Structure Refinement: NCAF, WISH¶

This example demonstrates a Rietveld refinement of Na2Ca3Al2F14 crystal structure using time-of-flight neutron powder diffraction data from WISH at ISIS.

Two datasets from detector banks 5+6 and 4+7 are used for joint fitting.

Import Library¶

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from easydiffraction import Experiment
from easydiffraction import Project
from easydiffraction import SampleModel
from easydiffraction import download_from_repository
from easydiffraction import Experiment
from easydiffraction import Project
from easydiffraction import SampleModel
from easydiffraction import download_from_repository

⚠️ 'pycrysfml' module not found. This calculation engine will not be available.
✅ 'cryspy' calculation engine is successfully imported.
✅ 'pdffit' calculation engine is successfully imported.

Define Sample Model¶

This section covers how to add sample models and modify their parameters.

Create Sample Model¶

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model = SampleModel('ncaf')
model = SampleModel('ncaf')

Set Space Group¶

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model.space_group.name_h_m = 'I 21 3'
model.space_group.it_coordinate_system_code = '1'
model.space_group.name_h_m = 'I 21 3'
model.space_group.it_coordinate_system_code = '1'

Set Unit Cell¶

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model.cell.length_a = 10.250256
model.cell.length_a = 10.250256

Set Atom Sites¶

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model.atom_sites.add('Ca', 'Ca', 0.4663, 0.0, 0.25, wyckoff_letter='b', b_iso=0.92)
model.atom_sites.add('Al', 'Al', 0.2521, 0.2521, 0.2521, wyckoff_letter='a', b_iso=0.73)
model.atom_sites.add('Na', 'Na', 0.0851, 0.0851, 0.0851, wyckoff_letter='a', b_iso=2.08)
model.atom_sites.add('F1', 'F', 0.1377, 0.3054, 0.1195, wyckoff_letter='c', b_iso=0.90)
model.atom_sites.add('F2', 'F', 0.3625, 0.3633, 0.1867, wyckoff_letter='c', b_iso=1.37)
model.atom_sites.add('F3', 'F', 0.4612, 0.4612, 0.4612, wyckoff_letter='a', b_iso=0.88)
model.atom_sites.add('Ca', 'Ca', 0.4663, 0.0, 0.25, wyckoff_letter='b', b_iso=0.92)
model.atom_sites.add('Al', 'Al', 0.2521, 0.2521, 0.2521, wyckoff_letter='a', b_iso=0.73)
model.atom_sites.add('Na', 'Na', 0.0851, 0.0851, 0.0851, wyckoff_letter='a', b_iso=2.08)
model.atom_sites.add('F1', 'F', 0.1377, 0.3054, 0.1195, wyckoff_letter='c', b_iso=0.90)
model.atom_sites.add('F2', 'F', 0.3625, 0.3633, 0.1867, wyckoff_letter='c', b_iso=1.37)
model.atom_sites.add('F3', 'F', 0.4612, 0.4612, 0.4612, wyckoff_letter='a', b_iso=0.88)

Define Experiment¶

This section shows how to add experiments, configure their parameters, and link the sample models defined in the previous step.

Download Measured Data¶

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download_from_repository(
    'wish_ncaf_5_6.xys',
    destination='data',
)
download_from_repository(
    'wish_ncaf_5_6.xys',
    destination='data',
)

⚠️ Warning
File 'data/wish_ncaf_5_6.xys' already exists and will not be overwritten.

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download_from_repository(
    'wish_ncaf_4_7.xys',
    destination='data',
)
download_from_repository(
    'wish_ncaf_4_7.xys',
    destination='data',
)

⚠️ Warning
File 'data/wish_ncaf_4_7.xys' already exists and will not be overwritten.

