for j in range(i + 1, len(V)):
mis.append(pyebsd.misorientation(V[i], V[j]))
return mis
if __name__ == '__main__':
fname = os.path.join('..', 'data', 'ADI_bcc_fcc.ang')
scan = pyebsd.load_scandata(fname)
sel = (scan.ph == 1) & (scan.CI > .2)
# First nearest neighbors
neighbors = scan.get_neighbors(1, sel=sel)
# Experimental misorientations
mis_exp = pyebsd.misorientation_neighbors(scan.M, neighbors,
sel=sel).ravel()
# Expected misorientations between KS variants
mis_calc = misorientation_between_variants(
pyebsd.OR()) # for KS OR variants
fig, ax = plt.subplots()
ax.hist(mis_exp[mis_exp > 2], bins=200, density=True, label='Experimental')
ax.hist(mis_calc, bins=500, density=True, label='Theoretical')
ax.legend()
ax.set_xlabel('Misorientation angle (deg)')
ax.set_ylabel('Frequency')
plt.show()
import numpy as np
import pandas as pd
import pyebsd
import matplotlib.pyplot as plt
if __name__ == '__main__':
# Symmetry operators sorted according to the KS variants convention
C = pyebsd.list_cubic_symmetry_operators_KS()
KS = pyebsd.OR(ps=[[1, 1, 1], [0, 1, 1]],
ds=[[-1, 0, 1], [-1, -1, 1]],
single=True) # only the first matrix
# The orientations in M_KS are in the order of the variants convetion
# published in papers such as:
# T. Furuhara, T. Chiba, T. Kaneshita, H. Wu, G. Miyamoto, Metall.
# Mater. Trans. A 48 (2017) 2739–2752.
M_KS = np.matmul(KS, C.transpose(0, 2, 1)) # KS * C^T
v = 0 # variant
variants_found = set()
variants = pd.DataFrame(index=range(len(M_KS)))
variants['Variant number'] = variants.index + 1
variants['CP group'] = np.repeat(range(4), 6)
variants['Bain group'] = -1
for group in range(3):
misang = [
pyebsd.misorientation(M_KS[j], M_KS[v]) for j in range(len(M_KS))
]
if v == 0:
variants['Rotation from variant 1 (deg)'] = misang
def plot_hist_misorientation_variants(V, ax, title=None):
mis = misorientation_between_variants(V)
ax.hist(mis, bins=100)
ax.set_xlabel('Misorientation angle (deg)')
ax.set_ylabel('Frequency')
ax.set_title(title)
if __name__ == '__main__':
from itertools import cycle
import matplotlib.pyplot as plt
fig, axes = plt.subplots(2, 2, figsize=(14, 10))
fig.subplots_adjust(hspace=.3)
cyaxes = cycle(axes.ravel())
V = pyebsd.OR() # KS
plot_hist_misorientation_variants(V, next(cyaxes), 'KS OR')
V = pyebsd.OR(ds=([1, 1, 0], [1, 0, 0])) # NW
plot_hist_misorientation_variants(V, next(cyaxes), 'NW OR')
V = pyebsd.OR(ps=([1, 0, 0], [1, 0, 0]), ds=([0, 1, 0], [0, 1, 1])) # Bain
plot_hist_misorientation_variants(V, next(cyaxes), 'Bain OR')
V = pyebsd.OR(ps=([0, 1, 0], [1, 0, 1]), ds=([1, 0, 1], [-1, 1,
1])) # Pitsch
plot_hist_misorientation_variants(V, next(cyaxes), 'Pitsch OR')
plt.show()
# fig1, ax1 = plt.subplots()
# pyebsd.initialize_frame_PF(ax1)
# pyebsd.plot_PF(R_bcc, ax=ax1, contour=True, cmap='Reds_r', proj=[1, 1, 0])
# pyebsd.plot_PF(R_fcc, ax=ax1, contour=True, cmap='Blues_r', proj=[1, 1, 1])
# fig2, ax2 = plt.subplots()
# pyebsd.initialize_frame_PF(ax2)
# pyebsd.plot_PF(R_bcc, ax=ax2, contour=True, cmap='Reds_r', proj=[1, 1, 1])
# pyebsd.plot_PF(R_fcc, ax=ax2, contour=True, cmap='Blues_r', proj=[1, 1, 0])
fig, ax = plt.subplots()
pyebsd.initialize_frame_PF(ax)
