The onset of collective diffusion in hcp-iron: a combined theory of soft-matter and solid-state physics

Lately, scientists have discovered the existence of collective diffusion in hcp-iron via machine-learning algorithms. This result has opened a promising avenue for geophysical studies on planetary cores. However, the crossover between collective and non-collective regimes remains very ambiguous. Based on the solid-liquid similarity, we develop a simple differential equation to infer the crossover temperature from the density scaling exponent, the isothermal bulk modulus, and the volumetric thermal expansivity. All necessary thermodynamic inputs are provided by the statistical moment method for nonlinear atomic vibrations. Our theoretical results are supported by the latest computational data on warm-dense iron crystals. From there, we find a possible explanation for prolonged controversies about melting relations in diamond-anvil-cell experiments. The potential impacts of collective diffusion on the core properties of icy, rocky, and gaseous planets are also considered by combining our mineral-physics calculations with modern geodynamic models.