Quasiharmonic Vibrational Properties of TiNiSn from Ab Initio Phonons DAEHYUN WEE, 1,4 BORIS KOZINSKY, 2 BARBARA PAVAN, 3 and MARCO FORNARI 3 1.—Department of Environmental Science and Engineering, Ewha Womans University, Seoul 120-750, Republic of Korea. 2.—Research and Technology Center, Robert Bosch LLC, Cambridge, MA 02142, USA. 3.—Department of Physics, Central Michigan University, Mt. Pleasant, MI 48859, USA. 4.—e-mail: dhwee@ewha.ac.kr We report an ab initio study of vibrational and thermodynamic properties of TiNiSn, a half-Heusler alloy that has been investigated in the context of thermoelectrics, based on density functional theory and density functional perturbation theory. The quasiharmonic approximation, where the Helmholtz free energy obtained from phonons of multiple strained structures is fitted to a model equation of state, is employed to estimate thermodynamic properties. Good quantitative correspondence is achieved between experimental obser- vations and our theoretical calculation for various thermodynamic quantities: lattice parameter, thermal expansion coefficient, and heat capacity. Estimates of lattice thermal conductivity are also provided by using a semianalytic model previously proposed in the literature. Though this yields good qualitative agreement, a more accurate ab initio approach that explicitly includes anharmonic interactions between atoms should be employed for quantitative predictions of thermal conductivity. Key words: Thermoelectrics, half-Heusler compound, thermal expansion, thermal conductivity INTRODUCTION Thermoelectric energy conversion provides a fully solid-state solution for power generation. Without any moving parts to be integrated, it is an attractive alternative option to conventional heat engines for compact waste heat recovery systems. Typically, the efficiency of thermoelectric energy conversion is presented in terms of the temperature of each heat reservoir and the thermoelectric figure of merit ZT = a 2 T/qj, where a is the Seebeck coefficient, q is the electric resistivity, j is the thermal conductivity, and T is the temperature, leading to the following traditional expression: g 0 ¼ T h  T c T h ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ZT þ 1 p  1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ZT þ 1 p þ T c =T h ; (1) where ZT is typically evaluated at the mean tem- perature (T m ) of the hot-side temperature T h and the cold-side temperature T c . An increase in ZT results in an increase in the conversion efficiency, and sig- nificant efforts have been exerted to create materials with high ZT values. Thin films 1 and materials with grain boundaries 2 have been investigated, showing various degrees of success in improving ZT. Several half-Heusler alloys are promising as high- performance thermoelectric materials and have been also widely studied. 3–12 Chemically, they form ternary compounds with equiatomic composition ABX, where A and B are transition metals, and X is usually a p-block element. The compositions most studied have the form MNiSn or MCoSb (M = Ti, Zr, Hf). The structural archetype of these half-Heusler alloys is MgAgAs, belonging to space group F  43m (no. 216). One conventional unit cell contains four primitive units, with A atoms in the 4b Wyckoff positions (1/2, 1/2, 1/2), B atoms at 4c (1/4, 1/4, 1/4), and X atoms at 4a (0, 0, 0), as shown in Fig. 1. Thermoelectric half-Heusler alloys typically exhibit good electronic properties but relatively high thermal conductivity. 3 Reduction of thermal (Received May 29, 2011; accepted November 23, 2011; published online December 9, 2011) Journal of ELECTRONIC MATERIALS, Vol. 41, No. 6, 2012 DOI: 10.1007/s11664-011-1833-4 Ó 2011 TMS 977