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Prog. Theor. Phys. Vol. 64 No. 6 (1980) pp. 1945-1958

[ Full Text PDF : FREE ACCESS (880K) ]

The Effect of External Force on Surface Stability by the Self-Consistent Einstein Model

Masaru Sugiyama and Hiroshi Okamoto

Department of Engineering Sciences, Nagoya Institute of Technology, Nagoya 466

(Received August 4, 1980)

Abstract:

Effects of an external force on the surface lattice dynamics, such as anharmonic surface vibration, surface relaxation of the lattice constant and thermal stability of the surface, are studied by the use of the one-dimensional self-consistent Einstein model with emphasis on material strength. A new numerical method to solve the basic equations revealed surface instability phenomena. Above a critical temperature determined by the external force, the mean square displacements and the lattice constants satisfying the basic equations are not found. Under a tensile force, the system is unstable and will fracture when the force is stronger than a critical one which is cosiderably lower than the ideal strength.


URL : http://ptp.ipap.jp/link?PTP/64/1945/
DOI : 10.1143/PTP.64.1945

[ Full Text PDF : FREE ACCESS (880K) ] Citation:

References:

  1. Y. Ohde and H. Okamoto, J. Mater. Sci. 15 (1980), 1539[CrossRef].
    H. Okamoto and Y. Ohde, Polymer 21 (1980), 859.
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  5. See, for example, Dynamical Properties of Solids, ed. G. K. Horton and A. A. Maradudin (North-Holland, Amsterdam, American Elsevier, New York, 1974, vol. 1).
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  7. An extension of the theory to the lower temperature side is studied in the last one of Ref. 6).
  8. S. Naya, M. Iziri and T. Ishii, Prog. Theor. Phys. 60 (1978), 1604[PTP].
  9. L. A. Girifalco and V. G. Weizer, Phys. Rev. 114 (1959), 687[APS].
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Citing Article(s) :

  1. 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
    Masaru Sugiyama
  2. Journal of the Physical Society of Japan 61 (1992) pp. 2260-2268 :
    A Unified Approach to Nonequilibrium Phenomena in a Crystalline Lattice. I. Formulation
    Masaru Sugiyama
  3. Journal of the Physical Society of Japan 64 (1995) pp. 1-4 :
    Reflection of Nonlinear Waves in Crystal Lattices at Finite Temperatures, and Dynamic Fracture
    Masaru Sugiyama, Naoki Kameyama and Kouji Mizuno
  4. 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
  5. 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
  6. 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

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