卷积神经网络辅助无机晶体弹性性质预测

刘宇杰; 王振宇; 雷航; 张国宇; 咸家伟; 高志斌; 孙军; 宋海峰; 丁向东

doi:10.7498/aps.74.20250127

摘要

无机晶体材料因具有优异的物理和化学特性, 在多个领域展现出广泛的应用潜力. 弹性性质(如体积模量和剪切模量)对预测材料的电导率、热导率及力学性能具有重要作用, 然而, 传统实验测量方法存在成本高、周期长等问题. 随着计算方法的进步, 理论模拟逐渐成为独立于实验的研究方法. 近年来, 基于图神经网络的机器学习方法在无机晶体材料的弹性性质预测中取得了显著成果, 尤其是晶体图卷积神经网络(CGCNN)在材料数据的预测和扩展方面表现出色. 本研究利用从Matbench v0.1数据集中收集的10987个材料的体积模量和剪切模量数据, 训练了两个CGCNN模型, 基于预训练的模型成功实现了对80664个无机晶体结构弹性模量的预测. 为保证数据质量, 筛选了材料电子带隙在0.1—3.0 eV之间, 并去除了含有放射性元素的化合物. 预测数据来源于两个主要数据集: 一是从Materials Project数据库中筛选出的54359个晶体结构, 构成MPED弹性数据集; 二是Merchant等(2023 Nature 624 80)通过深度学习和图神经网络方法发现的26305种晶体结构, 构成NED弹性数据集. 最终, 本研究预测了80664种无机晶体的体积模量和剪切模量, 丰富了现有的材料弹性数据资源, 并为材料设计提供了更多的数据支持. 本文数据集可在https://doi.org/10.57760/sciencedb.j00213.00104中访问获取.

关键词:

Abstract

Inorganic crystal materials have shown extensive application potential in many fields due to their excellent physical and chemical properties. Elastic properties, such as shear modulus and bulk modulus, play an important role in predicting the electrical conductivity, thermal conductivity and mechanical properties of materials. However, the traditional experimental measurement method has some problems such as high cost and low efficiency. With the development of computational methods, theoretical simulation has gradually become an effective alternative to experiments. In recent years, graph neural network-based machine learning methods have achieved remarkable results in predicting the elastic properties of inorganic crystal materials, especially, crystal graph convolutional neural networks (CGCNNs), which perform well in the prediction and expansion of material data.In this study, two CGCNN models are trained by using the shear modulus and bulk modulus data of 10987 materials collected in the Matbench v0.1 dataset. These models show high accuracy and good generalization ability in predicting shear modulus and bulk modulus. The mean absolute error (MAE) is less than 13 and the coefficient of determination ($ R^2$) is close to 1. Then, two datasets are screened for materials with a band gap between 0.1 and 3.0 eV and the compounds containing radioactive elements are excluded. The dataset consists of two parts: the first part is composed of 54359 crystal structures selected from the Materials Project database, which constitute the MPED dataset; the second part is the 26305 crystal structures discovered by Merchant et al. (2023 Nature 624 80) through deep learning and graph neural network methods, which constitute the NED dataset. Finally, the shear modulus and bulk modulus of 80664 inorganic crystals are predicted in this study This work enriches the existing material elastic data resources and provides more data support for material design. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00104.

Keywords:

作者及机构信息

1.
西安交通大学材料科学与工程学院, 金属多孔材料全国重点实验室, 西安　710049

2.
北京应用物理与计算数学研究所, 计算物理全国重点实验室, 北京　100088

3.
西安交通大学材料科学与工程学院, 金属材料强度全国重点实验室, 西安　710049

通信作者: 咸家伟, xian_jiawei@iapcm.ac.cn ; 高志斌, zhibin.gao@xjtu.edu.cn ;

基金项目: 国家自然科学基金(批准号: 12104356, 52250191)、计算物理全国重点实验室基金和国家重点研发计划(批准号: 2023YFB4604100) 资助的课题.

Authors and contacts

1.
State Key Laboratory of Porous Metal Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, China

2.
National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

3.
State Key Laboratory for Mechanical Behavior of Materials, School of Materials Science and Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

Corresponding author: XIAN Jiawei, xian_jiawei@iapcm.ac.cn ; GAO Zhibin, zhibin.gao@xjtu.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12104356, 52250191), the Funding of National Key Laboratory of Computational Physics, China, and the National Key Research and Development Program of China (Grant No. 2023YFB4604100).

