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¶

In [2]:

from easydiffraction import ExperimentFactory
from easydiffraction import Project
from easydiffraction import SampleModelFactory
from easydiffraction import download_from_repository

from easydiffraction import ExperimentFactory from easydiffraction import Project from easydiffraction import SampleModelFactory from easydiffraction import download_from_repository

Define Sample Model¶

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

Create Sample Model¶

In [3]:

model = SampleModelFactory.create(name='ncaf')

model = SampleModelFactory.create(name='ncaf')

Set Space Group¶

In [4]:

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¶

In [5]:

model.cell.length_a = 10.250256

model.cell.length_a = 10.250256

Set Atom Sites¶

In [6]:

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

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

In [7]:

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

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

Downloading...

File 'wish_ncaf_5_6.xys' from 'easyscience/diffraction-lib'

In [8]:

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

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

Downloading...

File 'wish_ncaf_4_7.xys' from 'easyscience/diffraction-lib'

Create Experiment¶

In [9]:

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

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

Data loaded successfully

Experiment 🔬 'wish_5_6'. Number of data points: 4121

In [10]:

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

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

Data loaded successfully

Experiment 🔬 'wish_4_7'. Number of data points: 4043

Set Instrument¶

In [11]:

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

In [12]:

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¶

In [13]:

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

In [14]:

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¶

In [15]:

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_from_args(x=x, y=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_from_args(x=x, y=y)

Background type for experiment 'wish_5_6' changed to

line-segment

In [16]:

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_from_args(x=x, y=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_from_args(x=x, y=y)

Background type for experiment 'wish_4_7' changed to

line-segment

Set Linked Phases¶

In [17]:

expt56.linked_phases.add_from_args(id='ncaf', scale=1.0)

expt56.linked_phases.add_from_args(id='ncaf', scale=1.0)

In [18]:

expt47.linked_phases.add_from_args(id='ncaf', scale=2.0)

expt47.linked_phases.add_from_args(id='ncaf', scale=2.0)

Set Excluded Regions¶

In [19]:

expt56.excluded_regions.add_from_args(start=0, end=10010)
expt56.excluded_regions.add_from_args(start=100010, end=200000)

expt56.excluded_regions.add_from_args(start=0, end=10010) expt56.excluded_regions.add_from_args(start=100010, end=200000)

In [20]:

expt47.excluded_regions.add_from_args(start=0, end=10006)
expt47.excluded_regions.add_from_args(start=100004, end=200000)

expt47.excluded_regions.add_from_args(start=0, end=10006) expt47.excluded_regions.add_from_args(start=100004, end=200000)

Define Project¶

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

Create Project¶

In [21]:

project = Project()

project = Project()

Set Plotting Engine¶

In [22]:

project.plotter.engine = 'plotly'

project.plotter.engine = 'plotly'

Add Sample Model¶

In [23]:

project.sample_models.add(model)

project.sample_models.add(model)

Add Experiment¶

In [24]:

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¶

In [25]:

project.analysis.current_calculator = 'cryspy'

project.analysis.current_calculator = 'cryspy'

Current calculator changed to

cryspy

Set Minimizer¶

In [26]:

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

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

Current minimizer changed to

lmfit (leastsq)

Set Fit Mode¶

In [27]:

project.analysis.fit_mode = 'joint'

project.analysis.fit_mode = 'joint'

Current fit mode changed to

joint

Set Free Parameters¶

In [28]:

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

In [29]:

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¶

In [30]:

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)

In [31]:

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¶

In [32]:

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	1	47.53
2	24	15.57	67.2% ↓
3	109	15.49

