Efficient Analytical Approach for High-Pressure Melting Properties of Iron

TL;DR

This paper introduces a simple analytical model to predict iron's high-pressure melting behavior, aiding understanding of Earth's core by aligning well with recent experimental and simulation data.

Contribution

The study develops a novel analytical approach using quantum statistical mechanics and the Lindemann criterion to accurately predict iron's melting properties under extreme conditions.

Findings

Quantitative agreement with recent experimental data

Predicts discontinuities in atomic volume, enthalpy, and entropy upon melting

Provides insights into Earth's core dynamics

Abstract

Iron represents the principal constituent of the Earth's core, but its high-pressure melting diagram remains ambiguous. Here we present a simple analytical approach to predict the melting properties of iron under deep-Earth conditions. In our model, anharmonic free energies of the solid phase are directly determined by the moment expansion technique in quantum statistical mechanics. This basis associated with the Lindemann criterion for a vibrational instability can deduce the melting temperature. Moreover, we correlate the thermal expansion process with the shear response to explain a discontinuity of atomic volume, enthalpy, and entropy upon melting. Our numerical calculations are quantitatively consistent with recent experiments and simulations. The obtained results would improve understanding of the Earth's structure, dynamics, and evolution.