hexrd.wppf.texture module

hexrd.wppf.texture.Blmn = {'oh': {2: array([[1.]]), 4: array([[-0.45643546, -0.76376262, -0.45643546]]), 6: array([[ 0.66143783, -0.35355339,  0.66143783]]), 8: array([[-0.41142537, -0.27003086, -0.71807033, -0.27003086, -0.41142537]]), 10: array([[-0.49344664, -0.4145781 ,  0.41142537, -0.4145781 , -0.49344664]]), 12: array([[-0.40844758, -0.04107687, -0.34173955, -0.65528215, -0.34173955,         -0.04107687, -0.40844758],        [ 0.        ,  0.61972161, -0.29796055,  0.2330864 , -0.29796055,          0.61972161,  0.        ]]), 14: array([[-0.42168205, -0.34728298, -0.32362992,  0.44009646, -0.32362992,         -0.34728298, -0.42168205]]), 16: array([[ 0.40826075,  0.00472499,  0.08080979,  0.37440899,  0.61088219,          0.37440899,  0.08080979,  0.00472499,  0.40826075],        [ 0.        , -0.51338891, -0.30018124,  0.31746607, -0.30178916,          0.31746607, -0.30018124, -0.51338891,  0.        ]])}, 'th': {2: array([[0., 1., 0.]]), 4: array([[0.45643546, 0.        , 0.76376262, 0.        , 0.45643546]]), 6: array([[-0.39528471,  0.        ,  0.58630197,  0.        ,  0.58630197,          0.        , -0.39528471],        [ 0.        ,  0.66143783,  0.        , -0.35355339,  0.        ,          0.66143783,  0.        ]]), 8: array([[0.41142537, 0.        , 0.27003086, 0.        , 0.71807033,         0.        , 0.27003086, 0.        , 0.41142537]]), 10: array([[-0.32179907, -0.30267051,  0.08783983, -0.25429409,  0.44789702,          0.25236027,  0.44789702, -0.25429409,  0.08783983, -0.30267051,         -0.32179907],        [ 0.24992195, -0.38971803, -0.06821991, -0.32742864, -0.34785463,          0.32493865, -0.34785463, -0.32742864, -0.06821991, -0.38971803,          0.24992195]]), 12: array([[-0.10774661,  0.35440528,  0.04218317, -0.56170293, -0.11564076,          0.14294419, -0.15291919,  0.14294419, -0.11564076, -0.56170293,          0.04218317,  0.35440528, -0.10774661],        [ 0.34110005,  0.10028706, -0.26204378, -0.15894666,  0.42787445,          0.04044932,  0.43577422,  0.04044932,  0.42787445, -0.15894666,         -0.26204378,  0.10028706,  0.34110005],        [ 0.19715691,  0.02017706,  0.56151209, -0.03197896, -0.09548337,          0.00813812,  0.52003895,  0.00813812, -0.09548337, -0.03197896,          0.56151209,  0.02017706,  0.19715691]]), 14: array([[-0.28955063, -0.29723045,  0.01011772, -0.24478887,  0.12465751,         -0.22811658,  0.38999832,  0.31021019,  0.38999832, -0.22811658,          0.12465751, -0.24478887,  0.01011772, -0.29723045, -0.28955063],        [ 0.28772628, -0.29911506, -0.01005397, -0.24634097, -0.12387209,         -0.22956297, -0.38754109,  0.31217709, -0.38754109, -0.22956297,         -0.12387209, -0.24634097, -0.01005397, -0.29911506,  0.28772628]]), 16: array([[ 0.16618906, -0.36544385, -0.05921307,  0.17954391, -0.0028519 ,          0.46105404,  0.19021432, -0.1780508 ,  0.21273106, -0.1780508 ,          0.19021432,  0.46105404, -0.0028519 ,  0.17954391, -0.05921307,         -0.36544385,  0.16618906],        [ 0.30796148,  0.16416755, -0.26096265, -0.08065612, -0.09371337,         -0.2071183 ,  0.44600261,  0.07998537,  0.30530525,  0.07998537,          0.44600261, -0.2071183 , -0.09371337, -0.08065612, -0.26096265,          0.16416755,  0.30796148],        [ 0.2102802 ,  0.04839014,  0.43815842, -0.02377425,  0.29639276,         -0.06105033, -0.07659623,  0.02357654,  0.57077837,  0.02357654,         -0.07659623, -0.06105033,  0.29639276, -0.02377425,  0.43815842,          0.04839014,  0.2102802 ]])}}

utility functions for texture computation

quick overview of different laue group symmetries

laue_1 = ‘ci’ # triclinic laue_2 = ‘c2h’ # monoclinic laue_3 = ‘d2h’ # Orthorhombic laue_4 = ‘c4h’ # cyclic tetragonal laue_5 = ‘d4h’ # dihedral tetragonal laue_6 = ‘s6’ # cyclic trigonal + inversion laue_7 = ‘d3d’ # dihedral trigonal laue_8 = ‘c6h’ # cyclic laue_9 = ‘d6h’ # dihedral hexagonal laue_10 = ‘th’ # cubic low laue_11 = ‘oh’ # cubic high

class hexrd.wppf.texture.HarmonicModel(material=None, ssym='axial', ell_max=10, bvec=array([-0., -0., -1.]), evec=array([1., 0., 0.]), sample_normal=array([-0., -0., -1.]), pfdata=None)

Bases: object

this is the abstract class which is used by both the harmonic model as well as the pole figure class

Parameters

materialmaterial_rietveld class

rietveld material class

ssymstr

string encoding sample symmetry. four allowed options – ‘monoclinic’, ‘orthorhombic’, ‘axial’ and ‘triclinic’

ell_max: int

maximum degree of spherical harmonic to use for texture computation

params: lmfit.Parameters

Parameter class for the refinement

bvec: numpy.ndarray

unit vector of xray beam in the lab frame. default value is -Z direction

evec: numpy.ndarray

direction which defines zero azimuth. default value is x direction

sample_normal: numpy.ndarray

inclination of sample frame about x direction. default value is 0, corresponding to no tilt.

