首先利用VASPKIT-204命令得到体弹性模量、杨氏模量、剪切模量及泊松比随角度的依赖关系，具体算法可参考文献【J. Phys. Condens. Matter, 28, 275201 (2016)和Comput. Phys. Commun. 181, 2102–2115 (2010)】。接下来我们以某单斜体系的弹性常数为例来演示如何进行材料力学量三维可视化。第一步：新建ELASTIC_TENSOR.in并输入6x6弹性常数矩阵，注意第一行是注释行不可省略。如果是二维体系，则输入文件为ELASTIC_TENSOR_2D.in，注意二维体系弹性常数矩阵大小为3x3。# comment line (in GPa) 228.38 85.741 81.503 0 -0.737 0 85.741 217.47 94.201 0 -20.213 0 81.503 94.201 178.81 0 -9.472 0 0 0 0 35.094 0 -17.851 -0.737 -20.213 -9.472 0 37.778 0 0 0 0 -17.851 0 42.708
第二步：运行VASPKIT 204命令得到MECHANICS_3D.dat------------>>204 +-------------------------- Warm Tips --------------------------+ See an example in vaspkit/examples/angular_dependent_mechanics. +---------------------------------------------------------------+ -->> (01) Reading Elastic-Tensor From ELASTIC_TENSOR.in File...
Stiffness Tensor C_ij (in GPa): 228.380 85.741 81.503 0.000 -0.737 0.000 85.741 217.470 94.201 0.000 -20.213 0.000 81.503 94.201 178.810 0.000 -9.472 0.000 0.000 0.000 0.000 35.094 0.000 -17.851 -0.737 -20.213 -9.472 0.000 37.778 0.000 0.000 0.000 0.000 -17.851 0.000 42.708
Compliance Tensor S_ij (in GPa^{-1}): 0.005594 -0.001532 -0.001804 0.000000 -0.001163 0.000000 -0.001532 0.006607 -0.002632 0.000000 0.002845 0.000000 -0.001804 -0.002632 0.007829 0.000000 0.000520 0.000000 0.000000 0.000000 0.000000 0.036189 0.000000 0.015126 -0.001163 0.002845 0.000520 0.000000 0.028100 0.000000 0.000000 0.000000 0.000000 0.015126 0.000000 0.029737 +---------------------------------------------------------------+ -->> (02) Written MECHANICS_3D.dat File!
打开MECHANICS_3D.dat可看到第一行给出了每一列数据所代表的物理量，第二行给出了球坐标系下分别划分仰角#Theta Phi Bulk Young Shear_min Shear_max Poisson_min Poisson_max Compressibility #Grid size: 181 361 0.00000 0.00000 98.24107 127.73352 27.63268 35.58671 0.23047 0.33613 0.00339 0.00000 1.00000 98.24107 127.73352 27.63268 35.58671 0.23047 0.33613 0.00339 0.00000 2.00000 98.24107 127.73352 27.63268 35.58671 0.23047 0.33613 0.00339 0.00000 3.00000 98.24107 127.73352 27.63268 35.58671 0.23047 0.33613 0.00339
第三步：从vaspkit/examples/angular_dependent_mechanics 文件夹中拷贝mechanics_3d_plot_matlab.m到当前目录，调用Matlab软件运行该脚本，得到以下信息(VASPKIT ver. >= 1.3.2) ======================= Plot Options =========================== 1) Bulk Modulus 2) Young's Modulus 3) Shear Modulus (minimum) 4) Shear Modulus (maximum) 5) Poisson's ratio (minimum) 6) Poisson's ratio (maximum) 7) Linear Compressibility Which mechanical quantity do you want to plot? 2
另外，以下两个软件也可以实现材料力学量三维可视化。http://progs.coudert.name/elateVASP+ElasticPost计算材料各向异性杨氏模量泊松比等ElasticPOST 弹性常数各向异性后处理软件(带图形界面)ElATools程序: 用于分析2D和3D材料各向异性弹性特性的工具最后，特别感谢廖名情博士和刘忠利教授的建议和讨论。如果您使用VASPKIT，请记得引用哦。V. Wang, N. Xu, J.-C. Liu, G. Tang, W.-T. Geng, VASPKIT: A User-Friendly Interface Facilitating High-Throughput Computing and Analysis Using VASP Code, Computer Physics Communications 267, 108033, (2021), https://doi.org/10.1016/j.cpc.2021.108033. 