The effect of clamped and free boundaries on long range strain coupling in structural phase transitions

In ferroelastic structural phase transitions, the atomic ordering in one cell creates a local strain field which is propagated elastically throughout the material, resulting in an effective or indirect coupling J(R _ij ) between the ordering in cells i and j. With free boundaries on the sample, the J(R _ij ) contains a Zener-Eshelby term J _Z of infinite range, which largely determines the transition temperature T _c. The present paper shows what happens when the boundaries are clamped. On cooling from a high temperature an anomaly takes place at more or less the same temperature as the phase transition for free boundaries. Cooling results in an irregular pattern of domains with positive and negative order parameter whose long range strains cancel. Two cases are distinguished. In the “tweed” case coherent domain boundaries form easily and result in fine lamellar domains. When coherent domain boundaries are not possible (the “non-Sapriel”) case, larger less regular domains are formed. In either case the macroscopic net strain adds up to zero.