氢化物超导体临界转变温度的机器学习模型

doi:10.11900/0412.1961.2024.00140

金属学报

2024, Vol. 60

Issue (10): 1418-1428 DOI: 10.11900/0412.1961.2024.00140

研究论文

本期目录 | 过刊浏览

氢化物超导体临界转变温度的机器学习模型

赵晋彬¹^,², 王建韬²^,³, 何东昌²^,³, 李俊林¹, 孙岩², 陈星秋²(

), 刘培涛²(

)

1 太原科技大学材料科学与工程学院太原 030024
2 中国科学院金属研究所沈阳材料科学国家研究中心沈阳 110016
3 中国科学技术大学材料科学与工程学院沈阳 110016

Machine Learning Model for Predicting the Critical Transition Temperature of Hydride Superconductors

ZHAO Jinbin¹^,², WANG Jiantao²^,³, HE Dongchang²^,³, LI Junlin¹, SUN Yan², CHEN Xing-Qiu²(

), LIU Peitao²(

)

1 School of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
2 Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
3 School of Materials Science and Engineering, University of Science and Technology of China, Shenyang 110016, China

引用本文:

赵晋彬, 王建韬, 何东昌, 李俊林, 孙岩, 陈星秋, 刘培涛. 氢化物超导体临界转变温度的机器学习模型[J]. 金属学报, 2024, 60(10): 1418-1428.
Jinbin ZHAO, Jiantao WANG, Dongchang HE, Junlin LI, Yan SUN, Xing-Qiu CHEN, Peitao LIU. Machine Learning Model for Predicting the Critical Transition Temperature of Hydride Superconductors[J]. Acta Metall Sin, 2024, 60(10): 1418-1428.

全文: PDF(1961 KB) HTML

摘要:

高压下发现的具有高临界转变温度(T_c)的氢化物超导体激起了研究者对常压室温超导材料探索的广泛兴趣。尽管第一性原理方法可以准确预测氢化物超导体的T_c，但电声耦合计算量巨大且十分昂贵，因此迫切需要建立一个既准确又高效的T_c预测模型。本工作利用随机森林算法，根据特征的重要性选择最关键的特征，开发了一个简单且物理可解释的机器学习模型。该模型利用所选择的4个关键特征(即组成元素价电子数标准差、共价半径平均值和门捷列夫数(Mendeleev数)范围，以及Fermi能级处H的态密度占比)实现了高的T_c预测精度(平均绝对误差为24.3 K，均方根误差为33.6 K)，这为氢化物超导体的高通量筛选提供了有效预测模型，有助于加速高T_c超导氢化物的发现。

关键词 ：氢化物超导体, 超导转变温度, 机器学习, 随机森林, 第一性原理计算

Abstract：

The discovery of hydride superconductors with high critical transition temperature (T_c) under high pressures has received considerable interest in developing superconducting materials that can operate at room temperature and ambient pressure. Although first-principles methods can accurately predict the critical temperature of hydride superconductors, the computational demands are significant because of the expensive calculation of electron-phonon coupling. Hence, constructing an accurate and efficient model for predicting T_c is highly desirable. In this study, a simple and interpretable machine learning (ML) model was developed using the random forest algorithm, which enables the selection of important features based on their importance. Using four physics-based features, namely, the standard deviation of the number of valence electrons, mean covalent radii, range of the Mendeleev number of constituent elements, and hydrogen fraction of the total density of states at the Fermi energy, the optimal ML model achieves high accuracy, with a mean absolute error of 24.3 K and a root-mean-square error of 33.6 K. The ML model developed in this study shows great application potential for high-throughput screening, thereby expediting the discovery of high-T_c superconducting hydrides.

