yy7752美女有哪些(原胞转化方法以及标准原胞在计算中的重要性)

通常我们从实验文献中得到的cif文件都是单胞，因此在做计算之前需要转换为原胞。今天我们以Si为例来讲述今天的问题，首先从Materials Project (https://materialsproject.org)下载所需的结构。步骤如下：

我们同时下载单胞和原胞两个结构(晶体结构如下图所示)，单胞结构用于后面转换为原胞用，原胞结构作为对比使用(请注意原胞的基矢形式)。

Si8-conventional cell1.05.4687280655 0.0000000000 0.00000000000.0000000000 5.4687280655 0.00000000000.0000000000 0.0000000000 5.4687280655Si8Direct0.000000000 0.000000000 0.000000000-0.000000000 0.500000000 0.5000000000.500000000 0.500000000 0.0000000000.500000000 -0.000000000 0.5000000000.750000044 0.250000000 0.7500000440.250000000 0.250000000 0.2500000000.250000000 0.750000044 0.7500000440.750000044 0.750000044 0.250000000

Si2-primitive cell1.03.8669745922 0.0000000000 0.00000000001.9334872961 3.3488982326 0.00000000001.9334872961 1.1162994109 3.1573715331Si2Direct0.749999979 0.749999983 0.7499999970.500000007 0.499999989 0.499999998

单胞转换为原胞第一种方法(使用VESTA软件)：

Si2-primitive cell from VESTA software1.03.8670001030 0.0000000000 0.00000000001.9335000515 3.3489203256 0.00000000001.9335000515 1.1163067752 3.1573923625Si2Direct0.125000001 0.125000002 0.1249999960.874999978 0.875000019 0.874999963

单胞转换为原胞第二种方法(使用Materials Studio软件)：

Si2-primitive cell from MS software1.03.8670001030 0.0000000000 0.00000000001.9335000515 3.3489203256 0.00000000001.9335000515 1.1163067752 3.1573923625Si2Direct0.000000000 0.000000000 0.0000000000.250000002 0.250000005 0.249999992

单胞转换为原胞第三种方法(使用AFLOW软件)：

Si2-primitive cell from AFLOW software1.224745 0.00000000000000 2.23259888375212 2.23259888375212 2.23259888375212 0.00000000000000 2.23259888375212 2.23259888375212 2.23259888375212 0.000000000000002 Direct(2) [A2]  0.00000000000000 0.00000000000000 0.00000000000000  0.75000000000000 0.75000008800000 0.75000000000000 

单胞转换为原胞第四种方法(使用VASPKIT软件)：

(echo 6; echo 602)|vaspkit

Si2-primitive cell from VASPKIT software 1.0000000.00000000000000 2.73436403275000 2.734364032750002.73436403275000 0.00000000000000 2.734364032750002.73436403275000 2.73436403275000 0.00000000000000Si2DIRECT0.0000000000000000 0.0000000000000000 0.0000000000000000 Si10.2500000000000000 0.2500000000000000 0.2500000000000000 Si2

根据附录1，我们可以知道只有AFLOW和VASPKIT软件给出的原胞才是标准基矢形式的原胞。而其它网站或者软件给出的原胞不具备标准基矢形式的原胞。原胞和单胞手动转换的矩阵变换请参考附录2。下面我们选取两种不同原胞通过计算弹性常数进行对比。

INCAR

(echo 1; echo 101; echo DC)|vaspkit

Global Parameters ISTART = 1 (Read existing wavefunction; if there) # ISPIN = 2 (Spin polarised DFT) # ICHARG = 11 (Non-self-consistent: GGA/LDA band structures) LREAL = .FALSE. (Projection operators: automatic) # ENCUT = 400 (Cut-off energy for plane wave basis set, in eV) PREC = Normal (Precision level)# LWAVE = .TRUE. (Write WAVECAR or not)# LCHARG = .TRUE. (Write CHGCAR or not) ADDGRID= .TRUE. (Increase grid; helps GGA convergence) # LVTOT = .TRUE. (Write total electrostatic potential into LOCPOT or not) # LVHAR = .TRUE. (Write ionic + Hartree electrostatic potential into LOCPOT or not) # NELECT = (No. of electrons: charged cells; be careful) # LPLANE = .TRUE. (Real space distribution; supercells) # NPAR = 4 (Max is no. nodes; don't set for hybrids) # NWRITE = 2 (Medium-level output) # KPAR = 2 (Divides k-grid into separate groups) # NGX = 500 (FFT grid mesh density for nice charge/potential plots) # NGY = 500 (FFT grid mesh density for nice charge/potential plots) # NGZ = 500 (FFT grid mesh density for nice charge/potential plots)EDIFF = 1E-6
Elastic constants Calculation # NGZ = 500 (FFT grid mesh density for nice charge/potential plots) IBRION = 6 (Determine the Hessian matrix) NFREE = 2 (How many displacements are used for each direction; 2-4) ISIF = 3 (Stress/relaxation: 3-Shape/Ions/V) NSW = 1 (Max ionic steps) PREC = High (High level) ENCUT = 700 (1.3 ~ 1.5 * default cutoff, need to check convergence)

