PHYSICAL REVIEW B 89, 205203 (2014) Thermal physics of the lead chalcogenides PbS, PbSe, and PbTe from first principles Jonathan M. Skelton, 1 Stephen C. Parker, 1 Atsushi Togo, 2 Isao Tanaka, 2, 3 and Aron Walsh 1 , * 1 Department of Chemistry, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom 2 Elements Strategy Initiative for Structural Materials, Kyoto University, Kyoto Prefecture 606-8501, Japan 3 Department of Materials Science and Engineering, Kyoto University, Kyoto Prefecture 606-8501, Japan (Received 12 March 2014; revised manuscript received 23 April 2014; published 15 May 2014) The lead chalcogenides represent an important family of functional materials, in particular due to the benchmark high-temperature thermoelectric performance of PbTe. A number of recent investigations, experimental and theoretical, have aimed to gather insight into their unique lattice dynamics and electronic structure. However, the majority of first-principles modeling has been performed at fixed temperatures, and there has been no comprehensive and systematic computational study of the effect of temperature on the material properties. We report a comparative lattice-dynamics study of the temperature dependence of the properties of PbS, PbSe, and PbTe, focusing particularly on those relevant to thermoelectric performance, viz. phonon frequencies, lattice thermal conductivity, and electronic band structure. Calculations are performed within the quasiharmonic approximation, with the inclusion of phonon-phonon interactions from many-body perturbation theory, which are used to compute phonon lifetimes and predict the lattice thermal conductivity. The results are critically compared against experimental data and other calculations, and add insight to ongoing research on the PbX compounds in relation to the off-centering of Pb at high temperatures, which is shown to be related to phonon softening. The agreement with experiment suggests that this method could serve as a straightforward, powerful, and generally applicable means of investigating the temperature dependence of material properties from first principles. DOI: 10.1103/PhysRevB.89.205203 PACS number(s): 05.70.−a, 31.15.A−, 72.20.Pa I. INTRODUCTION The lead chalcogenides have attracted much attention in recent years, in particular due to the excellent high-temperature thermoelectric performance of PbTe [1]. Thermoelectric ma- terials interconvert heat and electricity [2], and have important applications in the recovery of waste heat, e.g., from industrial processes, and “green” energy [3]. The figure of merit for thermoelectrics is ZT = S 2 σT/(κ L + κ E ), where S is the Seebeck coefficient, σ is the electrical conductivity, and κ L and κ E are the lattice and electronic thermal conductivities, respectively. Widespread application requires a ZT value above 2 at the target operating temperature [4]. The PbX materials have low intrinsic lattice thermal conductivities, and by reducing these further through nanostructuring, Biswas et al. recently achieved a breakthrough ZT value of 2.2 [5]. The chalcogenides also have interesting electrical properties, in particular a high-temperature band convergence that levels out the increase in the electronic gap with temperature [6–8]. Engineering the electronic structure by doping (e.g., with Tl) [9] can further improve the electrical properties, while alloys of the chalcogenides, e.g., PbTe 1−x Se x , can have improved electrical properties and reduced lattice thermal conductivity [7,10]. In a bid to further improve performance, and to identify similarly good thermoelectrics, much research has been under- taken to understand these unique properties at a fundamental level. Various experimental studies have found that the lead chalcogenides exhibit strongly anharmonic lattice dynamics [11–13], which are thought to contribute to their low lattice conductivity. Pronounced thermally induced distortions to * Author to whom correspondence should be addressed: a.walsh@bath.ac.uk the atomic positions have been observed experimentally [11,13,14] and in molecular-dynamics calculations [15], which would give rise to strong phonon-scattering mechanisms. Similarly, large off-centering of the Pb cation in the rocksalt lattice has been reported [11,13], even at moderate temper- atures, although the magnitude of the off-site displacement is still under debate [14]. Electrical properties are equally important to the thermoelectric activity, and as such the band convergence has been extensively characterized [6–8], and the effect of thermal disorder on the band structure has been studied theoretically [15]. A number of studies have made use of first-principles modeling to study the PbX systems, typically within the Kohn-Sham density-functional theory (DFT) formalism [16]. Most have focused either on the electronic structure [17,18], or on lattice dynamics and thermal conductivity [10,19–23]. Some studies have also considered the effect of pressure on material properties [19,22], and the studies in Refs. [15,21] and [24] used first-principles calculations to investigate the temperature dependence of some of the material properties. Aside from these latter works, first-principles electronic structure modeling typically does not take temperature into account explicitly, except through the use of experimental (e.g., room temperature) lattice constants. This is not ideal, since the equilibrium lattice constant at a given temperature can depend critically on the choice of DFT functional, and therefore calculations using the experimental lattice constant may be modeling a different temperature with respect to the DFT free-energy surface. Moreover, when modeling thermoelectric materials, particularly high-temperature thermoelectrics such as PbTe, it is important to complement fixed-temperature calculations with studies of the effect of temperature on the material properties. We have performed a comparative lattice-dynamics study of the effect of temperature on the physical properties, 1098-0121/2014/89(20)/205203(10) 205203-1 ©2014 American Physical Society