Modeling the pressure-dependent melting temperature of metals

Abstract

We present a model of pressure-dependent melting temperature to describe the physical fact that both cooling and pressurization can cause the solidification of liquid metal. Based on the Force-Heat Equivalence Energy Density Principle, an equivalent relationship between the heat energy variations during cooling and the mechanical work during pressurization is established as the molten metal solidifies. Then, this equivalent relationship is applied to develop a pressure-dependent melting temperature model without any adjustable parameter for metals. The model reveals the inner relationship between melting temperature, pressure, the bulk modulus and its first pressure derivative at zero pressure. The predicted results by our model are in good agreement with the available experimental data. Moreover, this study provides insights into the fundamental understanding of quantitative effect of pressure on melting temperature, which is in contrast to the well-known Lindemann's and Simon's equations that are both empirical melting temperature equations. It is worth noting that the melting curve of metals to very high pressure can be well predicted by our model only needing two experimental data at low pressures.