Create Experiment¶

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expt56 = Experiment(
    'wish_5_6',
    beam_mode='time-of-flight',
    data_path='data/wish_ncaf_5_6.xys',
)
expt56 = Experiment(
    'wish_5_6',
    beam_mode='time-of-flight',
    data_path='data/wish_ncaf_5_6.xys',
)

Data loaded successfully
Experiment 🔬 'wish_5_6'. Number of data points: 4121

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expt47 = Experiment(
    'wish_4_7',
    beam_mode='time-of-flight',
    data_path='data/wish_ncaf_4_7.xys',
)
expt47 = Experiment(
    'wish_4_7',
    beam_mode='time-of-flight',
    data_path='data/wish_ncaf_4_7.xys',
)

Data loaded successfully
Experiment 🔬 'wish_4_7'. Number of data points: 4043

Set Instrument¶

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expt56.instrument.setup_twotheta_bank = 152.827
expt56.instrument.calib_d_to_tof_offset = -13.5
expt56.instrument.calib_d_to_tof_linear = 20773.0
expt56.instrument.calib_d_to_tof_quad = -1.08308
expt56.instrument.setup_twotheta_bank = 152.827
expt56.instrument.calib_d_to_tof_offset = -13.5
expt56.instrument.calib_d_to_tof_linear = 20773.0
expt56.instrument.calib_d_to_tof_quad = -1.08308

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expt47.instrument.setup_twotheta_bank = 121.660
expt47.instrument.calib_d_to_tof_offset = -15.0
expt47.instrument.calib_d_to_tof_linear = 18660.0
expt47.instrument.calib_d_to_tof_quad = -0.47488
expt47.instrument.setup_twotheta_bank = 121.660
expt47.instrument.calib_d_to_tof_offset = -15.0
expt47.instrument.calib_d_to_tof_linear = 18660.0
expt47.instrument.calib_d_to_tof_quad = -0.47488

Set Peak Profile¶

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expt56.peak.broad_gauss_sigma_0 = 0.0
expt56.peak.broad_gauss_sigma_1 = 0.0
expt56.peak.broad_gauss_sigma_2 = 15.5
expt56.peak.broad_mix_beta_0 = 0.007
expt56.peak.broad_mix_beta_1 = 0.01
expt56.peak.asym_alpha_0 = -0.0094
expt56.peak.asym_alpha_1 = 0.1
expt56.peak.broad_gauss_sigma_0 = 0.0
expt56.peak.broad_gauss_sigma_1 = 0.0
expt56.peak.broad_gauss_sigma_2 = 15.5
expt56.peak.broad_mix_beta_0 = 0.007
expt56.peak.broad_mix_beta_1 = 0.01
expt56.peak.asym_alpha_0 = -0.0094
expt56.peak.asym_alpha_1 = 0.1

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expt47.peak.broad_gauss_sigma_0 = 0.0
expt47.peak.broad_gauss_sigma_1 = 29.8
expt47.peak.broad_gauss_sigma_2 = 18.0
expt47.peak.broad_mix_beta_0 = 0.006
expt47.peak.broad_mix_beta_1 = 0.015
expt47.peak.asym_alpha_0 = -0.0115
expt47.peak.asym_alpha_1 = 0.1
expt47.peak.broad_gauss_sigma_0 = 0.0
expt47.peak.broad_gauss_sigma_1 = 29.8
expt47.peak.broad_gauss_sigma_2 = 18.0
expt47.peak.broad_mix_beta_0 = 0.006
expt47.peak.broad_mix_beta_1 = 0.015
expt47.peak.asym_alpha_0 = -0.0115
expt47.peak.asym_alpha_1 = 0.1

Set Background¶

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expt56.background_type = 'line-segment'
for x, y in [
    (9162, 465),
    (11136, 593),
    (13313, 497),
    (14906, 546),
    (16454, 533),
    (17352, 496),
    (18743, 428),
    (20179, 452),
    (21368, 397),
    (22176, 468),
    (22827, 477),
    (24644, 380),
    (26439, 381),
    (28257, 378),
    (31196, 343),
    (34034, 328),
    (37265, 310),
    (41214, 323),
    (44827, 283),
    (49830, 273),
    (52905, 257),
    (58204, 260),
    (62916, 261),
    (70186, 262),
    (74204, 262),
    (82103, 268),
    (91958, 268),
    (102712, 262),
]:
    expt56.background.add(x, y)
expt56.background_type = 'line-segment'
for x, y in [
    (9162, 465),
    (11136, 593),
    (13313, 497),
    (14906, 546),
    (16454, 533),
    (17352, 496),
    (18743, 428),
    (20179, 452),
    (21368, 397),
    (22176, 468),
    (22827, 477),
    (24644, 380),
    (26439, 381),
    (28257, 378),
    (31196, 343),
    (34034, 328),
    (37265, 310),
    (41214, 323),
    (44827, 283),
    (49830, 273),
    (52905, 257),
    (58204, 260),
    (62916, 261),
    (70186, 262),
    (74204, 262),
    (82103, 268),
    (91958, 268),
    (102712, 262),
]:
    expt56.background.add(x, y)

