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近年来, 基于第一性原理的新型高性能合金的设计开发受到了广泛关注. 然而, 在纳观尺度上, 关于Cu-Zr合金的结构设计及其热力学性质的研究鲜有报道. 本文基于CuZr2的晶体结构特点, 采用Cr原子掺杂的方法, 通过基于密度泛函理论的第一性原理计算, 设计优化了12种Cr掺杂CuZr2结构, 发现了6种力学及动力学稳定的掺杂结构模型. 通过对CuZr2及其动力学稳定的Cr掺杂结构的电子结构、弹性性质和硬度的计算研究发现: 所有的研究对象均表现为金属性质, CuZr2对外不显示磁性. 然而, Cr原子的掺入, 增加了基体的元素种类, 除Cr原子d轨道电子带来的自旋电子差异外, 掺入的Cr原子还会破坏基体内Zr原子p和d轨道上不同自旋方向电子的对称性分布, 使设计的6种Cr掺杂CuZr2结构表现为铁磁性质, 其磁矩在0.303—5.243μB之间变化. 此外, 研究发现Cr元素可以改善CuZr2的力学性质. 当采用Cr原子替代基体内Zr原子时, 可以提高材料的弹性模量和硬度, 而采用Cr原子替代基体内Cu原子时, 由于硬度的降低, 则可以改善材料的加工性能. 本文数据集可在科学数据银行数据库
https://www.doi.org/10.57760/sciencedb.j00213.00122 中访问获取.In recent years, the design and development of new high-performance alloys based on first principles have received extensive attention. However, there are few reports on the structural design and thermodynamic properties of Cu-Zr alloys at nanoscale. In this work, based on the crystal structure characteristics of CuZr2, 12 kinds of Cr-doped CuZr2 structures are designed and optimized by the method of Cr atom doping through the first-principle calculation based on the density functional theory, and 6 kinds of mechanically and dynamically stable doped structure models are found. By calculating the electronic structure, elastic properties and hardness of the CuZr2 and its dynamically stable Cr-doped structure, it is found that the studied objects have all energy bands that pass through the Fermi energy level and are metallic. The main contributors to the metallic properties of the CuZr2 are the p and d orbital electrons of Zr, while the main contributors to the metallic properties of the 6 dynamically stable Cr-doped CuZr2 structures are the p and d orbital electrons of Cr and Zr. Meanwhile, CuZr2 has symmetrically distributed spin electrons, which do not show magnetism externally. However, the doping of Cr atoms increases the elemental species of the matrix. In addition to the difference of spin electrons brought by the d-orbital electrons of Cr atoms, the doped Cr atoms destroy the symmetrical distribution of electrons with different spin directions in the p- and d-orbitals of Zr atoms in the matrix, so that the designed 6 dynamically stable Cr-doped CuZr2 structures exhibit ferromagnetic properties with magnetic moments ranging from 0.303μB to 5.243μB. In addition, it is found that Cr atoms can improve the mechanical properties of CuZr2. When the Cr atom is used to replace the Zr atom in the matrix, the elastic modulus and hardness of the material can be improved, and when the Cr atom is used to replace the Cu atom in the matrix, the machining properties of the material can be improved due to the reduction of hardness. The datasets presented in this work, including the band structure, density of states, and phonon dispersion frequency, are available fromhttps://www.doi.org/10.57760/sciencedb.j00213.00122 .-
Keywords:
- first-principles /
- CuZr2 alloy /
- doping
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图 1 计算参数收敛性测试结果 (a) 截断能Ecut的测试结果; (b) k点网格的测试结果
Fig. 1. Convergence test results of the calculation parameters: (a) Energy cutoff; (b) k-point mesh.
图 2 设计的12种Cr掺杂CuZr2的晶体结构模型 (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) CuZrCr-2; (d) CuZr0.5Cr1.5; (e) Cu0.5Zr2Cr0.5; (f) Cu0.5Zr1.5Cr-1; (g) Cu0.5Zr1.5Cr-2; (h) Cu0.5ZrCr1.5-1; (i) Cu0.5ZrCr1.5-2; (j) Cu0.5ZrCr1.5-3; (k) Cu0.5Zr0.5Cr2-1; (l) Cu0.5Zr0.5Cr2-2
Fig. 2. Structural models of 12 Cr-doped CuZr2: (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) CuZrCr-2; (d) CuZr0.5Cr1.5; (e) Cu0.5Zr2Cr0.5; (f) Cu0.5Zr1.5Cr-1; (g) Cu0.5Zr1.5Cr-2; (h) Cu0.5ZrCr1.5-1; (i) Cu0.5ZrCr1.5-2; (j) Cu0.5ZrCr1.5-3; (k) Cu0.5Zr0.5Cr2-1; (l) Cu0.5Zr0.5Cr2-2.
图 3 DFPT方法计算得到的CuZr2的声子谱图
Fig. 3. Phonon spectra of CuZr2 calculated by the DFPT method.
