金属学报, 2024, 60(10): 1418-1428 DOI: 10.11900/0412.1961.2024.00140

研究论文

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-Qiu,2, LIU Peitao,2

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

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

收稿日期: 2024-05-08   修回日期: 2024-07-10  

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)

Corresponding authors: 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

Received: 2024-05-08   Revised: 2024-07-10  

Fund supported: National Natural Science Foundation of China(52188101,52201030)
National Key Research and Development Program of China(2021YFB3501503)
Key Research Program of Chinese Academy of Sciences(ZDRW-CN-2021-2-5)

作者简介 About authors

赵晋彬,男,1991年生,博士生

摘要

高压下发现的具有高临界转变温度(Tc)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Tc,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Tc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Tc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Tc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 (Tc) 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 Tc 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-Tc superconducting hydrides.

Keywords: hydride superconductor; superconducting transition temperature; machine learning; random forest; first-principles calculation

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本文引用格式

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 DOI:10.11900/0412.1961.2024.00140

ZHAO Jinbin, WANG Jiantao, HE Dongchang, LI Junlin, SUN Yan, CHEN Xing-Qiu, LIU Peitao. Machine Learning Model for Predicting the Critical Transition Temperature of Hydride Superconductors[J]. Acta Metallurgica Sinica, 2024, 60(10): 1418-1428 DOI:10.11900/0412.1961.2024.00140

材料的超导电性一直是凝聚态物理和材料领域的研究热点之一[1~4]。超导材料的零电阻特性和完美抗磁特性[5]使得超导体在许多领域具有广阔的应用前景[3,6],如高效的电力转换、无损的电力输出、超强磁铁、高灵敏度传感器材料等。但是,超导的形成机制依然是理论和实验研究的重大难题之一,尤其是如何突破温度的限制,使得超导体能够在高温(如≥ 40 K,BCS (Bardeen-Cooper-Schrieffer)理论预测的极限温度[7])甚至室温下获得应用,是科学人员一直在攻克的难题。在过去30余年里,科学人员对不能用传统BCS理论[7]解释的非常规超导体进行了广泛研究。目前,常压下铜基超导体的临界温度(Tc)在20~133 K范围[8~11],铁基超导体的Tc在26~77 K范围[12~14]。铜基超导体因其Tc可以超过77 K (液氮沸点),因此在某些领域获得了的应用[3,6]。近年,镍基超导体[15~19]成为新的研究热点。Sun等[16]报道了一种镍氧化物La3Ni2O7单晶在14 GPa压力下表现出超导电性,超导转变温度为80 K,是继铜基超导体之后再次在氧化物体系中发现的液氮温区的超导体。然而,由于非常规超导体的形成机制尚不明晰,目前仍存在争议[20~22],在关于超导转变温度研究上亟待突破。

因此,科研人员将目光转向了可以用理论解释的常规超导体上。但是在传统BCS理论框架下,很难在非氢化物常规超导体的Tc上取得突破。例如,目前Tc最高的非氢化物常规超导体为MgB2,常压下测得其Tc为39 K[23]。为寻求更高Tc的超导材料,Ashcroft[24,25]提出以H元素为主要成分的化合物有望实现这个目标。这是因为H是元素周期表中最轻的元素,根据Tc1/M (M为元素质量),所以氢化物可以实现高的Tc。此外,H原子提供了高Tc所必要的高频声子以及强的电声耦合作用。在氢化物中通过其他元素对H原子的化学压缩,可以实现超导的临界压力降低[24,25]。需要强调的是,氢化物超导体是唯一先通过理论预测、后被实验验证的超导材料。其中2个最为典型的例子为氢化物超导体H3S[26~28]和LaH10[29~31]。这重新激发了研究者对寻找高Tc超导体的浓厚兴趣[32,33]。随着超导理论的完善和计算能力的提升,许多氢化物超导体体系被理论预测并在实验中成功合成,如Y-H[34,35]、Th-H[36,37]、Ce-H[38,39]、Ca-H[40,41]等体系。

尽管如此,对氢化物超导体的研究仍面临着一些问题和挑战。例如,目前发现的大多数氢化物超导体都需要在高压条件下才能稳定存在,而且电声耦合的强度也依赖于高压。为了降低所需要的压力,研究者将重心转向三元或多元氢化物上,因为它们具有进一步提高Tc并降低金属化压强的潜力[42~51]。目前理论预测的最高Tc的氢化物超导材料为Sun等[43]预测的Li2MgH16,250 GPa下Tc高达473 K。目前已预测了一些可以在中低压区实现高Tc的氢化物超导材料。如,Gao等[52]预测KB2H8在12 GPa下Tc为134~146 K[52]。Zhang等[53]预测了一系列具有萤石型结构框架的AXH8 (A = Sc、Ca、Y、Sr、La、Ba,X = Be、B、Al)氢化物超导体,其中LaBeH8被预测在20 GPa下可以声子稳定,预测Tc约为185 K[53]。之后不久,LaBeH8被Song等[54]首次在实验上成功合成,在80 GPa下测得的Tc为110 K。Zhao等[55]研究了Y-Ca-H的体系结构和超导性,发现了4种笼型结构三元氢化物,经过计算,Y3CaH24的超导转变温度在150 GPa下为242~258 K[55]。Du等[56]通过将重稀土元素Yb/Lu加入类钠盐的六氢化物中,得到一系列可以在中压下稳定的高Tc氢化物超导体,其中Y3LuH24在120 GPa下Tc为283 K,YLuH12在140 GPa下Tc为275 K,YLu3H24在110 GPa下Tc为288 K。最近,Sanna等[57]理论预测了Mg2XH6 (X = Rh、Ir、Pd、Pt)常压超导家族,预测的常压下超导转变温度在45~80 K之间。同时期内,Dolui等[58]也独立地理论预测Mg2IrH6为常压超导材料,并提出了可能的实验合成路径。此外,一些学者对高Tc的成因进行了相关性研究。比如Belli等[59]利用第一性原理计算分析了100多种二元氢化物超导体的电子和结构特性,发现Tc与电子键合之间存在很强的相关性,并建立了一个基于电子局域函数网络的描述符来预测Tc。Liu等[60]提出了实现高Tc氢化物超导的2种规则(即最优价电子数规则和最优原子占据规则),并在此基础上预测了CaHfH12在300 GPa下Tc为360 K,CaZrH12在200 GPa下Tc为290 K。

