Tb2Ti2O7 - single-crystal neutron CW - isotropic extinction¶

Verifies the cryspy isotropic extinction model against a FullProf single-crystal reference with isotropic ADPs.

Refinement: the overall scale and the extinction radius. Known difference: cryspy and FullProf use different extinction conventions.

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='tbti')

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

structure.cell.length_a = 10.130  # FullProf a

structure.atom_sites.create(
    id='Tb',  # FullProf Atom
    type_symbol='Tb',  # 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=0.0,  # FullProf Biso
)
structure.atom_sites.create(
    id='Ti',  # FullProf Atom
    type_symbol='Ti',  # 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=0.0,  # FullProf Biso
)
structure.atom_sites.create(
    id='O1',  # FullProf Atom
    type_symbol='O',  # FullProf Typ
    fract_x=0.32804,  # FullProf X
    fract_y=0.125,  # FullProf Y
    fract_z=0.125,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.0,  # FullProf Biso
)
structure.atom_sites.create(
    id='O2',  # FullProf Atom
    type_symbol='O',  # FullProf Typ
    fract_x=0.375,  # FullProf X
    fract_y=0.375,  # FullProf Y
    fract_z=0.375,  # FullProf Z
    adp_type='Biso',  # FullProf Biso
    adp_iso=0.0,  # FullProf Biso
)

project.structures.add(structure)

structure = StructureFactory.from_scratch(name='tbti') structure.space_group.name_h_m = 'F d -3 m' # FullProf Space group symbol structure.cell.length_a = 10.130 # FullProf a structure.atom_sites.create( id='Tb', # FullProf Atom type_symbol='Tb', # 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=0.0, # FullProf Biso ) structure.atom_sites.create( id='Ti', # FullProf Atom type_symbol='Ti', # 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=0.0, # FullProf Biso ) structure.atom_sites.create( id='O1', # FullProf Atom type_symbol='O', # FullProf Typ fract_x=0.32804, # FullProf X fract_y=0.125, # FullProf Y fract_z=0.125, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=0.0, # FullProf Biso ) structure.atom_sites.create( id='O2', # FullProf Atom type_symbol='O', # FullProf Typ fract_x=0.375, # FullProf X fract_y=0.375, # FullProf Y fract_z=0.375, # FullProf Z adp_type='Biso', # FullProf Biso adp_iso=0.0, # FullProf Biso ) project.structures.add(structure)

In [5]:

structure.show_as_text()

structure.show_as_text()

Structure 🧩 'tbti' as text

	Edi
1	data_tbti
2
3	_cell.length_a 10.13
4	_cell.length_b 10.13
5	_cell.length_c 10.13
6	_cell.angle_alpha 90.
7	_cell.angle_beta 90.
8	_cell.angle_gamma 90.
9
10	_space_group.name_h_m "F d -3 m"
11	_space_group.coord_system_code 2
12
13	_geom.min_bond_distance_cutoff 0.
14	_geom.bond_distance_inc 0.25
15
16	loop_
17	_atom_site.id
18	_atom_site.type_symbol
19	_atom_site.fract_x
20	_atom_site.fract_y
21	_atom_site.fract_z
22	_atom_site.wyckoff_letter
23	_atom_site.multiplicity
24	_atom_site.occupancy
25	_atom_site.adp_iso
26	_atom_site.adp_type
27	Tb Tb 0.5 0.5 0.5 d 16 1. 0. Biso
28	Ti Ti 0. 0. 0. c 16 1. 0. Biso
29	O1 O 0.32804 0.125 0.125 f 48 1. 0. Biso
30	O2 O 0.375 0.375 0.375 b 8 1. 0. Biso

Load the FullProf reference¶

In [6]:

FULLPROF_PROJECT_DIR = 'sc-neut-cwl_tbti_isotropic-extinction'
FULLPROF_OUT_FILE = 'tbti.out'
FULLPROF_SCALE = 0.2609  # FullProf Scale
FULLPROF_WAVELENGTH = 0.7930  # FullProf Lambda
# cryspy uses Becker-Coppens isotropic extinction, not the one from
# FullProf.
EXTINCTION_RADIUS = 10.0
EXTINCTION_MOSAICITY = 35000.0

f2calc = verify.load_fullprof_sc_f2calc(FULLPROF_PROJECT_DIR, FULLPROF_OUT_FILE)
FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_OUT_FILE)

FULLPROF_PROJECT_DIR = 'sc-neut-cwl_tbti_isotropic-extinction' FULLPROF_OUT_FILE = 'tbti.out' FULLPROF_SCALE = 0.2609 # FullProf Scale FULLPROF_WAVELENGTH = 0.7930 # FullProf Lambda # cryspy uses Becker-Coppens isotropic extinction, not the one from # FullProf. EXTINCTION_RADIUS = 10.0 EXTINCTION_MOSAICITY = 35000.0 f2calc = verify.load_fullprof_sc_f2calc(FULLPROF_PROJECT_DIR, FULLPROF_OUT_FILE) FULLPROF_LABEL = verify.fullprof_label(FULLPROF_PROJECT_DIR, FULLPROF_OUT_FILE)

