Abstract:Volume Dependence of Melting Temperature at High Pressure and its Relation to a New Dimensionless Quantity​

U. Walzer. Volume dependence of melting temperature at high pressure and itsrelation to a new dimensionless quantity. Exp. Technik d. Physik, 31:33-51, 1983.

Volume Dependence of Melting Temperature at High Pressure and its Relation to a New Dimensionless Quantity

U. Walzer

Abstract

The dependence of melting temperature on the atomic volume is inferred in two separate ways from different assumptions. The first deduction is based on an interatomic pair potential and a dislocation model, while the second one is based on the equation of state by Ullmann and Pan'kov, on an expression for the dependence of the Grüneisen ratio on pressure and bulk modulus and on Lindemann's law. It is also possible to infer the equation of state from the lattice theory alone. From this, the exponents of the T_m(v) equations are independently determined. They are found to be in agreement. Reversing the sequence of conclusions, one may, if one accepts the other aforementioned premises, infer Lindemann's law. However, this applies only for high coordination numbers and high pressures, respectively. In a systematic manner, new dimensionless quantities Q_j containing the melting temperature are defined, and their pressure dependence is calculated analytically and numerically, there being no necessity of solving the equation of state so that density stands alone on one side of the sign of equality. The most simple one of these dimensionless quantities, Q₀, shows an interesting systematics for the elements of the Periodic Table. For high pressures, the Q₀ values of the metals are scattered around merely insignificantly variable average values which slightly depend on pressure. If one might proceed from the assumption that, at an appropriate pressure, but at an assumed zero temperature, the materials of the Earth's core would exist in the form of a close-packed structure, it is possible to determine the ratio of melting temperature to formula weight as a function of the pressure for the actual Earth's core.

Key words: melting temperature, high pressure, Lindemann's law, Grüneisen parameter, Grüneisen ratio, dimensionless quantity, Earth's core, Periodic Table, Cauchy's relation, Kuhlmann-Wilsdorf, Clausius-Clapeyron, pressure dependence, pressure, Leibfried number, Bragg number, equation of state, formula weight, core-mantle boundary, transition metals

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