def Sigma3CSL(left, right):
fcc_rotation_location = os.path.join(
os.path.dirname(inspect.getfile(GBpy)), 'pkl_files',
'cF_Id_csl_common_rotations.pkl')
with open(fcc_rotation_location) as infile:
fcc_rotations = pickle.load(infile)
# misorientation for sigma 3 boundary
sig3 = fcc_rotations['3']['N'][0] / fcc_rotations['3']['D'][0]
# create lattice instance and multiply by lattice parameter of nickel
Ni = lattice.Lattice()
a_Ni = 3.52
a_Al = 4.050
#4.032, LEA (Liu, Ercolessi, Adams) potential on NIST
a_ref = 1.
Ni.l_g_go *= a_Al
basis = [[0., 0.5, 0.5], [0.5, 0., 0.5], [0.5, 0.5, 0.]]
# get primitive CSL vectors and convert them to orthogonal basis
csl_p, __ = find_csl_dsc.find_csl_dsc(basis, sig3)
print csl_p
csl_o = np.dot(Ni.l_g_go, csl_p).T
# take boundary plane from orientation matrix, use it to get
# 2D CSL in boundary plane, and convert to orthogonal basis
boundary_plane = left[0]
gb = bp_basis.gb_2d_csl(boundary_plane, sig3, basis, 'normal_go', 'g1')
#print "gb =",gb
csl_2d = np.dot(Ni.l_g_go, gb[0]).T
#print "csl_2d =",csl_2d
# normalize orientation matrix to make it a rotation matrix,
# and rotate both CSL and 2D CSL into crystal frame
rotation_matrix = [list(np.array(i) / np.linalg.norm(i)) for i in left]
#print rotation_matrix
csl_2d = [np.dot(rotation_matrix, i) for i in csl_2d]
csl = [np.dot(rotation_matrix, i) for i in csl_o]
# iterate through the vertices of the CSL unit cell
# and use the highest and lowest x coordinates
# to calculate the period in the x direction
xlo, xhi = 0, 0
for i in product([0, 1], [0, 1], [0, 1]):
csl_vertex = np.sum(np.array(csl).T * i, axis=1)
xlo = min(xlo, csl_vertex[0])
xhi = max(xhi, csl_vertex[0])
x_period = xhi - xlo
# iterate through the vertices of the 2D CSL unit cell
# and use the highest and lowest y and z coordinates
# to calculate the period in the y and z directions
ylo, yhi, zlo, zhi = 0, 0, 0, 0
for i in product([0, 1], [0, 1]):
csl_2d_vertex = np.sum(np.array(csl_2d).T * i, axis=1)
ylo = min(ylo, csl_2d_vertex[1])
yhi = max(yhi, csl_2d_vertex[1])
zlo = min(zlo, csl_2d_vertex[2])
zhi = max(zhi, csl_2d_vertex[2])
y_period = yhi - ylo
z_period = zhi - zlo
return x_period, y_period, z_period
def plots(mesh_size, sigma_val, n, lat_type):
####################################################################################################################
### Creating an array of boundary plane miller indices in CSL lattice
mil_ind_csl = gen_miller_ind(mesh_size)
####################################################################################################################
### Creating an instance of lattice class
elem = GBl.Lattice(lat_type)
### Getting the primitive lattice in orthogonal frame
l_g_go = elem.l_g_go
### Extracting the sigma misorientation from the pickle file
### Misorientation is in the primitive frame of associated lattice
gb_dir = os.path.dirname(inspect.getfile(GBpy))
pkl_path = gb_dir + '/pkl_files/cF_Id_csl_common_rotations.pkl'
pkl_content = pickle.load(open(pkl_path))
sig_mis_N = pkl_content[str(sigma_val)]['N'][0]
sig_mis_D = pkl_content[str(sigma_val)]['D'][0]
