Elastic interaction of point defects in cubic and hexagonal crystals

The elastic interaction of two point defects in cubic and hexagonal structures has been considered. On the basis of the exact expression for the tensor Green’s function of the elastic field obtained by the Lifschitz–Rozentsveig for a hexagonal medium, an exact formula for the interaction energy of two point defects has been obtained. The solution is represented as a function of the angle of their relative position on the example of semiconductors such as III-nitrides and $\alpha$-SiC. For the cubic medium, the solution is found on the basis of the Lifschitz–Rozentsveig Green’s tensors corrected by Ostapchuk, in the weak-anisotropy approximation. It is proven that the calculation of the interaction energy by the original Lifschitz–Rozentsveig Green’s tensor leads to the opposite sign of the energy. On the example of the silicon crystal, the approximate solution is compared with the numerical solution, which is represented as an approximation by a series of spherical harmonics. The range of applicability of the continual approach is estimated by the quantum mechanical calculation of the lattice Green’s function.