LiF — powder X-ray CW — polarization¶

Verifies the X-ray polarization correction on the same single-wavelength LiF reference.

Refinement: the overall scale only; all other parameters are taken from the FullProf reference.

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='lif')

structure.space_group.name_h_m = 'F m -3 m'  # FullProf Space group symbol
structure.cell.length_a = 4.026700  # FullProf a

structure.atom_sites.create(
    id='Li1',  # FullProf Atom
    type_symbol='Li',  # FullProf Typ
    fract_x=0.0,  # FullProf X
    fract_y=0.0,  # FullProf Y
    fract_z=0.0,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=1.20000,  # FullProf Biso
)
structure.atom_sites.create(
    id='F1',  # FullProf Atom
    type_symbol='F',  # FullProf Typ
    fract_x=0.5,  # FullProf X
    fract_y=0.5,  # FullProf Y
    fract_z=0.5,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.80000,  # FullProf Biso
)

project.structures.add(structure)

structure = StructureFactory.from_scratch(name='lif') structure.space_group.name_h_m = 'F m -3 m' # FullProf Space group symbol structure.cell.length_a = 4.026700 # FullProf a structure.atom_sites.create( id='Li1', # FullProf Atom type_symbol='Li', # FullProf Typ fract_x=0.0, # FullProf X fract_y=0.0, # FullProf Y fract_z=0.0, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=1.20000, # FullProf Biso ) structure.atom_sites.create( id='F1', # FullProf Atom type_symbol='F', # FullProf Typ fract_x=0.5, # FullProf X fract_y=0.5, # FullProf Y fract_z=0.5, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=0.80000, # FullProf Biso ) project.structures.add(structure)

Load the FullProf reference¶

In [5]:

FULLPROF_PROJECT_DIR = 'pd-xray-cwl_lif'
FULLPROF_PRF_FILE = 'lif_single_polarized.prf'
FULLPROF_SUM_FILE = 'lif_single_polarized.sum'
FULLPROF_BAC_FILE = 'lif_single_polarized.bac'
FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE)

FULLPROF_ZERO = 0.0  # FullProf Zero
FULLPROF_SCALE = 0.01  # FullProf Scale
FULLPROF_WAVELENGTH = 1.540560  # FullProf Lambda1
FULLPROF_U = 0.048457  # FullProf U
FULLPROF_V = -0.083053  # FullProf V
FULLPROF_W = 0.040000  # FullProf W
FULLPROF_X = 0.0  # FullProf X
FULLPROF_Y = 0.049268  # FullProf Y
FULLPROF_WDT = 48.0  # FullProf Wdt
FULLPROF_POLARIZATION_COEFFICIENT = 0.5  # FullProf Rpolarz
FULLPROF_CTHM = 0.8  # FullProf Cthm
FULLPROF_MONOCHROMATOR_TWOTHETA = 26.5650511771  # acos(sqrt(Cthm)) in degrees

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

FULLPROF_PROJECT_DIR = 'pd-xray-cwl_lif' FULLPROF_PRF_FILE = 'lif_single_polarized.prf' FULLPROF_SUM_FILE = 'lif_single_polarized.sum' FULLPROF_BAC_FILE = 'lif_single_polarized.bac' FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_SUM_FILE) FULLPROF_ZERO = 0.0 # FullProf Zero FULLPROF_SCALE = 0.01 # FullProf Scale FULLPROF_WAVELENGTH = 1.540560 # FullProf Lambda1 FULLPROF_U = 0.048457 # FullProf U FULLPROF_V = -0.083053 # FullProf V FULLPROF_W = 0.040000 # FullProf W FULLPROF_X = 0.0 # FullProf X FULLPROF_Y = 0.049268 # FullProf Y FULLPROF_WDT = 48.0 # FullProf Wdt FULLPROF_POLARIZATION_COEFFICIENT = 0.5 # FullProf Rpolarz FULLPROF_CTHM = 0.8 # FullProf Cthm FULLPROF_MONOCHROMATOR_TWOTHETA = 26.5650511771 # acos(sqrt(Cthm)) in degrees 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='lif',
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='xray',
    scattering_type='bragg',
)
verify.set_reference_as_measured(experiment, x, calc_fullprof)

