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Figure_dislocation.py
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Figure_dislocation.py
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# -*- coding: utf-8 -*-
# ---
# jupyter:
# jupytext:
# formats: ipynb,py:percent
# text_representation:
# extension: .py
# format_name: percent
# format_version: '1.3'
# jupytext_version: 1.12.0
# kernelspec:
# display_name: Python [conda env:moire-figures]
# language: python
# name: conda-env-moire-figures-py
# ---
# %% [markdown]
# # Generate Figure 3: Dislocations
# %%
from skimage.io import imread
import os
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as patches
import matplotlib.ticker as ticker
import colorcet
from latticegen import hexlattice_gen, generate_ks
from latticegen.singularities import singularity_shift, refined_singularity
from latticegen.transformations import rotate
import pyGPA.geometric_phase_analysis as GPA
from pyGPA.imagetools import indicate_k, gauss_homogenize2
from pyGPA.property_extract import Kerelsky_plus
from pyGPA.mathtools import periodic_average
def sort_primary_ks(k_lists):
double_ks = np.stack([np.concatenate([x, -x]) for x in k_lists])
centerangle = periodic_average(np.arctan2(*double_ks.reshape((-1, 2)).T), period=np.pi/3)
return [x[np.argsort(np.arctan2(*rotate(x, -centerangle).T))][3:] for x in double_ks]
# %% [markdown]
# ## Getting experimental data and GPA
# %%
folder = "data"
name = "20200715_154404_0.66um_495.9_sweep-STAGE_X-STAGE_Y_highres_highE_stitch_v10_2020-11-20_1843_sobel_5_bw_200.tif"
NMPERPIXEL = 0.88
oimage = imread(os.path.join(folder, name)).squeeze()[2400:3400, 2250:3400].astype(np.float64)
# %%
mask = np.zeros_like(oimage, dtype=bool)
sigma = 18
dr = 2*sigma
mask[dr:-dr, dr:-dr] = 1.
# %%
image = gauss_homogenize2(oimage, mask, 15)
pks_exp, _ = GPA.extract_primary_ks(image[dr+100:-dr, dr+25:-dr-75], pix_norm_range=(4, 50), sigma=1.5)
# %%
u_exp, gs_exp = GPA.extract_displacement_field(image, pks_exp, sigma=sigma, kwscale=5, ksteps=3, return_gs=True)
# %%
zslices = slice(350, 750), slice(350, 750)
exx, eyy = np.mgrid[:oimage.shape[0], :oimage.shape[1]]
# %% [markdown]
# ## Rendering dislocation in moire lattice
# %%
S = 1024 # Size of visualization in pixels.
r_k = 0.1
a_0 = 0.246
xi0 = 0
alphai = 3
sshift = singularity_shift(r_k, xi0, S, alpha=2*np.pi*alphai/6) # + 0.3*np.array((2/3/r_k,0))[:,None,None]
iterated1 = 0.7 * hexlattice_gen(r_k, xi0, 3, S, shift=sshift, chunks=400).compute()
iterated1 -= iterated1.min()
theta = 4.5
shiftx = -1.5
shifty = -2
iterated2 = hexlattice_gen(r_k, xi0+theta, 3, S, shift=np.array((shiftx, shifty)), chunks=400).compute()
iterated2 -= iterated2.min()
moire = np.sqrt((iterated1)**2 + (iterated2)**2)
# %%
plt.figure()
im = plt.imshow(moire.T, cmap='cet_fire_r',
vmax=np.quantile(moire, 0.9),
vmin=np.quantile(moire, 0.1),
origin='lower',
)
