Melting temperature of iron under the Earth’s inner core condition from deep machine learning

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 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.

Keywords

Inner core boundary / Melting temperature / Machine learning / Solid-liquid coexistence / Free energy calculation / Molecular dynamics simulation

CRediT authorship contribution statement

Fulun Wu: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Formal analysis, Data curation. Shunqing Wu: Writing – review & editing, Supervision, Project administration, Funding acquisition. Cai-Zhuang Wang: Writing – review & editing, Software, Formal analysis. Kai-Ming Ho: Writing – review & editing, Validation, Methodology, Investigation, Formal analysis. Renata M. Wentzcovitch: Writing – review & editing, Supervision, Investigation, Formal analysis. Yang Sun: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Work at Xiamen University was supported by National Natural Science Foundation of China (Grant Nos. 42374108 and 12374015). Y.S. acknowledges support from Fundamental Research Funds for the Central Universities (Grant No. 20720230014). R.M.W. acknowledges support from NSF (Grant Nos. EAR-2000850 and EAR-1918126). K.M.H. acknowledges support from NSF (Grant No. EAR-1918134). Shaorong Fang and Tianfu Wu from the Information and Network Center of Xiamen University are acknowledged for their help with Graphics Processing Unit (GPU) computing. We acknowledge the supercomputing time supported by the Opening Project of the Joint Laboratory for Planetary Science and Supercomputing (Grant No. CSYYGS-QT-2024-15), Research Center for Planetary Science, and the National Supercomputing Center in Chengdu.

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