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

doi:10.15541/jim20250299

Abstract

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

CLC Number:

TB35

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.

Figures/Tables 10

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

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

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

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

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

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

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%

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

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

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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