Al-Cu金属间化合物的机器学习势构建及压缩力学性质

荆琳烁; 邵建立; 薛峰宁; 王裴; 徐利春

doi:10.11858/gywlxb.20251141

Al-Cu金属间化合物的机器学习势构建及压缩力学性质

doi: 10.11858/gywlxb.20251141

荆琳烁^1,,
邵建立^2,*, ,,
薛峰宁²,
王裴³,
徐利春^1,*, ,

1.
太原理工大学物理与光电工程学院, 山西太原　030024
2.
北京理工大学机电学院, 北京　100081
3.
北京应用物理与计算数学研究所, 北京　100094

基金项目: 国家重点研发计划（2021YFB3802300）

详细信息

作者简介:
荆琳烁（1998－），男，硕士，主要从事金属材料研究. E-mail：jls_tyut@163.com

通讯作者:
邵建立（1979－），男，博士，教授，主要从事材料动态力学响应理论研究. E-mail：shao_jianli@bit.edu.cn

徐利春（1985－），男，博士，副教授，主要从事新能源材料物性研究. E-mail：xulichun@tyut.edu.cn

中图分类号: TG146.2; O521.9
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- HTML全文浏览量: 152
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出版历程
- 收稿日期: 2025-07-22
- 修回日期: 2025-09-01
- 网络出版日期: 2025-09-17
- 刊出日期: 2025-11-05

Machine Learning Potential Construction and Compressive Mechanical Properties of Al-Cu Intermetallic Compounds

JING Linshuo^1
,,
SHAO Jianli^{2,*
, ,},
XUE Fengning²,
WANG Pei³,
XU Lichun^{1,*
, ,}

1.
College of Physics and Optoelectronic Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
2.
School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
3.
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

摘要

摘要: 研究Al-Cu金属间化合物对于Al-Cu合金的优化设计至关重要。分子动力学（molecular dynamics，MD）模拟可以给出Al-Cu合金力学行为的微观过程，而原子间作用势是保证模拟可靠性的关键物理基础。基于第一性原理计算数据构建了Al-Cu体系的深度势（deep potential，DP）函数，并将DP预测的物理性质（晶体结构、能量-体积曲线、压力-体积曲线和声子谱）与密度泛函理论（density functional theory，DFT）和嵌入原子势（embedded atom method，EAM）结果进行了对比分析，验证了DP模型的泛化能力和准确性。基于该DP模型，对5种Al-Cu金属间化合物（θ-Al₂Cu、θ′-Al₂Cu、Al₃Cu、Al₄Cu₉和AlCu₄相）进行了压缩过程MD模拟，给出了θ-Al₂Cu、θ′-Al₂Cu和AlCu₄等结构屈服时的特征规律：θ-Al₂Cu、θ′-Al₂Cu和AlCu₄的屈服应力和剪应力随应变率的升高而增大，屈服应变也相应提高。这一现象源于声子拖曳对原子滑移的阻碍增强。其中，θ-Al₂Cu的抗压缩性能最好，在4×10⁹ s⁻¹应变率下压缩到17.4%时屈服，屈服强度为51.15 GPa，并产生螺位错，原子沿着[$ \overline{1}11 $]、[111]和[$11 \overline{1} $]方向滑移；θ′-Al₂Cu压缩到10.0%时屈服，原子在垂直于压缩方向的平面内滑移；AlCu₄相压缩到13.4%时屈服，原子沿着[401]和[$40 \overline{1} $]方向滑移。
- Al-Cu合金 /
- 机器学习 /
- 分子动力学 /
- 力学性能 /
- 单轴压缩
Abstract: The optimization design of Al-Cu intermetallic compounds is crucial for the mechanical properties of Al-Cu alloys. Molecular dynamics (MD) simulation can provide microscopic processes of the mechanical behavior of Al-Cu alloys, and the interatomic potential is the key physical basis to ensure the reliability of the MD simulation. This work constructed a depth potential (DP) function for the Al-Cu system based on first-principles calculations, and compared the physical properties predicted by DP (crystal structure, energy-volume curve, pressure-volume curve, and phonon spectrum) with density functional theory (DFT) and embedded atom method (EAM) results. The generalization ability and accuracy of the DP model were verified. Based on the DP potential, MD simulations were conducted on the compression process of five Al-Cu intermetallic compounds (θ-Al₂Cu, θ′-Al₂Cu, Al₃Cu, Al₄Cu₉, and AlCu₄ phases). The characteristics and laws of yielding phenomena in structures such as θ-Al₂Cu, θ′-Al₂Cu and AlCu₄ were presented. The yield stress and shear stress of θ-Al₂Cu, θ′-Al₂Cu and AlCu₄ increase with the increase of strain rate, and the yield strain also increases correspondingly. This phenomenon arises from the enhancement of phonon drag obstruction to atomic slip. Among them, θ-Al₂Cu has the best compressive performance, yielding at a strain rate of 4×10⁹ s⁻¹ when compressed to 17.4%, with a yield strength of 51.15 GPa. Screw dislocations are produced, and the atoms slip along the [$ \overline{1} 11$], [111] and [$11 \overline{1} $] directions. θ′-Al₂Cu yields when compressed to 10.0%, and the atoms slip in the plane perpendicular to the compression. Yielding occurs when the AlCu₄ phase is compressed to 13.4% and the atoms slip along the [401] and [$40 \overline{1} $] directions.
- Al-Cu alloy /
- machine learning /
- molecular dynamics /
- mechanical properties /
- uniaxial compression

