A theory for elastic properties of single crystals with microstructure and its application to diffusion induced segregation

Abstract

In this article a general theory for elastically stressed single crystals in the presence of microstructure is presented and an explicit formula for the resulting non-linear stored mechanical energy is obtained. The optimal microstructure under applied stress is characterised and the optimal laminates are identified in 2D. The analysis is based on a sharp lower estimate of the energy that relies on relaxation. The new theory is then used to extend existing models for diffusion induced segregation (DIS) in the case of (Zn,Fe)S single crystals. Numerical simulations based on finite elements are carried out and the results are compared with former computations of the homogeneous case.

On the Allen—Cahn/Cahn—Hilliard system with a geometrically linear elastic energy

“…We point out that for the new cases (ii) and (iii), the formulas collected in Section 4 for the specific energy W are essential for any numerical studies of the AC-CH models extended to microstructure. For related investigations and numerical methods we refer the interested reader to [7] and [8]. Besides the limiting assumption of constant temperature (cf.…”