T_KS = pyebsd.OR()
# T_KS^-1 = T_KS^T
T_KS_T = T_KS.transpose([0, 2, 1])
M_KS = np.dot(T_KS, M_fcc_avg)
R_KS = M_KS.transpose(0, 2, 1)
# T_KS^T . M_bcc
M_KS_all = np.tensordot(C, M_KS,
axes=[[-1], [-2]]).transpose([2, 0, 1, 3])
R_fcc_inv = np.tensordot(T_KS_T, M_KS_all.reshape(-1, 3, 3),
axes=[[-1], [-2]]).transpose([2, 0, 3, 1])
# M_bcc_all = np.tensordot(C, M_bcc,
# axes=[[-1], [-2]]).transpose([2, 0, 1, 3])
import os
import sys
import numpy as np
import matplotlib.pyplot as plt
import pyebsd
T_KS = pyebsd.OR() # K-S
T_NW = pyebsd.OR(ds=[[1, 1, 0], [1, 0, 0]]) # N-W
proj = [1, 1, 1]
ax = pyebsd.plot_PF(M=T_KS,
mfc=[1, 1, 1, 0],
mec='r',
mew=1,
marker='s',
ms=5,
proj=proj,
label='KS')
pyebsd.plot_PF(M=T_NW,
mfc=[1, 1, 1, 0],
mec='g',
mew=1,
marker='D',
ms=5,
proj=proj,
label='NW',
ax=ax)
pyebsd.draw_std_traces(ax, lw=.2)
import numpy as np
import matplotlib.pyplot as plt
import pyebsd
if __name__ == '__main__':
# T. Furuhara, T. Maki, Mater. Sci. Eng. A 312 (2001) 145–154.
M_KS = []
M_KS.append(pyebsd.OR(ps=[[1, 1, 1], [0, 1, 1]], ds=[[-1, 0, 1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, 1], [0, 1, 1]], ds=[[-1, 0, 1], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, 1], [0, 1, 1]], ds=[[0, 1, -1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, 1], [0, 1, 1]], ds=[[0, 1, -1], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, 1], [0, 1, 1]], ds=[[1, -1, 0], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, 1], [0, 1, 1]], ds=[[1, -1, 0], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, -1, 1], [0, 1, 1]], ds=[[1, 0, -1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, -1, 1], [0, 1, 1]], ds=[[1, 0, -1], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, -1, 1], [0, 1, 1]], ds=[[-1, -1, 0], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, -1, 1], [0, 1, 1]], ds=[[-1, -1, 0], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, -1, 1], [0, 1, 1]], ds=[[0, 1, 1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, -1, 1], [0, 1, 1]], ds=[[0, 1, 1], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[-1, 1, 1], [0, 1, 1]], ds=[[0, -1, 1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[-1, 1, 1], [0, 1, 1]], ds=[[0, -1, 1], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[-1, 1, 1], [0, 1, 1]], ds=[[-1, 0, -1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[-1, 1, 1], [0, 1, 1]], ds=[[-1, 0, -1], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[-1, 1, 1], [0, 1, 1]], ds=[[1, 1, 0], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[-1, 1, 1], [0, 1, 1]], ds=[[1, 1, 0], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, -1], [0, 1, 1]], ds=[[-1, 1, 0], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, -1], [0, 1, 1]], ds=[[-1, 1, 0], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, -1], [0, 1, 1]], ds=[[0, -1, -1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, -1], [0, 1, 1]], ds=[[0, -1, -1], [-1, 1, -1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, -1], [0, 1, 1]], ds=[[1, 0, 1], [-1, -1, 1]], single=True))
M_KS.append(pyebsd.OR(ps=[[1, 1, -1], [0, 1, 1]], ds=[[1, 0, 1], [-1, 1, -1]], single=True))