高压下Nb<sub>3</sub>Sn单晶的超导相转变

石震天; 杨绪佳; 王豪阳; 乔力

doi:10.11858/gywlxb.20200615

高压下Nb₃Sn单晶的超导相转变

doi: 10.11858/gywlxb.20200615

太原理工大学机械与运载工程学院应用力学研究所，山西太原　030024

基金项目: 国家自然科学基金（11772212）

详细信息

作者简介:
石震天（1995－），男，硕士研究生，主要从事电磁固体力学研究. E-mail：384794451@qq.com

通讯作者:
乔　力（1984－），男，副教授，主要从事微纳米尺度结构材料力学、电磁固体力学研究. E-mail：qiaoli@tyut.edu.cn

中图分类号: O511.3；O521.2
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出版历程
- 收稿日期: 2020-09-21
- 修回日期: 2020-10-22

Superconducting Transition of Nb₃Sn Single Crystal under High-Pressure

Institute of Applied Mechanics, College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 研究高压下Nb₃Sn单晶的超导相转变行为对探究力学变形诱导的材料超导性能弱化机理有重要意义。通过分子动力学模拟研究了Nb₃Sn单晶在高压下的原子尺度变形和晶体结构变化，在此基础上，建立了高压下Nb₃Sn单晶的超导相转变模型，模型预测结果与实验观测结果吻合较好。结果表明：静水压作用下，Nb₃Sn单晶体发生了明显的晶格畸变，但晶体结构保持完整；压力诱导的费米面上电子态密度的变化在高压下Nb₃Sn单晶体超导相转变中起主导作用。所得研究结果为研究高压下Nb₃Sn多晶体以及复合多晶体的相转变行为奠定了基础，同时有助于进一步认识Nb₃Sn材料超导性能的弱化机理。
- Nb₃Sn单晶 /
- 静水压 /
- T²依赖性电阻率 /
- 分子动力学模拟
Abstract: Study on the superconducting transition of single crystal Nb₃Sn under high pressure is valuable to understand the mechanism of critical performance degradation in superconducting Nb₃Sn, which is induced by the mechanical deformation. In this paper, on the basis of molecular dynamics simulations, we studied high-pressure induced atomic scale deformation and crystal lattice distortions of single crystal Nb₃Sn. Following this analysis, we established a superconducting transition model of single crystal Nb₃Sn under high pressure. There is a good agreement between model predictions and experimental observations. The results show that the high pressure induces obvious lattice distortions in single crystal Nb₃Sn, the lattice structure, however, remains intact. Pressure-induced change in density of states at the Fermi surface is shown to play a dominate role in superconducting transition in single crystal Nb₃Sn. The results lay a foundation of understanding the high pressure induced superconducting transition of polycrystalline Nb₃Sn. At the same time, they provide some detailed information on understanding the mechanism controlling for strain-induced critical performance degradation in Nb₃Sn.
- single crystal Nb₃Sn /
- hydrostatic pressure /
- T² dependent resistivity /
- molecular dynamics simulation

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图 1 $ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $单晶体计算模型（a）和A15型晶格结构（b）

Figure 1. Calculation model of $ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $ single crystal (a) and A15 type lattice structure (b)

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图 2 $ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $单晶体积随温度的变化

Figure 2. Volume of $ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $ single crystal varies with temperature

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图 3 4.2 K时Nb₃Sn单晶体在静水压作用下的变形情况

Figure 3. Deformation of Nb₃Sn single crystal under hydrostatic pressure at 4.2 K

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图 4 静水压加载下$ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $单晶体的应力分布

Figure 4. Stress distribution of $ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $ single crystal under hydrostatic pressure

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图 5 $ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $单晶体xz面的主应力分布

Figure 5. Principal stresses distribution of $ {\mathrm{N}\mathrm{b}}_{3}\mathrm{S}\mathrm{n} $ single crystal on the right side under hydrostatic pressure

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图 6 静水压作用下Nb₃Sn单晶体在低温区的电阻率随温度的变化

