LBCO — powder neutron CW — preferred orientation¶

Verifies the March-Dollase preferred-orientation correction against a FullProf reference with orientation along [0 0 1]. The page refines the scale because cryspy's Modified March correction is not volume-normalised, so it differs from FullProf by a constant per-phase scale factor (the orientation coefficient itself transfers).

In [2]:

import easydiffraction as edi
from easydiffraction import ExperimentFactory
from easydiffraction import StructureFactory
from easydiffraction.analysis import verification as verify

import easydiffraction as edi from easydiffraction import ExperimentFactory from easydiffraction import StructureFactory from easydiffraction.analysis import verification as verify

Build the project¶

In [3]:

project = edi.Project()

project = edi.Project()

Define the structure¶

In [4]:

structure = StructureFactory.from_scratch(name='lbco')

structure.space_group.name_h_m = 'P m -3 m'  # FullProf Space group symbol

structure.cell.length_a = 3.890790  # FullProf a

structure.atom_sites.create(
    id='La',  # FullProf Atom
    type_symbol='La',  # FullProf Typ
    fract_x=0.0,  # FullProf X
    fract_y=0.0,  # FullProf Y
    fract_z=0.0,  # FullProf Z
    occupancy=0.5,  # FullProf Occ
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.57511,  # FullProf Biso
)
structure.atom_sites.create(
    id='Ba',  # FullProf Atom
    type_symbol='Ba',  # FullProf Typ
    fract_x=0.0,  # FullProf X
    fract_y=0.0,  # FullProf Y
    fract_z=0.0,  # FullProf Z
    occupancy=0.5,  # FullProf Occ
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.57511,  # FullProf Biso
)
structure.atom_sites.create(
    id='Co',  # FullProf Atom
    type_symbol='Co',  # FullProf Typ
    fract_x=0.5,  # FullProf X
    fract_y=0.5,  # FullProf Y
    fract_z=0.5,  # FullProf Z
    occupancy=1.0,  # FullProf Occ
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.26023,  # FullProf Biso
)
structure.atom_sites.create(
    id='O',  # FullProf Atom
    type_symbol='O',  # FullProf Typ
    fract_x=0.0,  # FullProf X
    fract_y=0.5,  # FullProf Y
    fract_z=0.5,  # FullProf Z
    occupancy=0.97856,  # FullProf Occ
    adp_type='Biso',  # FullProf Biso
    adp_iso=1.36662,  # FullProf Biso
)

project.structures.add(structure)

structure = StructureFactory.from_scratch(name='lbco') structure.space_group.name_h_m = 'P m -3 m' # FullProf Space group symbol structure.cell.length_a = 3.890790 # FullProf a structure.atom_sites.create( id='La', # FullProf Atom type_symbol='La', # FullProf Typ fract_x=0.0, # FullProf X fract_y=0.0, # FullProf Y fract_z=0.0, # FullProf Z occupancy=0.5, # FullProf Occ adp_type='Biso', # FullProf Biso adp_iso=0.57511, # FullProf Biso ) structure.atom_sites.create( id='Ba', # FullProf Atom type_symbol='Ba', # FullProf Typ fract_x=0.0, # FullProf X fract_y=0.0, # FullProf Y fract_z=0.0, # FullProf Z occupancy=0.5, # FullProf Occ adp_type='Biso', # FullProf Biso adp_iso=0.57511, # FullProf Biso ) structure.atom_sites.create( id='Co', # FullProf Atom type_symbol='Co', # FullProf Typ fract_x=0.5, # FullProf X fract_y=0.5, # FullProf Y fract_z=0.5, # FullProf Z occupancy=1.0, # FullProf Occ adp_type='Biso', # FullProf Biso adp_iso=0.26023, # FullProf Biso ) structure.atom_sites.create( id='O', # FullProf Atom type_symbol='O', # FullProf Typ fract_x=0.0, # FullProf X fract_y=0.5, # FullProf Y fract_z=0.5, # FullProf Z occupancy=0.97856, # FullProf Occ adp_type='Biso', # FullProf Biso adp_iso=1.36662, # FullProf Biso ) project.structures.add(structure)

Load the FullProf reference¶

In [5]:

FULLPROF_PROJECT_DIR = 'pd-neut-cwl_lbco_preferred-orientation'
FULLPROF_PRF_FILE = 'lbco.prf'
FULLPROF_SUM_FILE = 'lbco.sum'
FULLPROF_BAC_FILE = 'lbco.bac'
FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE)

FULLPROF_ZERO = 0.62040  # FullProf Zero
FULLPROF_SCALE = 9.405870  # FullProf Scale
FULLPROF_WAVELENGTH = 1.494000  # FullProf Lambda
FULLPROF_U = 0.081547  # FullProf U
FULLPROF_V = -0.115345  # FullProf V
FULLPROF_W = 0.121125  # FullProf W
FULLPROF_X = 0.0  # FullProf X
FULLPROF_Y = 0.083038  # FullProf Y
FULLPROF_WDT = 30.0  # FullProf Wdt
FULLPROF_PREF_1 = 1.2  # FullProf Pref1
FULLPROF_PREF_2 = 0.3  # FullProf Pref2
FULLPROF_PR_1 = 0  # FullProf Pr1
FULLPROF_PR_2 = 0  # FullProf Pr2
FULLPROF_PR_3 = 1  # FullProf Pr3

x, calc_fullprof = verify.load_fullprof_calc_profile(
    FULLPROF_PROJECT_DIR,
    FULLPROF_PRF_FILE,
    FULLPROF_BAC_FILE,
    FULLPROF_ZERO,
)

FULLPROF_PROJECT_DIR = 'pd-neut-cwl_lbco_preferred-orientation' FULLPROF_PRF_FILE = 'lbco.prf' FULLPROF_SUM_FILE = 'lbco.sum' FULLPROF_BAC_FILE = 'lbco.bac' FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE) FULLPROF_ZERO = 0.62040 # FullProf Zero FULLPROF_SCALE = 9.405870 # FullProf Scale FULLPROF_WAVELENGTH = 1.494000 # FullProf Lambda FULLPROF_U = 0.081547 # FullProf U FULLPROF_V = -0.115345 # FullProf V FULLPROF_W = 0.121125 # FullProf W FULLPROF_X = 0.0 # FullProf X FULLPROF_Y = 0.083038 # FullProf Y FULLPROF_WDT = 30.0 # FullProf Wdt FULLPROF_PREF_1 = 1.2 # FullProf Pref1 FULLPROF_PREF_2 = 0.3 # FullProf Pref2 FULLPROF_PR_1 = 0 # FullProf Pr1 FULLPROF_PR_2 = 0 # FullProf Pr2 FULLPROF_PR_3 = 1 # FullProf Pr3 x, calc_fullprof = verify.load_fullprof_calc_profile( FULLPROF_PROJECT_DIR, FULLPROF_PRF_FILE, FULLPROF_BAC_FILE, FULLPROF_ZERO, )

Create the experiment¶

In [6]:

experiment = ExperimentFactory.from_scratch(
    name='lbco',
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
    scattering_type='bragg',
)
verify.set_reference_as_measured(experiment, x, calc_fullprof)

experiment.linked_structures.create(structure_id='lbco', scale=FULLPROF_SCALE)

experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH
experiment.instrument.calib_twotheta_offset = FULLPROF_ZERO

experiment.peak.type = 'pseudo-voigt'
experiment.peak.broad_gauss_u = FULLPROF_U
experiment.peak.broad_gauss_v = FULLPROF_V
experiment.peak.broad_gauss_w = FULLPROF_W
experiment.peak.broad_lorentz_x = FULLPROF_X
experiment.peak.broad_lorentz_y = FULLPROF_Y

experiment.preferred_orientation.create(
    structure_id='lbco',
    march_r=FULLPROF_PREF_1,
    march_random_fract=FULLPROF_PREF_2,
    index_h=FULLPROF_PR_1,
    index_k=FULLPROF_PR_2,
    index_l=FULLPROF_PR_3,
)

experiment.peak.cutoff_fwhm = FULLPROF_WDT

project.experiments.add(experiment)

