布里渊区及能带路径的可视化（布里渊区k点范围）

先前本公众号已经介绍"五种方法生成能带结构计算的高对称点"，使用里面的方法即可获取相应晶体对应的布里渊区图。在VASPKIT 1.20新版本中即将实现布里渊区及能带路径的可视化。相应的脚本文件(见文末代码)已经开放内测，感兴趣的可以到VASPKIT FAQs QQ 群331895604群文件下载。相比其它软件，VASPKIT可以更加方便实现自动标记对应能带计算的k点路径。

晶体结构的第一布里渊区可通过调用Voronoi图算法实现，特别感谢中科大郑奇靖老师提供了关于实现算法的建议。接下来我们演示如何调用VASPKIT结合python脚本实现布里渊区及能带路径的可视化：

第一步：我们以Cu和graphene为例，准备好POSCAR文件，注意一定是原胞结构(primtive cell)。然后分别运行vaspkit -303 (Cu 体相)和vaspkit -302 (二维体系graphene)生成包含推荐能带路径的KPATH.in文件和高对称点HIGH_SYMMETRY_POINTS文件;

===================== Structural Options ======================== 01) VASP Input Files Generator 02) Elastic-Properties 03) K-Path Generator 04) Structure Editor 05) Catalysis-ElectroChem Kit 06) Symmetry Search ===================== Electronic Options ======================== 11) Density-of-States 21) DFT Band-Structure 23) 3D Band-Structure 25) Hybrid-DFT Band-Structure 26) Fermi-Surface 28) Band-Structure Unfolding =========== Charge & Potential & Wavefunction Options =========== 31) Charge & Spin Density 42) Potential-Related 51) Wave-Function Analysis ====================== Misc Utilities =========================== 71) Optical-Properties 72) Molecular-Dynamics Kit 73) VASP2other Interface 91) Semiconductor Calculator 92) 2D-Materials Kit 0) Quit------------>>302 +-------------------------- Warm Tips --------------------------+ See An Example in vaspkit/examples/seek_kpath/graphene_2D. More details are given in arXiv:1806.04285 (2018) and refs. This feature is still experimental & check PRIMCELL.vasp file. +---------------------------------------------------------------+-->> (01) Reading Structural Parameters from POSCAR File... +-------------------------- Summary ----------------------------+ The vacuum slab is supposed to be along z axis Prototype: AB2 Total Atoms in Input Cell: 3 Lattice Constants in Input Cell: 3.190 3.190 12.000 Lattice Angles in Input Cell: 90.000 90.000 120.000 Total Atoms in Primitive Cell: 3 Lattice Constants in Primitive Cell: 3.190 3.190 12.000 Lattice Angles in Primitive Cell: 90.000 90.000 120.0002D Bravais Lattice: Hexagonal Point Group: 26 [ D3h ] International: P-6m2 Symmetry Operations: 12 Suggested K-Path: (shown in the next line) [ GAMMA-M-K-GAMMA ] +---------------------------------------------------------------+-->> (02) Written PRIMCELL.vasp file.-->> (03) Written HIGH_SYMMETRY_POINTS File for Reference.-->> (04) Written KPATH.in File for Band-Structure Calculation. +----------------------------WARNING----------------------------+ | Do NOT forget to copy PRIMCELL.vasp to POSCAR unless you know | | what you are doing. Otherwise you might get wrong results! | +---------------------------------------------------------------+`

第二步，终端运行python3 visualize_BZ.py (代码见下面)得到下图：

import numpy as np, numpy.linalg as nplfrom scipy.spatial import Voronoifrom itertools import productfrom matplotlib.patches import FancyArrowPatchfrom mpl_toolkits.mplot3d import proj3dimport matplotlib as mplmpl.rcParams['font.size'] = 12.
def read_poscar(poscar, species=None): poscar = open(poscar,'r') title = poscar.readline.strip scale = float(poscar.readline.strip) s = float(scale) lattice_vectors = [[ float(v) for v in poscar.readline().split() ], [ float(v) for v in poscar.readline().split() ], [ float(v) for v in poscar.readline().split() ]] lattice_vectors = np.array(lattice_vectors) reciprocal_lattice_vectors= np.linalg.inv(lattice_vectors).T reciprocal_lattice_vectors=reciprocal_lattice_vectors*np.pi*2return reciprocal_lattice_vectors
def read_high_symmetry_points: f = open("HIGH_SYMMETRY_POINTS",'r')  fa=f.readline  n=0 hpts= while True:  fa=f.readline  hpts.append(fa)  n=n+1if fa.find('use') > 0: break f.close  kpts=  klabels= for i in range(0,n-3):  kpts.append(hpts[i].split[0:3]) klabels.append(hpts[i].split[3]) kpts=np.array(kpts,dtype=np.float64)return kpts, klabels
def is_greek_alphabets(klabels): Greek_alphabets=['Alpha','Beta','Gamma','Delta','Epsilon','Zeta','Eta','Theta', 'Iota','Kappa','Lambda','Mu','Nu','Xi','Omicron','Pi','Rho','Sigma','Tau','Upsilon','Phi','Chi','Psi','Pega'] group_labels=for i in range(len(klabels)):  klabel=klabels[i] for j in range(len(Greek_alphabets)):if (klabel.find(Greek_alphabets[j].upper)>=0): latex_exp=r''+'$\\'+str(Greek_alphabets[j])+'$' klabel=klabel.replace(str(Greek_alphabets[j].upper),str(latex_exp))if (klabel.find('_')>0): n=klabel.find('_') klabel=klabel[:n]+'