〈111〉方向单轴应变下金刚石和硅的广义层错能

黄丽丽 彭丽 陈实 张红平 李牧

黄丽丽, 彭丽, 陈实, 张红平, 李牧. 〈111〉方向单轴应变下金刚石和硅的广义层错能[J]. 高压物理学报, 2024, 38(3): 030107. doi: 10.11858/gywlxb.20240765
引用本文: 黄丽丽, 彭丽, 陈实, 张红平, 李牧. 〈111〉方向单轴应变下金刚石和硅的广义层错能[J]. 高压物理学报, 2024, 38(3): 030107. doi: 10.11858/gywlxb.20240765
HUANG Lili, PENG Li, CHEN Shi, ZHANG Hongping, LI Mu. Generalized Stacking Fault Energies of Diamond and Silicon under ⟨111⟩ Uniaxial Loading[J]. Chinese Journal of High Pressure Physics, 2024, 38(3): 030107. doi: 10.11858/gywlxb.20240765
Citation: HUANG Lili, PENG Li, CHEN Shi, ZHANG Hongping, LI Mu. Generalized Stacking Fault Energies of Diamond and Silicon under ⟨111⟩ Uniaxial Loading[J]. Chinese Journal of High Pressure Physics, 2024, 38(3): 030107. doi: 10.11858/gywlxb.20240765

〈111〉方向单轴应变下金刚石和硅的广义层错能

doi: 10.11858/gywlxb.20240765
基金项目: 国家自然科学基金(12204317,11974321,11972330)
详细信息
    作者简介:

    黄丽丽(1989-),女,博士,助理教授,主要从事位错结构的第一性原理计算研究. E-mail:huanglili@sztu.edu.cn

    通讯作者:

    李 牧(1979-),男,博士,教授,主要从事动高压物理研究. E-mail:limu@sztu.edu.cn

  • 中图分类号: O521.2; O344.1

Generalized Stacking Fault Energies of Diamond and Silicon under ⟨111⟩ Uniaxial Loading

  • 摘要: 晶体中原子层面剪切所带来的能量称为广义层错能,它是描述晶体中纳米尺度塑性变形的关键参数,如位错分解、成核和孪晶。在冲击加载过程中,弹塑性转变发生在一维弹性应变之后,因此,单轴应变下的广义层错能对于理解塑性流动的发生具有重要意义。应用基于密度泛函理论的第一性原理,计算了在$ \text{[}\text{111}\text{]} $方向单轴应变下硅和金刚石的glide (111)面的广义层错能面。基于广义层错能面的平移对称性,通过傅里叶级数展开,拟合得到了广义层错能面的表达式,并给出了$ [\overline{\text{1}}\text{10}\text{]} $ (111)和$ \text{[}\text{11}\overline{\text{2}}\text{]} $ (111)方向的广义层错能曲线。结果表明,随着应变的增加,本征层错能和不稳定层错能出现明显的变化,且不稳定层错能与本征层错能之比减小,说明在$ \left\langle{\text{111}}\right\rangle $方向的单轴应变下晶体中的位错不容易发生分解。该结果解释了在四代光源上开展的位错演化动态实验结果,即沿$ \left\langle{\text{111}}\right\rangle $方向加载的层错信号出现的速度和强度均远不如沿$\left\langle{\text{110}}\right\rangle $方向和$\left\langle{\text{100}}\right\rangle $方向加载的结果。

     

  • 图  glide (111)面示意图(蓝色原子为下半无限大晶体的最上层原子,灰色原子为上半无限大晶体的最下层原子,ROB的距离,C点为本征层错位置,D点为不稳定层错位置)

    Figure  1.  Schematic diagram of glide (111) surface (Blue atoms are the topmost layer of atoms in the lower half of the infinity crystal, and gray atoms are the bottom layer of atoms in the upper half of the infinity crystal; R is the distance of OB, the point C is the location of intrinsic stacking fault, and the point D is the location of unstable stacking fault.)

    图  基于DFT的第一性原理计算理想超胞模型

    Figure  2.  Ideal supercell model for the first principle computations based on DFT

    图  不同应变下由式(4)拟合得到的硅的glide (111)面的GSFE面(图中的点为第一性原理计算结果,[$ 11\overline{2} $]方向上的第1个能量峰值为不稳定层错能,第1个能量最小值为本征层错能,GSFE面沿[$ \overline{1}10 $]方向的投影是对称的)

    Figure  3.  GSFE surface of the glide (111) surface of silicon fitted by Eq. (4) for different strains (The points in the figures are the results of first principles calculations, the first energy peak in the [$ 11\overline{2} $] direction is the unstable stacking fault energy, the first energy minimum is the intrinsic stacking fault energy, and the GSFE surface is symmetric along the projection in the [$ \overline{1}10 $] direction.)

    图  不同应变下由式(4)拟合得到的金刚石的glide (111)面的GSFE面(图中的点为第一性原理计算结果,[$ 11\overline{2} $]方向上的第1个能量峰值为不稳定层错能,第1个能量最小值为本征层错能,GSFE面沿[$ \overline{1}10 $]方向的投影是对称的)

    Figure  4.  GSFE surface of the glide (111) surface of diamond fitted by Eq. (4) for different strains (The points in the figures are the results of first principles calculations, the first energy peak in the [$ 11\overline{2} $] direction is the unstable stacking fault energy, the first energy minimum is the intrinsic stacking fault energy, and the GSFE surface is symmetric along the projection in the [$ \overline{1}10 $] direction.)

