Estimation of suitable upper-limits for temperature, in stability comparisons between solid phases at high pressures. Study cases: carbon, oxygen, and fluorine

Abstract

For most solid materials the Quasi-Harmonic Approximation (QHA) is expected to stay valid in a wide range of temperatures that get extended as we increase pressure, reaching a limit that could vastly exceed the melting temperature of the material. Hence, it becomes relevant to develop additional criteria for constraining the maximum temperature under which it still makes sense to perform stability comparisons between crystalline phases, hopefully without paying the high computational price that is required to calculating the precise melting curve for each solid phase. In this work, we report that for crystalline systems in which QHA remains accurate at high temperature, an alternative and computationally inexpensive phenomenological approximation holds well for identifying the region in the pressure-temperature (P-T) space where melting is likely to occur, meaning, the Lindemann’s criteria. By quantifying how atoms deviate from their equilibrium positions upon increasing temperature in the solid phase, we were able to constrain their P-T region of stability to conditions that are located under a line that represents an 11% average deviation of the atoms with respect to their interatomic distances, therefore, providing an approximate but reliable lower limit for the melting line which is relatively easy to calculate, and also a very useful alternative when no accurate experimental data is available and calculations do not exist or are not conclusive.