Figure 6. Change of resistivity with temperature in low temperature area for Nb₃Sn single crystal under hydrostatic pressure

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图 7 静水压作用下Nb₃Sn单晶体临界温度变化预测结果与实验结果对比

Figure 7. Comparison between the predicted and measured critical temperature of Nb₃Sn single crystal under hydrostatic pressure

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表 1 Nb₃Sn单晶的力学性能参数

Table 1. Elastic constants and lattice constant of Nb₃Sn single crystal

Method	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	Lattice constant/Å
This work	284.1	95.8	53.76	5.21
First principle	284.3	107.7	67.07	5.32
Experiment	253.8	112.4	39.60	5.29

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表 2 电阻率模型相关参数

Table 2. Parameters of resistivity model

${\;\rho{_0} }$/(μΩ·cm)	${A}{_0}$/(μΩ·cm·K⁻²)	${T}{_{1/2}^{{0}}}/\mathrm{K}$	$ C $	$ \bar{K} $
1.17	6.4×10⁻³	17.82	−0.7	0.13×10⁻²

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表 3 态密度函数相关参数

Table 3. Parameters of density of state function

${\chi }{_1}$	$ {\chi }{_2}$	$ {\chi }{_3} $	$ {\kappa }{_1} $	$ {\kappa }{_2}$	$ {\kappa }{_3}$
0.975	12.570	−9.225	−35.500	−7.490	−5.650

$ {\;\beta }{_{11}}$	$ {\;\beta }{_{12}} $	$ {\;\beta }{_{21}} $	$ {\;\beta }{_{22}} $	$ {\;\beta }{_{31}} $	$ {\;\beta }{_{32}} $
0.004 75	0.002 00	0.015 28	0.002 00	0.012 80	0.001 00

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参考文献(36)