Key words： hydride superconductor superconducting transition temperature machine learning random forest first-principles calculation

收稿日期: 2024-05-08

ZTFLH:

TG132.26

基金资助:国家自然科学基金项目(52188101,52201030);国家重点研发计划项目(2021YFB3501503);中国科学院重点部署项目(ZDRW-CN-2021-2-5)

通讯作者: 刘培涛，ptliu@imr.ac.cn，主要从事材料的电子结构计算与原子模拟研究;
陈星秋，xingqiu.chen@imr.ac.cn，主要从事合金设计与计算研究

Corresponding author: LIU Peitao, professor, Tel: (024)23971560, E-mail: ptliu@imr.ac.cn;
CHEN Xing-Qiu, professor, Tel: (024)23971560, E-mail: xingqiu.chen@imr.ac.cn

作者简介: 赵晋彬，男，1991年生，博士生

	服务

	把本文推荐给朋友
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	赵晋彬
	王建韬
	何东昌
	李俊林
	孙岩
	陈星秋
	刘培涛
44.8K

链接本文:

https://www.ams.org.cn/CN/10.11900/0412.1961.2024.00140 或 https://www.ams.org.cn/CN/Y2024/V60/I10/1418

图1 氢化物超导体的分布情况

表1 随机森林算法在sklearn库中使用的超参数(其他未明确指出的参数使用了默认值)

图2 单次训练下临界温度(Tc)的模型测试误差与特征数量的关系，及10次独立训练下的平均模型测试集误差与训练集占比的关系

图3 递归筛选出的最重要的4个特征，及所获得的最精确的机器学习模型预测的Tc与真值对比

图4 Tc与组成元素的价电子数的标准差、平均共价半径、Mendeleev数范围，及Fermi能级处H的电子态密度占比4个特征的相关性

表2 针对数据集中6个Tc最高的氢化物超导材料的模型预测[43,59,60,70,89]