综上氢化物超导材料的研究发展可见理论预测的重要性。第一性原理方法(如Eliashberg理论[61,62]、McMillan-Allen-Dynes公式[63~65]及超导密度泛函理论[66~68])可以准确预测氢化物超导体的Tc,但计算量很大。尤其是在强电声耦合超导体[69]中,电声耦合矩阵计算十分昂贵。因此,开发准确且高效的氢化物超导转变温度预测模型是十分必要的。随着数据库和人工智能方法的快速发展,数据驱动和机器学习方法也逐渐被应用于超导领域。

在数据驱动方面,Shipley等[70]利用晶体结构预测方法搜索了整个元素周期表10~50 GPa下稳定的二元氢化物,对最佳超导候选材料进行了高通量计算,发现了36种Tc超过100 K的声子稳定的高压氢化物超导体。Choudhary和Garrity[69]针对常规超导体开发了一个高通量计算工作流,计算了超过1000个材料的Tc,建立了一个系统的BCS超导数据库,并基于此开发了深度学习预测模型。Saha等[71]基于现有氢化物超导体的结构框架,通过元素替换方式获得了139个新的氢化物超导体,并基于此创建了Superhydra数据库,目前仅限于在200 GPa下的二元氢化物。Sommer等[72]建立了“3DSC”超导数据库,其中包括Tc和结构数据,以便进行机器学习。Cerqueira等[73]对7000多个常规超导候选材料的Tc进行了高通量第一性原理计算,发现了许多之前尚未报道的新超导材料。

在机器学习预测方面,Stanev等[74]使用随机森林(random forest,RF)机器学习方法[75]对SuperCon数据库[76]中超过12000条的超导数据进行了训练,探索了超导电性与材料化学/结构特性之间的联系。Hutcheon等[77]针对二元氢化物EH n (其中E为除H元素以外的其他元素,如La、Mg等),将E元素的van der Waals半径、原子序数、原子质量、原子每个轨道上的电子数及H含量作为描述符,构建了一个基于神经网络的机器学习模型,模型均方根误差为34 K。Liu等[78]对轨道属性、电子壳层信息等具有物理意义的特征进行了排列组合,得到了140多个特征,对SuperCon数据库的Tc数据进行了回归预测,得出材料的超导转变温度上限与电子轨道杂化存在着很强的联系。Wines和Choudhary[79]使用第一性原理计算预测了900多种氢化物材料的Tc,发现了125种稳定的结构,并开发了图神经网络Tc预测模型,大大缩减了预测成本。

需要注意的是,上述工作都是利用大量的特征,通过强相关方法对超导转变温度进行拟合和预测。尽管发现了一些关联规律,但是过多的特征会增加模型的复杂度并降低模型的物理可解释性。本工作围绕已被理论预测或被实验证实的氢化物超导体,利用随机森林算法,开发了一个简单且物理可解释的Tc机器学习预测模型。随机森林算法可对特征按重要性进行排序,从而选取出最关键的特征,不仅可以降低模型过拟合的风险,同时可以增加模型的可解释性和泛化能力。结果发现,仅基于所选择的4个最关键的且具有物理意义的特征(包含组成元素的价电子数的标准差、共价半径的平均值和门捷列夫数(Mendeleev数)的范围,以及Fermi能级处H的态密度占比),所构建的机器学习模型便可以实现较高的Tc预测精度(平均绝对误差为24.3 K,均方根误差为33.6 K)。本工作开发的Tc机器学习模型和公式为氢化物超导体的高通量筛选提供了有效预测模型,进而有助于加速高Tc超导氢化物的发现。

1 计算方法

1.1 数据收集

本工作从文献中收集了258个Tc大于10 K的氢化物超导体,包含对应的压强和结构数据,详细数据汇总在补充材料表S1中。这是目前收集的较为齐全的氢化物超导体数据集。本工作仅聚焦氢化物超导体,这是因为氢化物超导体具有较高Tc的潜质,而且可以用理论来预测其Tc,理论预测数据多且较为干净,便于机器学习。所收集的氢化物超导体包含二元和三元氢化物,其数据分布见图1。可见,大多数氢化物超导体都需要一个很高的压力来实现超导电性。从Tc与压强的关系分布图(图1a)可以看出,三元氢化物超导体大都在二元氢化物超导体的左上方,意味着在相同Tc下三元氢化物超导体需要的临界压力相对较低,或者在相同压力下三元氢化物超导体表现出较高的Tc。这正是目前研究者把研究重心转到三元或多元氢化物的原因。从不同Tc分布区间的二元和三元氢化物的数量对比(图1b)可见,相比二元氢化物,三元氢化物超导体的数量较少,约占二元氢化物超导体的1/5,这意味着有更多的三元或多元氢化物超导体仍未被探索。

