Influence of elastic energy on the microstructure of nano TiNi₂Sn precipitates within a Half-Heusler TiNiSn matrix

The precipitation of the Heusler TiNi₂Sn phase in TiNiSn half-Heusler alloys during the aging treatment of the alloys has a beneficial effect on their thermoelectric properties. In this study, we estimate the role of elastic energy on the evolution of the precipitates' morphology in these alloys, emphasizing the influence of elastic inhomogeneity compared to published experimental observations. TiNi₂Sn precipitates exhibiting minimal elastic energy in the geometrical shape of a disk with a low aspect ratio at a {100} orientation. Experimentally, disk-shaped precipitates with an aspect ratio (c/a) of about 1/9 along different 〈100〉 directions are observed at the peak-aged condition. The restriction on a coherent thin precipitate necessitates a tetragonal deviation from the cubic structure. The calculated tetragonality for TiNi₂Sn precipitates is about 1.07, which agrees with the experiment. As is common in many metallic alloys, the precipitates in TiNiSn are partially ordered due to elastic interactions. Pair elastic interaction energy favors thin-face to thin-face configurations and a particular head-to-tail arrangement that is an outcome of the elastic inhomogeneity of the material. All these configurations align well with experimental observations.