HTML全文

图 1 (a)压缩的初始结构，(b) 5种金属间化合物在300 K下弛豫过程中σ_zz和温度随时间变化的曲线，(c) 5种金属间化合物的晶体结构

Figure 1. (a) Initial structure of compression; (b) curves of σ_zz and temperature over time during the relaxation process of five intermetallic compounds at 300 K; (c) crystal structures of five intermetallic compounds

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图 2 DP模型与DFT的预测结果对比

Figure 2. Comparison of the prediction results of DP model and DFT

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图 3 DP模型、EAM模型对8种Al-Cu金属间化合物的基态能量(a)和形成能(b)的预测结果与DFT模型预测结果的对比

Figure 3. Comparison of the prediction results of DP and EAM model for ground state energy (a) and formation energy (b) of eight Al-Cu intermetallic compounds with those of the DFT model

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图 4 8种Al-Cu金属间化合物的E-V曲线和p-V曲线

Figure 4. E-V and p-V curves of eight Al-Cu intermetallic compounds

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图 5 3种Al-Cu金属间化合物的声子谱

Figure 5. Phonon spectra of three Al-Cu intermetallic compounds

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图 6 300 K、不同应变率压缩下5种Al-Cu金属间化合物在[001]方向的应力-应变曲线和剪应力-应变曲线

Figure 6. Stress-strain curves and shear stress-strain curves of five intermetallic compounds subjected to compression at various strain rates in the [001] direction at 300 K

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图 7 Al₄Cu₉的(a) 应力-应变曲线，(b)原子应变切片，(c)剪应力分布，(d) σ_zz切片和(e)原子能量切片

Figure 7. (a) Stress-strain curve, (b) atomic strain slice, (c) shear stress distribution, (d) σ_zz slice and (e) atomic energy slice of Al₄Cu₉

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图 8 Al₄Cu₉相原子的能量(a)～(b)和温度(c)～(d)切片

Figure 8. (a)−(b) Energy and (c)−(d) temperature slices of Al₄Cu₉ phase atoms

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图 9 θ-Al₂Cu的(a) σ_zz-应变曲线、(b)剪应力分布、(c)原子移动轨迹和(d)原子应变切片

Figure 9. (a) σ_zz-strain curve, (b) shear stress distribution, (c) atomic movement trajectory and (d) atomic strain slice of θ-Al₂Cu

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图 10 θ-Al₂Cu相原子的温度、σ_zz和能量切片

Figure 10. Temperature, σ_zz, and energy slices of θ-Al₂Cu phase atoms

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图 11 θ′-Al₂Cu的(a) 应力 -应变曲线、(b)剪应力分布、(c)原子移动轨迹和(d)原子应变切片

Figure 11. (a) Stress-strain curve, (b) shear stress distribution, (c) atomic movement trajectory and (d) atomic strain slice of the θ′-Al₂Cu phase

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图 12 θ′-Al₂Cu相原子的温度、 σ_zz和能量切片

Figure 12. Temperature, σ_zz and energy slices of θ′-Al₂Cu phase atoms

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图 13 AlCu₄相的(a) 应力-应变曲线、(b)原子应变切片、(c)剪应力分布和(d)原子移动轨迹

Figure 13. (a) Stress-strain curve, (b) atomic strain slice, (c) shear stress distribution and (d) atomic movement trajectory of AlCu₄ phase

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图 14 AlCu₄相原子的温度、σ_zz和能量切片

Figure 14. Temperature, σ_zz and energy slices of AlCu₄ phase atoms

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图 15 Al₃Cu相的(a) 应力-应变曲线、(b) CNA分析、(c)相结构随应变的演化规律和(d)位错曲线

Figure 15. (a) Stress-strain curve, (b) CNA analysis, (c) evolution of phase structure with strain and (d) dislocation curves of Al₃Cu phase