图5 数据集中6个Tc最高的氢化物超导材料的晶体结构和电子态密度

1	De Nobel J, Lindenfeld P. The discovery of superconductivity [J]. Phys. Today, 1996, 49: 40
2	Boeri L, Hennig R, Hirschfeld P, et al. The 2021 room-temperature superconductivity roadmap [J]. J. Phys. Condens. Matter, 2022, 34: 183002
3	Kim C J. Superconductor Levitation: Concepts and Experiments [M]. Singapore: Springer, 2019: 1
4	Mangin P, Kahn R. Superconductivity: An introduction [M]. Cham: Springer, 2017: 1
5	Meissner W, Ochsenfeld R. Ein neuer effekt bei eintritt der supraleitfähigkeit [J]. Naturwissenschaften, 1933, 21: 787
6	Hirsch J E, Maple M B, Marsiglio F. Superconducting materials classes: Introduction and overview [J]. Physica, 2015, 514C: 1
7	Bardeen J, Cooper L N, Schrieffer J R. Microscopic theory of superconductivity [J]. Phys. Rev., 1957, 106: 162
8	Bednorz J G, Müller K A. Possible high T_c superconductivity in the Ba-La-Cu-O system [J]. Z. Phys., 1986, 64B: 189
9	Keimer B, Kivelson S A, Norman M R, et al. From quantum matter to high-temperature superconductivity in copper oxides [J]. Nature, 2015, 518: 179
10	Wu M K, Ashburn J R, Torng C J, et al. Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure [J]. Phys. Rev. Lett., 1987, 58: 908 pmid: 10035069
11	Schilling A, Cantoni M, Guo J D, et al. Superconductivity above 130 K in the Hg-Ba-Ca-Cu-O system [J]. Nature, 1993, 363: 56
12	Kamihara Y, Watanabe T, Hirano M, et al. Iron-based layered superconductor La[O_{1 -} _x F _x ]FeAs (x = 0.05-0.12) with T_c = 26 K [J]. J. Am. Chem. Soc., 2008, 130: 3296 doi: 10.1021/ja800073m pmid: 18293989
13	Paglione J, Greene R L. High-temperature superconductivity in iron-based materials [J]. Nat. Phys., 2010, 6: 645
14	Wang Q Y, Li Z, Zhang W H, et al. Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO₃ [J]. Chin. Phys. Lett., 2012, 29: 037402
15	Li D F, Lee K, Wang B Y, et al. Superconductivity in an infinite-layer nickelate [J]. Nature, 2019, 572: 624
16	Sun H L, Huo M W, Hu X W, et al. Signatures of superconductivity near 80 K in a nickelate under high pressure [J]. Nature, 2023, 621: 493
17	Li Q, Zhang Y J, Xiang Z N, et al. Signature of superconductivity in pressurized La₄Ni₃O₁₀ [J]. Chin. Phys. Lett., 2024, 41: 017401
18	Zhang M X, Pei C Y, Du X, et al. Superconductivity in trilayer nickelate La₄Ni₃O₁₀ under pressure [DB/OL]. arXiv: 2311. 07423, 2023
19	Wang M. Discovery of high-T_c superconductivity in a nickelate [J]. Physics, 2023, 52: 663
19	王猛. 液氮温区镍氧化物高温超导体的发现 [J]. 物理, 2023, 52: 663
20	Pickett W E. Colloquium: Room temperature superconductivity: The roles of theory and materials design [J]. Rev. Mod. Phys., 2023, 95: 021001
21	Hu J P. Searching for new unconventional high temperature superconductors [J]. Acta Phys. Sin., 2021, 70(1): 017101
21	胡江平. 探索非常规高温超导体 [J]. 物理学报, 2021, 70(1): 017101
22	Li J X. Spin fluctuations and uncoventional superconducting pairing [J]. Acta Phys. Sin., 2021, 70(1): 017408
22	李建新. 自旋涨落与非常规超导配对 [J]. 物理学报, 2021, 70(1): 017408
23	Nagamatsu J, Nakagawa N, Muranaka T, et al. Superconductivity at 39 K in magnesium diboride [J]. Nature, 2001, 410: 63
24	Ashcroft N W. Metallic hydrogen: A high-temperature superconductor? [J]. Phys. Rev. Lett., 1968, 21: 1748
25	Ashcroft N W. Hydrogen dominant metallic alloys: High temperature superconductors? [J]. Phys. Rev. Lett., 2004, 92: 187002
26	Duan D F, Liu Y X, Tian F B, et al. Pressure-induced metallization of dense (H₂S)₂H₂ with high-T_c superconductivity [J]. Sci. Rep., 2014, 4: 6968
27	Gor'kov L P, Kresin V Z. Pressure and high-T_c superconductivity in sulfur hydrides [J]. Sci. Rep., 2016, 6: 25608 doi: 10.1038/srep25608 pmid: 27167334
28	Drozdov A P, Eremets M I, Troyan I A, et al. Conventional superconductivity at 203 Kelvin at high pressures in the sulfur hydride system [J]. Nature, 2015, 525: 73
29	Liu H Y, Naumov I I, Geballe Z M, et al. Dynamics and superconductivity in compressed lanthanum superhydride [J]. Phys. Rev. B, 2018, 98: 100102
30	Somayazulu M, Ahart M, Mishra A K, et al. Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures [J]. Phys. Rev. Lett., 2019, 122: 027001
31	Drozdov A P, Kong P P, Minkov V S, et al. Superconductivity at 250 K in lanthanum hydride under high pressures [J]. Nature, 2019, 569: 528
32	Eremets M I, Minkov V S, Drozdov A P, et al. High-temperature superconductivity in hydrides: Experimental evidence and details [J]. J. Supercond. Novel Magn., 2022, 35: 965