Create the experiment¶

In [7]:

experiment = ExperimentFactory.from_scratch(
    name='tbti',
    sample_form='single crystal',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
    scattering_type='bragg',
)
experiment.linked_structure.structure_id = 'tbti'
experiment.linked_structure.scale = FULLPROF_SCALE
experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH
experiment.extinction.type = 'becker-coppens'
experiment.extinction.model = 'gauss'
experiment.extinction.radius.value = EXTINCTION_RADIUS
experiment.extinction.mosaicity.value = EXTINCTION_MOSAICITY

verify.set_reference_reflections(experiment, f2calc)

project.experiments.add(experiment)

experiment = ExperimentFactory.from_scratch( name='tbti', sample_form='single crystal', beam_mode='constant wavelength', radiation_probe='neutron', scattering_type='bragg', ) experiment.linked_structure.structure_id = 'tbti' experiment.linked_structure.scale = FULLPROF_SCALE experiment.instrument.setup_wavelength = FULLPROF_WAVELENGTH experiment.extinction.type = 'becker-coppens' experiment.extinction.model = 'gauss' experiment.extinction.radius.value = EXTINCTION_RADIUS experiment.extinction.mosaicity.value = EXTINCTION_MOSAICITY verify.set_reference_reflections(experiment, f2calc) project.experiments.add(experiment)

Extinction type changed to

becker-coppens

edi-cryspy VS FullProf¶

In [8]:

calc_ed_cryspy = verify.calculate_reflections(project, experiment, 'cryspy')
LABEL_ED_CRYSPY = verify.engine_label('cryspy')
reference, candidate = verify.align_reflections(f2calc, calc_ed_cryspy)

project.display.reflection_comparison(
    'tbti',
    reference=reference,
    candidate=candidate,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY,
)

calc_ed_cryspy = verify.calculate_reflections(project, experiment, 'cryspy') LABEL_ED_CRYSPY = verify.engine_label('cryspy') reference, candidate = verify.align_reflections(f2calc, calc_ed_cryspy) project.display.reflection_comparison( 'tbti', reference=reference, candidate=candidate, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY, )

Calculator for experiment 'tbti' already set to

cryspy

Loading plot…

Fit edi-cryspy to FullProf¶

In [9]:

experiment.calculator.type = 'cryspy'

experiment.linked_structure.scale.free = True
experiment.extinction.radius.free = True

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

calc_ed_cryspy_refined = verify.calculate_reflections(project, experiment, 'cryspy')
LABEL_ED_CRYSPY_REFINED = verify.engine_label('cryspy', note='scale + ext radius')
reference_refined, candidate_refined = verify.align_reflections(f2calc, calc_ed_cryspy_refined)

project.display.reflection_comparison(
    'tbti',
    reference=reference_refined,
    candidate=candidate_refined,
    reference_label=FULLPROF_LABEL,
    candidate_label=LABEL_ED_CRYSPY_REFINED,
)

verify.report_refinement_closeness(
    reference,
    candidate,
    candidate_refined,
)

experiment.calculator.type = 'cryspy' experiment.linked_structure.scale.free = True experiment.extinction.radius.free = True project.analysis.fit() project.display.fit.results() calc_ed_cryspy_refined = verify.calculate_reflections(project, experiment, 'cryspy') LABEL_ED_CRYSPY_REFINED = verify.engine_label('cryspy', note='scale + ext radius') reference_refined, candidate_refined = verify.align_reflections(f2calc, calc_ed_cryspy_refined) project.display.reflection_comparison( 'tbti', reference=reference_refined, candidate=candidate_refined, reference_label=FULLPROF_LABEL, candidate_label=LABEL_ED_CRYSPY_REFINED, ) verify.report_refinement_closeness( reference, candidate, candidate_refined, )

Calculator for experiment 'tbti' already set to

cryspy

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.01	559733.19
2	6	0.06	227010.05	59.4% ↓
3	10	0.10	123452.76	45.6% ↓
4	13	0.14	4334.85	96.5% ↓
5	16	0.16	1422.02	67.2% ↓
6	26	0.25	1416.64

🏆 Best goodness-of-fit (reduced χ²) is 1416.64 at iteration 25

✅ 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)	0.25
4	🔁 Iterations	23
5	📏 Goodness-of-fit (reduced χ²)	1416.64
6	📏 R-factor (Rf, %)	2.52
7	📏 R-factor squared (Rf², %)	4.34
8	📏 Weighted R-factor (wR, %)	4.34

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	tbti	extinction		radius	μm	10.0000	-20.0462	0.5414	300.46 % ↓
2	tbti	linked_structure		scale		0.2609	2.0598	0.0174	689.51 % ↑

• 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

Calculator for experiment 'tbti' already set to

cryspy

Loading plot…

	Metric	Before	After
1	Profile diff (%)	86.18	4.34
2	Max deviation (%)	85.73	9.92
3	Area ratio	0.1351	0.9985
4	Shape correlation	0.9982	0.9985

Agreement check¶

In [10]:

verify.assert_patterns_agree(
    [
        (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', reference_refined, candidate_refined),
    ],
    known_discrepancy=True,
    reason='cryspy and FullProf use different extinction conventions.',
)

verify.assert_patterns_agree( [ (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', reference_refined, candidate_refined), ], known_discrepancy=True, reason='cryspy and FullProf use different extinction conventions.', )

	Comparison	Metric	Expected	Actual	OK
1	edi 0.19.0 (cryspy 0.12.1, scale + ext radius) vs FullProf 8.40	Profile diff (%)	< 2.5	4.34	❌
2		Max deviation (%)	< 6	9.92	❌
3		Area ratio	0.99 to 1.01	0.9985	✅
4		Shape correlation	> 0.999	0.9985	❌

• Known discrepancy = cryspy and FullProf use different extinction conventions.

Out[10]:

True