Typical Metal Material Melting Curves And Multiphase Equation Of State Of The Theoretical Calculations

The study on the relation of pressure, density and temperature of condensed matter is a foundational task of condensed physics. The accurate phase boundary is a key element to found an applied equation of state (EOS). Melting phase transition is a common phynomenon for most of matters. So, the study on melting curves has important significance in science and application to found theoretical model of equation of state. Several classical metals' melting curves are investigated. Then the Gray's three-phase equation of state for metals and the calculated melting curves are combined to calculate the solid-liquid equation of state of some interesting metals.Several analytic formulas of dislocation-mediated melting law with some equations of state and equations of constitution and different values of their parameters are used to calculate several classical metals' melting curves at high pressures. The results are compared with the latest experimental data of shock wave and diamond anvil cell. We get some conclusions:①The melting curves of fcc metals Ag, Al, Cu, and Ni calculated with simple analytic model of dislocation-mediated melting law are good agreement with experimental data. The results show that dislocation-mediated melting law is fitting for describing the melting process of simple fcc metals. We get the optimized values of the parameters Bo, B₀', Go, and G₀' of Ag, Al, Cu, and Ni.②The melting curves of three metals Mg, Pb, and U, which have solid-solid phase transition at low pressures, are calculated with one-ambient-phase-approximation analytic model of dislocation-mediated melting law. The results show that the model is sensitive to G₀', and the value of G₀' has big effect on the calculated melting slope dT_m/dP. Choosing good value of G₀', the calculated melting curves are good agreement with experimental data. The optimized values of G₀' of Mg, Pb, and U are 1.7, 1.25, and 3.0 respectively.③Using "segmental calculating method", we determine that the melting point ofγ-Sn is 436K at ambient pressure, and calculate the melting curves ofβ-Sn andγ-Sn with dislocation-mediated melting law. Being compared with experimental melting data, the results show that our calculating method is logical, which is not published publicly up to now. It needs further theoretical and experimental evidences to verify that the method is fitting for calculating other complicated multi-phase materials' melting curves. ④The melting curves of bcc transition metals Mo, Ta, and W are calculated with analytic model of dislocation-mediated melting law. The results show that, choosing the values of parameters Bo, B₀', G₀, and G₀' logically, the shock-wave experimental melting data of bcc transition metals Mo, Ta, and W can be explained by the calculation of analytic model of dislocation-mediated melting law. But the calculated results have large discrypancy with diamond anvil cell experimental data. The melting slopes dT_m/dP of the three bcc transition metals calculated with dislocation-mediated melting law are larger than the values extrapolated from Vacancy model based on diamond anvil cell experimental data. The shear moduli models revised from SCG constitution model are combined with analytic model of dislocation-mediated melting law to calculate the melting curves of Mo, Ta, and W. The results are not improved.⑤The melting curves of Na, Rb, and Te, whose melting slopes change sharply with pressure going up, are calculated with analytic model of dialocation-mediated melting law. The results are agreement with experimental data at low pressures, but have large discrypancy at high pressures. The analytic model of dislocation-mediated melting law is not fitting for calculating such materials' melting curves. It is very difficult to describe the melting curuves of complicated alkaline metals by an analytic formula.⑥The solid-liquid equations of state of three classical metals Pb, Ta, and Sn are calculated based on Gray's three-phase equation of state for metals and their melting curves determined by analytic model of dislocation-mediated melting law. The theoretically calculated isothermal and Hugoniot curves of the three metals are agreement with experimental data. We get the phase diagrams of Pb, Ta and Sn at the pressure range 0～140GPa, 0～400GPa, and 0～85GPa respectively. The shock-melting pressure ranges of Pb, Ta, andγ-Sn are about 66～88GPa, 296³57GPa, 48⁶1GPa respectively, and the shock-melting temperature ranges are about 3777～4595K, 9227～10065K, 2178～2528K respectively.