Homogeneous deformation theory with three-body interaction: Second- and third-order elastic constants of noncentrosymmetric crystals

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Abstract
A general homogeneous deformation theory is developed for an arbitrary nonionic crystal structure, which lacks a center of inversion. The strain-energy density is expanded as a power series in macroscopic and internal strains. Expressions are derived for the second- and third-order elastic constants in terms of the coefficients of expansion, and for these coefficients in terms of the interaction potential. Two types of potentials are considered—a two-body central potential and a three-body potential that depends on two scalar distances between the interacting particles. The final expressions obtained are much simpler than those of previous work, in terms of force-constant matrix elements.