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First-principles study of, electronic structure, elastic properties and hardness of Cr-doped CuZr2

WANG Kun ,  XU Heyan ,  ZHENG Xiong ,  ZHANG Haifeng

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First-principles study of, electronic structure, elastic properties and hardness of Cr-doped CuZr2

WANG Kun, XU Heyan, ZHENG Xiong, ZHANG Haifeng
Acta Phys. Sin.,
doi: 10.7498/aps.74.20250264
cstr: 32037.14.aps.74.20250264
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  • Abstract

    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 0.303 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 from https://www.doi.org/10.57760/sciencedb.j00213.00122.

  • 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

    Figure 1.  Convergence test results of the calculation parameters: (a) Energy cutoff; (b) k-point mesh.

    DownLoad: Full-Size Img PowerPoint

    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

    Figure 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.

    DownLoad: Full-Size Img PowerPoint

    图 3  DFPT方法计算得到的CuZr2的声子谱图

    Figure 3.  Phonon spectra of CuZr2 calculated by the DFPT method.

    DownLoad: Full-Size Img PowerPoint

    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

    Figure 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.

    DownLoad: Full-Size Img PowerPoint

    图 5  CuZr2晶体的电子结构　(a) 能带结构; (b) 态密度

    Figure 5.  Electronic structure of CuZr2 crystal: (a) Energy band structure; (b) density of states.

    DownLoad: Full-Size Img PowerPoint

    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

    Figure 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.

    DownLoad: Full-Size Img PowerPoint

    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

    Figure 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.

    DownLoad: Full-Size Img PowerPoint

    图 8  计算得到的7种材料的德拜温度及维氏硬度

    Figure 8.  Calculation results of Debye temperature and Vickers hardness of 7 materials.

    DownLoad: Full-Size Img PowerPoint

    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
    DownLoad: CSV

    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
    CuZr2Tetragonal-I4/mmma = b = 3.233 Å; c = 11.207 Å
    CuZr2[50]Tetragonal-I4/mmma = b = 3.236 Å; c = 11.204 Å
    CuZr1.5Cr0.5Tetragonal-P4mma = b = 3.215 Å; c = 10.408 Å
    CuZrCr-1Tetragonal-P4/mmma = b = 3.178 Å; c = 9.715 Å
    CuZrCr-2Tetragonal-P4/nmma = b = 2.981 Å; c = 10.504 Å
    CuZr0.5Cr1.5Tetragonal-P4mma = b = 2.932 Å; c = 9.601 Å
    Cu0.5Zr2Cr0.5Tetragonal-P4mmma = b = 3.261 Å; c = 10.931 Å
    Cu0.5Zr1.5Cr-1Tetragonal-P4mma = b = 3.279 Å; c = 9.951 Å
    Cu0.5Zr1.5Cr-2Tetragonal-P4mma = b = 3.021 Å; c = 11.243 Å
    Cu0.5ZrCr1.5-1Tetragonal-P4mmma = b = 3.244 Å; c = 9.084 Å
    Cu0.5ZrCr1.5-2Tetragonal-P4mma = b = 3.039 Å; c = 10.117 Å
    Cu0.5ZrCr1.5-3Tetragonal-P4mma = b = 2.906 Å; c = 10.901 Å
    Cu0.5Zr0.5Cr2-1Tetragonal-P4mma = b = 2.901 Å; c = 9.558 Å
    Cu0.5Zr0.5Cr2-2Tetragonal-P4mma = b = 3.051 Å; c = 8.697 Å
    DownLoad: CSV

    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υ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 υ and elastic anisotropy factor AU of CuZr2 and its designed six dynamically stabilized Cu-Zr-Cr doped structures.

    C11C12C13C33C44C66EBGνAU
    Cu2Zr4177.8466.0390.74145.6963.5330.98120.58110.6745.730.3180.654
    Cu2Zr4[50]16974911506632121111460.319—
    CuZr1.5Cr0.5169.4671.0699.28131.7058.5540.31109.35112.1140.880.3371.086
    CuZrCr-1170.1379.3987.12154.6459.3454.67129.90111.3249.750.3060.207
    Cu0.5Zr2Cr0.5161.4682.8283.20129.2245.5830.0099.19104.9636.940.3430.239
    Cu0.5Zr1.5Cr-1156.4281.4082.94143.6444.4547.59108.49105.6040.820.3290.105
    Cu0.5ZrCr1.5-1169.53115.2867.77143.1243.5289.44123.36107.2947.140.3080.860
    Cu0.5Zr0.5Cr2-1284.53116.96112.07227.277.4829.1577.29163.2327.200.4214.800
    DownLoad: CSV

    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)    		nνl
    /(m·s–1)    		νt
    /(m·s–1)    		νm
    /(m·s–1)    		θD
    /K    		Hv
    /GPa
    Cu2Zr4491.986.9764960.792560.542866.83316.985.044
    CuZr1.5Cr0.5452.766.9964883.102418.772714.89308.804.042
    CuZrCr-1413.547.0065038.352666.232980.21349.555.853
    Cu0.5Zr2Cr0.5480.436.8664740.052319.932605.71288.853.614
    Cu0.5Zr1.5Cr-1441.216.8564833.712441.412737.16311.944.316
    Cu0.5ZrCr1.5-1401.996.9864936.622598.512905.58343.765.527
    Cu0.5Zr0.5Cr2-1362.777.4965161.511905.762163.55271.141.243
    DownLoad: CSV
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Metrics
  • Abstract views:  394
  • PDF Downloads:  18
  • Cited By: 0
Publishing process
  • Received Date:  03 March 2025
  • Accepted Date:  21 April 2025
  • Available Online:  29 April 2025

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