Many-body forces in solids and the Brugger elastic constants. II. Inner elastic constants

For pt.I see ibid., vol.8, no.18, p.2837 (1975). The method of homogeneous deformations is used to derive expressions for the first- and second-order inner elastic constants of a crystalline solid in which the energy density is composed of contributions from many-body interaction terms of various order. These results are obtained by a straightforward extension of the techniques of part I. The Lagrangian definition of strain is used to describe the macroscopic strain of the lattice, and a rotationally invariant measure of inner displacement is used for the internal strain. This ensures that the elastic constants have the symmetry properties commonly associated with rotational invariance, at both zero and finite strain.