铁的熔点：深度机器学习下地球内核条件

Aug 5, 2026

Constraining the melting temperature of iron under Earth’s inner-core conditions is essential for understanding core dynamics and planetary evolution. The study develops a deep potential (DP) model for iron that explicitly includes electronic entropy contributions to capture thermodynamics at extreme core pressures and temperatures. Benchmarking shows high fidelity across relevant iron phases and conditions. Thermodynamic integration and direct solid–liquid coexistence simulations yield inner-core-boundary melting temperatures consistent with prior ab initio results, resolving a previous DP–ab initio discrepancy and highlighting the role of electronic entropy.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Introduction

Inner core conditions and significance of iron melting

Simulation approaches: CMD vs ab initio

Thermodynamic integration and solid–liquid coexistence methods

arXiv :2404 . 17852v1 [physics .geo-ph] 27 Apr 2024 Melting Temperature of Iron Under the Earth’s Inner Core Condition from Deep Machine Learning Fulun Wu, 1 Shunqing Wu, 1 Cai-Zhuang Wang,2 Kai-Ming Ho,2 Renata M. Wentzcovitch,3, 4, 5 and Yang Sun 1 1 Department of Physics, Xiamen University, Xiamen 361005, China 2 Department of Physics, Iowa State University, Ames, IA 50011, USA 3 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA 4 Department of Earth and Environmental Sciences, Columbia University, New York, NY 10027, USA 5 Lamont–Doherty Earth Observatory, Columbia University, Palisades, NY 10964, USA 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 ab initio results. This resolves the previous discrepancy of iron’s melting temperature at ICB between the DP model and 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. I. INTRODUCTION The Earth’s core plays a critical role in the thermal and compositional evolution of our planet [1, 2] . The core contains a solid inner core and a liquid outer, which form a solid-liquid coexistence (SLC) at the inner-core boundary (ICB) . Both inner and outer cores are primarily made of iron. It’s generally believed iron has a hexagonal close-packed (hcp) phase under inner core conditions [3, 4], while the body-centered cubic (bcc) phase is also suggested to be relevant for the inner core structure [5– 7] . The melting temperature of iron, at which the solidliquid equilibria form, is a key factor for estimating the temperature of the Earth’s center and the solidification process of the inner core [8–18] . Despite its importance, the melting temperature of iron in the inner core was not well constrained. Experimental measurements reported different results ranging from 4,850 K to 7,600 K due to the difficulties in generating extreme conditions and detecting melts [19] . The recent experiments still have uncertainties of 500 K for the melting temperature measurement at ICB conditions [16, 20] . Another avenue for exploring the extreme pressuretemperature conditions within Earth’s interiors is through computer simulations. These simulations offer a valuable alternative to experimental methods, allowing us to probe the properties of iron under core conditions. Depending on the modeling approach used to describe interatomic interactions, these simulations can be categorized as classical or ab initio simulations. Classical molecular dynamics (CMD) simulations employ semi-empirical potentials to represent interatomic interactions. Due to the efficiency of these potentials, CMD can simulate atomic structures at large length scales andover significant time scales, such as millions of atoms over nanoseconds. This allows the direct simulation of solidliquid equilibria at the ICB conditions so that the melting temperature can be directly extracted [21] . However, the limitation of CMD is that the simulation results highly depend on the accuracy of the employed semi-empirical potential. Different semi-empirical potential simulations have yielded varying melting temperatures for iron at inner core pressures.

FAQs

Why is the melting temperature of iron under inner core conditions important?

It helps constrain the Earth’s center temperature estimates and the solidification process of the inner core, which depends on where solid–liquid equilibria form.

How does the deep potential (DP) model improve the prediction of iron melting temperatures?

It incorporates electronic entropy contributions explicitly, enabling more accurate thermodynamics at Earth-core conditions and leading to high-fidelity benchmarking across phases and extremes.

What computational strategies are used to obtain the melting temperature in the study?

Melting temperatures are predicted using thermodynamic integration and direct solid–liquid coexistence simulations, both designed to compare solid and liquid free energies under inner-core-boundary conditions.

Aug 5, 2026

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