图1

图1   氢化物超导体的分布情况

Fig.1   Distribution of hydride superconductors

(a) critical temperature (Tc) vs pressure

(b) number of binary and ternary hydrides in different Tc distribution intervals


1.2 特征获取

为了建立准确、可靠的机器学习模型,选取相关的重要特征是极为必要的。考虑的特征不仅应该能够唯一地表示每种材料,还应该容易计算,以便对新材料进行快速预测。本工作获取特征的方式有3种。第一,使用MATMINER软件包[80]获取。该软件包是一个很好的资源库,可以快速地生成特征,特别适用材料科学领域。同时,下载了材料的一系列广谱特征,如共价半径、原子质量、价电子数、配位数、Mendeleev数等。此外,还捕获了构成元素的s、p、d、f壳层中价电子的平均数量。第二,针对收集的氢化物超导体的晶体结构进行键长和配位数的计算,得到了键长(最短、最长及平均)和配位数特征。第三,引入具有物理意义的特征。受Belli等[59]和Liu等[78]工作的启发,本工作通过第一性原理计算得到最高饱和轨道和最低不饱和轨道之间的能级间隔ΔE[78]、Fermi能级处体系的总态密度(TDOS)、Fermi能级处H的态密度占比(HDOS Fraction)、氢化物中H原子的原子比例(Hf)等。通过这3种方式,本工作最终获得了共计133个特征。

1.3 第一性原理计算

使用基于密度泛函理论的VASP[81,82]软件计算电子态密度和ΔE。选用广义梯度近似下的Perdew-Burke-Ernzerhof (PBE)[83]电子交换关联泛函。平面波截断能设置为600 eV。结构优化和态密度计算分别使用了波矢k点间距为0.3 × 2π nm-1和0.2 × 2π nm⁻¹的格点。ΔE的具体计算公式如下[78]

ΔE=n1E1PDOS(E1)DOS(E1)-n2E2PDOS(E2)DOS(E2).

式中,E1代表氢化物中某一原子的最高占据轨道能量,E2表示H原子的s轨道能量;PDOS和DOS分别为各原子的轨道分辨投影态密度和总的态密度;n1n2表示原子个数。利用了vaspkit软件[84]提取了VASP计算的态密度信息,然后进行了更密格点的插值。

1.4 机器学习模型与训练

本工作主要使用SCIKIT-LEARN (sklearn)库[85]提供的随机森林算法。随机森林算法是一种基于决策树的集成学习算法,不论是在分类还是在回归方面都表现出良好的性能。它的优点是计算量小,适用于较少数据集的机器学习。最重要的是,随机森林算法可以评估每个特征对目标变量的重要性,这对关键特征筛选、提高机器学习模型泛化能力非常有用。本工作所用随机森林算法的超参数见表1。其中,n-estimators决定决策树的数量,增加树的数量可以提高模型的准确性和稳定性,但同时也会增加计算成本和过拟合风险。max-depth为决策树的最大深度,限制树的最大深度可以防止过拟合,但也可能导致欠拟合,如果没有特别指定,树会一直生长直到叶节点都是纯叶节点或者达到max-depth指定的最大深度。min-samples-split为分割内部节点所需的最小样本数,增加这个值可以使得树更加平滑,减少过拟合风险,但是可能导致模型变得过于简单。min-samples-leaf为叶节点最小样本数,这个参数控制着树的复杂度,增加它的值可以使模型更加稳定,但可能导致过拟合。

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)

Table 1  Hyper-parameters used in the sklearn library for the random forest algorithm (For other parameters that are not explicitly specified, default values are used)

ParameterMeaning of parameterValue
n-estimatorsNumber of decision trees10-30
Max-depthMaximum depth of decision treesNone, 1, 2, 4
Min-samples-splitMinimum number of samples required to split internal nodes2, 4, 8
Min-samples-leafMinimum number of samples at leaf nodes1, 2, 4, 8

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针对关键特征筛选,首先利用递归特征消除算法,将特征数量从初始的133个减少至55个。随后进行第二次递归特征消除计算,将55个特征再次降低至11个。这11个特征分别是:Fermi能级处的TDOS、Fermi能级处的HDOS Fraction、平均键长[Mean(length)]、平均配位数[Mean(cn)]、3个Mendeleev数特征[Mean(Mendeleev Number)、Range(Mendeleev Number)及Min(Mendeleev Number)]、平均族序数[Mean(column)]、平均共价半径[Mean(CovalentRadius)]、最小电负性[Min(Electronegativity)],及价电子数的标准差[Avg_dev(NValence)]。需要指出的是,Liu等[78]提出的ΔE因其重要性值较低而并未保留下来。这说明尽管ΔE与超导材料Tc的上限存在很强的相关性[78],但是ΔETc本身并不是一个重要的特征。

接下来,使用随机森林方法进行回归训练,按照重要性对特征进行排序及分析。在每一轮训练中,将特征进行重新组合,比如从11个特征中筛选出10个,一共有11种组合,然后选择其中测试误差最低的一组,再进行下一轮回归训练,直至在特征数量尽可能少的前提下训练的模型足够准确。