文章全文

补充材料

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施引文献

图 1 晶体图卷积神经网络　(a)晶体图的构造: 晶体结构被转换为图形, 其中节点代表单位原胞中的原子, 边缘则表示原子之间的连接. 每个节点和边都用对应于晶体中原子和化学键的向量进行表征; (b)晶体图顶部的卷积神经网络结构: 在每个节点上构建R个卷积层和$ L_1$个隐藏层, 从而形成一个新的图, 其中每个节点表示该原子的局部环境. 经过池化操作后, 将代表整个晶体的向量连接到$ L_2$隐藏层, 然后连接到输出层, 以进行预测^[26]

Fig. 1. Illustration of the crystal graph convolutional neural networks: (a) Construction of the crystal graph. Crystals are converted to graphs with nodes representing atoms in the unit cell and edges representing atom connections. Nodes and edges are characterized by vectors corresponding to the atoms and bonds in the crystal, respectively. (b) Structure of the convolutional neural network on top of the crystal graph. R convolutional layers and $ L_1$ hidden layers are built on top of each node, resulting in a new graph with each node representing the local environment of each atom. After pooling, a vector representing the entire crystal is connected to $ L_2$ hidden layers, followed by the output layer to provide the prediction^[26].

下载: 全尺寸图片幻灯片

图 2 剪切模量((a), (b))和体模量((c), (d))的训练集(Train)、验证集(Val)和测试集(Test)在晶体图卷积神经网络(CGCNN)、随机森林(random forest)、极限梯度提升(XGBoost)、支持向量回归(SVR)、梯度提升(gradient boosting)和决策树(decision tree)的平均绝对误差(MAE)和决定系数(R²)

Fig. 2. Mean absolute error (MAE) and coefficient of determination (R²) for the training set (Train), validation set (Val), and test set (Test) of shear modulus ((a), (b)) and bulk modulus ((c), (d)) in crystal graph convolutional neural network (CGCNN), random forest (RF), extreme gradient boosting (XGBoost), support vector regression (SVR), gradient boosting (GB), and decision tree (DT).

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图 3 利用CGCNN模型所预测的体积模量与剪切模量结果与DFT计算值对比分析　(a)和(b), (c)和(d)以及(e)和(f)分别为在训练集、验证集和测试集的结果

Fig. 3. Comparison between the volume modulus and shear modulus predicted by CGCNN model and the calculated values of DFT. (a) and (b), (c) and (d), (e) and (f) are the results in the train set, validation set, and test set, respectively.

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图 4 来自MPED数据集的预测数据集的统计分析　(a) 7种晶系分布, 单斜晶系最常见(16101个结构), 其次是三斜晶系(14461个结构), 最少的是六方晶系(1361个结构); (b)数据集原胞中的原子数范围(1—444个原子)的分布; (c)元素分布, 显示了77种不同元素的出现频率. 该数据集包括过渡金属、主族元素和稀土元素, 其中氧的出现频率最高

Fig. 4. Statistical analysis of predictive datasets from MPED: (a) The distribution of 7 crystal systems, with monoclinic being the most common (16101 structures), followed by triclinic (14461 structures), while hexagonal is the least one (1361 structures); (b) distribution of range of number of atoms in the primitive cell (1–444 atoms) across the dataset; (c) elemental distribution that illustrates the frequency of 77 distinct elements. The dataset encompasses transition metals, main group elements, and rare earth elements, with oxygen showing the highest frequency.

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图 5 来自NED数据集所预测数据集的统计分析　(a) 7种晶系分布, 单斜晶系最常见(8063个结构), 其次是三斜晶系(7491个结构), 最少的是六方晶系(779个结构); (b)数据集原胞内原子数范围(3—84个原子)的分布; (c)元素分布, 显示了76种不同元素的出现频率. 该数据集包括过渡金属、主族元素和稀土元素, 其中氧的出现频率最高

Fig. 5. Statistical analysis of predictive datasets from NED: (a) The distribution of 7 crystal systems, with monoclinic being the most common (8063 structures), followed by triclinic (7491 structures), while hexagonal is the least one (779 structures); (b) distribution of the range of the number of atoms in the primitive cell (3–84 atoms) across the dataset; (c) elemental distribution illustrating the frequency of 76 distinct elements. The dataset encompasses transition metals, main group elements, and rare earth elements, with oxygen showing the highest frequency.

