基于材料组分信息的高居里温度铁磁材料预测

孙敬淇; 吴绪才; 阙志雄; 张卫兵

doi:10.7498/aps.72.20230382

摘要

寻找具有高居里温度的铁磁材料是凝聚态物理的热点问题. 本文建立了有效的基于材料组分信息的居里温度机器学习模型, 并预测了多种高居里温度铁磁材料. 基于收集到的1568个铁磁材料数据, 并以铁磁材料的组分信息作为描述符, 通过超参数优化和十折交叉验证, 构建了支持向量回归、核岭回归、随机森林及极端随机树四种高效的机器学习模型. 这其中, 极端随机树模型具有最好的预测性能, 其交叉验证R²评分可达81.48%. 同时, 还应用极端随机树模型对Materials Project数据库36949种铁磁材料进行了预测, 发现了338个居里温度大于600 K的铁磁材料. 本文提出的方法可以为获取具有高居里温度的铁磁材料提供有价值的帮助, 加快铁磁材料设计的过程.

关键词:

Abstract

The search for ferromagnetic materials with high Curie temperature (T_c) is a hot issue in condensed matter physics. In this work, an effective machine learning model of Curie temperature based on material component information is established to predict a variety of ferromagnetic materials with high Curie temperature. Based on the collected data of 1568 ferromagnetic materials, and taking the component information of ferromagnetic materials as descriptors, in this work four efficient machine learning models are constructed, namely support vector regression, kernel ridge regression, random forest and extremely randomized trees, through hyperparameter optimization and ten-break cross-validation. Of them, extremely randomized tree model has the best prediction performance, and its cross-validation R² score can reach 81.48%. At the same time, the extremely randomized tree model is also used to predict 36949 materials in the materials project database, and 338 ferromagnetic materials with T_c greater than 600 K are found in this work. The method proposed in this paper can help obtain ferromagnetic materials with high Curie temperature and accelerate the process of ferromagnetic material design.

Keywords:

作者及机构信息

长沙理工大学物理与电子科学学院, 柔性电子材料基因工程湖南省重点实验室, 长沙　410004

通信作者: 张卫兵, zhangwb@csust.edu.cn

基金项目: 国家自然科学基金(批准号: 11874092)、霍英东教育基金会第十六届高等院校青年教师基金(批准号: 161005)和湖南省杰出青年科学基金(批准号: 2021JJ10039)资助的课题.

Authors and contacts

Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering, School of Physics & Electronic Science, Changsha University of Science and Technology, Changsha 410004, China

Corresponding author: Zhang Wei-Bing, zhangwb@csust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874092), the Fok Ying-Tong Education Foundation, China (Grant No. 161005), and the Science Fund for Distinguished Young Scholars of Hunan Province, China (Grant No. 2021JJ10039).