2 计算结果

对于特征的筛选过程,在每次随机森林训练结束时,剔除重要性最低的特征,并重新评估模型的精度。常用的精度评估方法包括平均绝对误差(MAE)和均方根误差(RMSE)。在特征数量递归降低过程中,固定训练集的比例为90%,其余10%的数据作为测试集。模型测试误差与特征数量的关系见图2a。可见,模型在特征数量为4时表现最好,测试集误差为MAE = 24.3 K,RMSE = 33.6 K。

图2

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

Fig.2   Model test errors as a function of number of features for one single training (a) and averaged model test errors of ten independent trainings as a function of training set ratio (b) (The shadow-filled areas show the standard deviation. MAE—mean absolute error, RMSE—root mean square error)


为了消除模型的偶然性并验证筛选出的4个特征是否是理想结果,利用这4个特征进行了第二项计算实验,即通过改变训练集的分布方式和训练集与测试集的占比来验证模型的稳定性。首先,在划分训练集和测试集的时候,使用sklearn库中的train_test_split函数,并对随机种子random_state进行修改。random_state通常用于控制随机数生产过程,使用相同的random_state值时会得到完全相同的训练集/测试集划分,这样会导致模型在测试集上的表现过于理想。因此,更改random_state值获取不同的训练集/测试集随机划分来验证模型的准确性是非常有必要的。本工作中,一共进行了10次修改(random_state = 10~100,间隔为10),取10次结果的平均值作为最终的模型测试结果,标准差作为误差区间。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见图2b。可见,随着训练集占比的提高,模型的精度会越来越好,但是当训练集占比过高时则会出现模型过拟合,导致模型测试集误差增大。在训练过程中,使用sklearn库中的GridSearchCV模块进行了参数搜索。GridSearchCV模块可以自动调参,其遍历所有可能参数组合,最终确定最优结果对应的组合参数。GridSearchCV模块里内置了交叉验证功能,本工作使用了五倍交叉验证(cv = 5)进行模型训练。需要指出的是,本工作也尝试了使用十倍交叉验证进行模型训练,最后发现其与五倍交叉验证相比,模型精度不受影响。通过对数据集进行十次划分,再结合五倍交叉验证的模型训练,大大消除了模型训练结果的偶然性。发现当训练集占比为90%时,模型测试集MAE和RMSE的均值最低,即MAE = (38.6 ± 7.8) K,RMSE = (56.2 ± 14.3) K。

图3a给出了递归筛选出的最重要的4个特征及其重要性值。按照重要性增加的顺序排序为:[Mean(CovalentRadius)]、[Avg_dev(NValence)]、[Range(Mendeleev Number)]及(HDOS Fraction)。图3b给出了基于这4个关键特征训练获得的最精确的机器学习模型(使用训练集占比0.9和n_estimators = 29获得)预测的Tc与真值对比。可见,预测的训练集和测试集的Tc大多集中在y = x两侧,因此不存在严重的模型过拟合问题。模型测试集误差为:MAE = 24.3 K,RMSE = 33.6 K。需要强调的是,在这4个关键特征的基础上减少特征数量或添加其他的特征都会降低模型的精度(图2a)。

图3

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

Fig.3   The most important 4 features by recursive selections (a) and Tc predicted by the most accurate machine learning model obtained vs the ground-truth values (b) ([Avg_dev(NValence)]—standard deviation of the number of valence electrons of constituent element, [Mean(CovalentRadius)]—mean covalent radius of constituent element, [Range(Mendeleev Number)]—range of the Mendeleev number of constituent element, HDOS Fraction—hydrogen fraction of the total density of states at the Fermi energy)


3 分析讨论

下文重点分析这4个特征并探讨它们与Tc的关系。

3.1 价电子数(NValence)

Stanev等[74]曾在自己的工作中提到“3个‘黄金描述符’将60个已知的Tc > 10 K的超导体限制在了特征空间的3个小岛上:平均价电子数、轨道半径差和金属电负性差”。选择这3个描述符是因为它们在二元、三元化合物的分类上以及稳态、亚稳态晶体的预测方面获得的成功[74]。Liu等[60]发现在金属氢化物超导体中,要使金属原子为H原子有效提供电子,那么金属原子应该具有价电子数3。由此可见,价电子数对氢化物超导是一个重要的特征。而在本工作开发的氢化物超导体Tc机器学习预测模型中,[Avg_dev(NValence)]被随机森林算法选为一个重要的特征。从图4a可以看出,高Tc氢化物超导体大多集中在Avg_dev(NValence) = 0~1的区域内。此外,通过绘制Tc与金属氢化物超导体中金属原子价电子数平均值的关系图,发现高Tc金属氢化物超导体大都分布在金属原子价电子数平均值为3的区域,这与Liu等[60]发现的最优价电子数规则高度一致。

图4

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

Fig.4   Correlation between Tc and four features of Avg_dev(NValence) (a), Mean(CovalentRadius) (b), Range(Mendeleev Number) (c), and HDOS Fraction (d)


3.2 平均原子半径(Mean CovalentRadius)

原子半径影响原子间的距离和相互作用强度,从而影响晶体结构和电子结构。对超导材料来说,晶体结构的变化会影响其中电子的相互作用方式,从而影响电子的运动和配对。在金属氢化物超导体中为了实现高的Tc,需要对H原子施加尽可能高的化学挤压,那么金属元素的原子半径需要在给定的晶格下使金属原子最大地填充晶格。这就是Liu等[60]提出的最优原子占据规则。此外,在Stanev等[74]和Hutcheon等[77]开发的机器学习模型中,平均原子半径亦作为一个重要的特征。图4b绘制了Tc与平均共价半径的关系。可见,高Tc氢化物超导体的平均共价半径一般在40~55 pm范围内。

