Direct derivation of anisotropic atomic displacement parameters from molecular dynamics simulations in extended solids with substitutional disorder using a neural network potential.

Atomic displacement parameters (ADPs) are crystallographic information describing the statistical distribution of atoms around an atom site. Anisotropic ADPs by atom were directly derived from classical molecular dynamics (MD) simulations using a universal machine-learned potential. The (co)valences of atom positions were taken over recordings at different time steps in a single MD simulation. The procedure is demonstrated on extended solids, namely rocksalt structure MgO and three thermoelectric materials, AgSnSe, NaInSn and BaCuInP. Unlike the very frequently used lattice dynamics approach, the MD approach can obtain ADPs in crystals with substitutional disorder and explicitly at finite temperature, but not under conditions where atoms migrate in the crystal. The calculated ADP approaches 0 when the temperature approaches 0, and the ADP is proportional to the temperature when the atom is in a harmonic potential and the sole contribution to the actual non-zero ADP is from the zero-point motion. The zero-point motion contribution can be estimated from the proportionality constant assuming this Einstein model. ADPs from MD simulations could act as a tool complementing experimental efforts to understand the crystal structure including the distribution of atoms around atom sites.