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图 16 Al₃Cu相原子的温度、σ_zz和能量切片

Figure 16. Temperature, σ_zz and energy slices of Al₃Cu phase atoms

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表 1 Al-Cu二元金属间化合物基态下的晶格常数、形成焓和结合能

Table 1. Lattice constants, enthalpy of formation, and binding energy of Al-Cu binary intermetallic compounds in the ground state

Compound	Space group	a/Å	b/Å	c/Å	ΔH/(eV/atom)	ΔE/eV	Source
θ-Al₂Cu	I4/mcm	6.075	6.075	4.870	−0.133	−3.146	This work
θ-Al₂Cu	I4/mcm	6.073	6.073	4.879	−0.163	−3.850	Ref. [46]
θ′-Al₂Cu	I4/mmm	4.061	4.061	5.702	−0.159	−3.173	This work
θ′-Al₂Cu	I4/mmm	4.087	4.087	5.822	−0.149	−3.836	Ref. [46]
Al₃Cu	Pm3m	3.924	3.924	3.924	−0.019	−2.953	This work
Al₃Cu	Pm3m	3.938	3.938	3.938	−0.029	−3.715	Ref. [46]
Ω-Al₂Cu	P4/mmm	4.105	4.105	2.891	−0.010	−3.024	This work
Ω-Al₂Cu	P4/mmm	4.137	4.137	2.875	−0.016	−3.704	Ref. [46]
1-AlCu₃	Pm3m	3.637	3.637	3.637	−0.168	−3.582	This work
	Pm3m	3.692	3.692	3.692	−0.170	−3.865	Ref. [46]
	Pm3m	3.641	3.641	3.641			Ref. [47]
1-AlCu	Pm3m	2.998	2.998	2.998	−0.136	−3.310	This work
1-AlCu	Pm3m	2.998	2.998	2.998	−0.136	−3.826	Ref. [46]
Al₃Cu₂	Pm3m1	4.092	4.092	4.993	−0.137	−3.215	This work
	Pm3m1	4.147	4.147	5.059	−0.145	−3.834	Ref. [46]
	Pm3m1	4.122	4.122	5.114			Ref. [48]
AlCu₄	P213	6.244	6.244	6.244	−0.111	−3.573	This work
AlCu₄	P213	6.331	6.331	6.331	−0.109	−3.804	Ref. [46]
2-AlCu₃	P63/mmc	5.138	5.138	4.206	−0.175	−3.590	This work
2-AlCu₃	P63/mmc	5.223	5.223	4.250	−0.178	−3.872	Ref. [46]
Al₄Cu₁₅	P4/mmm	3.609	3.609	18.456	−0.095	−3.548	This work
Al₄Cu₁₅	P4/mmm	3.677	3.677	18.034	−0.093	−3.788	Ref. [46]
3-AlCu₃	Fm3m	5.776	5.776	5.776	−0.154	−3.568	This work
	Fm3m	5.858	5.858	5.858	−0.163	−3.857	Ref. [46]
	Fm3m	5.798	5.798	5.798			Ref. [49]
4-AlCu₃	Pmmn	4.173	4.512	5.107	−0.180	−3.594	This work
2-AlCu	C12/m1	4.056	6.315	6.325	−0.199	−3.373	This work
Al₄Cu₉	P43m	8.618	8.618	8.618	−0.202	−3.561	This work
Al₄Cu₉	P43m	8.738	8.738	8.738	−0.203	−3.896	Ref. [46]
2-Al₃Cu	P4/mmm	2.778	2.778	7.513	−0.062	−2.995	This work
2-Al₃Cu	P4/mmm	2.802	2.802	7.732	−0.082	−3.768	Ref. [46]

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表 2 Al-Cu二元金属间化合物基态弹性模量

Table 2. Elastic modulus of Al-Cu binary intermetallic compounds in ground state

Compound	Space group	B/GPa	E_m/GPa	G/GPa	ν	B/G
θ-Al₂Cu	I4/mcm	76.10	119.43	48.22	0.24	1.58
θ′-Al₂Cu	I4/mmm	85.39	142.68	58.40	0.22	1.46
Al₃Cu	Pm3m	86.15	133.73	53.87	0.24	1.60
Ω-Al₂Cu	P4/mmm	88.10	93.80	35.46	0.32	2.48
2-AlCu	C12/m1	48.31	136.59	66.43	0.03	0.73
Al₃Cu₂	P3ml	77.21	104.28	40.90	0.27	1.89
AlCu₄	P213	80.98	112.41	44.30	0.27	1.83
Al₄Cu₉	P43m	106.51	191.91	79.98	0.20	1.33

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