sig_mis_g = sig_mis_N/sig_mis_D
### Converting the misorientation to orthogonal frame/superlattice of the crystal
### Done using similarity transformation
sig_mis_go = np.dot(np.dot(l_g_go, sig_mis_g), np.linalg.inv(l_g_go)).reshape(1,3,3)[0]
### Getting the csl basis in primitive frame
l_csl_g, l_dsc_g = GBfcd.find_csl_dsc(l_g_go, sig_mis_g)
### Converting the csl basis to orthogonal frame
l_csl_go = np.dot(l_g_go, l_csl_g)
### reciprocal csl basis in po frame
l_rcsl_go = GBfcd.reciprocal_mat(l_csl_go)
### Converting the miller indices to normals in po frame
bpn_go = np.dot(l_rcsl_go, mil_ind_csl.transpose()).transpose()
####################################################################################################################
### Finding the boundary plane normals in the FZ using five_param_fz
bp_fz_norms_go1, bp_symm_grp, symm_grp_ax = five_param_fz(sig_mis_go, bpn_go)
### Finding unique normals
bp_fz_norms_go1_unq, bfz_unq_ind = GBt.unique_rows_tol(bp_fz_norms_go1, return_index=True)
### Finding the input hkl indices corresponding to unique FZ normals
mil_ind_csl_unq = mil_ind_csl[bfz_unq_ind]
####################################################################################################################
### Calculating interplanar distance (d sigma hkl) for unique FZ bpn
l_rcsl_go = GBfcd.reciprocal_mat(l_csl_go)
mt_cslr_go = np.dot(l_rcsl_go.transpose(), l_rcsl_go)
d_inv_sqr = np.diag(np.dot(np.dot(mil_ind_csl_unq, mt_cslr_go),mil_ind_csl_unq.transpose()))
d_inv = np.sqrt(d_inv_sqr)
d_sig_hkl = np.true_divide(1, d_inv)
####################################################################################################################
### Calculating unit cell area for 2-D csl unit cells for unique FZ bpn
pl_den = []
num_bpn_unq = np.shape(bp_fz_norms_go1_unq)[0]
for ct1 in range(num_bpn_unq):
_, _, pl_den_csl = GBb2.bicryst_planar_den(bp_fz_norms_go1_unq[ct1, :], sig_mis_g, l_g_go, 'normal_go', 'g1')
pl_den.append(pl_den_csl)
pl_den = np.array(pl_den)
a_sig_hkl = np.true_divide(1, pl_den)
####################################################################################################################
### Checking the csl primitive unit cell volume equality
v_sig_hkl = np.multiply(d_sig_hkl, a_sig_hkl)
# print v_sig_hkl
v_basis = abs(np.linalg.det(l_csl_go))
if np.all(abs(v_sig_hkl-v_basis) < 1e-04):
print "The two volumes match!"
else:
print " Mismatch!"
####################################################################################################################
### Sorting attributes in increasing order of 2d csl primitive unit cell area
ind_area_sort = np.argsort(a_sig_hkl)
a_sig_hkl_sort = np.sort(a_sig_hkl)
d_sig_hkl_sort = d_sig_hkl[ind_area_sort]
bp_fz_norms_go1_unq_sort = bp_fz_norms_go1_unq[ind_area_sort]
####################################################################################################################
### Check to ensure required number of unique bpn are returned
if np.shape(bp_fz_norms_go1_unq_sort)[0] < n:
print "Please input a larger mesh grid or reduce the number of boundaries!"
