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Electronic Influence on Lattice Dynamics

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Elementary Excitations in Solids, Molecules, and Atom

Part of the book series: NATO Advanced Study Institutes Series ((ASIB,volume 2))

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Abstract

In a vibrating lattice, the effective force between two ions consists of (i) the direct ion-ion interaction and (ii) the interaction via mediating electrons. The electronic contribution to the lattice dynamics is very important in many classes of crystals spanning from metals to insulators. The electronic contribution in simple metals has been fairly satisfactorily treated by the method of pseudopotentials, essentially treating the electrons as nearly free. However, there remains an enormous class of transition metals, their compounds, covalent and ionic crystals, in which there are important electrons which are not nearly free nor yet so tightly bound so as to be moving rigidly with the ion. In section 2 we shall describe a method which takes into account the effects of these electrons on the lattice dynamics.

Research supported by the National Science Foundation, Grant No. GP-28997.

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References

  1. Sham, L.J. (1969). Modern Solid State Physics, Vol. II, Phonons and Their Interactions, (eds. Enns, R.H. and Haering, R.R.), (Gordon and Breach, London).

    Google Scholar 

  2. Maradudin, A.A., Montroll, E.W., Weiss, G.H. and Ipatova, I.P (1971). Theory of Lattice Dynamics in the Harmonic Approximation, (Academic Press, New York).

    Google Scholar 

  3. Pines, D. and Nozières, P. (1966). The Theory of Quantum Liquidsj Vol. I, (Benjamin, W.A. New York).

    Google Scholar 

  4. Ehrenreich, H. and Cohen, M.H. (1959). Phys. Rev., 115, 786.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. Sham, L.J. (1969). Phys. Rev., 188, 1431.

    Article  ADS  Google Scholar 

  6. Pick, R.M., Cohen, M.H. and Martin, R.M. (1970). Phys Rev., B1, 910.

    ADS  Google Scholar 

  7. Sham, L.J. (1972). Phys. Rev., B1, 3581.

    ADS  Google Scholar 

  8. Sinha, S.K. (1969). Phys. Rev., 177, 1256.

    Article  ADS  Google Scholar 

  9. Hayashi, E. and Shimizu, M. (1969). J. Phys. Soc. Japan, 26, 1396.

    Article  ADS  Google Scholar 

  10. Hanke, W. (1971). Phonons, (ed. Nusimovici, M.A.), (Flammarion Press, Paris), p. 294;

    Google Scholar 

  11. Hanke, W. and Bilz, H. (1972). Proceedings of the International Conference on Inelastic Scattering of Neutrons, (IAEA, Vienna); Hanke, W. Phys. Rev. (to be published).

    Google Scholar 

  12. Pick, R. (1971). Phonons, (ed. Nusimovici, M.A.), (Flammarion Press, Paris), p. 20.

    Google Scholar 

  13. Sham, L.J. (1971). Phys. Rev. Lett., 27, 1725; (1972).

    Article  ADS  Google Scholar 

  14. Sham, L.J. (1971). Phys. Rev., B6, 3584. (1972).

    ADS  Google Scholar 

  15. See also:Sham, L.J. (1971). Lattice Dynamics, (eds. Maradudin, A.A. and Horton, G.K.), (North-Holland, New York), (to be published).

    Google Scholar 

  16. Des Cloizeaux, J. (1963). Phys. Rev., 129, 554;

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. Des Cloizeaux, J. (1964). Phys. Rev., A135, 685, 698.