Background type for experiment 'wish_5_6' changed to
line-segment

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expt47.background_type = 'line-segment'
for x, y in [
    (9090, 488),
    (10672, 566),
    (12287, 494),
    (14037, 559),
    (15451, 529),
    (16764, 445),
    (18076, 460),
    (19456, 413),
    (20466, 511),
    (21880, 396),
    (23798, 391),
    (25447, 385),
    (28073, 349),
    (30058, 332),
    (32583, 309),
    (34804, 355),
    (37160, 318),
    (40324, 290),
    (46895, 260),
    (50631, 256),
    (54602, 246),
    (58439, 264),
    (66520, 250),
    (75002, 258),
    (83649, 257),
    (92770, 255),
    (101524, 260),
]:
    expt47.background.add(x, y)
expt47.background_type = 'line-segment'
for x, y in [
    (9090, 488),
    (10672, 566),
    (12287, 494),
    (14037, 559),
    (15451, 529),
    (16764, 445),
    (18076, 460),
    (19456, 413),
    (20466, 511),
    (21880, 396),
    (23798, 391),
    (25447, 385),
    (28073, 349),
    (30058, 332),
    (32583, 309),
    (34804, 355),
    (37160, 318),
    (40324, 290),
    (46895, 260),
    (50631, 256),
    (54602, 246),
    (58439, 264),
    (66520, 250),
    (75002, 258),
    (83649, 257),
    (92770, 255),
    (101524, 260),
]:
    expt47.background.add(x, y)

Background type for experiment 'wish_4_7' changed to
line-segment

Set Linked Phases¶

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expt56.linked_phases.add('ncaf', scale=1.0)
expt56.linked_phases.add('ncaf', scale=1.0)

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expt47.linked_phases.add('ncaf', scale=2.0)
expt47.linked_phases.add('ncaf', scale=2.0)

Set Excluded Regions¶

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expt56.excluded_regions.add(minimum=0, maximum=10010)
expt56.excluded_regions.add(minimum=100010, maximum=200000)
expt56.excluded_regions.add(minimum=0, maximum=10010)
expt56.excluded_regions.add(minimum=100010, maximum=200000)

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expt47.excluded_regions.add(minimum=0, maximum=10006)
expt47.excluded_regions.add(minimum=100004, maximum=200000)
expt47.excluded_regions.add(minimum=0, maximum=10006)
expt47.excluded_regions.add(minimum=100004, maximum=200000)

Define Project¶

The project object is used to manage the sample model, experiments, and analysis

Create Project¶

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project = Project()
project = Project()

Set Plotting Engine¶

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project.plotter.engine = 'plotly'
project.plotter.engine = 'plotly'

Current plotter changed to
plotly

Add Sample Model¶

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project.sample_models.add(model)
project.sample_models.add(model)

Add Experiment¶

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project.experiments.add(expt56)
project.experiments.add(expt47)
project.experiments.add(expt56)
project.experiments.add(expt47)

Perform Analysis¶

This section shows the analysis process, including how to set up calculation and fitting engines.