[1]	梁明, 张平祥, 卢亚锋, 等. 磁体用Nb₃Sn超导体研究进展 [J]. 材料导报, 2006, 20(12): 1–4. LIANG M, ZHANG P Y, LU Y F, et al. Advances in Nb₃Sn superconductor for magnet application [J]. Materials Review, 2006, 20(12): 1–4.
[2]	周又和, 王省哲. ITER超导磁体设计与制备中的若干关键力学问题 [J]. 中国科学(物理学·力学·天文学), 2013, 43(15): 1558–1569. ZHOU Y H, WANG X Z. Review on some key issues related to design and fabrication of superconducting magnets in ITER [J]. Scientia Sinica (Physica, Mechanica & Astronomica), 2013, 43(15): 1558–1569.
[3]	许少峰, 刘旭峰, 宋云涛. Nb₃Sn超导磁体低温冷却设计 [J]. 原子能科学技术, 2013, 43(15): 147–150. XU S F, LIU X F, SONG Y T. Cryogenic cooling design of Nb₃Sn superconducting magnet [J]. Atomic Energy Science and Technology, 2013, 43(15): 147–150.
[4]	王秋良. 高磁场超导磁体科学[M]. 北京: 科学出版社, 2008. WANG Q L. High-field superconducting magnets science [M]. Beijing: Science Press, 2008.
[5]	唐先德, 李春广, 武玉, 等. 核聚变用内Sn法Nb₃Sn股线的制备与性能 [J]. 低温物理学报, 2005, 27(A2): 936–931. TANG X D, LI C G, WU Y, et al. The manufacture and properties of the Nb₃Sn strand for ITER by the internal tin process [J]. Chinese Journal of Low Temperature Physics, 2005, 27(A2): 936–931.
[6]	蒋华伟. 应变对Nb₃Sn股线临界特性退化影响 [J]. 稀有金属材料与工程, 2015, 44(6): 1423–1426. JIANG H W. Effect of strain on critical properties degradation of Nb₃Sn strand [J]. Rare Metal Materials and Engineering, 2015, 44(6): 1423–1426.
[7]	LIU B, WU Y, LIU F, et al. Axial strain characterization of the Nb₃Sn strand used for China's TF conductor [J]. Fusion Engineering & Design, 2011, 86(1): 1–4.
[8]	TAYLOR J D M, HAMPSHIRE D P, et al. The scaling law for the strain dependence of the critical current density in Nb₃Sn superconducting wires [J]. Superconductor Science and Technology, 2006, 18(12): 241–252.
[9]	SUMMERS L T, GUINAN M W, MILLER J R, et al. A model for the prediction of Niobium-Tin (Nb₃Sn) critical current as a function of field, temperature, strain, and radiation damage [J]. IEEE Transactions on Magnetics, 1991, 27(2/3): 2041–2044.
[10]	HAKEN T, BERNARD, GODEKE A, et al. The influence of compressive and tensile axial strain on the critical properties of Nb₃Sn conductors [J]. IEEE Transactions on Applied Superconductivity, 1995, 5(5): 1909–1912.
[11]	EKIN J W. Unified scaling law for flux pinning in practical superconductors: I. separability postulate, raw scaling data and parameterization at moderate strains [J]. Superconductor Science & Technology, 2010, 23(8): 083001.
[12]	EKIN J W. Strain-scaling law for flux pinning in practical superconductors. part 1: basic relationship and application to niobium-tin (Nb₃Sn) conductors [J]. Cryogenics, 1980, 20(11): 611–624. doi: 10.1016/0011-2275(80)90191-5
[13]	CHU C W. Pressure-enhanced lattice transformation in Nb₃Sn single crystal [J]. Physical Review Letters, 1974, 33(21): 1283–1286. doi: 10.1103/PhysRevLett.33.1283
[14]	TANAKA S, HANDOKO, MIYAKE A, et al. Superconducting and martensitic transitions of V₃Si and Nb₃Sn under high pressure [J]. Journal of the Physical Society of Japan, 2012: 81.
[15]	LIM K C, THOMPSON J D, WEBB G W. Electronic density of states and T_c in niobium-tin (Nb₃Sn) under pressure [J]. Physical Review B: Condens Matter, 1983, 27(5): 2781–2787. doi: 10.1103/PhysRevB.27.2781
[16]	REN Z, GAMPERLE L, FETE A, et al. Evolution of T₂ resistivity and superconductivity in Nb₃Sn under pressure [J]. Physical Review B, 2017, 95(18): 184503. doi: 10.1103/PhysRevB.95.184503
[17]	WOODARD D W, CODY G D. Anomalous resistivity of Nb₃Sn [J]. Modern Language Review, 1964, 136(1): 166–168.
[18]	QIAO L, YANG L, ZHENG X J. A simple phenomenological model for characterizing the coupled effect of strain states and temperature on the normal-state electrical resistivity in Nb₃Sn superconductors [J]. Journal of Applied Physics, 2013, 114(3): 1–7.
[19]	WEBB G, FISK Z, ENGELHARDT J, et al. Apparent T₂ dependence of normal-state resistivities and lattice heat-capacities of high-T superconductors [J]. Bulletin of the American Physical Society, 1976, 21(11): 1285.