KPOINTS

(echo 1; echo 102; echo 2; echo 0.04)|vaspkit

K-Mesh Generated with KP-Resolved Value (Low=0.08~0.05, Medium=0.04~0.03, Fine=0.02~0.01): 0.0400Gamma5 5 50.0 0.0 0.0

POSCAR1

Si2-primitive cell from AFLOW software1.224745 0.00000000000000 2.23259888375212 2.23259888375212 2.23259888375212 0.00000000000000 2.23259888375212 2.23259888375212 2.23259888375212 0.000000000000002 Direct(2) [A2]  0.00000000000000 0.00000000000000 0.00000000000000  0.75000000000000 0.75000008800000 0.75000000000000 

POSCAR2

Si2-primitive cell1.03.8669745922 0.0000000000 0.00000000001.9334872961 3.3488982326 0.00000000001.9334872961 1.1162994109 3.1573715331Si2Direct0.749999979 0.749999983 0.7499999970.500000007 0.499999989 0.499999998

POSCAR1计算得到的弹性矩阵结果如下：

(echo 2; echo 203)|vaspkit

 Crystal Class: m-3m Space Group: Fd-3m Crystal System: Cubic system Including Point group classes: 23, 2/m-3, 432, -43m, 4/m-32/m There are 3 independent elastic constants C11 C12 C12 0 0 0 C12 C11 C12 0 0 0 C12 C12 C11 0 0 0 0 0 0 C44 0 0 0 0 0 0 C44 0 0 0 0 0 0 C44
 Stiffness Tensor C_ij (in GPa): 153.416 60.373 60.373 0.000 0.000 0.000 60.373 153.416 60.373 0.000 0.000 0.000 60.373 60.373 153.416 0.000 0.000 0.000 0.000 0.000 0.000 72.566 0.000 0.000 0.000 0.000 0.000 0.000 72.566 0.000 0.000 0.000 0.000 0.000 0.000 72.566

POSCAR2计算得到的弹性矩阵结果如下：

 +-------------------------- Summary ----------------------------+ Crystal Class: m-3m Space Group: Fd-3m Crystal System: Cubic system Including Point group classes: 23, 2/m-3, 432, -43m, 4/m-32/m There are 3 independent elastic constants C11 C12 C12 0 0 0 C12 C11 C12 0 0 0 C12 C12 C11 0 0 0 0 0 0 C44 0 0 0 0 0 0 C44 0 0 0 0 0 0 C44
 Stiffness Tensor C_ij (in GPa): 179.640 51.817 42.795 0.000 12.759 0.000 51.817 179.640 42.795 0.000 -12.759 0.000 42.795 42.795 188.662 0.000 0.000 0.000 0.000 0.000 0.000 63.911 0.000 12.759 12.759 -12.759 0.000 0.000 54.890 0.000 0.000 0.000 0.000 12.759 0.000 54.890

面心立方Si正确的弹性矩阵Cij应该具有附录3的形式，利用标准原胞计算得到的弹性矩阵Cij才符合，而利用标准原胞计算得到的Cij需要进行一定的矩阵变换才能得到正确的Cij形式。对于初学者来说，如果不知道这一点就容易犯错误！其实除了弹性常数，采用不同形式的原胞进行计算得到的介电、压电等性质均会有影响。

附录1：

Computational Materials Science 49 (2010) 299–312.

附录2：(版权归yyyu200，欢迎关注他的QE免费教程)

https://yyyu200.github.io/DFTbook/blogs/2019/04/07/TransCell/

附录3：

http://jerkwin.github.io/2014/04/17/材料弹性模量各向异性的三维图示方法/