3.3 Mendeleev(Mendeleev NumberMN)

Mendeleev数由Pettifor[86,87]在1984年首次提出,是晶体中每个化学元素分配的排列数,目的是使具有相似行为的化学元素归为一类[86,88]。在Pettifor图中,元素被排列成一条线或曲线,这条线上的元素按照它们的化合物形成能力进行排序。Pettifor图中位置接近的元素通常意味着具有相似的化合物形成能力。元素的电负性和原子半径也是排列元素时考虑的因素之一,这些物理化学性质影响元素之间的相互作用,从而影响化合物的形成和性质。换句话说,MN根据元素的电子结构和化学性质改变元素的顺序,使具有相似性质的元素彼此靠近。

在金属氢化物超导体中,Range(Mendeleev Number)表示氢化物中元素MN最大的数(即H的MN数92)减去元素MN最小的数。图4c展示了Tc与Range(Mendeleev Number)的关系。从图中的趋势可以看出,MN较小的金属元素有助于提高氢化物超导体的Tc。这是因为MN较小的金属元素通常具有较低的电负性、较大的原子半径及较低的价电子数,如Y、La等元素。这些金属元素可能更容易与H元素形成超氢化物,有助于提高Tc。这与文献[34,35,53,54]报道的高Tc氢化物超导体大都是钇或镧基超氢化物相一致。

3.4 Fermi能级处H的电子态密度占比(HDOS Fraction)

Fermi能级处电子的态密度D(Ef)对Tc的影响体现在简化的BCS公式[7]中:

Tcexp-1λD(Ef)

式中,λ是电声耦合系数。但是,Belli等[59]发现在部分氢化物超导材料中,Tc与体系总的电子态密度似乎没有太大的关联。与之相比,他们发现与Tc相关性更强的是HDOS[59]。从图4d中可以看出,Tc确实与HDOS存在着很强的正相关性,即HDOS越大,Tc通常也越高。这也与本工作中通过随机森林算法获得的特征重要性评价一致,表现出HDOS特征的重要性值最高(图3a)。需要强调的是,HDOS特征也蕴含了压强的信息。即随着压强的改变,材料的结构与DOS也随之变化。尽管Tc与压强的关系十分密切,但是在机器学习过程中,压强特征因重要性低而被筛选掉,而HDOS特征则因为具有更高的重要性而被保留下来。基于HDOS,Belli等提出了一个预测Tc的经验公式[59]

Tc=(750φHfHDOS3-85)

式中,φ是电子局域函数网络的描述符,Hf为H在氢化物中的原子分数。该经验公式是通过拟合178种超导材料(包含纯H和二元氢化物)获得的,预测精度约为60 K[59]

3.5 模型比较

为了比较构建的随机森林机器学习预测模型和Belli等[59]提出的经验 公式(3),作为例子,本工作仅针对数据集中6个Tc最高的氢化物超导材料的Tc进行了预测,具体对比结果见表2[43,59,60,70,89]。它们的晶体结构和电子态密度见图5。可见,随机森林机器学习预测模型最优,其性能要远优于Belli经验 公式(3)。从表2[43,59,60,70,89]也可以看到,高Tc氢化物超导体一般具有高的HDOS或Range(MN)。图5表明,6个Tc最高的氢化物超导材料都是具有笼型结构的超氢化物。

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]

Table 2  Model predictions for the six hydride superconductors with the highest Tc in the dataset[43,59,60,70,89]

Material

Pressure

GPa

HDOS

Range(Mendeleev Number)Mean(CovalentRadius)

Avg_dev

(NValence)

Tc (RF)

K

Tc (Belli)[59]

K

Tc (Expt.) K
Li2MgH162500.539147.00.10319.3298.3473.0[43]
CaHfH121900.288551.62.24324.9198.3363.0[60]
CaHfH183000.418545.51.62339.0332.0345.0[60]
CaZrH123000.318551.60.49308.2192.6343.0[60]
MgH125000.722439.50.14300.5522.4340.0[70]
YH102500.418045.60.33312.5259.6326.0[89]
MAE-----47.6125.3-
RMSE-----68.4140.3-

Note: RF—random forest, HDOS—hydrogen fraction of the total density of states at the Fermi energy

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图5

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

Fig.5   Crystal structures and electronic densities of states for the six hydride superconductors with the highest Tc in the dataset

(a) Li2MgH16 (250 GPa) (b) CaHfH12 (190 GPa) (c) CaHfH18 (300 GPa)

(d) CaZrH12 (300 GPa) (e) MgH12 (500 GPa) (f) YH10 (250 GPa)


4 结论

针对金属氢化物超导体的临界转变温度,本工作建立了一个简单、准确且物理可解释的随机森林机器学习预测模型。这得益于收集的数据集比较丰富全面,引入了具有物理意义的特征,以及充分运用了随机森林算法具有的特征重要性评估的特性。所构建的模型仅仅基于4个关键特征,即组成元素价电子数的标准差、共价半径的平均值和Mendeleev数范围,以及Fermi能级处H的电子态密度占比,便实现了测试集平均绝对误差为24.3 K、均方根误差为33.6 K高的模型预测精度。此外,通过深入分析这4个特征与超导临界转变温度的关系,发现高Tc金属氢化物超导体一般具有如下特性:(1) 金属元素的价电子数平均值为3,价电子数的标准差在0~1范围内;(2) 组成元素的平均共价半径在40~55 pm范围内;(3) 金属元素具有较小的Mendeleev数;(4) Fermi能级处具有较高的H的电子态密度占比。

文中补充材料可通过以下网址查看:https://www.ams.org.cn/CN/10.11900/0412.1961.2024.00140

参考文献

De Nobel J, Lindenfeld P.

