Contribution of shear strains to the vibrational entropy of defect configurations

Abstract

Calculating the vibrational entropy of an N-atom assembly in the harmonic approximation requires the diagonalization of a large matrix. This operation becomes rapidly time consuming when increasing the dimensions of the simulation cell. In studies of point defects, a widely used shortcut consists in calculating the eigenmodes of the atoms contained in an inner region, called the defect region, while the atoms belonging to the outer region are held fixed, and in applying an elastic correction to account for the entropy stored in the distortion of the outer region. A recent paper proposed basing the correction on the local pressure change experienced by each lattice site. The present contribution is an extension in the sense that it includes shears. We compared the two approximations for configurations which are currently encountered in defect studies, i.e. defect formation and migration. The studied defects are the single, di- and trivacancy, as well as the dumbbell interstitial, in a host matrix modelled by several empirical potentials mimicking pure copper. The inclusion of shears adds a noticeable contribution to the elastic correction for all configurations of low symmetry.

Acknowledgements

We thank E. Clouet, C. Marinica, B. Legrand, Y. Limoge and L. Proville for valuable discussions and suggestions and J.P. Poirier (Académie des Sciences) for drawing our attention to Brillouin's papers.