# %%
oks1 = generate_ks(r_k, xi0)[:3]
oks2 = generate_ks(r_k, xi0+theta)[:3]
pks1, _ = GPA.extract_primary_ks(iterated1, pix_norm_range=(3, 150), plot=True)
pks2, _ = GPA.extract_primary_ks(iterated2, pix_norm_range=(3, 150), plot=True)
pks, _ = GPA.extract_primary_ks(moire, pix_norm_range=(3, 50), plot=True, threshold=0.1, sigma=1)
pks1, pks2, pks_moire, pks_derived = sort_primary_ks([oks1, oks2, pks, pks1-pks2])
pks1, pks2, pks_moire, pks_derived = sort_primary_ks([pks1, pks2, pks, pks1-pks2])
# %%
u_disl, gs_disl = GPA.extract_displacement_field(iterated1, pks1, sigma=10, kwscale=4, return_gs=True)
# %%
phases_disl = np.stack([np.angle(g['lockin']) for g in gs_disl])
fig, axs = plt.subplots(ncols=3, nrows=1, figsize=[16, 5])
for i in range(len(gs_disl)):
im = axs[i].imshow(phases_disl[i][dr:-dr, dr:-dr].T, cmap='twilight',
interpolation='none', vmax=np.pi, vmin=-np.pi, origin='lower')
plt.colorbar(im, ax=axs[i])
axs[i].set_title((pks1)[i])
indicate_k((pks1), i, ax=axs[i], origin='lower')
# %%
msigma = 60
mdr = 2*msigma
u_moire, gs_moire = GPA.extract_displacement_field(moire, pks_derived, sigma=msigma, kwscale=4, return_gs=True)
moirephases = np.stack([np.angle(g['lockin']) for g in gs_moire])
# %%
fig, axs = plt.subplots(ncols=3, nrows=1, figsize=[16, 5])
for i in range(len(gs_moire)):
im = axs[i].imshow(moirephases[i][mdr:-mdr, mdr:-mdr].T, cmap='twilight',
interpolation='none', vmax=np.pi, vmin=-np.pi, origin='lower')
plt.colorbar(im, ax=axs[i])
axs[i].set_title((pks_derived)[i])
indicate_k((pks_derived), i, ax=axs[i], origin='lower')
# %%
z = 16
r = slice((z-1) * S // (2*z), (z+1) * S // (2*z))
w_in_nm = S*r_k*a_0//2
# %%
improved = refined_singularity(r_k/z*2, S=S)
improved_rot = hexlattice_gen(r_k/z*2, xi0+theta, 3, size=S, shift=np.array((shiftx, shifty))*z/2).compute()
rnew = slice(S//4, -S//4)
# %% [markdown]
# ## Generate Figure
#
# Arrows and inset indications as they appear in the paper were added afterwards using Illustrator
# %%
fig = plt.figure(figsize=[12.5, 7], constrained_layout=True)
gs0 = fig.add_gridspec(1, 2, width_ratios=[2.8, 9.8])
gsl = gs0[0].subgridspec(7, 3)
gsr = gs0[1].subgridspec(4, 6)
fig.set_constrained_layout_pads(w_pad=4 / 72, h_pad=4 / 72, hspace=0.0, wspace=0.0/72)
axmoire = fig.add_subplot(gsr[:3, :3])
axmoire.set_title('Stacked graphene layers')
axmoirephases = [fig.add_subplot(gsr[3, i]) for i in range(3)]
ax_exp = fig.add_subplot(gsr[:3, 3:])
ax_exp_phases = [fig.add_subplot(gsr[3, 3+i]) for i in range(3)]
axdisl = fig.add_subplot(gsl[:3, :3])
axdisl.set_title('Bottom layer: single dislocation')
axdislphases = [fig.add_subplot(gsl[3, i]) for i in range(3)]
axrotated = fig.add_subplot(gsl[-3:, :3])
axrotated.set_title(f'Top layer: rotated by θ$ = $4.5°')
axrotated.set_xlabel('nm')
edge = S*r_k*a_0/2
extent = np.array([-edge, edge, -edge, edge])
im = axdisl.imshow(improved[rnew, rnew].T, cmap='cet_fire_r', extent=extent/z,