The discovery of superconductivity

[J]. Phys. Today, 1996, 49: 40

[本文引用: 1]

Boeri L, Hennig R, Hirschfeld P, et al.

The 2021 room-temperature superconductivity roadmap

[J]. J. Phys. Condens. Matter, 2022, 34: 183002

Kim C J. Superconductor Levitation: Concepts and Experiments [M]. Singapore: Springer, 2019: 1

[本文引用: 2]

Mangin P, Kahn R. Superconductivity: An introduction [M]. Cham: Springer, 2017: 1

[本文引用: 1]

Meissner W, Ochsenfeld R.

Ein neuer effekt bei eintritt der supraleitfähigkeit

[J]. Naturwissenschaften, 1933, 21: 787

[本文引用: 1]

Hirsch J E, Maple M B, Marsiglio F.

Superconducting materials classes: Introduction and overview

[J]. Physica, 2015, 514C: 1

[本文引用: 2]

Bardeen J, Cooper L N, Schrieffer J R.

Microscopic theory of superconductivity

[J]. Phys. Rev., 1957, 106: 162

[本文引用: 3]

Bednorz J G, Müller K A.

Possible high Tc superconductivity in the Ba-La-Cu-O system

[J]. Z. Phys., 1986, 64B: 189

[本文引用: 1]

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

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     

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

[本文引用: 1]

Kamihara Y, Watanabe T, Hirano M, et al.

Iron-based layered superconductor La[O1 - x F x ]FeAs (x = 0.05-0.12) with Tc = 26 K

[J]. J. Am. Chem. Soc., 2008, 130: 3296

DOI      PMID      [本文引用: 1]

Paglione J, Greene R L.

High-temperature superconductivity in iron-based materials

[J]. Nat. Phys., 2010, 6: 645

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

[本文引用: 1]

Li D F, Lee K, Wang B Y, et al.

Superconductivity in an infinite-layer nickelate

[J]. Nature, 2019, 572: 624

[本文引用: 1]

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

[本文引用: 1]

Li Q, Zhang Y J, Xiang Z N, et al.

Signature of superconductivity in pressurized La4Ni3O10

[J]. Chin. Phys. Lett., 2024, 41: 017401

Zhang M X, Pei C Y, Du X, et al.

Superconductivity in trilayer nickelate La4Ni3O10 under pressure

[DB/OL]. arXiv: 2311. 07423, 2023

Wang M.

Discovery of high-Tc superconductivity in a nickelate

[J]. Physics, 2023, 52: 663

[本文引用: 1]

王 猛.

液氮温区镍氧化物高温超导体的发现

[J]. 物理, 2023, 52: 663

[本文引用: 1]

Pickett W E.

Colloquium: Room temperature superconductivity: The roles of theory and materials design

[J]. Rev. Mod. Phys., 2023, 95: 021001

[本文引用: 1]

Hu J P.

Searching for new unconventional high temperature superconductors

[J]. Acta Phys. Sin., 2021, 70(1): 017101

胡江平.

探索非常规高温超导体

[J]. 物理学报, 2021, 70(1): 017101

Li J X.

Spin fluctuations and uncoventional superconducting pairing

[J]. Acta Phys. Sin., 2021, 70(1): 017408

[本文引用: 1]

李建新.

自旋涨落与非常规超导配对

[J]. 物理学报, 2021, 70(1): 017408

[本文引用: 1]

Nagamatsu J, Nakagawa N, Muranaka T, et al.

Superconductivity at 39 K in magnesium diboride

[J]. Nature, 2001, 410: 63

[本文引用: 1]

Ashcroft N W.

Metallic hydrogen: A high-temperature superconductor?

[J]. Phys. Rev. Lett., 1968, 21: 1748

[本文引用: 2]

Ashcroft N W.

Hydrogen dominant metallic alloys: High temperature superconductors?

[J]. Phys. Rev. Lett., 2004, 92: 187002

[本文引用: 2]

Duan D F, Liu Y X, Tian F B, et al.

Pressure-induced metallization of dense (H2S)2H2 with high-Tc superconductivity

[J]. Sci. Rep., 2014, 4: 6968

[本文引用: 1]

Gor'kov L P, Kresin V Z.

Pressure and high-Tc superconductivity in sulfur hydrides

[J]. Sci. Rep., 2016, 6: 25608

DOI      PMID     

The paper discusses fundamentals of record-T-C superconductivity discovered under high pressure in sulfur hydride. The rapid increase of T-C with pressure in the vicinity of P-cr approximate to 123GPa is interpreted as the fingerprint of a first-order structural transition. Based on the cubic symmetry of the high-T-C phase, it is argued that the lower-T-C phase has a different periodicity, possibly related to an instability with a commensurate structural vector. In addition to the acoustic branches, the phonon spectrum of H3S contains hydrogen modes with much higher frequencies. Because of the complex spectrum, usual methods of calculating T-C are here inapplicable. A modified approach is formulated and shown to provide realistic values for T-C and to determine the relative contributions of optical and acoustic branches. The isotope effect ( change of T-C upon Deuterium for Hydrogen substitution) originates from high frequency phonons and differs in the two phases. The decrease of T-C following its maximum in the high-T-C phase is a sign of intermixing with pairing at hole-like pockets which arise in the energy spectrum of the cubic phase at the structural transition. On-pockets pairing leads to the appearance of a second gap and is remarkable for its non-adiabatic regime: hydrogen mode frequencies are comparable to the Fermi energy.