Set Calculator¶

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project.analysis.current_calculator = 'cryspy'
project.analysis.current_calculator = 'cryspy'

Current calculator changed to
cryspy

Set Minimizer¶

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project.analysis.current_minimizer = 'lmfit (leastsq)'
project.analysis.current_minimizer = 'lmfit (leastsq)'

Current minimizer changed to
lmfit (leastsq)

Set Fit Mode¶

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project.analysis.fit_mode = 'joint'
project.analysis.fit_mode = 'joint'

Current fit mode changed to
joint

Set Free Parameters¶

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model.atom_sites['Ca'].b_iso.free = True
model.atom_sites['Al'].b_iso.free = True
model.atom_sites['Na'].b_iso.free = True
model.atom_sites['F1'].b_iso.free = True
model.atom_sites['F2'].b_iso.free = True
model.atom_sites['F3'].b_iso.free = True
model.atom_sites['Ca'].b_iso.free = True
model.atom_sites['Al'].b_iso.free = True
model.atom_sites['Na'].b_iso.free = True
model.atom_sites['F1'].b_iso.free = True
model.atom_sites['F2'].b_iso.free = True
model.atom_sites['F3'].b_iso.free = True

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expt56.linked_phases['ncaf'].scale.free = True
expt56.instrument.calib_d_to_tof_offset.free = True
expt56.instrument.calib_d_to_tof_linear.free = True
expt56.peak.broad_gauss_sigma_2.free = True
expt56.peak.broad_mix_beta_0.free = True
expt56.peak.broad_mix_beta_1.free = True
expt56.peak.asym_alpha_1.free = True

expt47.linked_phases['ncaf'].scale.free = True
expt47.instrument.calib_d_to_tof_linear.free = True
expt47.instrument.calib_d_to_tof_offset.free = True
expt47.peak.broad_gauss_sigma_2.free = True
expt47.peak.broad_mix_beta_0.free = True
expt47.peak.broad_mix_beta_1.free = True
expt47.peak.asym_alpha_1.free = True
expt56.linked_phases['ncaf'].scale.free = True
expt56.instrument.calib_d_to_tof_offset.free = True
expt56.instrument.calib_d_to_tof_linear.free = True
expt56.peak.broad_gauss_sigma_2.free = True
expt56.peak.broad_mix_beta_0.free = True
expt56.peak.broad_mix_beta_1.free = True
expt56.peak.asym_alpha_1.free = True

expt47.linked_phases['ncaf'].scale.free = True
expt47.instrument.calib_d_to_tof_linear.free = True
expt47.instrument.calib_d_to_tof_offset.free = True
expt47.peak.broad_gauss_sigma_2.free = True
expt47.peak.broad_mix_beta_0.free = True
expt47.peak.broad_mix_beta_1.free = True
expt47.peak.asym_alpha_1.free = True

Plot Measured vs Calculated¶

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project.plot_meas_vs_calc(expt_name='wish_5_6', show_residual=True)
project.plot_meas_vs_calc(expt_name='wish_5_6', show_residual=True)

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project.plot_meas_vs_calc(expt_name='wish_4_7', show_residual=True)
project.plot_meas_vs_calc(expt_name='wish_4_7', show_residual=True)

Run Fitting¶

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project.analysis.fit()
project.analysis.fit()

Using all experiments 🔬 ['wish_5_6', 'wish_4_7'] for 'joint' fitting
🚀 Starting fit process with 'lmfit (leastsq)'...
📈 Goodness-of-fit (reduced χ²) change:

iteration	χ²	improvement [%]
1	47.53
24	15.57	67.2% ↓
109	15.49

🏆 Best goodness-of-fit (reduced χ²) is 15.49 at iteration 98
✅ Fitting complete.

