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Chinese Physics, 2006, Vol. 15(6): 1301-1309    DOI: 10.1088/1009-1963/15/6/028
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Dislocation energy and Peierls stress: a rigorous calculation from the lattice theory

Wang Shao-Feng (王少峰)
Institute for Structure and Function, Chongqing University, Chongqing 400044, China
Abstract  In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.
Keywords:  dislocation energy      Peierls stress      lattice theory  
Received:  10 June 2005      Revised:  14 February 2006      Accepted manuscript online: 
PACS:  61.72.Lk (Linear defects: dislocations, disclinations)  
  61.72.Bb (Theories and models of crystal defects)  
  62.20.D- (Elasticity)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10274057).

Cite this article: 

Wang Shao-Feng (王少峰) Dislocation energy and Peierls stress: a rigorous calculation from the lattice theory 2006 Chinese Physics 15 1301

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