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

[本文引用: 1]

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

[本文引用: 1]

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

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

[本文引用: 1]

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

[本文引用: 1]

Zhang S B, Zhang M, Liu H Y.

Superconductive hydrogen-rich compounds under high pressure

[J]. Appl. Phys., 2021, 127A: 684

[本文引用: 1]

Troyan I A, Semenok D V, Kvashnin A G, et al.

Anomalous high-temperature superconductivity in YH6

[J]. Adv. Mater., 2021, 33: 2006832

[本文引用: 2]

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

[本文引用: 2]

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

[本文引用: 1]

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

[本文引用: 1]

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

[本文引用: 1]

Chen W H, Semenok D V, Huang X L, et al.

High-temperature superconducting phases in cerium superhydride with a Tc up to 115 K below a pressure of 1 megabar

[J]. Phys. Rev. Lett., 2021, 127: 117001

[本文引用: 1]

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      PMID      [本文引用: 1]

Hydrogen-rich compounds hold promise as high-temperature superconductors under high pressures. Recent theoretical hydride structures on achieving high-pressure superconductivity are composed mainly of H(2) fragments. Through a systematic investigation of Ca hydrides with different hydrogen contents using particle-swam optimization structural search, we show that in the stoichiometry CaH(6) a body-centered cubic structure with hydrogen that forms unusual "sodalite" cages containing enclathrated Ca stabilizes above pressure 150 GPa. The stability of this structure is derived from the acceptance by two H(2) of electrons donated by Ca forming an "H(4)" unit as the building block in the construction of the three-dimensional sodalite cage. This unique structure has a partial occupation of the degenerated orbitals at the zone center. The resultant dynamic Jahn-Teller effect helps to enhance electron-phonon coupling and leads to superconductivity of CaH(6). A superconducting critical temperature (T(c)) of 220-235 K at 150 GPa obtained from the solution of the Eliashberg equations is the highest among all hydrides studied thus far.

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      PMID      [本文引用: 1]

Searching for superconductivity with T near room temperature is of great interest both for fundamental science & many potential applications. Here we report the experimental discovery of superconductivity with maximum critical temperature (T) above 210 K in calcium superhydrides, the new alkali earth hydrides experimentally showing superconductivity above 200 K in addition to sulfur hydride & rare-earth hydride system. The materials are synthesized at the synergetic conditions of 160~190 GPa and ~2000 K using diamond anvil cell combined with in-situ laser heating technique. The superconductivity was studied through in-situ high pressure electric conductance measurements in an applied magnetic field for the sample quenched from high temperature while maintained at high pressures. The upper critical field Hc(0) was estimated to be ~268 T while the GL coherent length is ~11 Å. The in-situ synchrotron X-ray diffraction measurements suggest that the synthesized calcium hydrides are primarily composed of CaH while there may also exist other calcium hydrides with different hydrogen contents.© 2022. The Author(s).

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

[本文引用: 1]

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

[本文引用: 6]

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

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

Grockowiak A D, Ahart M, Helm T, et al.

Hot hydride superconductivity above 550 K

[J]. Front. Electron. Mater., 2022, 2: 837651

Di Cataldo S, Boeri L.

Metal borohydrides as ambient-pressure high-Tc superconductors

[J]. Phys. Rev., 2023, 107B: L060501

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

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

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      PMID     

Ternary hydrides are regarded as an important platform for exploring high-temperature superconductivity at relatively low pressures. Here, we successfully synthesized the hcp-(La,Ce)H at 113 GPa with the initial La/Ce ratio close to 3:1. The high-temperature superconductivity was strikingly observed at 176 K and 100 GPa with the extrapolated upper critical field H(0) reaching 235 T. We also studied the binary La-H system for comparison, which exhibited a T of 103 K at 78 GPa. The T and H(0) of the La-Ce-H are respectively enhanced by over 80 K and 100 T with respect to the binary La-H and Ce-H components. The experimental results and theoretical calculations indicate that the formation of the solid solution contributes not only to enhanced stability but also to superior superconducting properties. These results show how better superconductors can be engineered in the new hydrides by large addition of alloy-forming elements.© 2023. The Author(s).

Zhao W D, Huang X L, Zhang Z H, et al.

Superconducting ternary hydrides: Progress and challenges

[J]. Natl. Sci. Rev., 2024, 11: nwad307

[本文引用: 1]

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

[本文引用: 2]

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

[本文引用: 3]

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

[本文引用: 2]

Zhao W D, Duan D F, Du M Y, et al.