文章全文 : translate this paragraph

参考文献

[1]	Sanvito S, Oses C, Xue J, Tiwari A, Zic M, Archer T, Tozman P, Venkatesan M, Coey M, Curtarolo S 2017 Sci. Adv. 3 e1602241 Google Scholar
[2]	Jiang Z, Wang P, Jiang X, Zhao J 2018 Nanoscale Horiz. 3 335 Google Scholar
[3]	Lu X, Fei R, Yang L 2019 Phys. Rev. B 100 205409 Google Scholar
[4]	Claussen N, Bernevig B A 2020 Phys. Rev. B 101 245117 Google Scholar
[5]	Jiang Z, Wang P, Xing J, Jiang X, Zhao J 2018 ACS Appl. Mater. Interfaces 10 39032 Google Scholar
[6]	Kabiraj A, Kumar M, Mahapatra S 2020 npj Comput. Mater. 6 35 Google Scholar
[7]	Lu S H, Zhou Q H, Guo Y, Wang J L 2022 Chem 8 769 Google Scholar
[8]	Lu S H, Zhou Q H, Guo Y L, Zhang Y H, Wu Y L, Wang J L 2020 Adv. Mater. 32 2002658.Google Scholar
[9]	Nelson J, Sanvito S 2019 Phys. Rev. Mater. 3 104405 Google Scholar
[10]	Xue Y F, Shen Z, Wu Z B, Song C S 2022 J. Appl. Phys. 132 053901 Google Scholar
[11]	Zhang B, Zheng X Q, Zhao T Y, Hu F X, Sun J R, Shen B G 2018 Chin. Phys. B 27 067503 Google Scholar
[12]	Vishina A, Vekilova O Y, BJörkman T, Bergman A, Herper H C, Eriksson O 2020 Phys. Rev. B 101 094407 Google Scholar
[13]	Kwon H Y, Kim N J, Lee C K, Won C 2019 Phys. Rev. B 99 024423 Google Scholar
[14]	Choudhary K, Garrity K F, Ghimire N J, Anand N, Tavazza F 2021 Phys. Rev. B 103 155131 Google Scholar
[15]	Coey J M D 2011 IEEE Trans. Magn. 47 4671 Google Scholar
[16]	Buschow K J 2003 Handbook of Magnetic Materials (Amsterdam: Elsevier) pp293–456
[17]	Connolly T F 2012 Bibliography of Magnetic Materials and Tabulation of Magnetic Transition Temperatures (New York: Springer Science & Business Media) pp1–30
[18]	Long T, Fortunato N M, Zhang Y, Gutfleisch O 2021 Mater. Res. Lett. 9 169 Google Scholar
[19]	Zhai X, Chen M, Lu W 2018 Comput. Mater. Sci. 151 41 Google Scholar
[20]	Fabian P, Gaël V, Alexandre G, Vincent M, Bertrand T, Olivier G, Mathieu B, Peter P, Ron W, Vincent D, Jake V, Alexandre P, David C, Matthieu B, Matthieu P, Duchesnay É 2011 J. Mach. Learn. Res. 12 2825
[21]	Mirjalili 2019 Enetic Algorithm (Berlin: Springer) pp43–55
[22]	Syarif I, Prugel A, Wills G 2016 Telecommun. Comput. Electron. Control 14 1502 Google Scholar
[23]	杨自欣, 高章然, 孙晓帆, 蔡宏灵, 张凤鸣, 吴小山 2019 物理学报 68 210502 Google Scholar Yang Z X, Gao Z R, Sun X F, Cai H L, Zhang F M, Wu X S 2019 Acta Phys. Sin. 68 210502 Google Scholar
[24]	Benesty J, Chen J, Huang Y, Cohen I 2009 Pearson Correlation Coefficient (Berlin: Springer) pp1–4
[25]	Jain A, Ong S P, Hautie G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G 2013 APL Mater. 1 011002 Google Scholar
[26]	Popoel E, Tuszynski M, Zarek W, Rendecki T 1989 J. Less-Common Met. 146 127 Google Scholar
[27]	Li J G, Pan M X, Sun J R, Zhang F X, Li S P, Zhao D Q, Yu X H, Zhao S X, Chen X C 1996 Solid State Commun. 97 pp1047 Google Scholar
[28]	Dang M Z, Rancourt D G 1996 Phys. Rev. B 53 2291 Google Scholar
[29]	Miyata N, Kamimori T, Goto M 1986 J. Phys. Soc. Jpn. 55 2037 Google Scholar
[30]	Trumpy G, Both E, Djéga-Mariadassou C, Lecocq P 1970 Phys. Rev. B 2 3477 Google Scholar
[31]	Meinert M 2016 J. Phys. Condens. Matter 28 056006 Google Scholar

施引文献

图 1 1568个铁磁材料数据集T_c的分布情况

Fig. 1. Distribution of T_c in 1568 ferromagnetic material data sets.

下载: 全尺寸图片幻灯片

图 2 数据集中铁磁材料的元素分布情况　(a) T_c大于300 K时元素分布; (b) T_c大于600 K时元素分布

Fig. 2. Element distribution of ferromagnetic materials in data set: (a) Element distribution when T_c is greater than 300 K; (b) element distribution when T_c is greater than 600 K.

