Modeling the high-pressure solid and liquid phases of tin from deep potentials with ab initio accuracy

Constructing an accurate atomistic model for the high-pressure phases of tin (Sn) is challenging because the properties of Sn are sensitive to pressures. We develop machine-learning-based deep potentials for Sn with pressures ranging from 0 to 50 GPa and temperatures ranging from 0 to 2000 K. In particular, we find the deep potential, which is obtained by training the ab initio data from density functional theory calculations with the state-of-the-art SCAN exchange-correlation functional, is suitable to characterize high-pressure phases of Sn. We systematically validate several structural and elastic properties of the α (diamond structure), β, bct, and bcc structures of Sn, as well as the structural and dynamic properties of liquid Sn. The thermodynamics integration method is further utilized to compute the free energies of the α, β, bct, and liquid phases, from which the deep potential successfully predicts the phase diagram of Sn including the existence of the triple-point that qualitatively agrees with the experiment.