Fit results
✅ Success: True
⏱️ Fitting time: 64.44 seconds
📏 Goodness-of-fit (reduced χ²): 15.49
📏 R-factor (Rf): 6.98%
📏 R-factor squared (Rf²): 8.05%
📏 Weighted R-factor (wR): 9.15%
📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	ncaf	atom_sites	Ca	b_iso	0.9200	0.9340	0.0448	Å²	1.52 % ↑
2	ncaf	atom_sites	Al	b_iso	0.7300	0.7330	0.0569	Å²	0.41 % ↑
3	ncaf	atom_sites	Na	b_iso	2.0800	2.0474	0.1082	Å²	1.57 % ↓
4	ncaf	atom_sites	F1	b_iso	0.9000	0.9389	0.0373	Å²	4.32 % ↑
5	ncaf	atom_sites	F2	b_iso	1.3700	1.3442	0.0408	Å²	1.88 % ↓
6	ncaf	atom_sites	F3	b_iso	0.8800	0.8481	0.0551	Å²	3.62 % ↓
7	wish_5_6	instrument		d_to_tof_linear	20773.0000	20773.0394	0.3051	µs/Å	0.00 % ↑
8	wish_5_6	instrument		d_to_tof_offset	-13.5000	-13.6260	0.4257	µs	0.93 % ↑
9	wish_5_6	linked_phases	ncaf	scale	1.0000	1.1029	0.0035		10.29 % ↑
10	wish_5_6	peak		asym_alpha_1	0.1000	0.1094	0.0012		9.43 % ↑
11	wish_5_6	peak		gauss_sigma_2	15.5000	15.6543	0.7398	µs²/Å²	1.00 % ↑
12	wish_5_6	peak		mix_beta_0	0.0070	0.0067	0.0000	deg	4.54 % ↓
13	wish_5_6	peak		mix_beta_1	0.0100	0.0101	0.0002	deg	1.46 % ↑
14	wish_4_7	instrument		d_to_tof_linear	18660.0000	18660.1028	0.3625	µs/Å	0.00 % ↑
15	wish_4_7	instrument		d_to_tof_offset	-15.0000	-14.9768	0.5084	µs	0.15 % ↓
16	wish_4_7	linked_phases	ncaf	scale	2.0000	2.5216	0.0077		26.08 % ↑
17	wish_4_7	peak		asym_alpha_1	0.1000	0.1222	0.0018		22.15 % ↑
18	wish_4_7	peak		gauss_sigma_2	18.0000	18.2604	0.8685	µs²/Å²	1.45 % ↑
19	wish_4_7	peak		mix_beta_0	0.0060	0.0065	0.0000	deg	7.52 % ↑
20	wish_4_7	peak		mix_beta_1	0.0150	0.0148	0.0003	deg	1.38 % ↓

Plot Measured vs Calculated¶

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project.plot_meas_vs_calc(expt_name='wish_5_6', show_residual=True)
project.plot_meas_vs_calc(expt_name='wish_5_6', show_residual=True)

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project.plot_meas_vs_calc(expt_name='wish_4_7', show_residual=True)
project.plot_meas_vs_calc(expt_name='wish_4_7', show_residual=True)

Summary¶

This final section shows how to review the results of the analysis.

Show Project Summary¶

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project.summary.show_report()
project.summary.show_report()

*** PROJECT INFO ***

Title
Untitled Project

*** CRYSTALLOGRAPHIC DATA ***

Phase datablock
🧩 ncaf

Space group
I 21 3

Cell parameters

alpha	90.00000
beta	90.00000
gamma	90.00000
a	10.25026
b	10.25026
c	10.25026

Atom sites

Label	Type	fract_x	fract_y	fract_z	Occupancy	B_iso
Ca	Ca	0.46630	0.00000	0.25000	1.00000	0.93400
Al	Al	0.25210	0.25210	0.25210	1.00000	0.73301
Na	Na	0.08510	0.08510	0.08510	1.00000	2.04740
F1	F	0.13770	0.30540	0.11950	1.00000	0.93890
F2	F	0.36250	0.36330	0.18670	1.00000	1.34424
F3	F	0.46120	0.46120	0.46120	1.00000	0.84814

*** EXPERIMENTS ***

Experiment datablock
🔬 wish_5_6

Experiment type
powder, neutron, time-of-flight

Profile type
pseudo-voigt * ikeda-carpenter

Experiment datablock
🔬 wish_4_7

Experiment type
powder, neutron, time-of-flight

Profile type
pseudo-voigt * ikeda-carpenter

*** FITTING ***

Calculation engine
cryspy

Minimization engine
lmfit (leastsq)

Fit quality

Goodness-of-fit (reduced χ²)

15.49