Viscosity of liquid gallium: Neural network potential molecular dynamics and experimental study

Abstract

Gallium traditionally comprises a difficult object for theoretical description due to its complex short-range order structure. In this paper, deep learning potential for liquid gallium was developed, which allowed to significantly increase spatiotemporal scale of molecular dynamics (MD) simulation with preserving ab initio accuracy. Such increasing of performance of MD simulations allowed to calculate temperature dependence of viscosity value for liquid Ga, for which there is a considerable ambiguity in the available literature data, especially in low temperature range. Since direct ab initio viscosity calculations are not possible, as they do not allow enough statistical data to be collected, we combine several theoretical approaches: ab initio MD, for the implementation of which we used the VASP program code; the method of artificial neural networks (ANN) to obtain an effective interatomic interaction potential (ANN potential) using the DeePMD program; a classical MD method (LAMMPS program code); and the recently proposed viscosity calculation approach – time-decomposition method, which uses averaging over a large number of trajectories obtained by the MD. Ab initio MD calculations for liquid gallium were conducted in a temperature range from 303 to 1400 K (500 atoms were used in a supercell and 10,000 of 1 fs steps were performed for each temperature). The obtained data for the surface of potential energy and forces acting on atoms were used as a training set for constructing the ANN potential, whose high quality is confirmed by its almost ideal reproduction of ab initio structure at the level of pair correlations. In turn, the ab initio radial distribution functions are close to the results of other works. Self-diffusion coefficient, calculated via MD with developed deep learning potential, coincides well with the theoretical and experimental results of other authors. Temperature dependence of the viscosity was also computed via MD with developed potential using 10 independent trajectories (4000 atoms and 200,000 fs each) for every temperature point. Calculated viscosity data is in a good agreement with literature data at high temperatures, however at low temperatures some literature data agrees with our computational result, while the others – not. To check the results of our simulation, we experimentally measured viscosity from the melting point to 1270 K using an original setup based on oscillating cup method. Obtained experimental results are in excellent agreement with the results of our simulations. Thus, since both methods (experimental and computational) are modern and independent, presented at this work temperature dependence of viscosity is probably the most reliable at this moment.