A weak compatibility condition for precipitation with application to the microstructure of PbTe-Sb2Te3 thermoelectrics

In martensitic phase transformations it has been appreciated since the 1950s that elastic compatibility plays an important role in determining the morphology of microstructure resulting from the phase transformation [1, 2, 3, 4]. Recently, new links have been established between conditions of compatibility and other properties, such as hysteresis [5, 6], thermal stability and fatigue under repeated transformation [7], and functional properties [8, 9, 10] of transforming materials. For example, in alloys of TiNiCuPd whose composition has been tuned to satisfy the special compatibility condition λ2 = 1, where λ2 is the middle eigenvalue of the transformation stretch matrix [2, 5], it is found that the thermal hysteresis drops precipitously from about 60 K to near zero as λ2 → 1. In TiNiPd the existence of the corresponding compatible interface between austenite and a single variant of martensite was confirmed [11] by high-resolution transmission electron microscopy. Other examples of a significant relation between λ2 ≈ 1 and properties are emerging in Heusler alloys [12, 13], oxides [14], multiferroic materials [15], battery materials [16] and oxyacid materials used in fuel cells [17]. Diffusional phase transformations, particularly those which show clear evidence of dislocations at the boundary of precipitates and therefore are considered semi-coherent at best, are not thought to be influenced by conditions of elastic compatibility. We explore in this paper a weaker condition of compatibility between phases than λ2 = 1 in the context of a diffusional phase transformation in the thermoelectric system PbSbTe. In this system Sb2Te3 Widmanstätten type precipitates grow in a ∗now at the Department of Metallic Materials, School of Materials Science and Engineering, South China University of Technology, 381 Wushan Road, Guangzhou 510640, PR China