Elastic modeling of point-defects and their interaction

Abstract

Different descriptions used to model a point-defect in an elastic continuum are reviewed. The emphasis is put on the elastic dipole approximation, which is shown to be equivalent to the infinitesimal Eshelby inclusion and to the infinitesimal dislocation loop. Knowing this elastic dipole, a second rank tensor fully characterizing the point-defect, one can directly obtain the long-range elastic field induced by the point-defect and its interaction with other elastic fields. The polarizability of the point-defect, resulting from the elastic dipole dependence with the applied strain, is also introduced. Parameterization of such an elastic model, either from experiments or from atomic simulations, is discussed. Different examples, like elastodiffusion and bias calculations, are finally considered to illustrate the usefulness of such an elastic model to describe the evolution of a point-defect in a external elastic field.

A multi-scale model for stresses, strains and swelling of reactor components under irradiation

“…The addition of the two terms in (27) gives the density of body forces resulting from the accumulation of defects in the material…”

“…The availability of such data is still relatively limited as the majority of density functional calcul ations of defects performed so far focused on the accurate evaluation of energies of defects [42][43][44][45], rather than on the evaluation of elastic properties of defects [7,8,27,29,46]. The relaxation volume of a Frenkel pair can be approximated by the sum of relaxation volumes of an SIA and a vacancy.…”

“…The fundamental notions relating macroscopic strains and stresses to microstructure are the dipole tensor and relaxation volume of a defect object, which can be an individual point defect or a large cluster of such defects formed in a collision cascade. We show that the dipole tensor of a defect, which has so far only been applied to nano-scale point defects [7,25,27], can in fact be used for characterizing defect objects of arbitrary size. This is a mere consequence of the fact that there is no characteristic spatial scale in elasticity equations.…”

“…Equation (1) fully defines the strain field generated by a defect cluster at distances that are much greater than its characteristic spatial extent. It is well established how to compute elastic dipole tensors of point defects [7,27,29]. Below, we show how elastic dipole tensors can be defined and evaluated for defect clusters produced by the collapse of entire high-energy collision cascades.…”

“…The volume dipole tensor density, and the density of relaxation volumes of defects, vary from one point in the material to another, depending on the local degree of exposure of a material to irradiation. The dipole tensor can be defined independently of the nature of a defect object, for example, it can be defined for a point defect, a dislocation loop [7,27,31], or a fairly complex configuration of atomic displacements produced by a collision cascade as a whole. In the latter case, although the volume of the spatial region involved in the calculation of P kl contains a large number of atoms, it is still small in comparison with the size of a reactor component, justifying the fundamental approximation on which equation (1) is based.…”