图 4 DFPT方法计算得到的12种Cr掺杂CuZr2的声子谱图 (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) CuZrCr-2; (d) CuZr0.5Cr1.5; (e) Cu0.5Zr2Cr0.5; (f) Cu0.5Zr1.5Cr-1; (g) Cu0.5Zr1.5Cr-2; (h) Cu0.5ZrCr1.5-1; (i) Cu0.5ZrCr1.5-2; (j) Cu0.5ZrCr1.5-3; (k) Cu0.5Zr0.5Cr2-1; (l) Cu0.5Zr0.5Cr2-2
Fig. 4. Phonon spectra of 12 Cr-doped CuZr2 calculated by the DFPT method: (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) CuZrCr-2; (d) CuZr0.5Cr1.5; (e) Cu0.5Zr2Cr0.5; (f) Cu0.5Zr1.5Cr-1; (g) Cu0.5Zr1.5Cr-2; (h) Cu0.5ZrCr1.5-1; (i) Cu0.5ZrCr1.5-2; (j) Cu0.5ZrCr1.5-3; (k) Cu0.5Zr0.5Cr2-1; (l) Cu0.5Zr0.5Cr2-2.
图 5 CuZr2晶体的电子结构 (a) 能带结构; (b) 态密度
Fig. 5. Electronic structure of CuZr2 crystal: (a) Energy band structure; (b) density of states.
图 6 动力学稳定的Cu-Zr-Cr掺杂体系的能带结构 (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) Cu0.5Zr2Cr0.5; (d) Cu0.5Zr1.5Cr-1; (e) Cu0.5ZrCr1.5-1; (f) Cu0.5Zr0.5Cr2-1
Fig. 6. Band structure of dynamically stabilized Cu-Zr-Cr doped structures: (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) Cu0.5Zr2Cr0.5; (d) Cu0.5Zr1.5Cr-1; (e) Cu0.5ZrCr1.5-1; (f) Cu0.5Zr0.5Cr2-1.
图 7 动力学稳定的Cu-Zr-Cr掺杂体系的态密度 (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) Cu0.5Zr2Cr0.5; (d) Cu0.5Zr1.5Cr-1; (e) Cu0.5ZrCr1.5-1; (f) Cu0.5Zr0.5Cr2-1
Fig. 7. Density of states of dynamically stabilized Cu-Zr-Cr doped structures: (a) CuZr1.5Cr0.5; (b) CuZrCr-1; (c) Cu0.5Zr2Cr0.5; (d) Cu0.5Zr1.5Cr-1; (e) Cu0.5ZrCr1.5-1; (f) Cu0.5Zr0.5Cr2-1.
图 8 计算得到的7种材料的德拜温度及维氏硬度
Fig. 8. Calculation results of Debye temperature and Vickers hardness of seven materials.
表 1 CuZr2的晶体结构信息
Table 1. Crystal structure information of CuZr2 alloy.
CuZr2 
空间群 Tetragonal-I4/mmm 晶格常数 实验值
a = b = 3.2204 Å; c = 11.1832 Å
α = β = γ = 90°原子数 Cu 2 Zr 4 Wyckoff
占位x y z Cu(2a) 0 0 0 Zr(4e) 0 0 0.346 
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表 2 CuZr2及其设计的12种Cr掺杂结构的晶格信息
Table 2. Lattice information of CuZr2 and its designed 12 Cr-doped structures.
化合物 空间群 晶格常数 CuZr2 Tetragonal-I4/mmm a = b = 3.233 Å; c = 11.207 Å CuZr2[50] Tetragonal-I4/mmm a = b = 3.236 Å; c = 11.204 Å CuZr1.5Cr0.5 Tetragonal-P4mm a = b = 3.215 Å; c = 10.408 Å CuZrCr-1 Tetragonal-P4/mmm a = b = 3.178 Å; c = 9.715 Å CuZrCr-2 Tetragonal-P4/nmm a = b = 2.981 Å; c = 10.504 Å CuZr0.5Cr1.5 Tetragonal-P4mm a = b = 2.932 Å; c = 9.601 Å Cu0.5Zr2Cr0.5 Tetragonal-P4mmm a = b = 3.261 Å; c = 10.931 Å Cu0.5Zr1.5Cr-1 Tetragonal-P4mm a = b = 3.279 Å; c = 9.951 Å Cu0.5Zr1.5Cr-2 Tetragonal-P4mm a = b = 3.021 Å; c = 11.243 Å Cu0.5ZrCr1.5-1 Tetragonal-P4mmm a = b = 3.244 Å; c = 9.084 Å Cu0.5ZrCr1.5-2 Tetragonal-P4mm a = b = 3.039 Å; c = 10.117 Å Cu0.5ZrCr1.5-3 Tetragonal-P4mm a = b = 2.906 Å; c = 10.901 Å Cu0.5Zr0.5Cr2-1 Tetragonal-P4mm a = b = 2.901 Å; c = 9.558 Å Cu0.5Zr0.5Cr2-2 Tetragonal-P4mm a = b = 3.051 Å; c = 8.697 Å
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表 3 CuZr2及其设计的6种动力学稳定的Cu-Zr-Cr掺杂结构的弹性常数Cij、弹性模量E, B和G (单位: GPa)、泊松比ν以及各向异性因子AU
Table 3. Elastic constants Cij, elastic modulus E, B and G (unit: GPa), Poisson’s ratio ν and elastic anisotropy factor AU of CuZr2 and its designed six dynamically stabilized Cu-Zr-Cr doped structures.
