Melting Temperature of Iron Under the Earth's Inner Core Condition from Deep Machine Learning

TL;DR

This paper develops a deep machine learning model to accurately predict iron's melting temperature under Earth's inner core conditions, incorporating electronic entropy effects and aligning with ab initio results.

Contribution

A novel deep potential model for iron that explicitly includes electronic entropy, improving melting temperature predictions under extreme core conditions.

Findings

DP model accurately predicts melting temperatures at ICB.

Electronic entropy significantly influences melting behavior.

Model aligns with previous ab initio calculations.

Abstract

Constraining the melting temperature of iron under Earth's inner core conditions is crucial for understanding core dynamics and planetary evolution. Here, we develop a deep potential (DP) model for iron that explicitly incorporates electronic entropy contributions governing thermodynamics under Earth's core conditions. Extensive benchmarking demonstrates the DP's high fidelity across relevant iron phases and extreme pressure and temperature conditions. Through thermodynamic integration and direct solid-liquid coexistence simulations, the DP predicts melting temperatures for iron at the inner core boundary, consistent with previous \textit{ab initio} results. This resolves the previous discrepancy of iron's melting temperature at ICB between the DP model and \textit{ab initio} calculation and suggests the crucial contribution of electronic entropy. Our work provides insights into machine learning melting behavior of iron under core conditions and provides the basis for future development of binary or ternary DP models for iron and other elements in the core.