J(params)

this is the texture index for the harmonic model. A value of 1 is a random texture and any value > 1 is preferred orientation.

property angs

property bvec

calc_new_pfdata(params, hkls, pfgrid=None)

this routine computes the new pfdata which will will be used in computing pole figures for a new hkl pole

calc_new_pole_figure(params, hkls=None, pfgrid=None, plot=False)

calculate pole figure for new poles given by hkls. the data will be computed on the same grid as the input grid. this is done so that the spherical harmonics don’t have to be recomputed.

by default, we will pick the pf grid 5 degrees in theta and 10 degrees in azimuth

hkls has the shape nx3

calc_pf_rings(params, eta_min=-3.141592653589793, eta_max=3.141592653589793, eta_step=0.0017453292519943296, calc_type='texture_factor')

this functin computes the intensity variation along the debye-scherrer rings for each hkl in the material. the intensity variation around the ring is computed between eta_min and eta_max. Default values are (-pi,pi) which gives the full ring. eta_step is the angular step size in azimuth. Default value is 0.1 degrees for eta_step

calc_ref_frame()

calc_residual(params)

get the difference between the input pole figures and the calculated pole figures

calc_texture_factor(params, eta_min=-3.141592653589793, eta_max=3.141592653589793, eta_step=0.017453292519943295)

calculate_harmonic_coefficients(params, hkls=None)

precompute the spherical harmonics for the given hkls and sample directions

convert_hkls_to_cartesian(hkls)

this routine converts hkls in the crystallographic frame to the cartesian frame and normalizes them

property csym

property densest_grid

property ell_max

property etavec

get_c_matrix(params, ell)

get_parameters(params=None, vary=True)

make lmfit parameter class for refinement

get_sph_c_matrix(h, ell, gridtype=None)

get_sph_s_matrix(h, ell, gridtype=None)

get_total_sym_harm(symtype)

function to return the total symmetrized harmonics for a given degree and symmetry

property gvecs

property intensities

property material

property new_pf_plots_visible

property num_pfs

number of pole figures (read only)

property parameter_names

property pfdata

plot_new_pf(filled=False, grid=False, cmap='jet', colorbar=True, colorbar_label='m.r.d.', show=True)

first get the layout of the subplot

plot_pf(filled=False, grid=False, cmap='jet', colorbar=True, colorbar_label='m.r.d.', show=True, recalculated=False)

# FIXME: there is a bug during plots when the 0/2pi or -pi/pi points are not filled in for some set of inputs. need to come up with a fix for this

08/25/25 SS added a fix which seems to work for some cases. needs more extensive testing

precompute_spherical_harmonics(eta_min, eta_max, eta_step, calc_type='texture_factor')

this function precomputes the spherical harmonic functions so we don’t keep repeating the calculations

recalculated_pf(params, new=False)

property ref_frame_rmat

property rotated_angs

property sample_normal

property ssym

property stereo_radius

stereographic_radius(new=False)

update_new_pf_plot_data(params)

update_new_pf_plots()

property weights

write_data(prefix)

write out the data in text format the prefix goes in front of the names name will be “<prefix>_hkl.txt”

class hexrd.wppf.texture.InversePoleFigures(sample_dir, sampling='equiangular', resolution=5.0)

Bases: object

this class deals with everything related to inverse pole figures.

property angs

initialize_crystal_dir(samplingtype, resolution=5.0)

this function prepares the unit vectors of the stereogram

property resolution

property sample_dir

sample direction for IPF

property sampling

hexrd.wppf.texture.SYMLIST = ['ci', 'c2h', 'd2h', 'c4h', 'd4h', 's6', 'd3d', 'c6h', 'd6h', 'th', 'oh', 'monoclinic', 'orthorhombic', 'triclinic', 'axial']

in this section we will list the constants we need for symmetrizing the spherical harmonics for the cubic crystals (sgnum 195-230). For cyclic and dihedral symmetries, the symmetrization is done by selection rules, so they don’t need to be explicitly written here

we will list all constants up to degree 16. If the user asks for anything more than that, we will need to compute it on the fly using the spherical python package. However, this will build an extra dependency, so not sure if we need that

hexrd.wppf.texture.calc_sym_sph_harm(deg, theta, phi, sym='oh')

get symmetrized harmonics with given degree and set of coefficients

Parameters

degint

degree of the symmetrized harmonic.

coeffnumpy.ndarray

coefficeints to get symmetrized harmonic only for cubic symmetry size is nx1

thetanumpy.ndarray

polar angle in radians size is nx1

phinumpy.ndarray

co-latiture in radians size is nx1

Returns

numpy.ndarray

spherical harmonics

hexrd.wppf.texture.check_degrees(ell, sym)

hexrd.wppf.texture.check_symmetry(sym, symtype='either')

helper functio to check crystal and sample symmetry

hexrd.wppf.texture.get_num_sym_harm(ell, sym='oh')

hexrd.wppf.texture.harmonic_model

alias of HarmonicModel

hexrd.wppf.texture.inverse_polar_figures

alias of InversePoleFigures