experiment = ExperimentFactory.from_scratch( name='lbco', sample_form='powder', beam_mode='constant wavelength', radiation_probe='neutron', scattering_type='bragg', ) verify.set_reference_as_measured(experiment, x, calc_fullprof) experiment.linked_structures.create(structure_id='lbco', scale=FULLPROF_SCALE) experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH experiment.instrument.calib_twotheta_offset = FULLPROF_ZERO experiment.peak.type = 'pseudo-voigt' experiment.peak.broad_gauss_u = FULLPROF_U experiment.peak.broad_gauss_v = FULLPROF_V experiment.peak.broad_gauss_w = FULLPROF_W experiment.peak.broad_lorentz_x = FULLPROF_X experiment.peak.broad_lorentz_y = FULLPROF_Y experiment.preferred_orientation.create( structure_id='lbco', march_r=FULLPROF_PREF_1, march_random_fract=FULLPROF_PREF_2, index_h=FULLPROF_PR_1, index_k=FULLPROF_PR_2, index_l=FULLPROF_PR_3, ) experiment.peak.cutoff_fwhm = FULLPROF_WDT project.experiments.add(experiment)

Peak profile type for experiment 'lbco' changed to

pseudo-voigt

edi-cryspy VS FullProf¶

In [7]:

experiment.calculator.type = 'cryspy'

project.analysis.calculate()
calc_ed_cryspy = experiment.data.intensity_calc
LABEL_ED_CRYSPY = verify.engine_label('cryspy')

project.display.pattern_comparison(
    'lbco',
    reference=calc_fullprof,
    candidate=calc_ed_cryspy,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY,
)

experiment.calculator.type = 'cryspy' project.analysis.calculate() calc_ed_cryspy = experiment.data.intensity_calc LABEL_ED_CRYSPY = verify.engine_label('cryspy') project.display.pattern_comparison( 'lbco', reference=calc_fullprof, candidate=calc_ed_cryspy, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY, )

Calculator for experiment 'lbco' already set to

cryspy

Loading plot…

Fit edi-cryspy to FullProf¶

cryspy uses the reciprocal March coefficient (g₁ = 1/r, converted automatically) and does not volume-normalise the correction, so it differs from FullProf by a constant per-phase scale factor. Refining the scale absorbs that factor and recovers the FullProf profile.

In [8]:

experiment.linked_structures['lbco'].scale.free = True

project.analysis.fit()
project.display.fit.results()

project.analysis.calculate()
calc_ed_cryspy_refined = experiment.data.intensity_calc
LABEL_ED_CRYSPY_REFINED = verify.engine_label('cryspy', note='refined')

project.display.pattern_comparison(
    'lbco',
    reference=calc_fullprof,
    candidate=calc_ed_cryspy_refined,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY_REFINED,
)

experiment.linked_structures['lbco'].scale.free = True project.analysis.fit() project.display.fit.results() project.analysis.calculate() calc_ed_cryspy_refined = experiment.data.intensity_calc LABEL_ED_CRYSPY_REFINED = verify.engine_label('cryspy', note='refined') project.display.pattern_comparison( 'lbco', reference=calc_fullprof, candidate=calc_ed_cryspy_refined, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY_REFINED, )

Standard fitting

📋 Using experiment 🔬 'lbco' for 'single' fitting

🚀 Starting fit process with 'lmfit (leastsq)'...

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.28	3816.37
2	5	1.70	4.07	99.9% ↓
3	8	3.09	4.07

🏆 Best goodness-of-fit (reduced χ²) is 4.07 at iteration 7

✅ Fitting complete.

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	3.09
4	🔁 Iterations	5
5	📏 Goodness-of-fit (reduced χ²)	4.07
6	📏 R-factor (Rf, %)	1.42
7	📏 R-factor squared (Rf², %)	0.72
8	📏 Weighted R-factor (wR, %)	0.72

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	lbco	linked_structure	lbco	scale		9.4059	7.7117	0.0010	18.01 % ↓

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

Loading plot…

Agreement check¶

In [9]:

verify.assert_patterns_agree(
    [
        (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', calc_fullprof, calc_ed_cryspy_refined),
    ],
)

verify.assert_patterns_agree( [ (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', calc_fullprof, calc_ed_cryspy_refined), ], )

	Comparison	Metric	Expected	Actual	OK
1	edi 0.19.0 (cryspy 0.12.1, refined) vs FullProf 8.40	Profile diff (%)	< 2.5	0.72	✅
2		Max deviation (%)	< 6	0.58	✅
3		Area ratio	0.99 to 1.01	0.9918	✅
4		Shape correlation	> 0.999	1.0000	✅

Out[9]:

True