Calculation of elastic constants by the method of crystal static deformation

The contribution of homogeneous lattice deformations (neglecting internal strains) to elastic properties of crystals with triclinic or higher symmetry is examined. The deformed lattice constants are expressed as functions of the components of the finite Lagrangian strain tensor, and their derivatives are calculated. Thus equations are obtained that relate the second-order elastic constants to first and second partial derivatives of the static crystal energy with respect to unit-cell parameters. With the assumption of a two-body Born-type interatomic potential, the energy derivatives were calculated analytically, and a rigid-body approximation was introduced to account for molecular groups in the crystal structure. Test computations of elastic constants were performed for MgF₂ (rutile-type), benzene and naphthalene, using literature potential parameters optimized on structural data; results are discussed with respect to adequacy of the potentials and of the approximations of the model used.