33	Zhang S B, Zhang M, Liu H Y. Superconductive hydrogen-rich compounds under high pressure [J]. Appl. Phys., 2021, 127A: 684
34	Troyan I A, Semenok D V, Kvashnin A G, et al. Anomalous high-temperature superconductivity in YH₆ [J]. Adv. Mater., 2021, 33: 2006832
35	Snider E, Dasenbrock-Gammon N, McBride R, et al. RETRACTED: Synthesis of yttrium superhydride superconductor with a transition temperature up to 262 K by catalytic hydrogenation at high pressures [J]. Phys. Rev. Lett., 2021, 126: 117003
36	Semenok D V, Kvashnin A G, Ivanova A G, et al. Synthesis of ThH₄, ThH₆, ThH₉ and ThH₁₀: A route to room-temperature superconductivity [DB/OL]. arXiv: 1902. 10206, 2019
37	Semenok D V, Kvashnin A G, Ivanova A G, et al. Superconductivity at 161 K in thorium hydride ThH₁₀: Synthesis and properties [J]. Mater. Today, 2020, 33: 36
38	Li B, Miao Z L, Ti L, et al. Predicted high-temperature superconductivity in cerium hydrides at high pressures [J]. J. Appl. Phys., 2019, 126: 235901
39	Chen W H, Semenok D V, Huang X L, et al. High-temperature superconducting phases in cerium superhydride with a T_c up to 115 K below a pressure of 1 megabar [J]. Phys. Rev. Lett., 2021, 127: 117001
40	Wang H, Tse J S, Tanaka K, et al. Superconductive sodalite-like clathrate calcium hydride at high pressures [J]. Proc. Natl. Acad. Sci. USA, 2012, 109: 6463 doi: 10.1073/pnas.1118168109 pmid: 22492976
41	Li Z W, He X, Zhang C L, et al. Superconductivity above 200 K discovered in superhydrides of calcium [J]. Nat. Commun., 2022, 13: 2863 doi: 10.1038/s41467-022-30454-w pmid: 35606357
42	Flores-Livas J A, Boeri L, Sanna A, et al. A perspective on conventional high-temperature superconductors at high pressure: Methods and materials [J]. Phys. Rep., 2020, 856: 1
43	Sun Y, Lv J, Xie Y, et al. Route to a superconducting phase above room temperature in electron-doped hydride compounds under high pressure [J]. Phys. Rev. Lett., 2019, 123: 097001
44	Di Cataldo S, Von Der Linden W, Boeri L. Phase diagram and superconductivity of calcium borohyrides at extreme pressures [J]. Phys. Rev., 2020, 102B: 014516
45	Geng N S, Bi T G, Zurek E. Structural diversity and superconductivity in S-P-H ternary hydrides under pressure [J]. J. Phys. Chem., 2022, 126C: 7208
46	Grockowiak A D, Ahart M, Helm T, et al. Hot hydride superconductivity above 550 K [J]. Front. Electron. Mater., 2022, 2: 837651
47	Di Cataldo S, Boeri L. Metal borohydrides as ambient-pressure high-T_c superconductors [J]. Phys. Rev., 2023, 107B: L060501
48	Song P, Hou Z F, Baptista De Castro P, et al. High-pressure Mg-Sc-H phase diagram and its superconductivity from first-principles calculations [J]. J. Phys. Chem., 2022, 126C: 2747
49	Shutov G M, Semenok D V, Kruglov I A, et al. Ternary superconducting hydrides in the La-Mg-H system [J]. Mater. Today Phys., 2024, 40: 101300
50	Chen W H, Huang X L, Semenok D V, et al. Enhancement of superconducting properties in the La-Ce-H system at moderate pressures [J]. Nat. Commun., 2023, 14: 2660 doi: 10.1038/s41467-023-38254-6 pmid: 37160883
51	Zhao W D, Huang X L, Zhang Z H, et al. Superconducting ternary hydrides: Progress and challenges [J]. Natl. Sci. Rev., 2024, 11: nwad307
52	Gao M, Yan X W, Lu Z Y, et al. Phonon-mediated high-temperature superconductivity in the ternary borohydride KB₂H₈ under pressure near 12 GPa [J]. Phys. Rev., 2021, 104B: L100504
53	Zhang Z H, Cui T, Hutcheon M J, et al. Design principles for high-temperature superconductors with a hydrogen-based alloy backbone at moderate pressure [J]. Phys. Rev. Lett., 2022, 128: 047001
54	Song Y G, Bi J K, Nakamoto Y, et al. Stoichiometric ternary superhydride LaBeH₈ as a new template for high-temperature superconductivity at 110 K under 80 GPa [J]. Phys. Rev. Lett., 2023, 130: 266001
55	Zhao W D, Duan D F, Du M Y, et al. Pressure-induced high-T_c superconductivity in the ternary clathrate system Y-Ca-H [J]. Phys. Rev., 2022, 106B: 014521
56	Du M Y, Song H, Zhang Z H, et al. Room-temperature superconductivity in Yb/Lu substituted clathrate hexahydrides under moderate pressure [J]. Research, 2022, 2022: 9784309
57	Sanna A, Cerqueira T F T, Fang Y W, et al. Prediction of ambient pressure conventional superconductivity above 80 K in hydride compounds [J]. npj Comput. Mater., 2024, 10: 44
58	Dolui K, Conway L J, Heil C, et al. Feasible route to high-temperature ambient-pressure hydride superconductivity [J]. Phys. Rev. Lett., 2024, 132: 166001
