Phase diagram of uranium from ab initio calculations and machine learning

Experimental studies of materials at extreme conditions are challenging, and as a consequence, P-T phase diagrams are still unknown for many elements and materials. In this work, we present the P-T phase diagram of uranium calculated up to extreme conditions. First, we searched for possible crystal structures using the evolutionary algorithm USPEX. Their free energies were then calculated using thermodynamic integration (TI) and temperature-dependent effective potential techniques. TI was performed using molecular dynamics, employing a machine learning (ML) force field trained on energies and forces from density-functional calculations at the generalized gradient approximation level. The prediction error of the ML force field for the energy was less than 10 meV/atom. Using thermodynamic perturbation theory (including first and second order corrections), from the free energies of the ML force field, we obtained free energies and phase diagram at the level of quality of the underlying density-functional calculations at pressures up to 800 GPa and temperatures up to 16 000 K.