    Article  ADS  Google Scholar 

  18. Sinha, S.K., Gupta, R.P. and Price, D.L. (1971). Phys. Rev. Lett., 26, 1324.

    Article  ADS  Google Scholar 

  19. Weger, M. and Goldberg, I.B. Solid State Phys., (to be published).

    Google Scholar 

  20. Testardi, L.R. (to be published).

    Google Scholar 

  21. Batterman, B.W. and Barrett, C.S. (1964). Phys. Rev. Lett., 13, 390;

    Article  ADS  Google Scholar 

  22. Batterman, B.W. and Barrett, C.S. (1966). Phys. Rev., 149, 296.

    Article  ADS  Google Scholar 

  23. Mailfert, R., Batterman, B.W. and Hanak, J.J. (1967). Phys. Lett., A24, 315;

    ADS  Google Scholar 

  24. Vieland, L.J. (1972). J. Phys. Chem. Solids, 33, 581.

    Article  ADS  Google Scholar 

  25. For V3Si: Testardi, L.R. and Bateman, T.B. (1967). Phys. Rev., 154, 402.

    Article  ADS  Google Scholar 

  26. For Nb3Sn: Keller, K.R. and Hanak, J.J. (1967). Phys. Rev., 154, 628;

    Article  ADS  Google Scholar 

  27. Rehwald, W. (1968). Phys. Lett., A27, 287.

    ADS  Google Scholar 

  28. Shirane, G., Axe, J.D. and Birgeneau, R.J. (1971). Solid State Commun., 9, 347.

    Article  Google Scholar 

  29. Shirane, G. and Axe, J.D. (1971). Phys. Rev. Lett., 27, 1803.

    Article  ADS  Google Scholar 

  30. Kodess, B.N., Kurithzin, V.B. and Tretjakov, B.N. (1971). Phys. Lett., A37, 415;

    ADS  Google Scholar 

  31. Kodess, B.N. and Shekhtman, V.Sh. (1971). Sov. Phys. JETP Lett., 14, 225.

    ADS  Google Scholar 

  32. Matthias, B.T., Geballe, T.H., Longinotti, L.D., Corenzwit, E., Hull, G.W. and Maita, J.P. (1967). Science, 156, 645;

    Article  ADS  Google Scholar 

  33. Arrhenius, G., Corenzwit, E.., Fitzgerald, R., Hull Jr., G.W., Luo, H.L., Matthias, B.T. and Zachariasen, W.H. (1968). Proc. Nat. Acad. Sci., 61, 621.

    Article  ADS  Google Scholar 

  34. Willens, R.H., Geballe, T.H., Gossard, A.C., Maita, J.P., Menth, A., Hull Jr., G.H. and Soden, R.R. (1970). Solid State Commun., 7, 837.

    Article  Google Scholar 

  35. Webb, G.W., Vieland, L.J., Miller, R.E. and Wicklund, A. (1971). Solid State Commun., 9, 1769.

    Article  ADS  Google Scholar 

  36. Weger, M. (1964). Rev. Mod. Phys., 36, 176,

    Article  ADS  Google Scholar 

  37. Labbé, J. and Friedel, J. (1966). J. Phys. (Paris), 17, 153, 303.

    Google Scholar 

  38. Berko, S. and Weger, M. (1970). Phys. Rev. Lett., 24, 55;

    Article  ADS  Google Scholar 

  39. Berko, S. and Weger, M. (1972). Computational Physios, (eds. Herman, F., Dalton, N.W. and Koehler, T.R.), (Plenum Press), p. 59.