下载: 全尺寸图片幻灯片

图 3 均匀网格搜索　(a) 随机森林参数优化图; (b) 极端随机树参数优化图

Fig. 3. Uniform grid search: (a) Random forest parameter optimization map; (b) extreme random tree parameter optimization map

下载: 全尺寸图片幻灯片

图 4 四种机器学习模型实验值和预测值对比的二维散点图　(a) 核岭回归; (b) 支持向量机; (c) 随机森林; (d) 极端随机树

Fig. 4. Two-dimensional scatter plots comparing experimental and predicted values of four machine learning models: (a) Kernel ridge regression; (b) support vector machine; (c) random forests; (d) extremely random tree.

下载: 全尺寸图片幻灯片

图 5 基于极端随机数模型的特征重要性排序图

Fig. 5. Feature importance ranking graph based on extreme random number model.

下载: 全尺寸图片幻灯片

图 6 预测集中铁磁材料元素分布情况　(a) 2531个T_c大于300 K数据的元素分布图; (b) 338个T_c大于600 K数据的元素分布图

Fig. 6. Element distribution of ferromagnetic materials in prediction set: (a) Element distribution of 2531 data with T_c greater than 300 K; (b) element distribution of 338 data with T_c greater than 600 K.

下载: 全尺寸图片幻灯片

图 7 预测集中338个T_c > 600 K的铁磁材料的T_c分布情况

Fig. 7. Curie temperature distribution of 338 ferromagnetic materials with T_c >600 K in prediction set.

下载: 全尺寸图片幻灯片

表 1 本研究中四种机器学习模型的超参数

Table 1. Hyperparameters of four machine learning models in this study.

模型	超参数
KRR	alpha = 0.00567165, kernel = “rbf”
SVR	kernel = “rbf”, C = 181.8797945, gamma = 0.18646131
RF	n_estimators = 170, max_features = 0.30, min_samples_leaf = 0.001
EXT	n_estimators = 180, max_features = 0.58, min_samples_leaf = 0.001

下载: 导出CSV

表 2 基于特征筛选获得的化学参数描述符

Table 2. Chemical parameter descriptors obtained based on feature screening.

No.	Meanings	Features
1	Mean atomic number	MAN
2	Mean IonicRadius	MIR
3	Mean Modulus of Elasticity	MME
4	Mean melting point	MMP
5	Mean GSmagmom	MGSM
6	Mean covalentradius	MCR
7	Mean IonizationEnergy	MIE
8	Mean ElectronAffinity	MEA
9	Mean AtomicVolume	MAV
10	Mean MendeleevNumber	MMN
11	Composition of Mn	CMn
12	Composition of Fe	CFe
13	Composition of Co	CCo
14	Composition of Ni	CNi
15	range AtomicRadius	RAR
16	range Electronegativity	REE
17	avg p valence electrons	ApV
18	avg d valence electrons	AdV
19	frac f valence electrons	FfV
20	transition metal fraction	TMF
21	2-norm	2N

下载: 导出CSV

表 3 本研究中四种机器学习模型的最终评估结果

Table 3. Final evaluation results of four machine learning models in this study.

	KRR	SVR	RF	EXT
MAE	89.43	83.21	76.52	70.86
RMSE	125.50	125.77	114.71	109.32
R²/%	80.75	80.67	83.92	85.39
CS MAE	95.41	88.64	81.18	74.04
CS RMSE	141.21	137.62	124.13	117.98
CS R²/%	73.70	74.92	79.45	81.48

