Fundamentals of the anisotropy of elastic interactions between dilating particles in a cubic material

The anisotropic nature of the elastic interaction that prevails between point defects or precipitates, associated with pure dilational misfit strains, within an elastically linear cubic material, is well established theoretically as well as experimentally. In most natural materials the interaction is attractive when the particles are arranged along the <100> direction of the matrix. It is repulsive when they are arranged along the <110> or <111> directions. A detailed study of the elastic fields associated with the presence of a spherical dilating particle allows to provide insight into this anisotropic nature of the elastic interaction energy. The displacement fields, the strain fields and the stress fields associated with a dilating sphere in an isotropic and in a cubic matrix were calculated by direct three-dimensional integration using a Fast Fourier Transform algorithm. The sphere exerts a uniform radial pressure on its surroundings and the primary strains at each point can be traced back as being directly related to the elastic compliance in the radial direction. Continuity of displacements and system symmetry induce, however, significant changes in the elastic fields. The origin of these changes lies in the small strains along the hard <111> and <110> directions. A simple explanation to the elastic anisotropic interaction between neighbouring point defects or precipitates ensues from the dependence of the interaction energy on the sum of the normal stresses within neighbouring particles.