Created
June 19, 2024 14:30
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Plot real cell and Brillouin zone.
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#!/usr/bin/env python3 | |
import numpy as np | |
import matplotlib.pyplot as plt | |
import matplotlib as mpl | |
from scipy.spatial import Voronoi | |
def get_reduced_voronoi(cell): | |
assert cell.shape == (2,2) | |
points = np.tensordot( | |
cell, np.mgrid[-1:2, -1:2], axes=(0,0) | |
).reshape(2,-1).T | |
vor = Voronoi(points) | |
bz_facets = [] | |
bz_ridges = [] | |
bz_vertices = [] | |
for pid, rid in zip(vor.ridge_points, vor.ridge_vertices): | |
if 4 in pid: | |
bz_ridges.append(vor.vertices[np.r_[rid, [rid[0]]]]) | |
bz_facets.append(vor.vertices[rid]) | |
bz_vertices += rid | |
bz_vertices = list(set(bz_vertices)) | |
return (vor.vertices[bz_vertices], # V | |
bz_ridges, # E | |
bz_facets) # F | |
def plot_reduced_voronoi(cell, ax, lc, lw, ls, reci=False): | |
# icell = np.linalg.inv(cell).T | |
icell = cell | |
V, E, F = get_reduced_voronoi(icell) | |
# l1, l2 = np.linalg.norm(icell, axis=1) | |
xmin = min(ax.get_xlim()[0], icell[:,0].min()) | |
xmax = max(ax.get_xlim()[1], icell[:,0].max()) | |
ymin = min(ax.get_ylim()[0], icell[:,1].min()) | |
ymax = max(ax.get_ylim()[1], icell[:,1].max()) | |
for xx in E: | |
ax.plot(xx[:,0], xx[:,1], color=lc, lw=lw, ls=ls) | |
xmin = min(xmin, xx[:,0].min()) | |
xmax = max(xmax, xx[:,0].max()) | |
ymin = min(ymin, xx[:,1].min()) | |
ymax = max(ymax, xx[:,1].max()) | |
arrowprops = dict(arrowstyle="->", | |
shrinkA=0, | |
shrinkB=0, | |
color=lc) | |
s = "b" if reci else "a" | |
print(icell, tuple(icell[0,:]), tuple(icell[1,:])) | |
ax.text(*icell[0,:], s+"1", color=lc) | |
ax.annotate("", xy=tuple(icell[0,:]), xytext=(0,0), arrowprops=arrowprops) | |
ax.text(*icell[1,:], s+"2", color=lc) | |
ax.annotate("", xy=tuple(icell[1,:]), xytext=(0,0), arrowprops=arrowprops) | |
ax.set_xlim(xmin-0.02, xmax+0.02) | |
ax.set_ylim(ymin-0.02, ymax+0.02) | |
if '__main__' == __name__: | |
# 2D system only | |
# cell_primitive = np.array([[ 3.1903157000000002, 0.0000000000000000], | |
# [-1.5951578500000001, 2.7628944419999999]]); | |
cell_primitive = np.array([[ 2.7628944419999999,-1.5951578500000001], | |
[ 0.0000000000000000, 3.1903157000000002]]); | |
transform_matrix = np.array([[4, 2], | |
[0, 3]]) | |
cell_supercell = transform_matrix @ cell_primitive | |
icell_primitive = np.linalg.inv(cell_primitive).T | |
icell_supercell = np.linalg.inv(cell_supercell).T | |
fig, axs = plt.subplots(ncols=2, figsize=(8, 4), dpi=400) | |
ax = axs[0] | |
ax.set_xlim(0,0.00001) | |
ax.set_ylim(0,0.00001) | |
plot_reduced_voronoi(cell_primitive, ax, lc="k", lw=1.0, ls='-', reci=False) | |
plot_reduced_voronoi(cell_supercell, ax, lc="b", lw=1.0, ls='-', reci=False) | |
ax.set_aspect('equal') | |
ax.axis('off') | |
ax = axs[1] | |
ax.set_xlim(0,0.00001) | |
ax.set_ylim(0,0.00001) | |
plot_reduced_voronoi(icell_primitive, ax, lc="k", lw=1.0, ls='-', reci=True) | |
plot_reduced_voronoi(icell_supercell, ax, lc="b", lw=1.0, ls='-', reci=True) | |
ax.set_aspect('equal') | |
ax.axis('off') | |
fig.tight_layout(pad=0.0) | |
fig.savefig("bz.png", dpi=400) |
Author
Ionizing
commented
Jun 19, 2024
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