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Chinese Physics, 2002, Vol. 11(4): 332-338    DOI: 10.1088/1009-1963/11/4/305
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A general Möbius inversion transform formula for hcp lattices and its application

Li Mi (李泌)a, Li Yi-Shan (李一山)b
a  Department of Physics, Beijing University of Science and Technology, Beijing 100083, China;  College of Applied Sciences, Beijing Polytechnic University, Beijing 100022, China
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.
Keywords:  lattice theory      interatomic potentials and forces      phonon dispersions  
Received:  08 October 2001      Revised:  11 December 2001      Accepted manuscript online: 
PACS:  63.20.D- (Phonon states and bands, normal modes, and phonon dispersion)  
  61.50.Lt (Crystal binding; cohesive energy)  
  05.50.+q (Lattice theory and statistics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 59771044).

Cite this article: 

Li Mi (李泌), Li Yi-Shan (李一山) A general Möbius inversion transform formula for hcp lattices and its application 2002 Chinese Physics 11 332

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