Modeling the high-pressure solid and liquid phases of tin from deep potentials with <i>ab initio</i> accuracy
Tao Chen, Fengbo Yuan, Jianchuan Liu, Hua-Yun Geng, Linfeng Zhang, Han Wang, Mohan Chen
Abstract
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 $\ensuremath{\alpha}$ (diamond structure), $\ensuremath{\beta}$, 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 $\ensuremath{\alpha}, \ensuremath{\beta}$, 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.