Ab initio calculations of pressure and temperature dependent elastic constants of lead.

Abstract

In the framework of DFT, we present a methodology that is as ab initio as possible for calculating the elastic constants in pressure and temperature. In this context, elastic constants are derived via the strain-fluctuation formalism involving Born, kinetic and stress fluctuation terms. AIMD trajectories in the isokinetic (NVT) ensemble are performed using the Abinit software to evaluate each term. Stress fluctuations are obtained directly from the trajectories. The Born term, on the other hand, is obtained by extracting several uncorrelated configurations from the trajectories and applying the energy-strain method. Bayesian inference is used to quantify the uncertainties associated with this procedure. As a result, the methodology enables elastic constants and their uncertainties to be evaluated for a wide range of materials. Admittedly, the whole approach has a high computational cost. In this paper, the method is then applied to solid lead in the fcc and hcp phases at various pressures and temperatures. The elastic constants obtained are linear as a function of temperature and pressure, and are qualitatively consistent with the experimental results available for the fcc phase. The major computational effort involved in obtaining a numerical ab initio reference database for lead can be used to test the accuracy of other approaches using surrogate models. .