下载: 导出CSV

[1]	Sanvito S, Oses C, Xue J, Tiwari A, Zic M, Archer T, Tozman P, Venkatesan M, Coey M, Curtarolo S 2017 Sci. Adv. 3 e1602241 Google Scholar
[2]	Jiang Z, Wang P, Jiang X, Zhao J 2018 Nanoscale Horiz. 3 335 Google Scholar
[3]	Lu X, Fei R, Yang L 2019 Phys. Rev. B 100 205409 Google Scholar
[4]	Claussen N, Bernevig B A 2020 Phys. Rev. B 101 245117 Google Scholar
[5]	Jiang Z, Wang P, Xing J, Jiang X, Zhao J 2018 ACS Appl. Mater. Interfaces 10 39032 Google Scholar
[6]	Kabiraj A, Kumar M, Mahapatra S 2020 npj Comput. Mater. 6 35 Google Scholar
[7]	Lu S H, Zhou Q H, Guo Y, Wang J L 2022 Chem 8 769 Google Scholar
[8]	Lu S H, Zhou Q H, Guo Y L, Zhang Y H, Wu Y L, Wang J L 2020 Adv. Mater. 32 2002658.Google Scholar
[9]	Nelson J, Sanvito S 2019 Phys. Rev. Mater. 3 104405 Google Scholar
[10]	Xue Y F, Shen Z, Wu Z B, Song C S 2022 J. Appl. Phys. 132 053901 Google Scholar
[11]	Zhang B, Zheng X Q, Zhao T Y, Hu F X, Sun J R, Shen B G 2018 Chin. Phys. B 27 067503 Google Scholar
[12]	Vishina A, Vekilova O Y, BJörkman T, Bergman A, Herper H C, Eriksson O 2020 Phys. Rev. B 101 094407 Google Scholar
[13]	Kwon H Y, Kim N J, Lee C K, Won C 2019 Phys. Rev. B 99 024423 Google Scholar
[14]	Choudhary K, Garrity K F, Ghimire N J, Anand N, Tavazza F 2021 Phys. Rev. B 103 155131 Google Scholar
[15]	Coey J M D 2011 IEEE Trans. Magn. 47 4671 Google Scholar
[16]	Buschow K J 2003 Handbook of Magnetic Materials (Amsterdam: Elsevier) pp293–456
[17]	Connolly T F 2012 Bibliography of Magnetic Materials and Tabulation of Magnetic Transition Temperatures (New York: Springer Science & Business Media) pp1–30
[18]	Long T, Fortunato N M, Zhang Y, Gutfleisch O 2021 Mater. Res. Lett. 9 169 Google Scholar
[19]	Zhai X, Chen M, Lu W 2018 Comput. Mater. Sci. 151 41 Google Scholar
[20]	Fabian P, Gaël V, Alexandre G, Vincent M, Bertrand T, Olivier G, Mathieu B, Peter P, Ron W, Vincent D, Jake V, Alexandre P, David C, Matthieu B, Matthieu P, Duchesnay É 2011 J. Mach. Learn. Res. 12 2825
[21]	Mirjalili 2019 Enetic Algorithm (Berlin: Springer) pp43–55
[22]	Syarif I, Prugel A, Wills G 2016 Telecommun. Comput. Electron. Control 14 1502 Google Scholar
[23]	杨自欣, 高章然, 孙晓帆, 蔡宏灵, 张凤鸣, 吴小山 2019 物理学报 68 210502 Google Scholar Yang Z X, Gao Z R, Sun X F, Cai H L, Zhang F M, Wu X S 2019 Acta Phys. Sin. 68 210502 Google Scholar
[24]	Benesty J, Chen J, Huang Y, Cohen I 2009 Pearson Correlation Coefficient (Berlin: Springer) pp1–4
[25]	Jain A, Ong S P, Hautie G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G 2013 APL Mater. 1 011002 Google Scholar
[26]	Popoel E, Tuszynski M, Zarek W, Rendecki T 1989 J. Less-Common Met. 146 127 Google Scholar
[27]	Li J G, Pan M X, Sun J R, Zhang F X, Li S P, Zhao D Q, Yu X H, Zhao S X, Chen X C 1996 Solid State Commun. 97 pp1047 Google Scholar
[28]	Dang M Z, Rancourt D G 1996 Phys. Rev. B 53 2291 Google Scholar
[29]	Miyata N, Kamimori T, Goto M 1986 J. Phys. Soc. Jpn. 55 2037 Google Scholar
[30]	Trumpy G, Both E, Djéga-Mariadassou C, Lecocq P 1970 Phys. Rev. B 2 3477 Google Scholar
[31]	Meinert M 2016 J. Phys. Condens. Matter 28 056006 Google Scholar

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