高熵硼化物陶瓷机器学习力场的构建与高温性能计算

doi:10.15541/jim20250299

无机材料学报 ›› 2026, Vol. 41 ›› Issue (4): 455-461.DOI: 10.15541/jim20250299 CSTR: 32189.14.jim20250299

高熵硼化物陶瓷机器学习力场的构建与高温性能计算

龚焕¹(), 张旭¹^,², 张小锋³, 李蓓¹^,²(), 刘凯¹

¹ 武汉理工大学材料科学与工程学院, 武汉 430070
² 武汉理工大学材料复合新技术全国重点实验室, 武汉 430070
³ 广东省科学院新材料研究所特种材料表面工程全国重点实验室, 广州 510650

收稿日期:2025-07-17 修回日期:2025-09-15 出版日期:2026-04-20 网络出版日期:2025-09-27
通讯作者: 李蓓, 副教授. E-mail: libei@whut.edu.cn
作者简介:龚焕(1997-), 男, 硕士研究生. E-mail: 1252744637@qq.com
基金资助:
国家自然科学基金(52202066)

Machine Learning Potential Development and High-temperature Property Calculation for High-entropy Boride Ceramics

GONG Huan¹(), ZHANG Xu¹^,², ZHANG Xiaofeng³, LI Bei¹^,²(), LIU Kai¹

¹ School of Materials Science and Engineering, Wuhan University of Technology, Wuhan 430070, China
² State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China
³ National Key Laboratory of Special Materials Surface Engineering, Institute of New Materials, Guangdong Academy of Sciences, Guangzhou 510650, China

Received:2025-07-17 Revised:2025-09-15 Published:2026-04-20 Online:2025-09-27
Contact: LI Bei, associate professor. E-mail: libei@whut.edu.cn
About author:GONG Huan (1997-), male, Master candidate. E-mail: 1252744637@qq.com
Supported by:
National Natural Science Foundation of China(52202066)

摘要/Abstract

摘要：

高熵硼化物陶瓷(High-entropy Boride Ceramics, HEBCs)在极端高温环境中的分子动力学模拟受限于经验力场的精度与温度适用性。本研究针对(Hf_0.2Zr_0.2Ta_0.2Ti_0.2Nb_0.2)B₂体系, 基于第一性原理计算与深度学习方法, 开发了高精度深度学习势能。通过主动学习优化训练数据集, 显著提升了模型在高温(~3000 K)下的模拟稳定性。该力场在模拟中兼具高精度与高效率。验证结果表明, 体积状态方程预测结果与第一性原理计算结果较为吻合, 证明了模型具有良好的可扩展性; 计算所得晶格常数及力学性能参数与实验值的误差<2%。尤为重要的是, 本研究成功揭示了HEBCs热膨胀各向异性规律, 修正了已有研究中的反常趋势。这项成果为极端条件下HEBCs的原子尺度模拟提供了可靠工具, 对深入理解其高温服役行为具有重要的科学价值。

关键词: 高熵硼化物陶瓷, 分子动力学, 深度学习势能, 高温性能

Abstract:

Molecular dynamics simulations of high-entropy boride ceramics (HEBCs) in extreme high-temperature environments are constrained by limited accuracy and temperature stability of empirical force fields. In this work, a high-accuracy deep-learning potential (DP) was proposed and developed for (Hf_0.2Zr_0.2Ta_0.2Ti_0.2Nb_0.2)B₂ systems via first-principles calculations and deep learning method. It is shown that, through expanding datasets via the active learning strategy, the DP model stability under high-temperature conditions (i.e., ~3000 K) could be significantly enhanced. The developed DP achieves high accuracy while maintaining computational efficiency. Validation results from the developed DP manifest that predictions of the volumetric equation of state align well with first-principles calculations, demonstrating the model’s good scalability. The lattice constants and mechanical properties predicted by DP-enabled molecular dynamics simulations show excellent agreements with experimental observations, with relative errors within 2%. Furthermore, the simulations successfully reveal the anisotropic thermal expansion behavior of HEBCs and rectify the anomalous trends reported in previous research. Therefore, this developed DP model provides a reliable tool for atomic-scale simulations of high-entropy boride ceramics under extreme conditions, and holds significant scientific value for advancing the in-depth understanding of their high-temperature service behavior.