vmax=np.quantile(improved, 0.9552),
# interpolation='none',
origin='lower',
)
im = axmoire.imshow(moire[mdr:-mdr, mdr:-mdr].T, cmap='cet_fire_r', extent=extent*(S-2*mdr)/S,
vmax=np.quantile(moire, 0.99),
vmin=np.quantile(moire, 0.01),
interpolation='none',
origin='lower',
)
im = axrotated.imshow(improved_rot[rnew, rnew].T, cmap='cet_fire_r', extent=extent/z,
vmax=np.quantile(improved_rot, 0.95),
vmin=np.quantile(improved_rot, 0.1),
# interpolation='none',
origin='lower'
)
mxx, myy = np.mgrid[:moire.shape[0], :moire.shape[1]]
dxx, dyy = np.mgrid[:iterated1.shape[0], :iterated1.shape[1]]
for i in range(3):
im = axmoirephases[i].imshow(moirephases[i][mdr:-mdr, mdr:-mdr].T,
cmap='twilight', interpolation='none',
vmax=np.pi, vmin=-np.pi,
extent=extent*(S-2*mdr) / S,
origin='lower')
kx, ky = pks_derived[i]
mrecon = np.exp(np.pi*2*1j*(mxx*kx + myy*ky)) / np.exp(1j*moirephases[i])
mrecon = mrecon.real
axmoirephases[i].yaxis.tick_right()
axmoirephases[i].yaxis.set_label_position("right")
axmoirephases[i].tick_params(axis='y', which='both',
labelleft=False, labelright=False)
axmoirephases[i].imshow(mrecon[mdr:-mdr, mdr:-mdr].T, cmap='gray_r',
extent=extent*(S-2*mdr)/S,
alpha=0.1, origin='lower',
interpolation='none'
)
iax = indicate_k((pks_derived), i, ax=axmoirephases[i], origin='lower', s=8)
iax.margins(0.1)
kx, ky = pks1[i]
drecon = np.exp(np.pi*2*1j*(dxx*kx + dyy*ky)) / np.exp(1j*phases_disl[i])
drecon = drecon.real
axdislphases[i].tick_params(axis='y', which='both',
labelleft=False, labelright=False)
imdisl = axdislphases[i].imshow(phases_disl[i][r, r].T,
cmap='twilight', interpolation='none',
vmax=np.pi, vmin=-np.pi,
extent=extent/z,
origin='lower')
axdislphases[i].imshow(drecon[r, r].T, cmap='gray_r',
extent=extent/z,
alpha=0.2, origin='lower',
interpolation='none'
)
axdislphases[i].axes.xaxis.set_visible(False)
axdislphases[i].axes.yaxis.set_visible(False)
axdislphases[0].tick_params(axis='y', which='both', labelleft=True, labelright=False)
for ax in [axdisl, axrotated] + axdislphases:
for axis in ['top', 'bottom', 'left', 'right']:
ax.spines[axis].set_linewidth(2)
ax.spines[axis].set_color("green")
axmoire.yaxis.tick_right()
axmoire.set_ylabel('nm')
axmoire.yaxis.set_label_position("right")
axmoire.tick_params(axis='y', which='both', labelleft=False, labelright=True)
rect = patches.Rectangle((-(1)/z*w_in_nm, -(1)/z*w_in_nm), 2/z*w_in_nm, 2/z*w_in_nm,
linewidth=2, edgecolor='g', facecolor='none')
axmoire.add_patch(rect)
axmoirephases[1].set_title('GPA phases moiré')
axdislphases[1].set_title('GPA phases bottom layer')
axmoirephases[1].set_xlabel('nm')
# Experimental data
###################
im = ax_exp.imshow(oimage[zslices].T, cmap='gray',
vmax=np.quantile(oimage[zslices], 0.9999),
vmin=np.quantile(oimage[zslices], 0.0001), origin='lower')
exp_extent = np.array(im.get_extent()) * NMPERPIXEL-175
im.set_extent(exp_extent)