🏆 Best goodness-of-fit (reduced χ²) is 15.49 at iteration 94

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 79.70 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_site	Ca	b_iso	0.9200	0.9340	0.0448	Ų	1.52 % ↑
2	ncaf	atom_site	Al	b_iso	0.7300	0.7330	0.0569	Ų	0.41 % ↑
3	ncaf	atom_site	Na	b_iso	2.0800	2.0474	0.1082	Ų	1.57 % ↓
4	ncaf	atom_site	F1	b_iso	0.9000	0.9389	0.0373	Ų	4.32 % ↑
5	ncaf	atom_site	F2	b_iso	1.3700	1.3442	0.0408	Ų	1.88 % ↓
6	ncaf	atom_site	F3	b_iso	0.8800	0.8481	0.0551	Ų	3.62 % ↓
7	wish_5_6	peak	None	gauss_sigma_2	15.5000	15.6543	0.7398	µs²/Ų	1.00 % ↑
8	wish_5_6	peak	None	mix_beta_0	0.0070	0.0067	0.0000	deg	4.54 % ↓
9	wish_5_6	peak	None	mix_beta_1	0.0100	0.0101	0.0002	deg	1.46 % ↑
10	wish_5_6	peak	None	asym_alpha_1	0.1000	0.1094	0.0012		9.43 % ↑
11	wish_5_6	linked_phases	ncaf	scale	1.0000	1.1029	0.0035		10.29 % ↑
12	wish_5_6	instrument	None	d_to_tof_offset	-13.5000	-13.6260	0.4257	µs	0.93 % ↑
13	wish_5_6	instrument	None	d_to_tof_linear	20773.0000	20773.0394	0.3051	µs/Å	0.00 % ↑
14	wish_4_7	peak	None	gauss_sigma_2	18.0000	18.2604	0.8685	µs²/Ų	1.45 % ↑
15	wish_4_7	peak	None	mix_beta_0	0.0060	0.0065	0.0000	deg	7.52 % ↑
16	wish_4_7	peak	None	mix_beta_1	0.0150	0.0148	0.0003	deg	1.38 % ↓
17	wish_4_7	peak	None	asym_alpha_1	0.1000	0.1222	0.0018		22.15 % ↑
18	wish_4_7	linked_phases	ncaf	scale	2.0000	2.5216	0.0077		26.08 % ↑
19	wish_4_7	instrument	None	d_to_tof_offset	-15.0000	-14.9768	0.5084	µs	0.15 % ↓
20	wish_4_7	instrument	None	d_to_tof_linear	18660.0000	18660.1028	0.3625	µs/Å	0.00 % ↑

Plot Measured vs Calculated¶

In [33]:

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)

In [34]:

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¶

In [35]:

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

	Parameter	Value
1	a	10.25026
2	b	10.25026
3	c	10.25026
4	alpha	90.00000
5	beta	90.00000
6	gamma	90.00000

Atom sites

	label	type	x	y	z	occ	Biso
1	Ca	Ca	0.46630	0.00000	0.25000	1.00000	0.93400
2	Al	Al	0.25210	0.25210	0.25210	1.00000	0.73301
3	Na	Na	0.08510	0.08510	0.08510	1.00000	2.04740
4	F1	F	0.13770	0.30540	0.11950	1.00000	0.93890
5	F2	F	0.36250	0.36330	0.18670	1.00000	1.34424
6	F3	F	0.46120	0.46120	0.46120	1.00000	0.84814

EXPERIMENTS
━━━━━━━━━━━

Experiment datablock

🔬 wish_5_6

Experiment type

SampleFormEnum.POWDER, RadiationProbeEnum.NEUTRON, time-of-flight

Profile type

PeakProfileTypeEnum.PSEUDO_VOIGT_IKEDA_CARPENTER

Experiment datablock

🔬 wish_4_7

Experiment type

SampleFormEnum.POWDER, RadiationProbeEnum.NEUTRON, time-of-flight

Profile type

PeakProfileTypeEnum.PSEUDO_VOIGT_IKEDA_CARPENTER

FITTING
━━━━━━━

Calculation engine

cryspy

Minimization engine

lmfit (leastsq)

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	15.49