A first-principles study of the temperature-dependent diffusion coefficients of silver in the thermoelectric compound PbTe

PbTe-based compounds establish an important class of thermoelectric (TE) materials due to their relatively high thermal-to-electrical energy conversion efficiency at the mid-temperature range (600 – 800 K). The Pb-Te-Ag system is of prime interest due to its potential of forming Ag-rich precipitates dispersed in the PbTe-matrix. Investigation of the microstructure evolution of this system enables us to predict the applicability regime of this system in service temperatures, and this involves both thermodynamic and kinetic aspects. Herein, we apply first-principles calculations to evaluate the diffusion coefficients of Ag in a PbTe matrix. Based on unique combination between calculations of point defect formation energies, electronic density of states (DOS), and electron localization function (ELF), we conclude that diffusion of Ag in PbTe in the interstitial mechanism is preferable compared to the vacancy or substitutional mechanism. We determine both the activation energy for diffusion and the pre-exponential diffusion coefficient for an interstitial mechanism, applying the transition state theory (TST), to be 1.08 × 10⁻⁵ cm²·s⁻¹ and 52.9 kJ·mole⁻¹, respectively. This study provides us with practical tools to evaluate the kinetics of phase transformations in these compounds by improving our ability to control nucleation and growth of Ag-rich precipitates in PbTe. This, eventually, provides us with predictive information on the thermal stability of PbTe-based compounds.