    图  不同应变下glide (111)面的GSFE面在$ \text{[}\text{11}\overline{\text{2}}\text{]} $滑移方向上的投影

    Figure  5.  Projections of the GSFE surface on the $ \text{[}\text{11}\overline{\text{2}}\text{]} $ slip direction for different strains on the glide (111) surface

    图  不同应变下glide (111)面的GSFE面在[$ \overline{1}10 $]滑移方向上的投影

    Figure  6.  Projections of the GSFE surface on the [$ \overline{1}10 $] slip direction for different strains on the glide (111) surface

    图  不同应变下硅的glide (111)面的本征层错能(γI)、不稳定层错能(γus)以及两者的比值

    Figure  7.  Intrinsic stacking fault energy (γI) and unstable stacking fault energy (γus) and the ratio of them for the glide (111) surface of silicon at different strains

    图  不同应变下金刚石的glide (111)面的本征层错能(γI )、不稳定层错能(γus)以及两者的比值

    Figure  8.  Intrinsic stacking fault energy (γI) and unstable stacking fault energy (γus) and the ratio of them for the glide (111) surface of dimond at different strains

    表  1  不同超胞的硅的本征层错能和不稳定层错能

    Table  1.   Intrinsic stacking faults energies and unstable stacking faults energies for silicon with different supercells

    Layers γI/(eV·Å−2) γus/(eV·Å−2) Layers γI/(eV·Å−2) γus/(eV·Å−2)
    6 0.002 0.085 18 0.003 0.106
    10 0.004 0.098 22 0.003 0.107
    14 0.004 0.104
    下载: 导出CSV

    表  2  不同应变下由式(4)描述的GSFE面的拟合参数

    Table  2.   Fitting parameters of the GSFE surface described by Eq. (4) for different strains

    Material ε Fitting parameters/(J·m−2)
    c0 c1 c2 c3 c4 c5
    Silicon 0 24.085 −12.658 7.490 −2.221 −0.471 0.257
    0.03 25.623 −13.568 8.163 −2.439 −0.521 0.295
    0.06 27.235 −14.531 8.882 −2.674 −0.573 0.337
    0.09 28.911 −15.538 9.646 −2.924 −0.631 0.383
    0.12 30.631 −16.577 10.446 −3.183 −0.696 0.432
    0.15 32.372 −17.634 11.265 −3.445 −0.764 0.482
    0.18 34.143 −18.720 12.112 −3.720 −0.834 0.537
    Material ε Fitting parameters/(J·m−2)
    c6 s1 s2 s3 s4 s5
    Silicon 0 0.046 21.901 −3.797 0.849 −0.020 −0.013
    0.03 0.050 23.465 −4.160 0.944 −0.026 −0.016
    0.06 0.054 25.114 −4.548 1.046 −0.033 −0.020
    0.09 0.059 26.835 −4.960 1.157 −0.041 −0.023
    0.12 0.064 28.604 −5.391 1.275 −0.046 −0.025
    0.15 0.069 30.395 −5.833 1.397 −0.048 −0.027
    0.18 0.077 32.225 −6.289 1.527 −0.054 −0.032
    Material ε Fitting parameters/(J·m−2)
    c0 c1 c2 c3 c4 c5
    Diamond 0 55.327 −29.945 20.276 −6.548 −1.668 0.852
    0.03 62.026 −34.033 23.583 −7.701 −1.944 1.084
    0.06 69.519 −38.668 27.417 −9.054 −2.268 1.371
    0.09 77.951 −43.959 31.877 −10.654 −2.641 1.717
    0.12 87.438 −50.002 37.078 −12.544 −3.070 2.129
    0.15 97.852 −56.793 43.166 −14.733 −3.638 2.648
    0.18 109.070 −64.368 50.293 −17.270 −4.382 3.312
    Material ε Fitting parameters/(J·m−2)
    c6 s1 s2 s3 s4 s5
    Diamond 0 0.260 51.709 −11.059 3.080 −0.125 −0.059
    0.03 0.278 58.586 −12.938 3.634 −0.175 −0.079
    0.06 0.297 66.292 −15.122 4.294 −0.238 −0.102
    0.09 0.318 74.966 −17.651 5.078 −0.325 −0.133
    0.12 0.335 84.742 −20.561 5.996 −0.439 −0.167
    0.15 0.369 95.601 −23.980 7.099 −0.515 −0.208
    0.18 0.441 107.721 −28.001 8.429 −0.528 −0.264
    下载: 导出CSV

    表  3  在不同应变下式(6)描述的$ [\overline{{\boldsymbol{1}}}{\boldsymbol{10}}] $ (111)方向的GSFE面的拟合参数

    Table  3.   Fitting parameters of the GSFE surface for $ [\overline{{\boldsymbol{1}}}{\boldsymbol{10}}] $ (111) slip direction described by Eq. (6) at different strains

    Material ε μγ/(GJ·m−3) $\varDelta_1 $ $\varDelta_2 $ Material ε μγ/(GJ·m−3) $\varDelta_1 $ $\varDelta_2 $
    Silicon 0 16.297 −1.002 0.495 Dimond 0 121.297 −1.149 0.850
    0.03 16.612 −1.013 0.496 0.03 125.646 −1.150 0.825
    0.06 16.898 −1.025 0.496 0.06 129.464 −1.150 0.797
    0.09 17.151 −1.035 0.495 0.09 132.670 −1.148 0.768
    0.12 17.369 −1.045 0.492 0.12 135.093 −1.145 0.735
    0.15 17.545 −1.053 0.489 0.15 136.433 −1.141 0.694
    0.18 17.665 −1.060 0.481 0.18 136.151 −1.129 0.629
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-03-28
  • 修回日期:  2024-04-16
  • 网络出版日期:  2024-05-28
  • 刊出日期:  2024-06-03

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