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图 6 MPED数据集中不同材料的剪切模量与体模量分布　(a)所有材料的剪切模量与体模量分布, 不同颜色代表不同的晶系; (b)三斜晶系; (c)单斜晶系; (d)正交晶系; (e)三方晶系; (f)四方晶系; (g)六方晶系; (h)立方晶系. 条形图展示了各晶系材料的剪切模量和体模量的统计分布

Fig. 6. Shear modulus and bulk modulus distributions of different materials in the MPED dataset: (a) Shear modulus vs. bulk modulus distributions for all materials, with different colors representing different crystal systems; (b) triclinic; (c) monoclinic; (d) orthorhombic; (e) trigonal; (f) tetragonal; (g) hexagonal; (h) cubic. The bar graphs show the statistical distribution of shear and bulk moduli for each crystal system material.

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图 7 NED数据集中各晶体结构材料的模量分布　(a)整体剪切模量-体模量分布(颜色区分晶系); (b)三斜晶系; (c)单斜晶系; (d) 正交晶系; (e)三方晶系; (f)四方晶系; (g)六方晶系; (h)立方晶系. 条形图统计了各晶系材料的剪切模量和体模量分布

Fig. 7. Distribution of moduli for various crystal structure materials in the NED dataset: (a) Overall shear modulus-bulk modulus distribution (color-coded by crystal system); (b) triclinic system; (c) monoclinic system; (d) orthorhombic system; (e) trigonal system; (f) tetragonal system; (g) hexagonal system; (h) cubic system. Bar charts illustrate the distribution of shear modulus and bulk modulus for materials in each crystal system.

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表 A1 MPED数据集无机晶体材料基础物理特性及预测值(部分). 这里, ID-number和Formula分别是材料编号和化学式

Table A1. Fundamental physical properties (partial) and predicted values of inorganic crystalline materials from MPED datasets. The CIF files of these materials were obtained from the Materials Project. Here, ID-number and Formula represent the material ID and chemical formula, respectively.

ID-number	Formula	N	ρ	V	M	B	G	$ \upsilon_{\rm{l}} $	$ \upsilon_{\rm{t}} $	$ \upsilon_{\rm{s}} $	ν	$ \theta_{\rm{D}} $
mp-1000	BaTe	2	4.938	89.094	264.927	31.764	23.469	2180.121	3573.541	2407.744	0.204	160.498
mp-10009	GaTe	8	5.1549	254.251	789.292	24.095	16.757	1802.955	3001.379	1994.276	0.218	93.722
mp-1001012	Sc₂ZnSe₄	14	3.254	289.440	567.162	53.623	32.397	3155.374	5454.806	3502.473	0.249	157.640
mp-1001015	Y₂ZnS₄	14	3.675	335.691	742.961	60.652	25.843	2651.771	5087.157	2967.069	0.314	127.104
mp-1001016	Sc₂ZnSe₄	14	4.687	333.879	942.322	54.940	22.543	2193.172	4258.659	2455.876	0.320	105.395
mp-1001019	MgSc₂Se₄	14	4.086	349.578	860.114	52.875	22.985	2371.850	4521.352	2652.741	0.310	112.113
mp-1001021	Y₂ZnSe₄	14	4.811	385.950	1118.121	55.070	22.939	2183.662	4219.640	2444.462	0.317	99.958
mp-1001023	BeC₂	6	1.879	58.402	66.067	132.395	102.494	7386.608	11967.830	8148.016	0.192	625.248
mp-1001024	Y₂MgS₄	14	3.173	345.765	660.753	56.994	26.037	2864.435	5375.943	3200.229	0.302	135.747
mp-1001034	MgIn₂Se₄	14	5.031	376.146	1139.562	39.515	21.476	2066.136	3680.578	2299.251	0.270	94.830
mp-1001069	Li₄₈P₁₆S₆₁	125	1.743	2652.952	2784.713	19.812	7.267	2041.845	4114.028	2291.557	0.337	49.283
mp-1001079	LiC₂N₂	10	1.505	130.116	117.952	56.823	20.405	3681.742	7471.454	4133.696	0.340	242.869
mp-10013	SnS	2	3.596	69.620	150.775	17.613	5.617	1249.772	2642.016	1406.249	0.356	101.772
mp-1001594	C₄O₃	84	1.656	1155.735	1152.492	19.101	12.904	2791.530	4682.464	3090.023	0.224	87.663
mp-1001604	LuTlS₂	4	7.377	99.825	443.480	49.490	20.396	1662.754	3224.127	1861.754	0.319	119.486
mp-1001611	LuTlSe₂	4	8.001	111.508	537.270	43.737	22.793	1687.844	3043.848	1880.122	0.278	116.295
mp-1001780	LuCuS₂	4	6.522	77.056	302.643	74.239	35.316	2327.021	4313.132	2597.493	0.295	181.731
mp-1001786	LiScS₂	4	2.700	71.362	116.027	58.972	36.372	3670.409	6309.130	4072.100	0.244	292.285
mp-1001790	LiO₃	4	2.130	42.828	54.939	46.463	28.415	3652.317	6292.720	4052.874	0.246	344.878
mp-1001831	LiB	4	2.099	28.090	35.504	111.075	134.490	8004.910	11762.661	8727.079	0.069	854.731

