Estimating thermal conductivity and thermoelectricity in PbTiO$_3$ from first principles

A combination of density functional theory and Boltzmann transport equation is used in this study to calculate the lattice thermal conductivity ($\kappa_{\rm L}$) of PbTiO$_3$ (PTO). We cannot apply this procedure to determine $\kappa_{\rm L}$ in presence of imaginary phonon modes ("soft modes"). Hence the tetragonal structure of PTO is used in these calculations, and the predicted $\kappa_{\rm L}$ is extrapolated to higher temperature using insights from experiments. The computed $\kappa_{\rm L}$ of PTO is low, possibly due to the anharmonicity associated with the ferroelectric/paraelectric transition. Electronic transport parameters such as the Seebeck coefficient and the electrical conductivity are also determined (under constant scattering time approximation in semiclassical Boltzmann theory) for PTO. The low $\kappa_{\rm L}$ and the electronic transport parameters together indicate excellent thermoelectric properties of PTO ($zT >$ 1.5 at 1000 K). As a technologically important ferroelectric/piezoelectric material, PTO is used in alloys and in layered structures. These morphologies could bring down the $\kappa_{\rm L}$ further, improving its thermoelectric performance. Synthesis of electrically conducting samples of PTO would allows us to verify the above predictions.