C11 C12 C13 C33 C44 C66 E B G ν AU Cu2Zr4 177.84 66.03 90.74 145.69 63.53 30.98 120.58 110.67 45.73 0.318 0.654 Cu2Zr4[50] 169 74 91 150 66 32 121 111 46 0.319 — CuZr1.5Cr0.5 169.46 71.06 99.28 131.70 58.55 40.31 109.35 112.11 40.88 0.337 1.086 CuZrCr-1 170.13 79.39 87.12 154.64 59.34 54.67 129.90 111.32 49.75 0.306 0.207 Cu0.5Zr2Cr0.5 161.46 82.82 83.20 129.22 45.58 30.00 99.19 104.96 36.94 0.343 0.239 Cu0.5Zr1.5Cr-1 156.42 81.40 82.94 143.64 44.45 47.59 108.49 105.60 40.82 0.329 0.105 Cu0.5ZrCr1.5-1 169.53 115.28 67.77 143.12 43.52 89.44 123.36 107.29 47.14 0.308 0.860 Cu0.5Zr0.5Cr2-1 284.53 116.96 112.07 227.27 7.48 29.15 77.29 163.23 27.20 0.421 4.800
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表 4 计算得到的CuZr2及其Cr掺杂结构的声速、德拜温度及维氏硬度
Table 4. Calculated sound velocity, Debye temperature and Vickers hardness of CuZr2 and its Cr-doped structures.
M/(g·mol–1) ρ/(g·cm–3) n νl/(m·s–1) νt/(m·s–1) νm/(m·s–1) θD/K Hv/GPa Cu2Zr4 491.98 6.97 6 4960.79 2560.54 2866.83 316.98 5.044 CuZr1.5Cr0.5 452.76 6.99 6 4883.10 2418.77 2714.89 308.80 4.042 CuZrCr-1 413.54 7.00 6 5038.35 2666.23 2980.21 349.55 5.853 Cu0.5Zr2Cr0.5 480.43 6.86 6 4740.05 2319.93 2605.71 288.85 3.614 Cu0.5Zr1.5Cr-1 441.21 6.85 6 4833.71 2441.41 2737.16 311.94 4.316 Cu0.5ZrCr1.5-1 401.99 6.98 6 4936.62 2598.51 2905.58 343.76 5.527 Cu0.5Zr0.5Cr2-1 362.77 7.49 6 5161.51 1905.76 2163.55 271.14 1.243
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Google Scholar
[2] Zhao Y, Pang T, He J, Tao X, Chen H, Ouyang Y, Du Y 2018 Calphad 61 92
Google Scholar
[3] Wang T, Cullinan T E, Napolitano R E 2014 Acta Mater. 62 188
Google Scholar
[4] Nishiyama N, Amiya K, Inoue A 2007 J. Non-Cryst. Solids 353 3615
Google Scholar
[5] Inoue A 2000 Acta Mater. 48 279
Google Scholar
[6] 余健, 赵峰, 杨惠雅, 刘嘉斌, 马吉恩, 方攸同 2023 浙江大学学报-科学A 24 206
Google Scholar
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Google Scholar
[7] Zeng K J, Hämäläinen M 1995 J. Alloys Compd. 220 53
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[11] Zinkle S J 2016 Phys. Scr. T167 014004
Google Scholar
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Google Scholar
[13] Taubin M L, Solntseva E S, Chesnokov D A 2017 Int. J. Hydrogen Energy 42 24541
Google Scholar
[14] Solntceva E S, Taubin M L, Bochkov N A, Solntsev V A, Yaskolko A A 2016 Int. J. Hydrogen Energy 41 7206
Google Scholar
[15] Higashino S, Miyashita D, Ishimoto T, Miyoshi E, Nakano T, Tane M 2025 Addit. Manuf. 102 104720
Google Scholar
[16] Lu Y, Xie G, Wang D, Zhang S, Zheng W, Shen J, Lou L, Zhang J 2018 Mater. Sci. Eng., A 720 69
Google Scholar
[17] 路甬祥, 白春礼, 施尔畏, 方新, 李志刚 2009 中国至2050年先进材料科技发展路线图 (北京: 科学出版社) 第79页
Lu Y X, Bai C L, Shi E W, Fang X, Li Z G 2009 China's Advanced Materials Science and Technology Development Roadmap to 2050 (Beijing: Science Press) p79
[18] Wu M M, Jiang Y, Wang J W, Wu J, Tang B Y, Peng L M, Ding W J 2011 J. Alloys Compd. 509 2885
Google Scholar
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Google Scholar
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Google Scholar
[21] Zhang W H, Halet J F, Mori T 2023 J. Mater. Chem. A 11 24228
Google Scholar
[22] Caliskan S, Almessiere M A, Baykal A, Slimani Y 2023 Comput. Mater. Sci. 226 112243
Google Scholar
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Google Scholar
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