下载: 导出CSV

表 A2 NED数据集无机晶体材料基础物理特性及预测值(部分). 这里, Filename表示文件名

Table A2. Basic physical properties and predicted values of inorganic crystalline materials (part) from NED datasets. Here, Filename represents the file name.

Filename	N	ρ	V	M	G	B	$ \upsilon_\mathrm{l} $	$ \upsilon_\mathrm{t} $	$ \upsilon_\mathrm{s} $	ν	$ \theta_\mathrm{D} $
FIrS	3	7.798	51.805	243.280	28.413	54.027	3433.128	1908.824	2125.825	0.276	244.862
AuGeP	3	7.381	67.619	300.580	23.064	55.970	3427.627	1767.655	1979.213	0.319	208.603
GdHO	3	7.384	39.190	174.257	62.945	113.409	5169.778	2919.774	3247.588	0.266	410.537
LiPrPtSn	4	9.285	82.565	461.643	31.112	78.216	3590.578	1830.554	2051.127	0.324	222.617
ErLiPdSn	4	8.792	75.424	399.330	36.874	81.235	3851.257	2047.962	2288.361	0.303	255.968
BaBiHgNa	4	6.817	138.827	569.887	11.187	24.989	2419.500	1281.048	1431.855	0.305	130.688
BeGeHLa	4	5.801	63.421	221.566	49.688	90.981	5206.069	2926.621	3256.448	0.269	385.920
AlHKSb	4	3.004	104.402	188.848	14.352	23.461	3765.877	2185.915	2425.631	0.246	243.454
EuHgNaSb	4	7.135	115.739	497.304	15.654	30.762	2690.122	1481.228	1650.873	0.282	160.097
LiNiSmSn	4	7.617	72.963	334.704	36.441	70.798	3958.873	2187.199	2437.061	0.280	275.632
DyLiPdSn	4	8.557	76.573	394.571	35.786	81.074	3879.627	2045.067	2286.509	0.308	254.475
N₂SSe₂	5	2.175	166.436	217.998	2.459	2.521	1632.981	1063.352	1165.878	0.132	107.904
LiNaSe₂Zn	5	3.916	107.396	253.260	17.754	31.924	3767.961	2129.286	2368.236	0.265	253.647
BrGeLa₂Rh	5	6.436	137.585	533.260	27.302	50.532	3675.249	2059.620	2292.318	0.271	226.057
CsHgNaS₂	5	4.774	146.289	420.615	9.852	18.449	2572.057	1436.510	1599.245	0.273	154.518
AlAs₂CsMg	5	3.863	143.606	334.035	20.025	28.181	3769.434	2276.944	2517.185	0.213	244.713
Br₂GeSmY	5	4.803	163.091	471.714	19.469	32.496	3488.675	2013.383	2235.315	0.250	208.287
As₂Ca₂Sr	5	3.392	155.481	317.619	28.093	37.392	4697.360	2877.774	3176.871	0.200	300.774
KLiMnTe₂	5	3.860	153.218	356.177	12.890	26.438	3361.705	1827.331	2038.601	0.290	193.953
Al₂C₂Yb	5	6.426	64.862	251.024	88.642	125.838	6162.150	3713.927	4106.697	0.215	520.350

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