Sn is commonly used in shock simulations to study the behaviour of metals under shock loading. However, there has been a tough problem of the complex phase transitions of Sn under high pressure. Current empirical potentials for Sn can not accurately describe the phase transitions of Sn. For instance, the embedded atom method (EAM) model by F. Sapozhnikov et al. [1] is fitted to bct and bcc phases at high pressure, but fails to describe phase at lower pressure. The modified embedded atom method (MEAM) model parameterized by Ravelo and Baskes et al.[2] are mostly fitted to low pressure phases of  and β, but cannot ensure accuracy on bct and bcc states. On the other hand,  ab initio methods such as density functional theory (DFT) can describe phase transitions under static states, but are too expensive to be applied to shock simulations.  Deep Potential (DP) method points out a new solution to the trade-off between accuracy and efficiency with the assistance of machine learning. We construct a DP model for Sn intended for shock simulation by training the data labeled with DFT calculations with SCAN exchange-correlation functional. The data covers a range of 0 - 100 GPa and 0 - 5000 K, including the common phases of Sn under both low and high pressure. To better describe dissociation from the surface, structures with a vacancy layer are also added into training data. Examinations show that our DP model can reproduce both the static properties of DFT calculation and the dynamic behaviour in experiments including Hugoniot curve and high pressure melting points, indicating it a promising trial to introduce ab initio accuracy into shock simulations.

References [2]  R. Ravelo and M. Baskes, Equilibrium and thermodynamic properties of grey, white, and liquid tin, Phys. Rev. Lett. 79, 2482 (1997).
 

tin,deep learning,density functional theory,meta-GGA,high temperature and high pressure,molecular dynamics