Effect of intrinsic defects on the thermal conductivity of PbTe from classical molecular dynamics simulations

Abstract

Despite being the archetypal thermoelectric material, still today some of the most exciting advances in the efficiency of these materials are being achieved by tuning the properties of PbTe. Its inherently low lattice thermal conductivity can be lowered to its fundamental limit by designing a structure capable of scattering phonons over a wide range of length scales. Intrinsic defects, such as vacancies or grain boundaries, can and do play the role of these scattering sites. Here we assess the effect of these defects by means of molecular dynamics simulations. For this we purposely parametrize a Buckingham potential that provides an excellent description of the thermal conductivity of this material over a wide temperature range. Our results show that intrinsic point defects and grain boundaries can reduce the lattice conductivity of PbTe down to a quarter of its bulk value. By studying the size dependence we also show that typical defect concentrations and grain sizes realized in experiments normally correspond to the bulk lattice conductivity of pristine PbTe.

Thermal conductivity of porous polycrystalline PbTe

“…For this study, we ran MD simulations using a bicrystal, the force field of Ref. [10], and an additional artificial potential, u ξ , applied to the atoms of one of the grains forming the simulation box. This artificial potential corresponds to predefined forces added to the atoms at the grain boundary to favor the growth of one grain.…”

“…In an MD simulation at constant temperature, the diffusion coefficient is calculated from the mean square displacements of the closest atom to each of the n vacancies in the simulation box for a time t. r i (t) is the position of the atom i at time t. All MD simulations performed in the present study were run using the force field of Ref. [10]. These simulations were run for up to 10 ns, with the longest simulations at lower temperatures, where the number of vacancy jumps is smaller, as in this case the diffusion coefficient may be overestimated.…”

“…Note that while κ b (T ) depends on the fast phonon dynamics, the processes of grain growth happen on much longer time scales described by our phase-field simulations and are irreversible. The grain boundary width δ gb and Kapitza resistance R K were studied using MD by the direct method with voids at the grain boundary [56,10]. δ gb increases with temperature as δ gb = δ 0 (T m − T ) −1/2 , where T m = 924 • C is the melting temperature [57] and δ 0 = 289 nm K 1/2 is a fitting parameter for data collected from Ref.…”

“…δ gb increases with temperature as δ gb = δ 0 (T m − T ) −1/2 , where T m = 924 • C is the melting temperature [57] and δ 0 = 289 nm K 1/2 is a fitting parameter for data collected from Ref. [10]. R K is inversely proportional to the heat capacity and is constant above the Debye temperature [58].…”

“…In this work, we implement a phase-field method whose materialspecific parameters are determined from MD simulations and energy-minimization calculations. For concreteness, we focus on one material: lead telluride (PbTe), one of the most widely studied and used thermoelectric material at intermediate temperatures, largely thanks to its low lattice thermal conductivity, with κ ≈ 2 Wm −1 K −1 at 300 K. This thermal conductivity can be reduced in the presence of vacancies and grain boundaries, which can separately bring this value down to ∼ 0.5 Wm −1 K −1 [10]. In the regimes of high densities of point or planar defects, this conductivity becomes practically independent of temperature, as predicted by phenomenological models.…”