59	Belli F, Novoa T, Contreras-García J, et al. Strong correlation between electronic bonding network and critical temperature in hydrogen-based superconductors [J]. Nat. Commun., 2021, 12: 5381 doi: 10.1038/s41467-021-25687-0 pmid: 34531389
60	Liu L L, Peng F, Song P, et al. Generic rules for achieving room-temperature superconductivity in ternary hydrides with clathrate structures [J]. Phys. Rev., 2023, 107B: L020504
61	Marsiglio F. Eliashberg theory: A short review [J]. Ann. Phys., 2020, 417: 168102
62	Éliashberg G M. Interactions between electrons and lattice vibrations in a superconductor [J]. Sov. Phys. JETP, 1960, 11: 696
63	Dynes R C. McMillan's equation and the T_c of superconductors [J]. Solid State Commun., 1972, 10: 615
64	Allen P B, Dynes R C. Transition temperature of strong-coupled superconductors reanalyzed [J]. Phys. Rev., 1975, 12B: 905
65	McMillan W L. Transition temperature of strong-coupled superconductors [J]. Phys. Rev., 1968, 167: 331
66	Oliveira L N, Gross E K U, Kohn W. Density-functional theory for superconductors [J]. Phys. Rev. Lett., 1988, 60: 2430 pmid: 10038349
67	Marques M A L, Lüders M, Lathiotakis N N, et al. Ab initio theory of superconductivity. II. Application to elemental metals [J]. Phys. Rev., 2005, 72B: 024546
68	Lüders M, Marques M A L, Lathiotakis N N, et al. Ab initio theory of superconductivity. I. Density functional formalism and approximate functionals [J]. Phys. Rev., 2005, 72B: 024545
69	Choudhary K, Garrity K. Designing high-T_C superconductors with BCS-inspired screening, density functional theory, and deep-learning [J]. npj Comput. Mater., 2022, 8: 244
70	Shipley A M, Hutcheon M J, Needs R J, et al. High-throughput discovery of high-temperature conventional superconductors [J]. Phys. Rev., 2021, 104B: 054501
71	Saha S, Di Cataldo S, Giannessi F, et al. Mapping superconductivity in high-pressure hydrides: The Superhydra project [J]. Phys. Rev. Mater., 2023, 7: 054806
72	Sommer T, Willa R, Schmalian J, et al. 3DSC—A dataset of superconductors including crystal structures [J]. Sci. Data, 2023, 10: 816 doi: 10.1038/s41597-023-02721-y pmid: 37990027
73	Cerqueira T F T, Sanna A, Marques M A L. Sampling the materials space for conventional superconducting compounds [J]. Adv. Mater., 2024, 36: 2307085
74	Stanev V, Oses C, Kusne A G, et al. Machine learning modeling of superconducting critical temperature [J]. npj Comput. Mater., 2018, 4: 29
75	Breiman L. Random forests [J]. Mach. Learn., 2001, 45: 5
76	MDR. MDR SuperCon Datasheet Ver.220808 [EB/OL]. (2022-16-12)[Date·Cite].
77	Hutcheon M J, Shipley A M, Needs R J. Predicting novel superconducting hydrides using machine learning approaches [J]. Phys. Rev., 2020, 101B: 144505
78	Liu Y, Huang H Y, Yuan J, et al. Upper limit of the transition temperature of superconducting materials [J]. Patterns, 2023, 4: 100841
79	Wines D, Choudhary K. Data-driven design of high pressure hydride superconductors using DFT and deep learning [J]. Mater. Futures, 2024, 3: 025602
80	Ward L, Dunn A, Faghaninia A, et al. Matminer: An open source toolkit for materials data mining [J]. Comput. Mater. Sci., 2018, 152: 60
81	Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set [J]. Phys. Rev., 1996, 54B: 11169
82	Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals [J]. Phys. Rev., 1993, 47B: 558
83	Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple [J]. Phys. Rev. Lett., 1996, 77: 3865 doi: 10.1103/PhysRevLett.77.3865 pmid: 10062328
84	Wang V, Xu N, Liu J C, et al. VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code [J]. Comput. Phys. Commun., 2021, 267: 108033
85	Pedregosa F, Varoquaux G, Gramfort A, et al. Scikit-learn: Machine learning in python [J]. J. Mach. Learn. Res., 2011, 12: 2825
86	Pettifor D G. A chemical scale for crystal-structure maps [J]. Solid State Commun., 1984, 51: 31
87	Pettifor D G. The structures of binary compounds. I. Phenomenological structure maps [J]. J. Phys., 1986, 19C: 285
88	Villars P, Cenzual K, Daams J, et al. Data-driven atomic environment prediction for binaries using the Mendeleev number: Part 1. Composition AB [J]. J. Alloys Compd., 2004, 367: 167
89	Liu H Y, Naumov I I, Hoffmann R, et al. Potential high-T_c superconducting lanthanum and yttrium hydrides at high pressure [J]. Proc. Natl. Acad. Sci. USA, 2017, 114: 6990

