基于神经网络势函数计算地球内核条件下的铁-硫合金黏度

徐云帆; 何宇; 张为; 李和平

doi:10.11858/gywlxb.20251221

基于神经网络势函数计算地球内核条件下的铁-硫合金黏度

doi: 10.11858/gywlxb.20251221

徐云帆^{1, 2, 3,},
何宇^{1, 2, 3,*, ,},
张为⁴,
李和平^{1, 2}

1.
中国科学院地球化学研究所关键矿产成矿与预测全国重点实验室, 贵州贵阳　550081
2.
中国科学院地球化学研究所地球内部物质高温高压重点实验室, 贵州贵阳　550081
3.
中国科学院大学, 北京　100049
4.
贵州师范大学喀斯特研究院, 贵州贵阳　550025

基金项目: 国家自然科学基金（42350002，42074104）；中国科学院青年交叉团队项目（JCTD-2022-1）；中国科学院青年创新促进会项目（2020394）；贵州省2020年科技专项补助项目（NGZ2020SIG）

详细信息

作者简介:
徐云帆（1997－），男，博士研究生，主要从事高温高压下地球内部物质性质的计算模拟研究. E-mail：xuyunfan@mail.gyig.ac.cn

通讯作者:
何　宇（1985－），男，博士，研究员，主要从事高温高压下地球内部物质性质的计算模拟研究. E-mail：heyu@mail.gyig.ac.cn

中图分类号: O521.2
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出版历程
- 收稿日期: 2025-10-09
- 修回日期: 2025-12-11
- 录用日期: 2025-12-12
- 网络出版日期: 2025-11-26

Viscosity of Iron-Sulfur Alloy under the Conditions of the Earth Inner Core Calculated Based on the Neural Network Potential

XU Yunfan^{1, 2, 3
,},
HE Yu^{1, 2, 3,*
, ,},
ZHANG Wei⁴,
LI Heping^{1, 2}

1.
State Key Laboratory of Critical Mineral Research and Exploration, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, Guizhou, China
2.
Key Laboratory of High-Temperature and High-Pressure Study of the Earth’s Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550081, Guizhou, China
3.
University of Chinese Academy of Sciences, Beijing 100049, China
4.
School of Karst Science, Guizhou Normal University, Guiyang 550025, Guizhou, China

摘要

摘要: 地球内核的密度较纯铁低，表明其中存在轻元素。碳、氢、氧、硫、硅被认为是最可能存在于内核的轻元素。黏度是反映地球内核动力学和演化历史的关键物理量，对于地球内核波速各向异性的成因具有重要影响。前人已对内核条件下纯铁的六方密堆积相（hexagonal close-packed, HCP）和体心立方相（body-centered cubic, BCC）的黏度进行了模拟计算。然而，目前仍然缺乏针对地球内核中轻元素对地球内核黏度影响的系统性研究。为此，构建了内核条件下铁-硫合金的神经网络势函数，利用该方法实现了对铁-硫体系的大规模分子动力学模拟，研究了空位浓度低至0.01%时对该合金离子输运性质的影响。利用晶格中铁的自扩散系数研究了内核铁-硫合金的蠕变机制和黏度，将地球内核条件下铁-硫合金的黏度限定为1×10¹⁴～2×10¹⁶ Pa·s，与自由核章动以及地震波观测结果一致。
- 神经网络势函数 /
- 地球内核 /
- 自扩散系数 /
- 黏度 /
- 分子动力学
Abstract: The density of the Earth’s inner core is lower than that of pure iron, indicating the presence of light elements. Among the candidate elements, carbon, hydrogen, oxygen, sulfur, and silicon are considered the most likely. Viscosity is a key physical property controlling the dynamics and evolutionary history of the inner core, and it has significant implications for the origin of seismic anisotropy. Previous studies have investigated the viscosity of pure iron in its hexagonal close-packed (HCP) and body-centered cubic (BCC) phases under inner-core conditions through computational simulations. However, the influence of light elements on the viscosity of the inner core remains insufficiently constrained. In this study, we constructed a neural-network potential (NNP) for Fe-S alloy under inner-core conditions and employed it to perform large-scale molecular dynamics simulations. We systematically examined the impact of vacancy concentrations as low as 0.01% on the ionic transport properties of Fe-S alloy. Based on the self-diffusion coefficients of Fe in the lattice, we further explored the creep mechanisms and viscosity of Fe-S alloy under core conditions. Our results indicate that dislocation creep dominates the rheological behavior, yielding viscosities of 1×10¹⁴–2×10¹⁶ Pa·s, consistent with constraints from free-core nutation and seismic observations.
- neural-network potential /
- Earth’s inner core /
- self-diffusion coefficient /
- viscosity /
- molecular dynamics

HTML全文

图 1 初始结构

Figure 1. Original structure

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图 2 流程图

Figure 2. Flow chart

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图 3 势函数模拟的能量、受力、应力的均方根误差

Figure 3. Energy, force and stress root mean squared error of potential function

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图 4 6 000 K和360 GPa下的神经网络势的RDF^[76]

Figure 4. RDF of neural-network potential at 6 000 K and 360 GPa^[76]

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图 5 360 GPa和6 000 K条件下空位浓度为0.01%的Fe-S合金经10 ps弛豫后的结构

Figure 5. Structure of the Fe-S alloy with a vacancy concentration of 0.01% after 10 ps relaxation at 360 GPa and 6 000 K

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图 6 360 GPa和6 000 K条件下Fe₄₀₅₀S₂₇₀无空穴和Fe₄₀₄₉S₂₇₀含空穴体系的轨迹叠加图像

Figure 6. Trajectories of Fe₄₀₅₀S₂₇₀ without vacancies and Fe₄₀₄₉S₂₇₀ with vacancies at 360 GPa and 6 000 K

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图 7 360 GPa、不同温度下Fe原子的扩散系数随空位浓度的变化

Figure 7. Variation of the diffusion coefficient of Fe iron with vacancy concentrations at different temperatures at 360 GPa

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图 8 360 GPa下不同空穴浓度下2种组分的自扩散系数

Figure 8. Diffusion coefficients of two elements at different vacancy concentrations at 360 GPa

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图 9 340和360 GPa下不同空位浓度铁的自扩散系数

Figure 9. Iron diffusion coefficients at 340 and 360 GPa with different vacancy concentrations

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图 10 340和 360 GPa条件下不同蠕变模型预测的黏度结果（粉色区域表示自由核章动对地球内核黏度的约束^[85]，绿色区域表示核幔引力耦合对地球内核黏度的约束^[84]）

Figure 10. Viscosities predicted by different creap models at 340 and 360 GPa (The pink region represents the constraint on inner-core viscosity from free-core nutation^[85], while the green region denotes the constraint from core-mantle gravitational coupling^[84].)

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表 1 不同训练模型的参数

Table 1. Parameters of different training model

Model	Descriptor	Rcut_smth/Å	Rcut/Å	Neuron	Learning rate type	Start_lr
DP-GEN	se_e2_a	1.5	6.0	[240, 240, 240]	Exp.	0.001
DeePMD-kit	se_e2_a	1.5	6.0	[240, 240, 240]	Exp.	0.001

Model	Stop_lr	Start_pref_e	Limit_pref_e	Start_pref_f	Limit_pref_f	Stop_batch
DP-GEN	3.54×10^–7	0.02	1	1 000	1	8×10⁵
DeePMD-kit	3.54×10^–7	0.02	1	1 000	1	1×10⁷

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