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Prog. Theor. Phys. Vol. 58 No. 3 (1977) pp. 767-776

[ Full Text PDF : FREE ACCESS (624K) ]

Self-Consistent Einstein Model and Theory of Anharmonic Surface Vibration. I

— One-Dimensional Model —

Takeo Matsubara and Kenji Kamiya

Department of Physics, Kyoto University, Kyoto 606

(Received March 29, 1977)

Abstract:

Softening of the surface lattice vibration and surface lattice relaxation are discussed on the basis of a self-consistent Einstein model, laying emphasis on the anharmonic effect. One-dimensional model is considered for the illustrative purpose. It is shown that the anharmonic effect is much more enhanced on and near the surface than in the interior.


URL : http://ptp.ipap.jp/link?PTP/58/767/
DOI : 10.1143/PTP.58.767

[ Full Text PDF : FREE ACCESS (624K) ] Citation:

References:

  1. See, for instance,
    R. E. Allen and F. W. de Wette, Phys. Rev. 180 (1969), 71[APS].
    R. F. Wallis, B. C. Clark and R. Herman, Phys. Rev. 167 (1968), 652[APS].
    R. E. Allen, F. W. de Wette and A. Rahman, Phys. Rev. 179 (1969), 887[APS].
  2. A. Blandin, Collective Properties of Physical System (Nobel Symposium 24) edited by B. Lundqvist and S. Lundqvist, (1974), p. 194.
  3. A. Nakanishi and T. Matsubara, J. Phys. Soc. Jpn. 39 (1975), 1415[JPSJ].
  4. T. Matsubara, J. Phys. Soc. Jpn. 40 (1976), 603[JPSJ].
  5. A similar argument based on the Debye model has been applied to a theory of melting:
    H. Fukuyama and O. M. Platzman, Solid State Commun. 15 (1974), 677[CrossRef].
  6. L. A. Girifalco and V. G. Weizer, Phys. Rev. 114 (1959), 687[APS].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 58 (1989) pp. 2612-2614 :
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    Masaru Sugiyama
  2. Journal of the Physical Society of Japan 59 (1990) pp. 833-842 :
    A Systematic Approach to the Evolution Equation of a Probability Distribution of a Deterministic Dynamical System
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  3. Journal of the Physical Society of Japan 59 (1990) pp. 4366-4375 :
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    Shinji Nambu and Masaki Oiji
  4. Journal of the Physical Society of Japan 61 (1992) pp. 2260-2268 :
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  5. Journal of the Physical Society of Japan 61 (1992) pp. 2269-2279 :
    A Unified Approach to Nonequilibrium Phenomena in a Crystalline Lattice. II. Linear-Wave-Analysis
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  6. Journal of the Physical Society of Japan 61 (1992) pp. 4367-4380 :
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  7. Journal of the Physical Society of Japan 62 (1993) pp. 163-169 :
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  8. Journal of the Physical Society of Japan 64 (1995) pp. 1-4 :
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    Masaru Sugiyama, Naoki Kameyama and Kouji Mizuno
  9. Journal of the Physical Society of Japan 68 (1999) pp. 1859-1863 :
    Statistical-Mechanical Study of the Collision between a Crystal Lattice and a Rigid Wall
    Masaru Sugiyama and Noriaki Sasaki
  10. Journal of the Physical Society of Japan 72 (2003) pp. 545-550 :
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  11. Journal of the Physical Society of Japan 74 (2005) pp. 631-637 :
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  12. Progress of Theoretical Physics Vol. 58 No. 4 (1977) pp. 1102-1113 :
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    Takeo Matsubara, Yūjirō Iwase and Akitaka Momokita
  13. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1407-1417 :
    Self-Consistent Einstein Model and Theory of Anharmonic Surface Vibration. II
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  14. Progress of Theoretical Physics Vol. 60 No. 5 (1978) pp. 1604-1605 :
    Note on the Penetration of Surface Vibration and the Melting Based on the Self-Consistent Einstein Model
    Shigeo Naya, Masaharu Iziri and Tetsuo Ishii
  15. Progress of Theoretical Physics Vol. 61 No. 4 (1979) pp. 1266-1268 :
    Comments on the Melting and the Size Dependence of Melting Temperature in Metallic Fine Particles
    Masaharu Iziri and Shigeo Naya
  16. Progress of Theoretical Physics Vol. 63 No. 2 (1980) pp. 357-367 :
    Note on Inverse Isotope Effect in Superconducting PdHx System. I
    Eiko Matsushita and Takeo Matsubara
  17. Progress of Theoretical Physics Vol. 64 No. 6 (1980) pp. 1945-1958 :
    The Effect of External Force on Surface Stability by the Self-Consistent Einstein Model
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  18. Progress of Theoretical Physics Vol. 68 No. 2 (1982) pp. 349-362 :
    Coninuum Approximation of the Self-Consistent Einstein Model under an External Force
    Masaru Sugiyama
  19. Progress of Theoretical Physics Vol. 69 No. 4 (1983) pp. 1074-1084 :
    A Simplified Theory of Melting for Lennard-Jones and Ionic Crystals Based on the Self-Consistent Einstein Model
    Tetsuo Ishii, Shigeo Naya and Satoshi Tanaka
  20. Progress of Theoretical Physics Vol. 71 No. 2 (1984) pp. 399-401 :
    Theory of Temperature Dependence of Surface Reconstruction
    Takeo Matsubara

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