. C. Decius, and P. C. Cross, 1955, Molecular Vibrations (McGraw-Hill, New York)
  131. Winston, J., and R. S. Halford, 1949, J. Chem. Phys. 17, 607
  132. Wolfram, T., G. W. Lehman, and R. E. DeWames, 1963, Phys. Rev. 129, 2483
  133. Woods, A. D. B., W. Cochran, and B. N. Brockhouse, 1960, Phys. Rev. 119, 980
  134. Woods, A. D. B., B. N. Brockhouse, M. Sakamoto, and R. N. Sinclair, 1961, in Inelastic Scattering of Neutrons (International Atomic Energy Agency, Vienna) p. 487
  135. Wright, G. B., 1969, Light Scattering Spectra of Solids (Springer, Berlin)
  136. Zak, J., 1969, Irreducible Representations of Space Groups (W. A. Benjamin, New York)
  137. Ziman, J. M., 1965, Principles of the Theory of Solids (Cambridge U. P., Cambridge)

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