Tb2Ti2O7 - single-crystal neutron CW - anisotropic ADPs¶

Verifies calculated F2 values for a no-extinction neutron single-crystal reference with anisotropic ADPs.

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='tbti')

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

structure.cell.length_a = 10.130  # FullProf a

# Anisotropic sites carry the FullProf beta tensor directly: ``adp_type``
# is set to ``'beta'`` and the dimensionless beta components are assigned
# verbatim. F d -3 m is cubic, so site symmetry links the remaining beta
# components and only the independent ones are set. FullProf occupancy is
# the site multiplicity over the general multiplicity; CIF/EasyDiffraction
# use 1.0 for a fully occupied site.
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='beta',  # FullProf beta tensor
)
aniso = structure.atom_site_aniso['Tb']
aniso.adp_11 = 0.00098991673  # FullProf beta11
aniso.adp_12 = -0.00047650724  # FullProf beta12

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='beta',  # FullProf beta tensor
)
aniso = structure.atom_site_aniso['Ti']
aniso.adp_11 = 0.00090989727  # FullProf beta11
aniso.adp_12 = -0.00016990340  # FullProf beta12

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='beta',  # FullProf beta tensor
)
aniso = structure.atom_site_aniso['O1']
aniso.adp_11 = 0.0012294180  # FullProf beta11
aniso.adp_22 = 0.00078215479  # FullProf beta22
aniso.adp_23 = 0.00041246481  # FullProf beta23

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='beta',  # FullProf beta tensor
)
aniso = structure.atom_site_aniso['O2']
aniso.adp_11 = 0.00060762477  # FullProf beta11

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 # Anisotropic sites carry the FullProf beta tensor directly: ``adp_type`` # is set to ``'beta'`` and the dimensionless beta components are assigned # verbatim. F d -3 m is cubic, so site symmetry links the remaining beta # components and only the independent ones are set. FullProf occupancy is # the site multiplicity over the general multiplicity; CIF/EasyDiffraction # use 1.0 for a fully occupied site. 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='beta', # FullProf beta tensor ) aniso = structure.atom_site_aniso['Tb'] aniso.adp_11 = 0.00098991673 # FullProf beta11 aniso.adp_12 = -0.00047650724 # FullProf beta12 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='beta', # FullProf beta tensor ) aniso = structure.atom_site_aniso['Ti'] aniso.adp_11 = 0.00090989727 # FullProf beta11 aniso.adp_12 = -0.00016990340 # FullProf beta12 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='beta', # FullProf beta tensor ) aniso = structure.atom_site_aniso['O1'] aniso.adp_11 = 0.0012294180 # FullProf beta11 aniso.adp_22 = 0.00078215479 # FullProf beta22 aniso.adp_23 = 0.00041246481 # FullProf beta23 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='beta', # FullProf beta tensor ) aniso = structure.atom_site_aniso['O2'] aniso.adp_11 = 0.00060762477 # FullProf beta11 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. 0.00514621 beta
28	Ti Ti 0. 0. 0. c 16 1. 0.00473022 beta
29	O1 O 0.32804 0.125 0.125 f 48 1. 0.00484119 beta
30	O2 O 0.375 0.375 0.375 b 8 1. 0.00315882 beta
31
32	loop_
33	_atom_site_aniso.id
34	_atom_site_aniso.adp_11
35	_atom_site_aniso.adp_22
36	_atom_site_aniso.adp_33
37	_atom_site_aniso.adp_12
38	_atom_site_aniso.adp_13
39	_atom_site_aniso.adp_23
40	Tb 0.00098992 0.00098992 0.00098992 -0.00047651 -0.00047651 -0.00047651
41	Ti 0.0009099 0.0009099 0.0009099 -0.0001699 -0.0001699 -0.0001699
42	O1 0.00122942 0.00078215 0.00078215 0. 0. 0.00041246
43	O2 0.00060762 0.00060762 0.00060762 0. 0. 0.

Load the FullProf reference¶

In [6]:

FULLPROF_PROJECT_DIR = 'sc-neut-cwl_tbti_anisotropic-adp'
FULLPROF_OUT_FILE = 'tbti.out'
FULLPROF_SCALE = 0.28749475  # FullProf Scale
FULLPROF_WAVELENGTH = 0.7930  # FullProf Lambda

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_anisotropic-adp' FULLPROF_OUT_FILE = 'tbti.out' FULLPROF_SCALE = 0.28749475 # FullProf Scale FULLPROF_WAVELENGTH = 0.7930 # FullProf Lambda 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

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 verify.set_reference_reflections(experiment, f2calc) project.experiments.add(experiment)

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

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 only')
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 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 only') 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	0.04	516632.99
2	5	0.19	0.02	100.0% ↓
3	8	0.31	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)	0.31
4	🔁 Iterations	5
5	📏 Goodness-of-fit (reduced χ²)	0.02
6	📏 R-factor (Rf, %)	0.02
7	📏 R-factor squared (Rf², %)	0.02
8	📏 Weighted R-factor (wR, %)	0.02

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	tbti	linked_structure		scale		0.2875	2.3007	0.0000	700.27 % ↑

• 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 (%)	87.50	0.02
2	Max deviation (%)	87.51	0.03
3	Area ratio	0.1250	1.0001
4	Shape correlation	1.0000	1.0000

Agreement check¶

In [10]:

verify.assert_patterns_agree([
    (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', reference_refined, candidate_refined),
])

verify.assert_patterns_agree([ (f'{LABEL_ED_CRYSPY_REFINED} vs {FULLPROF_LABEL}', reference_refined, candidate_refined), ])

	Comparison	Metric	Expected	Actual	OK
1	edi 0.19.0 (cryspy 0.12.1, scale only) vs FullProf 8.40	Profile diff (%)	< 2.5	0.02	✅
2		Max deviation (%)	< 6	0.03	✅
3		Area ratio	0.99 to 1.01	1.0001	✅
4		Shape correlation	> 0.999	1.0000	✅

Out[10]:

True