中国物理B ›› 2002, Vol. 11 ›› Issue (4): 332-338.doi: 10.1088/1009-1963/11/4/305

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A general M?bius inversion transform formula for hcp lattices and its application

李一山1, 李泌2   

  1. (1)College of Applied Sciences, Beijing Polytechnic University, Beijing 100022, China; (2)Department of Physics, Beijing University of Science and Technology, Beijing 100083, China
  • 收稿日期:2001-10-08 修回日期:2001-12-11 出版日期:2002-04-13 发布日期:2005-06-13
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 59771044).

A general Möbius inversion transform formula for hcp lattices and its application

Li Mi (李泌)a, Li Yi-Shan (李一山)b   

  1. a  Department of Physics, Beijing University of Science and Technology, Beijing 100083, China; b  College of Applied Sciences, Beijing Polytechnic University, Beijing 100022, China
  • Received:2001-10-08 Revised:2001-12-11 Online:2002-04-13 Published:2005-06-13
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 59771044).

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摘要： In this paper, we present a general M?bius inversion transform formula for hcp lattices. This formula can be applied to hcp lattices with a non-ideal c/a value and to obtain the pair potential between atoms in these lattices from the cohesive energy. Also, the three-body interaction among atoms in the lattices can be taken into account in the method. This method gives a useful means to obtain interatomic interactions in the interatomic force model. The method has been applied to zinc, and the pair potential obtained is used to calculate the phonon dispersion relations for some high-symmetry directions. It is found that, by properly considering a three-body interaction, one can acquire satisfactory results.

Abstract: In this paper, we present a general M?bius inversion transform formula for hcp lattices. This formula can be applied to hcp lattices with a non-ideal c/a value and to obtain the pair potential between atoms in these lattices from the cohesive energy. Also, the three-body interaction among atoms in the lattices can be taken into account in the method. This method gives a useful means to obtain interatomic interactions in the interatomic force model. The method has been applied to zinc, and the pair potential obtained is used to calculate the phonon dispersion relations for some high-symmetry directions. It is found that, by properly considering a three-body interaction, one can acquire satisfactory results.

Key words: lattice theory, interatomic potentials and forces, phonon dispersions

中图分类号:  (Phonon states and bands, normal modes, and phonon dispersion)

  • 63.20.D-
61.50.Lt (Crystal binding; cohesive energy) 05.50.+q (Lattice theory and statistics)