n = np.shape(bp_fz_norms_go1_unq_sort)[0]
####################################################################################################################
### Selecting the lowest 'n' area boundaries and their attributes for plotting
a_plot = a_sig_hkl_sort[:n]
pd_plot = np.true_divide(1, a_plot)
d_plot = d_sig_hkl_sort[:n]
bp_fz_plot = bp_fz_norms_go1_unq_sort[:n]
####################################################################################################################
### d vs pd plot
fig1 = plt.figure(figsize=(12, 12), facecolor='w')
plt.margins(0.05)
plt.xlabel('Interplanar spacing')
plt.ylabel('Planar density of 2D-CSL')
plt.plot(d_plot, pd_plot, 'ro')
# plt.show()
plt.savefig('d_vs_pd_' + str(mesh_size) + '_' + str(n)+ '.png', dpi=100, bbox_inches='tight')
####################################################################################################################
### FZ plot for the sorted and selected boundaries
na = '_'+ str(mesh_size) + '_'+ str(n)
plot_fig(symm_grp_ax, bp_fz_plot, np.pi/6, na)
# plt.show()
return
def pick_uni_bpn(num, sigma_val, lat_type, bound=10, plot_sw=False):
### Creating an instance of lattice class
elem = GBl.Lattice(lat_type)
### Getting the primitive lattice in orthogonal frame
l_g_go = elem.l_g_go
### Extracting the sigma misorientation from the pickle file
### Misorientation is in the primitive frame of associated lattice
gb_dir = os.path.dirname(inspect.getfile(GBpy))
pkl_path = gb_dir + "/pkl_files/cF_Id_csl_common_rotations.pkl"
pkl_content = pickle.load(open(pkl_path))
pub_out = []
for i in range(len(pkl_content[str(sigma_val)]["N"])):
sig_mis_N = pkl_content[str(sigma_val)]["N"][i]
sig_mis_D = pkl_content[str(sigma_val)]["D"][i]
sig_mis_g = sig_mis_N / sig_mis_D
sig_mis_go = np.dot(np.dot(l_g_go, sig_mis_g), np.linalg.inv(l_g_go)).reshape(1, 3, 3)[0]
### Getting the csl basis in primitive frame
l_csl_g, l_dsc_g = GBfcd.find_csl_dsc(l_g_go, sig_mis_g)
### Converting the csl basis to orthogonal frame
l_csl_go = np.dot(l_g_go, l_csl_g)
### reciprocal csl basis in po frame
l_rcsl_go = GBfcd.reciprocal_mat(l_csl_go)
mt_rcsl_go = np.dot(l_rcsl_go.transpose(), l_rcsl_go)
bp_fz, bp_symm_grp, symm_grp_ax, cube_grid, gs = est_bound(bound, mt_rcsl_go, l_rcsl_go, sig_mis_go, num)
bpn_sphr = fz2sphr(bp_fz, bp_symm_grp, symm_grp_ax)
bpn = csl_area_sort(bpn_sphr, l_rcsl_go, mt_rcsl_go)
bpn_grid = bpn_in_grid(bpn, cube_grid, gs, l_rcsl_go, mt_rcsl_go)
bpn_grid_fz, _, _ = fpf.five_param_fz(sig_mis_go, bpn_grid)
bpn_grid_fz = GBt.unique_rows_tol(bpn_grid_fz, tol=1e-06)
bpn_sort, hkl_sort = csl_area_sort(bpn_grid_fz, l_rcsl_go, mt_rcsl_go, return_hkl=True)
#### Preparing to pickle the contents
num_hkl = len(hkl_sort)
print num_hkl, "\n"
hkl_save = np.hstack((np.arange(1, num_hkl + 1, 1).reshape(num_hkl, 1), hkl_sort))
bpn_save = np.hstack((np.arange(1, num_hkl + 1, 1).reshape(num_hkl, 1), bpn_sort))
mis_id = "Sig_" + str(sigma_val) + "_" + str(i)
symm_ax = np.dot(np.linalg.inv(l_g_go), symm_grp_ax)
sig_attr = [mis_id, hkl_save, bpn_save, sig_mis_g, bp_symm_grp, symm_ax]
# pkl_file = mis_id + '.pkl'
# jar = open(pkl_file, 'wb')
# pickle.dump(sig_attr, jar)
# jar.close()
if plot_sw == True:
plot_2d(bpn_grid, gs)
grid_lines_sphr = grid(gs)
plot_3d(grid_lines_sphr, bpn_grid)
plot_3d(grid_lines_sphr, bpn)
pub_out.append(sig_attr)
# print pub_out, '\n'
return pub_out
