Unified Analytic Melt-Shear Model in the Limit of Quantum Melting

Abstract

Quantum melting is the phenomenon of cold (zero-temperature) melting of a pressure-ionized substance which represents a lattice of bare ions immersed in the background of free electrons, i.e., the so-called one-component plasma (OCP). It occurs when the compression of the substance corresponds to the zero-point fluctuations of its ions being so large that the ionic ordered state can no longer exist. Quantum melting corresponds to the classical melting curve reaching a turnaround point beyond which it starts going down and eventually terminates, when zero temperature is reached, at some critical density. This phenomenon, as well as the opposite phenomenon of quantum crystallization, may occur in dense stellar objects such as white dwarfs, and may play an important role in their evolution that requires a reliable thermoelasticity model for proper physical description. Here we suggest a modification of our unified analytic melt-shear thermoelasticity model in the region of quantum melting, and derive the corresponding Grüneisen parameters. We demonstrate how the new functional form for the cold shear modulus can be combined with a known equation of state. One of the constituents of the new model is the melting curve of OCP crystal which we also present. The inclusion of quantum melting implies that the modified model becomes applicable in the entire density range of the existence of the solid state, up to the critical density of quantum melting above which the solid state does not exist. Our approach can be generalized to model melting curves and cold shear moduli of different solid phases of a multi-phase material over the corresponding ranges of mechanical stability.