Pressure-induced high-Tc superconductivity in the ternary clathrate system Y-Ca-H

[J]. Phys. Rev., 2022, 106B: 014521

[本文引用: 2]

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

[本文引用: 1]

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

[本文引用: 1]

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

[本文引用: 1]

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      PMID      [本文引用: 12]

By analyzing structural and electronic properties of more than a hundred predicted hydrogen-based superconductors, we determine that the capacity of creating an electronic bonding network between localized units is key to enhance the critical temperature in hydrogen-based superconductors. We define a magnitude named as the networking value, which correlates with the predicted critical temperature better than any other descriptor analyzed thus far. By classifying the studied compounds according to their bonding nature, we observe that such correlation is bonding-type independent, showing a broad scope and generality. Furthermore, combining the networking value with the hydrogen fraction in the system and the hydrogen contribution to the density of states at the Fermi level, we can predict the critical temperature of hydrogen-based compounds with an accuracy of about 60 K. Such correlation is useful to screen new superconducting compounds and offers a deeper understating of the chemical and physical properties of hydrogen-based superconductors, while setting clear paths for chemically engineering their critical temperatures.© 2021. The Author(s).

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

[本文引用: 11]

Marsiglio F.

Eliashberg theory: A short review

[J]. Ann. Phys., 2020, 417: 168102

[本文引用: 1]

Éliashberg G M.

Interactions between electrons and lattice vibrations in a superconductor

[J]. Sov. Phys. JETP, 1960, 11: 696

[本文引用: 1]

Dynes R C.

McMillan's equation and the Tc of superconductors

[J]. Solid State Commun., 1972, 10: 615

[本文引用: 1]

Allen P B, Dynes R C.

Transition temperature of strong-coupled superconductors reanalyzed

[J]. Phys. Rev., 1975, 12B: 905

McMillan W L.

Transition temperature of strong-coupled superconductors

[J]. Phys. Rev., 1968, 167: 331

[本文引用: 1]

Oliveira L N, Gross E K U, Kohn W.

Density-functional theory for superconductors

[J]. Phys. Rev. Lett., 1988, 60: 2430

PMID      [本文引用: 1]

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

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

[本文引用: 1]

Choudhary K, Garrity K.

Designing high-TC superconductors with BCS-inspired screening, density functional theory, and deep-learning

[J]. npj Comput. Mater., 2022, 8: 244

[本文引用: 2]

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

[本文引用: 6]

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

[本文引用: 1]

Sommer T, Willa R, Schmalian J, et al.

3DSC—A dataset of superconductors including crystal structures

[J]. Sci. Data, 2023, 10: 816

DOI      PMID      [本文引用: 1]

Data-driven methods, in particular machine learning, can help to speed up the discovery of new materials by finding hidden patterns in existing data and using them to identify promising candidate materials. In the case of superconductors, the use of data science tools is to date slowed down by a lack of accessible data. In this work, we present a new and publicly available superconductivity dataset ('3DSC'), featuring the critical temperature T of superconducting materials additionally to tested non-superconductors. In contrast to existing databases such as the SuperCon database which contains information on the chemical composition, the 3DSC is augmented by approximate three-dimensional crystal structures. We perform a statistical analysis and machine learning experiments to show that access to this structural information improves the prediction of the critical temperature T of materials. Furthermore, we provide ideas and directions for further research to improve the 3DSC. We are confident that this database will be useful in applying state-of-the-art machine learning methods to eventually find new superconductors.© 2023. The Author(s).

Cerqueira T F T, Sanna A, Marques M A L.

Sampling the materials space for conventional superconducting compounds

[J]. Adv. Mater., 2024, 36: 2307085

[本文引用: 1]

Stanev V, Oses C, Kusne A G, et al.

Machine learning modeling of superconducting critical temperature

[J]. npj Comput. Mater., 2018, 4: 29

[本文引用: 4]

Breiman L.

Random forests

[J]. Mach. Learn., 2001, 45: 5

[本文引用: 1]

MDR.

MDR SuperCon Datasheet Ver

.220808 [EB/OL]. (2022-16-12)[Date·Cite].

[本文引用: 1]

Hutcheon M J, Shipley A M, Needs R J.

Predicting novel superconducting hydrides using machine learning approaches

[J]. Phys. Rev., 2020, 101B: 144505

[本文引用: 2]

Liu Y, Huang H Y, Yuan J, et al.

Upper limit of the transition temperature of superconducting materials

[J]. Patterns, 2023, 4: 100841

[本文引用: 6]

Wines D, Choudhary K.

Data-driven design of high pressure hydride superconductors using DFT and deep learning

[J]. Mater. Futures, 2024, 3: 025602

[本文引用: 1]

Ward L, Dunn A, Faghaninia A, et al.

Matminer: An open source toolkit for materials data mining

[J]. Comput. Mater. Sci., 2018, 152: 60

[本文引用: 1]

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

[本文引用: 1]

Kresse G, Hafner J.

Ab initio molecular dynamics for liquid metals

[J]. Phys. Rev., 1993, 47B: 558

[本文引用: 1]

Perdew J P, Burke K, Ernzerhof M.

Generalized gradient approximation made simple

[J]. Phys. Rev. Lett., 1996, 77: 3865

DOI      PMID      [本文引用: 1]

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

[本文引用: 1]

Pedregosa F, Varoquaux G, Gramfort A, et al.

Scikit-learn: Machine learning in python

[J]. J. Mach. Learn. Res., 2011, 12: 2825

[本文引用: 1]

Pettifor D G.

A chemical scale for crystal-structure maps

[J]. Solid State Commun., 1984, 51: 31

[本文引用: 2]

Pettifor D G.

The structures of binary compounds. I. Phenomenological structure maps

[J]. J. Phys., 1986, 19C: 285

[本文引用: 1]

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

[本文引用: 1]

Liu H Y, Naumov I I, Hoffmann R, et al.

Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure

[J]. Proc. Natl. Acad. Sci. USA, 2017, 114: 6990

[本文引用: 5]

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