[20]	GURVITCH M, GHOSH A K, LUTZ H, et al. Low-temperature resistivity of ordered and disordered A15 compounds [J]. Physical Review B, 1980, 22(1): 128–136. doi: 10.1103/PhysRevB.22.128
[21]	ZHANG Y, ASHCRAFT R, MENDELEV M I, et al. Experimental and molecular dynamics simulation study of structure of liquid and amorphous Ni₆₂Nb₃₈ alloy [J]. The Journal of Chemical Physics, 2016, 145(20): 204505. doi: 10.1063/1.4968212
[22]	KO W S, KIM D H, KWON Y J, et al. Atomistic simulations of pure tin based on a new modified embedded-atom method interatomic potential [J]. Metals-Basel, 2018, 8(11): 900. doi: 10.3390/met8110900
[23]	CHUDINOV V G, GOGOLIN V P, GOSHCHITSKII B N, et al. Simulation of collision cascades in intermetallic Nb₃Sn compounds [J]. Physica Status Solidi C, 1981, 67(1): 61–67. doi: 10.1002/pssa.2210670103
[24]	PAPADIMITRIOU I, UTTON C, TSAKIROPOULOS P. Ab initio investigation of the intermetallics in the Nb-Sn binary system [J]. Acta Materialia, 2015, 86: 23–33. doi: 10.1016/j.actamat.2014.12.017
[25]	SUNDARESWARI M, RAMASUBRAMANIAN S, RAJAGOPALAN M. Elastic and thermodynamical properties of A15 Nb₃X (X = Al, Ga, In, Sn and Sb) compounds-first principles DFT study [J]. Solid State Communications, 2010, 150(41/42): 2057–2060.
[26]	ZHANG R, GAO P F, WANG X Z, et al. First-principles study on elastic and superconducting properties of Nb₃Sn and NbAl under hydrostatic pressure [J]. AIP Advances, 2015, 5(10): 1–9.
[27]	WIESMANN H, GURVITCH M, LUTZ H, et al. Simple model for characterizing the electrical resistivity in A-15 superconductors [J]. Physical Review Letters, 1977, 38(14): 782–785. doi: 10.1103/PhysRevLett.38.782
[28]	YANG L, DING H, ZHANG X, et al. A multiple-field coupled resistive transition model for superconducting Nb₃Sn [J]. AIP Advances, 2016, 6(12): 125101. doi: 10.1063/1.4971214
[29]	CATON R, VISWANATHAN R. Analysis of the normal-state resistivity for the neutron-irradiated A15 superconductors vanadium silicide (V₃Si), niobium-platinum (Nb₃Pt), and niobium aluminide (Nb₃Al) [J]. Physical Review B: Condens Matter, 1982, 25(1): 179–193. doi: 10.1103/PhysRevB.25.179
[30]	RAMAKRISHNAN S, NIGAM A K, CHANDRA G. Resistivity and magnetoresistance studies on superconducting A15 V₃Ga, V₃Au, and V₃Pt compounds [J]. Physical Review B: Condens Matter, 1986, 34(9): 6166–6171. doi: 10.1103/PhysRevB.34.6166
[31]	QIAO L, ZHANG X, DING H, et al. An intrinsic model for strain tensor effects on the density of states in A15 Nb₃Sn [J]. Cryogenics, 2019, 97: 50–54. doi: 10.1016/j.cryogenics.2018.11.002
[32]	KIM D H, GRAY K E, KAMPWIRTH R T, et al. Possible origins of resistive tails and critical currents in high-temperature superconductors in a magnetic field [J]. Physical Review B: Condens Matter, 1990, 42(10): 6249–6258. doi: 10.1103/PhysRevB.42.6249
[33]	GODEKE A, JEWELL M C, GOLUBOV A A, et al. Inconsistencies between extrapolated and actual critical fields in Nb₃Sn wires as demonstrated by direct measurements of H_c2, H^* and T_c [J]. Superconductor Science & Technology, 2003, 16(9): 1019–1025.
[34]	何宇新, 乔力, 石震天, 等. 静水压作用下Nb₃Sn多晶体超导临界温度退化的耦合模型 [J]. 固体力学学报, 2020, 41(4): 334–342. HE Y X, QIAO L, SHI Z T, et al. A coupling model for hydrostatic pressure-induced critical temperature degradation of Nb₃Sn polycrystalline superconductors [J]. Acta Mechanica Solida Sinica, 2020, 41(4): 334–342.
[35]	TINKHAM M. Resistive transition of high-temperature superconductors [J]. Physical Review Letters, 1988, 61(14): 1658–1661. doi: 10.1103/PhysRevLett.61.1658
[36]	CHU C, TESTARDI L. Hydrostatic-pressure enhanced lattice transformation and hydrostatic-pressure suppressed superconducting transition in Nb₃Sn single-crystal [J]. Bulletin of the American Physical Society, 1974, 19(3): 228.