axs = ax_exp_phases
for i in range(len(gs_exp)):
phase = gs_exp[i]['lockin']
kx, ky = pks_exp[i]
recon = np.exp(np.pi*2*1j*(exx*kx + eyy*ky))/phase
recon = recon.real
im = axs[i].imshow(np.angle(phase)[zslices].T, cmap='twilight',
interpolation='none', extent=exp_extent, origin='lower', vmax=np.pi, vmin=-np.pi)
indicate_k(pks_exp, i, ax=axs[i], origin='lower', s=8)
axs[i].imshow(recon[zslices].T,
cmap='gray',
alpha=0.4,
interpolation='none',
extent=exp_extent, origin='lower')
axs[1].set_title('Experimental GPA phases')
axs[1].set_xlabel('nm')
for i in range(3):
axs[i].tick_params(axis='y', which='both', labelleft=False, labelright=False)
ax_exp.set_ylabel('nm')
props = Kerelsky_plus(pks_exp, nmperpixel=NMPERPIXEL, sort=1)
angle = props[0]
ax_exp.set_title(f"Twist angle θ $\\approx${angle:.2f}°")
ax_exp.yaxis.tick_right()
ax_exp.yaxis.set_label_position("right")
ax_exp.tick_params(axis='y', which='both', labelleft=False, labelright=True)
ax_exp.tick_params(axis='x', which='both', labelleft=False, labeltop=False)
phasecbar = plt.colorbar(im, ax=axs[2], ticks=[-np.pi, 0, np.pi], shrink=0.78)
phasecbar.ax.set_yticklabels(['-π', '0', 'π'])
for ax in axmoirephases:
ax.xaxis.set_major_locator(ticker.MultipleLocator(8))
ax.xaxis.set_minor_locator(ticker.MultipleLocator(2))
ax.yaxis.set_major_locator(ticker.MultipleLocator(8))
ax.yaxis.set_minor_locator(ticker.MultipleLocator(2))
axmoire.xaxis.set_major_locator(ticker.MultipleLocator(2))
axmoire.yaxis.set_major_locator(ticker.MultipleLocator(2))
for ax in axs:
ax.xaxis.set_minor_locator(ticker.MultipleLocator(50))
ax.yaxis.set_minor_locator(ticker.MultipleLocator(50))
axdisl.text(0.03, 0.97, 'a', transform=axdisl.transAxes,
fontsize=14, fontweight='bold', va='top', ha='left',
bbox=dict(facecolor='white', alpha=0.9, edgecolor='none'))
axdislphases[0].text(-0.08, 1.08, 'b', transform=axdislphases[0].transAxes,
fontsize=14, fontweight='bold', va='bottom', ha='right')
axrotated.text(0.03, 0.97, 'c', transform=axrotated.transAxes,
fontsize=14, fontweight='bold', va='top', ha='left',
bbox=dict(facecolor='white', alpha=0.9, edgecolor='none'))
axmoire.text(0.02, 0.98, 'd', transform=axmoire.transAxes,
fontsize=14, fontweight='bold', va='top', ha='left',
bbox=dict(facecolor='white', alpha=0.9, edgecolor='none'))
axmoirephases[0].text(0.1, 1.05, 'e', transform=axmoirephases[0].transAxes,
fontsize=14, fontweight='bold', va='bottom', ha='right')
ax_exp.text(0.02, 0.98, 'f', transform=ax_exp.transAxes,
fontsize=14, fontweight='bold', va='top', ha='left',
bbox=dict(facecolor='white', alpha=0.9, edgecolor='none'))
axs[0].text(0.1, 1.05, 'g', transform=axs[0].transAxes,
fontsize=14, fontweight='bold', va='bottom', ha='right')
#fig.set_constrained_layout_pads(hspace=-1, h_pad=0.5/72)
plt.savefig(os.path.join('figures', 'dislocation2.pdf'))
plt.savefig(os.path.join('figures', 'dislocation2.png'), dpi=300)
# %%