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Theory of the Interaction of Vacancies with Stress Fields in Metals. II. The Interaction between Vacancies and Dislocations

 

作者: D. Kuhlmann‐Wilsdorf,  

 

期刊: Journal of Applied Physics  (AIP Available online 1965)
卷期: Volume 36, issue 2  

页码: 637-646

 

ISSN:0021-8979

 

年代: 1965

 

DOI:10.1063/1.1714042

 

出版商: AIP

 

数据来源: AIP

 

摘要:

The theory developed in Part I is applied to the interaction energy between vacancies and dislocations for the case of elastic isotropy. In the elastic stress fields of dislocations, outside the dislocation cores, the vacancies are attracted into regions of compressional strain, as expected from the analogy with the Cottrell interaction between dislocations and substitutional atoms of a size smaller than the matrix atoms. Within dislocation cores, strains are much larger than in the elastic regions, but stresses are only moderately higher. Consequently, the two contributions to the binding energy which depend on normal strains rather than on normal stresses, namely, the electronic interaction energy and the change in the vibrational entropy, are much more important within cores than outside them and repel vacancies from regions of compressional strain. With the best possible estimates of core stresses and strains it is found that the electronic term is dominant in the cores at low temperatures, and the entropy term at high temperatures; therefore, vacancies are attracted into the dilated regions of dislocation cores with an interaction energy which rises linearly with the temperature.In near‐screw dislocations and in a range of mixed dislocations, the nominally ``compressed'' regions of the core are in fact dilated, because non‐Hookean behavior, superimposed on the symmetric strains which may be extrapolated from conditions existing outside the core, results in an over‐all dilatation. The interaction energy between vacancies and the cores of screw dislocations can therefore be significant, even though the contribution to it arising from the reduction of stored strain energy is small, and no Cottrell‐type interaction energy exists. According to the above results, climb of edge dislocations and of a range of mixed dislocations is more difficult than expected on the basis of previous theories, inasmuch as the vacancies are repelled from the most compressed region of the dislocation cores, which they must traverse if a dislocation is to climb by the absorption or emission of vacancies. This repulsion is smaller and may even be replaced by an attraction in mixed dislocations with predominant screw character, depending on the angle between the Burgers vector and the dislocation axis, and would explain why climb of edge dislocations sometimes seems to be inhibited whereas mixed and near‐screw dislocations climb. The interaction energies in the elastic stress field of dislocations at all temperatures, and in the cores at very low temperatures, is quite small, below 0.1 eV; at high temperatures in the cores, it may exceed 0.5 eV.

 

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