Key words: high-entropy boride ceramic, molecular dynamics, deep-learning potential, high temperature property

中图分类号:

TB35

龚焕, 张旭, 张小锋, 李蓓, 刘凯. 高熵硼化物陶瓷机器学习力场的构建与高温性能计算[J]. 无机材料学报, 2026, 41(4): 455-461.

GONG Huan, ZHANG Xu, ZHANG Xiaofeng, LI Bei, LIU Kai. Machine Learning Potential Development and High-temperature Property Calculation for High-entropy Boride Ceramics[J]. Journal of Inorganic Materials, 2026, 41(4): 455-461.

图/表 10

图1 (a)六方晶胞与正交晶胞的转换关系示意图; (b) (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2的初始原子构型

Fig. 1 (a) Schematic illustration of transformation relationship between hexagonal and orthorhombic unit cells; (b) Initial atomic configuration of (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2

图2 基于DP-1测试集的DFT和DPMD计算结果对比

Fig. 2 Comparison of DFT and DPMD calculation results based on the DP-1 test set (a) Energy; (b) Atomic force; (c) Virial stress

图3 基于DP-2测试集的DFT和DPMD计算结果对比

Fig. 3 Comparison of DFT and DPMD calculation results based on the DP-2 test set (a) Energy; (b) Atomic force; (c) Virial stress

图4 DP-1力场在升温过程中温度、势能及原子结构随时间的演变

Fig. 4 Evolution of temperature, potential energy, and atomic structure during heating using the DP-1 force field

图5 DP-2力场在升温过程中温度、势能及原子结构随时间的演变

Fig. 5 Evolution of temperature, potential energy, and atomic structure during heating using the DP-2 force field

图6 DFT和DPMD计算(Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2的能量-体积状态方程对比

Fig. 6 Comparative evaluation of the energy-volume equation of state for (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2 calculated by DFT and DPMD

表1 DPMD计算与第一性原理及实验的晶格常数和力学性能指标对比

Table 1 Comparative assessment of lattice constants and mechanical properties from DPMD simulations, DFT calculations and experimental data

Parameter	DPMD (~0 K)	DFT^[8] (~0 K)	Error (~0 K)	DPMD (300 K)	Exp. (300 K)	Error (300 K)
a/Å	3.119	3.116	0.10%	3.117	3.1062^[17]	0.35%
c/Å	3.386	3.391	0.15%	3.399	3.3755^[17]	0.70%
C₁₁/GPa	587.81	604	2.68%	570.94	-	-
C₃₃/GPa	420.37	449	6.38%	409.82	-	-
C₄₄/GPa	243.86	243	0.35%	233.08	-	-
C₁₂/GPa	83.70	87	3.79%	83.08	-	-
C₁₃/GPa	152.10	143	6.36%	148.23	-	-
E/GPa	530.62	537.99	1.37%	505.33	508.53^[18]	0.63%
B/GPa	262.93	265.93	1.13%	255.81	259.86^[18]	1.56%
G/GPa	228.00	231.33	1.44%	215.81	216.61^[18]	0.37%

图7 (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2的晶格常数和热膨胀系数随温度的变化曲线

Fig. 7 Change curves of lattice constants and thermal expansion coefficients of (Hf0.2Zr0.2Ta0.2Ti0.2Nb0.2)B2 as a function of temperature

图S1 不同随机构型测试中DP-1力场在升温过程中温度、势能及原子结构随时间的演变

Fig. S1 Evolution of temperature, potential energy and atomic structure over time during the heating process in DP-1 force field under different random initial configuration tests

图S2 不同随机构型测试中DP-2力场在升温过程中温度、势能及原子结构随时间的演变

Fig. S2 Evolution of temperature, potential energy and atomic structure over time during the heating process in DP-2 force field under different random initial configuration tests

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高熵硼化物陶瓷机器学习力场的构建与高温性能计算

Machine Learning Potential Development and High-temperature Property Calculation for High-entropy Boride Ceramics

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