Ural Federal University Scientists Obtain Neural Network To Create A Molecular Dynamics Model Of Liquid Gallium
Scientists at the Institute of Metallurgy, Ural Branch of the Russian Academy of Sciences, and Ural Federal University have developed a method for theoretically high-precision determination of the viscosity of liquid metals using a trained artificial neural network. The method was successfully tested in the process of building the deep learning potential of the neural network on the example of liquid gallium. Scientists were able to significantly increase the spatiotemporal scale of the simulation. The results of molecular dynamics modeling of liquid gallium are particularly accurate. Previous calculations were notoriously inaccurate, especially in the low temperature range. An article describing the research was published in the journal Computational Materials Science.
“First, liquids are in principle difficult to be described theoretically. The reason, in our opinion, lies in the absence of a simple initial approximation for this class of systems (for example, the initial approximation for gases is the ideal gas model). Secondly, the atomistic calculation of viscosity requires processing of a large volume of statistical data and, at the same time, a large accuracy of description of the potential energy surface and forces acting on atoms. Direct calculations cannot achieve such an effect. Thirdly, gallium in the liquid state is difficult to describe theoretically, because, due to certain features, its structure differs from that of most other metals,” explains Vladimir Filippov, Senior Researcher at the Department of Rare Metals and Nanomaterials at UrFU, research participant and co-author of the article.
Ural scientists solved the problem of modeling the molecular dynamics of liquid gallium by training an artificial neural network, which had previously been successfully applied to a wide range of materials. According to Vladimir Filippov, data from quantum-chemical simulations of energy and forces acting on atoms were used as a training set. Several thousand configurations of 500 atoms in the range from 303 (melting point) to 1400 kelvin (about 30-1130 degrees Celsius) were simulated.
“In a physical experiment, at temperatures above 1300 kelvin, liquid gallium vaporizes intensely, which leads to an uncontrollable change in the mass of the sample and, consequently, to a large error in the experiment. In molecular dynamic calculations, there is no such limitation,” explains Vladimir Filippov.
For each selected temperature value (303, 400, 600, 800, 1000, 1200, 1400 K), 4000 atoms and 10 different trajectories – successive positions of atoms in the system over time, calculated from equations of motion with different initial conditions for the velocity and coordinates of the atoms – were used.
“500 atoms were used to accurately calculate the total energy and forces acting on each atom using first-principle molecular dynamics and to create a deep learning potential for the neural network. In a system of 4,000 atoms, the resulting machine learning potential was used to calculate viscosity using classical molecular dynamics,” comments Vladimir Filippov.
The use of the created deep learning potential of the neural network for liquid gallium made it possible to increase the spatial and temporal scales of modeling. At the same time, the accuracy of molecular dynamics calculations corresponded to the first-principle one, which is based on calculations according to the laws of nature, without assuming additional assumptions.
To verify the simulation results, the scientists experimentally measured the viscosity of liquid gallium from the melting point (when viscosity values are at their highest) to 1270 K. For this purpose, they used an original automated apparatus for measuring the viscosity of high-temperature metallic melts, based on the method of attenuated torsional oscillations of a cylindrical crucible (beaker).
“In the experiment using this method, two quantities are measured: period and decrement of oscillations damping of the suspension system (decrement of damping is a quantitative characteristic of the speed of oscillations damping). The crucible with the investigated liquid is suspended on an elastic string inside a furnace with an inert helium atmosphere. During free torsional oscillatory movements of the suspension system, the internal friction, occurring in the liquid, causes attenuation of torsional oscillations and change of the oscillation period as compared to the period with an empty crucible,” describes Vladimir Filippov, who took part in creation of the experimental setup.
The higher the viscosity of the liquid, the faster the oscillations are attenuated, the scientist adds. Viscosity calculations also take into account frictional forces due to the gas environment around the crucible and imperfections in the suspension filament. This makes it necessary to measure the period and decrement of damping with an empty crucible under the same conditions as the liquid experiments. Viscosity measurements of liquid gallium were made in temperature steps of 10-50 K near the melting point and 100-150 K at high temperatures. At each temperature, the period and decrement of attenuation were measured after holding the liquid gallium for 30-40 minutes, until stable values of the measured quantities were obtained.
Verification showed that the viscosity calculations based on the simulation results are in excellent agreement with the data obtained in the experiment and, in the high temperature region, with the most reliable experimental data of other researchers. Moreover, the results obtained allow us to eliminate the ambiguity of the literature data on the viscosity of liquid gallium in the low-temperature range.
“Thus, it can be argued that the temperature dependence of the viscosity of liquid gallium presented in the article is the most reliable to date and can be used in further calculations of the phenomena and properties of liquid gallium, for example, in the search for regularities and anomalies in the relations of structural and dynamic features of the system. A file with the parameters of the developed – developed and effective – deep learning potential of the neural network to calculate the interatomic interaction in liquid gallium is available online,” emphasizes Vladimir Filippov.
The work was carried out within the framework of the state assignment of the Institute of Metallurgy, Ural Branch of RAS, and with the financial support of the Russian Foundation for Basic Research (Project No. 20-03-00370). An automated unit for measuring the viscosity of metal melts was created with the financial support of the Russian Science Foundation (Project No. 14-13-00676) and the Russian Foundation for Basic Research (Project No. 14-03-01126-a). Scientists from the Ural Branch of the Russian Academy of Sciences and Ural Federal University are planning to improve the developed deep learning capability of the neural network.