def pick_uni_mis(lat_type, n=70): elem = GBl.Lattice(lat_type) l_g_go = elem.l_p_po l_go_g = np.linalg.inv(l_g_go) gb_dir = os.path.dirname(inspect.getfile(GBpy)) pkl_path = gb_dir + '/pkl_files/symm_mats_O.pkl' symm_O = pickle.load(open(pkl_path)) symm_O_inv = np.linalg.inv(symm_O) mis_g, id = extract_mis(99, gb_dir) mis_go = np.tensordot(np.tensordot(l_g_go, mis_g.transpose(1, 2, 0), 1).transpose(2, 0, 1), l_go_g, 1) mis_go_inv = np.linalg.inv(mis_go) num = len(symm_O)*len(symm_O_inv) mis_go_symm1 = np.tensordot(np.tensordot(symm_O_inv, mis_go.transpose(1, 2, 0), 1).transpose(3, 0, 1, 2), symm_O.transpose(1, 2, 0), 1).transpose(0, 1, 4, 2, 3) mis_go_symm2 = np.tensordot(np.tensordot(symm_O_inv, mis_go_inv.transpose(1, 2, 0), 1).transpose(3, 0, 1, 2), symm_O.transpose(1, 2, 0), 1).transpose(0, 1, 4, 2, 3) mis_go_symm = np.concatenate((mis_go_symm1, mis_go_symm2)) mis_go_symm = mis_go_symm.reshape(len(mis_go_symm)*num, 3, 3) id_attr3 = np.tile(np.arange(1, num+1, 1).reshape(num, 1), (len(id), 1)) id_attr3 = np.vstack([id_attr3, -id_attr3]) id_symm = np.tile(np.repeat(id, num, axis=0), (2, 1)) id_symm = np.hstack([id_symm, id_attr3]) quat_go_symm = GBq.mat2quat(mis_go_symm) quat_go_symm_fil = GBq.antipodal(quat_go_symm) ### Add code for pi rotations quat_t = quat_go_symm_fil.transpose() quat_t_unq, ind = GBt.unique_rows_tol(quat_t, tol=1e-06, return_index=True) id_unq = id_symm[ind] ind_id_sort = np.argsort(id_unq[:, 0]) id_sort = id_unq[ind_id_sort] quat_sort = quat_t_unq[ind_id_sort].transpose() ### sort again according to sig vals mis_c = mf.sphr2cube_3d(quat_sort) ### testing # mis_r = mf.cube2sphr_3d(mis_c) grid, gce = make_grid(n) mis_gr_c, id_g = mis_in_grid(mis_c, id_sort, grid, gce) id_g_unq = GBt.unique_rows_tol(id_g[:, [0, 1]], 1e-06) ind_id_unq_sort = np.argsort(id_g_unq[:, 0]); id_g_unq = id_g_unq[ind_id_unq_sort] mis_pick_ind = mf.set_int_ind(id, id_g_unq) mis_pick = mis_g[mis_pick_ind] print '\n', len(mis_pick), '\n', id_g_unq # mis_gr_quat = mf.cube2sphr_3d(mis_gr_c) # mis_gr_go = GBq.quat2mat(mis_gr_quat) # mis_gr = np.tensordot(np.tensordot(l_go_g, mis_gr_go.transpose(1, 2, 0), 1).transpose(2, 0, 1), l_g_go, 1) # ### convert to g frame # ### pick in fz, check the code !! # dum = 0 return [mis_pick, mis_pick_ind]
def gen_hkl(bound, mt_tensor): m = 1.0 * bound h = math.ceil(math.sqrt(m / mt_tensor[0][0])) k = math.ceil(math.sqrt(m / mt_tensor[1][1])) l = math.ceil(math.sqrt(m / mt_tensor[2][2])) print h, k, l, "\n" x_csl = np.arange(-h, h + 1, 1.0) y_csl = np.arange(-k, k + 1, 1.0) z_csl = np.arange(-l, l + 1, 1.0) num_mi = np.size(x_csl) * np.size(y_csl) * np.size(z_csl) xx_csl, yy_csl, zz_csl = np.meshgrid(x_csl, y_csl, z_csl, indexing="xy") xx_csl, yy_csl, zz_csl = xx_csl.reshape(1, num_mi)[0], yy_csl.reshape(1, num_mi)[0], zz_csl.reshape(1, num_mi)[0] mil_ind = np.column_stack([xx_csl, yy_csl, zz_csl]) ind = np.where((mil_ind[:, 0] == 0) & (mil_ind[:, 1] == 0) & (mil_ind[:, 2] == 0))[0][0] ### deleting (0 0 0) mil_ind = np.delete(mil_ind, ind, 0) ### finding the unique miller indices mil_ind = GBim.int_finder(mil_ind, tol=1e-06, order="rows") mil_ind_csl = GBt.unique_rows_tol(mil_ind, tol=1e-06) ### Antipodal symmetry (h k l) ~ (-h -k -l) return mil_ind_csl
def grid(gs): g = gs + 1 beta = math.sqrt(np.pi / 6) num = 300 h_x = np.linspace(-beta, beta, g) h_y = np.linspace(-beta, beta, num) hl = np.transpose([np.tile(h_x, len(h_y)), np.repeat(h_y, len(h_x))]) h_z = np.zeros(len(hl)) h_z.fill(beta) hln = np.column_stack((hl[:, 0], hl[:, 1], h_z)) hln = np.concatenate((hln, np.column_stack((hl[:, 0], hl[:, 1], -h_z)))) hln = np.concatenate((hln, np.column_stack((hl[:, 0], h_z, hl[:, 1])))) hln = np.concatenate((hln, np.column_stack((hl[:, 0], -h_z, hl[:, 1])))) hln = np.concatenate((hln, np.column_stack((h_z, hl[:, 0], hl[:, 1])))) hln = np.concatenate((hln, np.column_stack((-h_z, hl[:, 0], hl[:, 1])))) v_x = np.linspace(-beta, beta, num) v_y = np.linspace(-beta, beta, g) vl = np.transpose([np.tile(v_x, len(v_y)), np.repeat(v_y, len(v_x))]) vln = np.column_stack((vl[:, 0], vl[:, 1], h_z)) vln = np.concatenate((vln, np.column_stack((vl[:, 0], vl[:, 1], -h_z)))) vln = np.concatenate((vln, np.column_stack((vl[:, 0], h_z, vl[:, 1])))) vln = np.concatenate((vln, np.column_stack((vl[:, 0], -h_z, vl[:, 1])))) vln = np.concatenate((vln, np.column_stack((h_z, vl[:, 0], vl[:, 1])))) vln = np.concatenate((vln, np.column_stack((-h_z, vl[:, 0], vl[:, 1])))) grid_lines = np.concatenate((hln, vln)) grid_lines_sphr = GBt.unique_rows_tol(mf.cube2sphr_2d(grid_lines), tol=1e-06) return grid_lines_sphr
def fz2sphr(bpn, bp_symm_grp, symm_grp_ax): gb_dir = os.path.dirname(inspect.getfile(GBpy)) pkl_path = gb_dir + "/pkl_files/" if bp_symm_grp == "C_s": file_name = "symm_mats_Cs.pkl" file_path = pkl_path + file_name elif bp_symm_grp == "C_2h": file_name = "symm_mats_C2h.pkl" file_path = pkl_path + file_name elif bp_symm_grp == "D_3d": file_name = "symm_mats_D3d.pkl" file_path = pkl_path + file_name elif bp_symm_grp == "D_2h": file_name = "symm_mats_D2h.pkl" file_path = pkl_path + file_name elif bp_symm_grp == "D_4h": file_name = "symm_mats_D4h.pkl" file_path = pkl_path + file_name elif bp_symm_grp == "D_6h": file_name = "symm_mats_D6h.pkl" file_path = pkl_path + file_name elif bp_symm_grp == "D_8h": file_name = "symm_mats_D8h.pkl" file_path = pkl_path + file_name elif bp_symm_grp == "O_h": file_name = "symm_mats_Oh.pkl" file_path = pkl_path + file_name rot_mat = np.linalg.inv(symm_grp_ax) bpn_rot = np.dot(rot_mat, bpn.transpose()).transpose() symm_mat = pickle.load(open(file_path, "rb")) symm_bpn_rot_gop1 = np.tensordot(symm_mat, bpn_rot.transpose(), 1).transpose((1, 2, 0)) symm_bpn_go1 = np.tensordot(np.linalg.inv(rot_mat), symm_bpn_rot_gop1, 1).transpose(2, 1, 0) dim1, dim2, dim3 = np.shape(symm_bpn_go1) symm_bpn_go1 = np.reshape(symm_bpn_go1, ((dim1 * dim2), dim3)) symm_bpn_go1_unq = GBt.unique_rows_tol(symm_bpn_go1, tol=1e-06) return symm_bpn_go1_unq
