Anharmonicity effects and thermal expansion of thermoelectric (M,M’,M”)NiSn (M,M’,M”=Ti, Zr, Hf) half-Heusler alloys

Abstract

High-resolution synchrotron radiation X-ray powder diffraction was used for the structural characterization of half-Heusler alloys with compositions MNiSn, M0.5M′0.5NiSn, and M0.5M′0.25M”0.25NiSn ((M, M′, M”) = Ti, Zr, Hf). These alloys were synthesized by arc melting and subsequent thermal annealing. Rietveld refinements of the room temperature patterns revealed that the unit cell parameter is larger for ZrNiSn and smaller for TiNiSn, in accordance with the respective atomic radii. The site occupation of each atomic species exhibited similar trends to those reported in the literature. The values of the linear coefficient of thermal expansion (α) for all the investigated phases within the alloys are < 10−5 K−1. In addition, the value of the Debye temperature (θD) is estimated by analyzing the temperature dependence of the isotropic atomic displacement parameters. In the case of these half-Heusler alloys, it is observed that a lower θD corresponds to a lower α. The good agreement between the temperature dependence of the Debye temperature and the calculated values using the Thirring-Stern expansion enables us to demonstrate the significant role of anharmonicity: the lighter the compound, the lower the anharmonicity. Furthermore, we also discuss the implications of anharmonicity on the thermal conductivity of this family of half-Heusler compounds at room temperature.