Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals

TL;DR

This paper extends the elastostatic Green function tensor method to analyze electrostriction in cubic, hexagonal, and orthorhombic crystals, providing explicit tensor derivations and emphasizing the importance of polarization gradient coupling.

Contribution

It introduces a generalized tensor approach for electrostriction in various crystal symmetries and highlights the significance of polarization gradient coupling in free energy models.

Findings

Explicit tensor kernels derived for different crystal symmetries

Illustration of physical meaning through simple examples

Emphasis on the systematic inclusion of polarization gradient coupling

Abstract

The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials.