Sc、Ti、V、Zr掺杂Cr2B3高压力学性质的第一性原理计算

张畅 孙小伟 宋婷 田俊红 刘子江

张畅, 孙小伟, 宋婷, 田俊红, 刘子江. Sc、Ti、V、Zr掺杂Cr2B3高压力学性质的第一性原理计算[J]. 高压物理学报, 2022, 36(4): 042201. doi: 10.11858/gywlxb.20210916
引用本文: 张畅, 孙小伟, 宋婷, 田俊红, 刘子江. Sc、Ti、V、Zr掺杂Cr2B3高压力学性质的第一性原理计算[J]. 高压物理学报, 2022, 36(4): 042201. doi: 10.11858/gywlxb.20210916
ZHANG Chang, SUN Xiaowei, SONG Ting, TIAN Junhong, LIU Zijiang. First-Principles Study on Mechanical Properties of Sc, Ti, V, Zr-Doped Cr2B3 at High Pressure[J]. Chinese Journal of High Pressure Physics, 2022, 36(4): 042201. doi: 10.11858/gywlxb.20210916
Citation: ZHANG Chang, SUN Xiaowei, SONG Ting, TIAN Junhong, LIU Zijiang. First-Principles Study on Mechanical Properties of Sc, Ti, V, Zr-Doped Cr2B3 at High Pressure[J]. Chinese Journal of High Pressure Physics, 2022, 36(4): 042201. doi: 10.11858/gywlxb.20210916

Sc、Ti、V、Zr掺杂Cr2B3高压力学性质的第一性原理计算

doi: 10.11858/gywlxb.20210916
基金项目: 甘肃省高等学校创新基金(2020A-039);甘肃省自然科学基金重点项目(20JR5RA427);甘肃省杰出青年科学基金(145RJDA323)
详细信息
    作者简介:

    张 畅(1996-),女,硕士研究生,主要从事功能新材料高压物性研究.E-mail:zhangch_lzjtu@126.com

    通讯作者:

    孙小伟(1979-),男,博士,教授,主要从事材料高压物性、声子晶体和声学超材料研究.E-mail:sunxw_lzjtu@yeah.net

  • 中图分类号: O521.2; O482.1

First-Principles Study on Mechanical Properties of Sc, Ti, V, Zr-Doped Cr2B3 at High Pressure

  • 摘要: 采用基于密度泛函理论的第一性原理方法,计算了掺杂Sc、Ti、V和Zr的Cr2B3在零压下的晶体结构和电子结构及其在0~150 GPa压力范围内的弹性常数和维氏硬度。结果表明:Cr2B3及其掺杂化合物均具备力学稳定性;在零压下,添加Sc、Ti、V和Zr元素均可提高Cr2B3的维氏硬度,其中Ti掺杂Cr2B3的硬度由26.3 GPa提高至40.2 GPa,提高52.9%,达到超硬材料标准,且 Ti和V掺杂Cr2B3的剪切模量分别提高14.3%和16.2%,杨氏模量分别提高8.2%和12.0%;由电子结构分析可知,Sc、Ti、V和 Zr元素可以加强B与B之间的电子局域化程度,从而增强共价键结合强度,使Cr2B3的硬度升高;Cr2B3的弹性常数、体积弹性模量、剪切模量、杨氏模量以及硬度随着压力的增加而增加,但其硬度仍较低,150 GPa下仅为28.3 GPa,而掺杂V的Cr2B3的硬度在整个压力范围内约为37 GPa。研究结果可为Cr2B3在高压等特殊条件下的应用提供理论参考。

     

  • 图  (a) Cr2B3 和 (b) CrMB3(M = Sc, Ti, V, Zr)的晶体结构(蓝色、绿色和粉色小球分别代表 Cr、B 和过渡金属原子)

    Figure  1.  Crystal structures of (a) Cr2B3 and (b) CrMB3 (M=Sc, Ti, V, Zr), where the blue, green and pink spheres represent Cr, B and transition metal atoms, respectively

    图  Cr2B3的弹性常数随压力的变化

    Figure  2.  Pressure dependence of the elastic constants for Cr2B3

    图  CrMB3(M=Sc, Ti, V, Zr)的弹性常数随压力的变化

    Figure  3.  Pressure dependence of the elastic constants for CrMB3 (M=Sc, Ti, V, Zr)

    图  Cr2B3在零压(a)和 150 GPa (b)下的声子色散曲线

    Figure  4.  Phonon-dispersion curves of Cr2B3 at (a) 0 GPa and (b) 150 GPa

    图  (a) CrScB3、(b) CrTiB3、(c) CrVB3、(d) CrZrB3在零压下的声子色散曲线

    Figure  5.  Phonon-dispersion curves of (a) CrScB3, (b) CrTiB3, (c) CrVB3 and (d) CrZrB3 at 0 GPa

    图  Cr2B3和 CrMB3(M=Sc, Ti, V, Zr)的体积弹性模量(a)、剪切模量(b)和杨氏模量(c)随压力的变化

    Figure  6.  Pressure dependence of (a) the bulk moduli, (b) the shear moduli, (c) the Young’s moduli for Cr2B3 and CrMB3 (M=Sc, Ti, V, Zr)

    图  Cr2B3和 CrMB3(M=Sc, Ti, V, Zr)的维氏硬度随压力的变化

    Figure  7.  Pressure dependence of the Vicker’s hardness for Cr2B3 and CrMB3 (M=Sc, Ti, V, Zr)

    图  Cr2B3及 CrMB3(M=Sc, Ti, V, Zr)的B/G 随压力的变化

    Figure  8.  Pressure dependence of the B/G for Cr2B3 and CrMB3 (M=Sc, Ti, V, Zr)

    图  零压下 Cr2B3的体积弹性模量的三维表示(a)及其在 xyxzyz 面上的投影(b)

    Figure  9.  (a) 3D representation and (b) 2D projections on xy, xz and yz planes of the bulk modulus for Cr2B3 at 0 GPa

    图  10  零压下 Cr2B3的杨氏模量的三维表示(a)及其在 xyxzyz 面上的投影(b)

    Figure  10.  (a) 3D representation and (b) 2D projections on xy, xz and yz planes of the Young’s modulus for Cr2B3 at 0 GPa

    图  11  零压下 CrMB3(M=Sc, Ti, V, Zr)的体积弹性模量在 xyxzyz 面的投影

    Figure  11.  2D projections of the bulk modulus for CrMB3 (M=Sc, Ti, V, Zr) on xy, xz and yz planes at 0 GPa

    图  12  零压下 CrMB3(M=Sc, Ti, V, Zr)的杨氏模量在 xyxzyz 面的投影

    Figure  12.  2D projections of the Young’s modulus for CrMB3 (M=Sc, Ti, V, Zr) on xy, xz and yz planes at 0 GPa

    图  13  零压下 Cr2B3的总态密度以及分波态密度

    Figure  13.  Total density of states and partial density of states for Cr2B3 at 0 GPa

    图  14  零压下 CrMB3(M=Sc, Ti, V, Zr)的总态密度以及分波态密度

    Figure  14.  Total density of states and partial density of states for CrMB3 (M=Sc, Ti, V, Zr) at 0 GPa

    图  15  零压下(a) Cr2B3、(b) CrScB3、(c) CrTiB3、(d) CrVB3、(e) CrZrB3在(100)平面的 ELF 以及零压下(f) Cr2B3、(g) CrScB3、(h) CrTiB3、(i) CrVB3和(j) CrZrB3在($00 \overline 1 $)平面的 ELF

    Figure  15.  Electronic local functions contours for (a) Cr2B3, (b) CrScB3, (c) CrTiB3, (d) CrVB3 and (e) CrZrB3 in plane (100) at 0 GPa, and electronic local functions contours for (f) Cr2B3, (g) CrScB3, (h) CrTiB3, (i) CrVB3 and (j) CrZrB3 in plane ($00 \overline 1 $) at 0 GPa

    表  1  零压下Cr2B3及掺杂结构CrMB3(M=Sc, Ti, V, Zr)的晶格常数、形成焓及掺杂结构的形成能

    Table  1.   Lattice constants, formation enthalpy of Cr2B3 and CrMB3 (M = Sc, Ti, V, Zr), and impurity formation energy ofCrMB3 (M=Sc, Ti, V, Zr) at zero pressure

    Compounds Doping-site positionSpace groupLattice constantsEf/eVΔH/(eV∙atom−1)
    abc
    Cr2B3 Cmcm2.898318.04642.9286−0.4731
    CrScB3 Cr1Cmcm3.220718.52223.0293−0.9713−0.6653
    Cr2
    CrTiB3 Cr1Cmcm3.064818.16692.9746−1.9192−0.8561
    Cr2Cmcm3.054118.59002.9883−0.6876−0.6118
    CrVB3 Cr1Cmcm2.954618.08742.9436−1.1856−0.7092
    Cr2Cmcm2.954718.22542.9489−0.6797−0.6101
    CrZrB3 Cr1Cmcm3.297218.58723.0702−1.2236−0.7181
    Cr2Cmcm3.176320.01363.0524 0.1705−0.4424
    下载: 导出CSV

    表  2  Cr2B3中B―B键的键长以及布居数随压力的变化

    Table  2.   Pressure dependence of B―B bond length and population for Cr2B3

    Pressure/GPaBond length/Å Population
    B1―B1B1―B2B2―B3B1―B1B1―B2B2―B3
    01.695861.719711.75978 1.590.631.36
    251.661811.683551.723691.620.641.40
    501.634741.655591.694621.650.651.44
    751.612371.632141.670121.680.661.47
    1001.592981.612251.649311.700.671.50
    1251.575891.595061.630981.730.681.53
    1501.560581.579501.614421.750.691.56
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-12-10
  • 修回日期:  2022-02-06
  • 录用日期:  2022-02-06
  • 网络出版日期:  2022-06-30
  • 刊出日期:  2022-07-28

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