A theory of anharmonic lattice statics for analysis of defective crystals
This paper develops a theory of anharmonic lattice statics for the analysis of defective complex lattices. This theory differs from the classical treatments of defects in lattice statics in that it does not rely on harmonic and homogenous force constants. Instead, it starts with an interatomic potential, possibly with infinite range as appropriate for situations with electrostatics, and calculates the equilibrium states of defects. In particular, the present theory accounts for the differences in the force constants near defects and in the bulk. The present formulation reduces the analysis of defective crystals to the solution of a system of nonlinear difference equations with appropriate boundary conditions. A harmonic problem is obtained by linearizing the nonlinear equations, and a method for obtaining analytical solutions is described in situations where one can exploit symmetry. It is then extended to the anharmonic problem using modified Newton–Raphson iteration. The method is demonstrated for model problems motivated by domain walls in ferroelectric materials.
© 2006 Springer Science + Business Media B.V. Received: 10 October 2005; Accepted: 19 August 2006; Published online: 27 October 2006. The financial support of the Army Research Office under MURI grant No. DAAD19-01-1-0517 is gratefully acknowledged. We benefited from a discussion on polarization catastrophe with Professor P.B. Allen.