Modeling the molecular dynamics of liquid metals at high pressures: Liquid potassium

A way of building potassium models by molecular dynamics using the embedded atom model (EAM) is developed. The contribution from pairwise interaction is presented as power series at an interpartial distance. Embedded potential parameters are determined by the experimental dependence of pressure on volume for a static compression of potassium at 300 K to a pressure of 53 GPa (potential A). By using potential A to describe shock compression and choosing the appropriate temperature at given degree of compression (up to 40000 K at compression to 0.29 of initial volume) it is shown that the model pressure can be made equal to the pressure indicated by the Rankine-Hugoniot relations. The model energy is lower than the actual energy determined by the relations, and the difference in energies increases with temperature almost linearly; such growth corresponds to an excess average heat capacity of about 11.6 J/(mol K), compared to the model heat capacity. It is established that the reasons for this divergence are the inability of the EAM potential to describe the temperature dependency of metal properties precisely, and the appearance of an energy contribution upon heating that is dependent on temperature but not on atom coordinates. Adding another summand to the potential energy (which is dependent on temperature only) allows us to match the heat capacities of real potassium and the models. The dependence of potassium's melting temperature on pressure is calculated. The calculated melting temperature at 41.2 GPa is 1231 K. Additional data (e.g., the actual temperature on the Rankine-Hugoniot curve and precise quantum mechanics calculations of heat capacity at extreme conditions) is required to eliminate potential ambiguity.