def est_bound(bound, mt_rcsl_go, l_rcsl_go, sig_mis_go, num): dum_bpn = np.array([[0, 0, 1]]) _, bp_symm_grp, _ = fpf.five_param_fz(sig_mis_go, dum_bpn) cube_grid, gs = make_grid(num, bp_symm_grp) req_bpn = 6 * gs * gs flag = True while flag: mil_ind_csl = gen_hkl(bound, mt_rcsl_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 = fpf.five_param_fz(sig_mis_go, bpn_go) bp_fz_norms_go1_unq = GBt.unique_rows_tol(bp_fz_norms_go1, tol=1e-06) num_bpn_fz = len(bp_fz_norms_go1_unq) est_para = 20 if bp_symm_grp == "C_s": num_bpn_sp = 2 * num_bpn_fz elif bp_symm_grp == "C_2h": est_para = 50 num_bpn_sp = 4 * num_bpn_fz elif bp_symm_grp == "D_3d": num_bpn_sp = 12 * num_bpn_fz elif bp_symm_grp == "D_2h": num_bpn_sp = 8 * num_bpn_fz est_para = 200 elif bp_symm_grp == "D_4h": num_bpn_sp = 16 * num_bpn_fz elif bp_symm_grp == "D_6h": num_bpn_sp = 24 * num_bpn_fz elif bp_symm_grp == "D_8h": num_bpn_sp = 32 * num_bpn_fz elif bp_symm_grp == "O_h": num_bpn_sp = 48 * num_bpn_fz # para_1 = len(bp_fz_norms_go1)/num_bpn_fz if num_bpn_sp >= est_para * req_bpn: flag = False else: bound = bound * 2 print bound return bp_fz_norms_go1_unq, bp_symm_grp, symm_grp_ax, cube_grid, gs
def gen_miller_ind(mesh_size): """ Returns an array of unique miller indices Parameters ---------- mesh_size: size of the mesh grid to create the indices array * positive integer Returns ------- mil_ind: array of unique miller indices stored row wise * numpy array of size (m x 3) * m is the number of unique indices created for a given mesh_size See Also -------- * GBpy.integer_manipulations.int_finder * GBpy.tools.unique_rows_tol """ ### Creating an array of boundary plane miller indices r = mesh_size x_csl = np.arange(-r, r+1, 1.0) y_csl = np.arange(-r, r+1, 1.0) z_csl = np.arange(-r, r+1, 1.0) num_mi = np.size(x_csl)*np.size(y_csl)*np.size(z_csl) xx_csl, yy_csl, zz_csl = np.meshgrid(x_csl, y_csl, z_csl, indexing='xy') xx_csl, yy_csl, zz_csl = xx_csl.reshape(1, num_mi)[0], yy_csl.reshape(1, num_mi)[0], zz_csl.reshape(1, num_mi)[0] mil_ind = np.column_stack([xx_csl, yy_csl, zz_csl]) ind = np.where((mil_ind[:, 0] == 0) & (mil_ind[:, 1] == 0) & (mil_ind[:, 2] == 0))[0][0] ### deleting (0 0 0) mil_ind = np.delete(mil_ind, ind, 0) ### finding the unique miller indices mil_ind = GBim.int_finder(mil_ind, tol=1e-06, order='rows') mil_ind = GBt.unique_rows_tol(mil_ind) # Try to remove (-h -k -l) for all (h k l) !!! return mil_ind
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