Lattice distortion around a vacancy in magnesium

Using the D₃ₕ point-group symmetry of an atom in magnesium and the defect-space matrix-partitioning technique, the perfect- and defect-crystal Green's functions are calculated in a two-neighbor defect-space model in an axially symmetric host lattice. The magnitude of the lattice distortions for the first two shells is found to be {~} 0.004 times the basal lattice constant, and the relaxation energy Eᵣ of the vacancy is 0.0026 eV. Approximating the medium by an elastic continuum, but using values of the strength tensor corresponding to four different lattice models, the change in volume ΔV of the medium is found to vary from -0.03 to -0.11 times the atomic volume and the relaxation energy is found to vary from 0.0014 to 0.014 eV. In the above approximation, expressions for ΔV and Eᵣ involving the bond-bending force constants are derived.