[1]

补充材料

Download

[1]	王京京, 姚志浩, 张鹏, 赵杰, 张迈, 王蕾, 董建新, 陈迎. 镍基高温合金中S元素对基体与热障涂层界面稳定性的影响[J]. 金属学报, 2024, 60(9): 1250-1264.
[2]	周彦余, 李江旭, 刘晨, 赖俊文, 高强, 马会, 孙岩, 陈星秋. 金属间化合物Pt₇Sb投影Berry相位与析氢催化关联的第一性原理计算[J]. 金属学报, 2024, 60(6): 837-847.
[3]	刘壮壮, 丁明路, 谢建新. 金属3D打印数字化制造研究进展[J]. 金属学报, 2024, 60(5): 569-584.
[4]	李志尚, 赵龙, 宗洪祥, 丁向东. 机器学习型分子力场在金属材料相变与变形领域的研究进展[J]. 金属学报, 2024, 60(10): 1388-1404.
[5]	陈名毅, 胡俊伟, 余耀辰, 牛海洋. 机器学习分子动力学辅助材料凝固形核研究进展[J]. 金属学报, 2024, 60(10): 1329-1344.
[6]	刘仕, 黄佳玮, 武静. 机器学习势在铁电材料研究中的应用[J]. 金属学报, 2024, 60(10): 1312-1328.
[7]	文通其, 刘怀忆, 龚小国, 叶贝琳, 刘思宇, 李卓远. 深度势能方法在材料科学中的应用[J]. 金属学报, 2024, 60(10): 1299-1311.
[8]	沈雪阳, 褚瑞轩, 蒋宜辉, 张伟. 相变存储器材料设计与多尺度模拟的研究进展[J]. 金属学报, 2024, 60(10): 1362-1378.
[9]	王冠杰, 刘盛咸, 周健, 孙志梅. 材料研究中的可解释机器学习[J]. 金属学报, 2024, 60(10): 1345-1361.
[10]	穆亚航, 张雪, 陈梓名, 孙晓峰, 梁静静, 李金国, 周亦胄. 基于热力学计算与机器学习的增材制造镍基高温合金裂纹敏感性预测模型[J]. 金属学报, 2023, 59(8): 1075-1086.
[11]	冀秀梅, 侯美伶, 王龙, 刘玠, 高克伟. 基于机器学习的中厚板变形抗力模型建模与应用[J]. 金属学报, 2023, 59(3): 435-446.
[12]	杨累, 赵帆, 姜磊, 谢建新. 机器学习辅助2000 MPa级弹簧钢成分和热处理工艺开发[J]. 金属学报, 2023, 59(11): 1499-1512.
[13]	高建宝, 李志诚, 刘佳, 张金良, 宋波, 张利军. 计算辅助高性能增材制造铝合金开发的研究现状与展望[J]. 金属学报, 2023, 59(1): 87-105.
[14]	何兴群, 付华栋, 张洪涛, 方继恒, 谢明, 谢建新. 机器学习辅助高性能银合金电接触材料的快速发现[J]. 金属学报, 2022, 58(6): 816-826.
[15]	王硕, 王俊升. Al-Li合金中 δ′/θ′/δ′复合沉淀相结构演化及稳定性的第一性原理探究[J]. 金属学报, 2022, 58(10): 1325-1333.

Viewed

Full text

Abstract

Cited

Shared

Discussed