    Google Scholar 

  40. Weger, M. (1970). J. Phys. Chem. Solids, 31, 1621;

    Article  ADS  Google Scholar 

  41. Goldberg, I.B. and Weger, M. (1971). J. Phys., C4, 188L.

    ADS  Google Scholar 

  42. Clogston, A.M. and Jaccarino, V. (1961). Phys. Rev., 121, 1357.

    Article  ADS  Google Scholar 

  43. Barisić, S. and Labbé, J. (1967). J. Phys. Chem. Solids, 28, 2477;

    Article  ADS  Google Scholar 

  44. Cohen, R.W., Cody, G.D. and Halloran, J.J. (1967). Phys. Rev. Lett., 19, 840.

    Article  ADS  Google Scholar 

  45. Kunzler, J.E., Maita, J.P., Levinstein, H.J. and Ryder, E.J. (1966). Phys. Rev., 143, 390;

    Article  ADS  Google Scholar 

  46. Vieland, L.J. and Wicklund, A.W. (1968). Phys. Rev., 166, 424.

    Article  ADS  Google Scholar 

  47. Anderson, P.W. and Blount, E.I. (1965). Phys.Rev. Lett., 14, 217.

    Article  MATH  ADS  Google Scholar 

  48. Birman, J.L. (1966). Phys. Rev. Lett., 17, 1216.

    Article  ADS  Google Scholar 

  49. Perel, J., Batterman, B.W. and Blount, E.I. (1968). Phys. Rev., 166, 616.

    Article  ADS  Google Scholar 

  50. Vieland, L.J., Cohen, R.W. and Rehwald, W. (1971). Phys. Rev. Lett., 26, 373;

    Article  ADS  Google Scholar 

  51. Vieland, L.J. (1972). J. Phys. Chem. Solids, 33, 581.

    Article  ADS  Google Scholar 

  52. Shirane, G. and Axe, J.D. (1971). Phys. Rev., B4, 2957.

    ADS  Google Scholar 

  53. Dieterich, W. and Fülde, P. (1971). Z. Phys., 248, 154.

    Article  ADS  Google Scholar 

  54. Noolandi, J. and Sham, L.J. Phys. Rev., (in press).

    Google Scholar 

  55. Maita, J.P. and Bucher, E. (1972). Phys. Rev. Lett., 29, 931.

    Article  ADS  Google Scholar 

  56. Ferraris, J., Cowan, D.O., Walatka, V. Jr. and Perlstein, J.H. (1973). J. Amer. Chem. Soc., 95, 948.

    Article  Google Scholar 

  57. Coleman, L.B., Cohen, M.J., Sandman, D.J., Yamagishi, F.G., Garito, A.F. and Heeger, A.J. Solid State Commun..

    Google Scholar 

  58. Peierls, R.E. (1953). Quantum Theory of Solids, (Oxford, London), p. 108.

    Google Scholar 

  59. Phillips, T.E., Kristenmacher, T.J., Ferraris, J.P. and Cowan, D.O. Chem. Commun., (submitted for publication).

    Google Scholar 

  60. Bardeen, J. (to be published).

    Google Scholar 

  61. Fröhlich, H. (1954). Proo. Roy. Soc., A223, 296.

    Article  ADS  Google Scholar 

  62. Bardeen, J., Cooper, L.N. and Schrieffer, J.R. (1957). Phys. Rev. 108, 1175.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  63. (1973); New York Times, March 25, p. 43; (1973). Phys. Today, May Issue, p.17.

    Google Scholar 

  64. Bloch, A.N., Ferraris, J.P., Cowan, D.O. and Poehler, T.O. Solid State Commun., (submitted for publication).

    Google Scholar 

  65. Patton, B.R. and Sham. L.J. (to be published).

    Google Scholar 

  66. Epstein, A.J., Etemad, S., Garito, A.F. and Heeger, A.J. (1972). Phys. Rev., C5, 952.

    ADS  Google Scholar 

  67. Vegler, J.G., Kommandeur, J. and Fedders, P.A. (1973). Phys. Rev., B1, 2929.

    ADS  Google Scholar 

  68. Abrikosov, A.A., Gorkov, L.P. and Dzyaloshinski, I.E. (1963). Methods of Quantum Field Theory in Statistical Mechanics, (Prentice Hall, New Jersey), chapter 7.

    Google Scholar 

  69. Bogoliubov, N.N. (1959). Usp. Fiz. Nauk., 67, 843;

    Google Scholar 

  70. Valatin, J.G. (1958). Nuovo Cim., 7, 843.

    Article  MathSciNet  Google Scholar 

  71. Kuper, CG. (1955). Froc. Roy. Soc, A227, 214.

    Article  ADS  Google Scholar 

  72. Kohn, W. (1959). Phys. Rev. Lett., 2, 393.

    Article  ADS  Google Scholar 

  73. Ovchinnikov, A.A. (1965). Sov. Phys. Solid State, 7, 664.

    Google Scholar 

  74. Afanasev, A.M. and Kagan, Yu. (1963). Sov. Phys. JETP, 16, 1030;

    ADS  Google Scholar 

  75. Kaganov, M.I. and Semenenko, A.I. (1966). Sov. Phys. JETP, 23, 419.

    ADS  Google Scholar 

  76. Patton, B.R. (1971). Phys. Rev. Lett., 27, 1273.

    Article  ADS  Google Scholar 

  77. Labbé, J. and Friedel, J. (1966). J. Phys. (Paris), 27, 708.

    Article  Google Scholar 

  78. Horovitz, B., Gutfreund, H. and Weger, M. (1972). Solid State Commun., 11, 1361.

    Article  ADS  Google Scholar 

  79. Appel, J. (1968). Phys. Rev. Lett., 21, 1164.

    Article  ADS  Google Scholar 

  80. Allen, P.B. (1973). Solid State Commun., 12, 379.

    Article  ADS  Google Scholar 

  81. Rice, M.J. and Strässler, S. (Preprint). I wish to thank Professor D. Scalapino for bringing this to my notice.

    Google Scholar 

  82. Kohn, W. and Sherrington, D. (1970). Rev. Mod. Phys., 42, 1.

    Article  MATH  ADS  Google Scholar 

  83. Aslamazov, L.G. and Larkin, A.I. (1968). Sov. Phys. Solid State, 10, 875.

    Google Scholar 

  84. Furry, W.H. (1937). Phys. Rev., 51, 125.

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, University of California, San Diego, La Jolla, California, 92037, USA

    L. J. Sham

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  1. L. J. Sham
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Editors and Affiliations

  1. Department of Physics and Institute for Applied Mathematics, University of Antwerp, Antwerp, Belgium

    J. T. Devreese

  2. Department of Physics, University of Illinois, Urbana, Illinois, USA

    A. B. Kunz

  3. Research Laboratories, A.R.L., Solid State Physics, Dayton, Ohio, USA

    T. C. Collins

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© 1974 Plenum Press, London

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Sham, L.J. (1974). Electronic Influence on Lattice Dynamics. In: Devreese, J.T., Kunz, A.B., Collins, T.C. (eds) Elementary Excitations in Solids, Molecules, and Atom. NATO Advanced Study Institutes Series, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2823-0_1

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  • DOI: https://doi.org/10.1007/978-1-4684-2823-0_1

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