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

experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH
experiment.instrument.calib_twotheta_offset = FULLPROF_ZERO
experiment.instrument.setup_polarization_coefficient = FULLPROF_POLARIZATION_COEFFICIENT
experiment.instrument.setup_monochromator_twotheta = FULLPROF_MONOCHROMATOR_TWOTHETA

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.peak.cutoff_fwhm = FULLPROF_WDT

project.experiments.add(experiment)

experiment = ExperimentFactory.from_scratch( name='lif', sample_form='powder', beam_mode='constant wavelength', radiation_probe='xray', scattering_type='bragg', ) verify.set_reference_as_measured(experiment, x, calc_fullprof) experiment.linked_structures.create(structure_id='lif', scale=FULLPROF_SCALE) experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH experiment.instrument.calib_twotheta_offset = FULLPROF_ZERO experiment.instrument.setup_polarization_coefficient = FULLPROF_POLARIZATION_COEFFICIENT experiment.instrument.setup_monochromator_twotheta = FULLPROF_MONOCHROMATOR_TWOTHETA 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.peak.cutoff_fwhm = FULLPROF_WDT project.experiments.add(experiment)

Peak profile type for experiment 'lif' 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(
    'lif',
    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( 'lif', reference=calc_fullprof, candidate=calc_ed_cryspy, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY, )

Calculator for experiment 'lif' already set to

cryspy

Loading plot…

Fit edi-cryspy to FullProf¶

Cryspy applies polarization natively from the K and cthm values passed by EasyDiffraction. FullProf's characteristic X-ray convention for Rpolarz = 0.5 uses the same polarization expression multiplied by two, so the seeded FullProf scale leaves the native Cryspy pattern half as intense. This fit documents the convention mismatch by letting the scale absorb that factor.

In [8]:

experiment.linked_structures['lif'].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(
    'lif',
    reference=calc_fullprof,
    candidate=calc_ed_cryspy_refined,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY_REFINED,
)

experiment.linked_structures['lif'].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( 'lif', reference=calc_fullprof, candidate=calc_ed_cryspy_refined, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY_REFINED, )

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.04	687.66
2	5	0.16	0.02	100.0% ↓
3	8	0.29	0.02

🏆 Best goodness-of-fit (reduced χ²) is 0.02 at iteration 5

✅ 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)	0.29
4	🔁 Iterations	5
5	📏 Goodness-of-fit (reduced χ²)	0.02
6	📏 R-factor (Rf, %)	0.62
7	📏 R-factor squared (Rf², %)	0.28
8	📏 Weighted R-factor (wR, %)	0.28

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	lif	linked_structure	lif	scale		0.0100	0.0200	0.0000	99.90 % ↑

• 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} vs {FULLPROF_LABEL}',
            calc_fullprof,
            calc_ed_cryspy,
        ),
    ],
    known_discrepancy=True,
    reason=(
        'Cryspy applies the native K/cthm polarization factor directly, '
        'while FullProf multiplies the characteristic X-ray Rpolarz=0.5 '
        'form by two; before scale refinement the Cryspy pattern is '
        'therefore half as intense.'
    ),
)

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} vs {FULLPROF_LABEL}', calc_fullprof, calc_ed_cryspy, ), ], known_discrepancy=True, reason=( 'Cryspy applies the native K/cthm polarization factor directly, ' 'while FullProf multiplies the characteristic X-ray Rpolarz=0.5 ' 'form by two; before scale refinement the Cryspy pattern is ' 'therefore half as intense.' ), ) 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 0.20.1 (cryspy 0.13.0) vs FullProf 8.40	Profile diff (%)	< 2.5	49.98	❌
2		Max deviation (%)	< 6	49.99	❌
3		Area ratio	0.99 to 1.01	0.5001	❌
4		Shape correlation	> 0.999	1.0000	✅

• Known discrepancy = Cryspy applies the native K/cthm polarization factor directly, while FullProf multiplies the characteristic X-ray Rpolarz=0.5 form by two; before scale refinement the Cryspy pattern is therefore half as intense.

	Comparison	Metric	Expected	Actual	OK
1	edi 0.20.1 (cryspy 0.13.0, refined) vs FullProf 8.40	Profile diff (%)	< 2.5	0.28	✅
2		Max deviation (%)	< 6	0.20	✅
3		Area ratio	0.99 to 1.01	0.9998	✅
4		Shape correlation	> 0.999	1.0000	✅

Out[9]:

True