A machine learning methodology to investigate the lattice thermal conductivity of defected PbTe

Defect engineering, used to scatter phonons, is a widely used methodology to suppress the lattice thermal conductivity and improve the thermoelectric performance. Thus, understanding the effects of defects on the lattice thermal conductivity is an essential issue. However, the current thermal conductivity calculation methods are limited by either efficiency or accuracy in dealing with the defects: achieving the high order force constants for solving the phonon Boltzmann transport equations is time consuming; the traditional Debye-Callaway (DC) model ignores the local geometry relaxations around defects. The potentials used in molecular dynamics simulations are usually the empirical potentials. Utilizing the machine learning methodology, we train the deep neural network potential (NNP) for the defected PbTe compound, a remarkable thermoelectric material with large potential applications. The NNP is validated using the static energy, mechanical properties, kinetic properties, and phonon dispersions of PbTe systems. With the accurate NNP, the corresponding lattice thermal conductivity is then calculated using the molecular simulations (MD) under the Green-Kubo (GK) approximations, which balances the computational cost and accuracy. For the pristine PbTe compound, the simulated lattice thermal conductivities are in good agreement with experimental measurements. For the intrinsic point defected PbTe system, our NNP + MD + GK produces reasonable lattice thermal conductivities compared to those from the DC model. By comparing the simulated results with those using the DC model, we provide a strain correction factor f(0) in the DC model of defect strain effects on the lattice thermal conductivity. From our simulations, the grain boundaries in PbTe scatter the medium wavelength phonons and significantly suppress the lattice thermal conductivity. In addition, the synergistic effect of twin boundaries and point defects could further reduce the lattice thermal conductivity. Our work provides a theoretical methodology not only to simulate heat transport in the defected material but also understand the phonon scattering behaviors of different defects.