Structure Refinement: Co2SiO4, D20¶

This example demonstrates a Rietveld refinement of Co2SiO4 crystal structure using constant wavelength neutron powder diffraction data from D20 at ILL.

Import Library¶

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from easydiffraction import ExperimentFactory
from easydiffraction import Project
from easydiffraction import StructureFactory
from easydiffraction import download_data
from easydiffraction import ExperimentFactory
from easydiffraction import Project
from easydiffraction import StructureFactory
from easydiffraction import download_data

Define Structure¶

This section shows how to add structures and modify their parameters.

Create Structure¶

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structure = StructureFactory.from_scratch(name='cosio')
structure = StructureFactory.from_scratch(name='cosio')

Set Space Group¶

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structure.space_group.name_h_m = 'P n m a'
structure.space_group.it_coordinate_system_code = 'abc'
structure.space_group.name_h_m = 'P n m a'
structure.space_group.it_coordinate_system_code = 'abc'

Set Unit Cell¶

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structure.cell.length_a = 10.3
structure.cell.length_b = 6.0
structure.cell.length_c = 4.8
structure.cell.length_a = 10.3
structure.cell.length_b = 6.0
structure.cell.length_c = 4.8

Set Atom Sites¶

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structure.atom_sites.create(
    label='Co1',
    type_symbol='Co',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='Co2',
    type_symbol='Co',
    fract_x=0.279,
    fract_y=0.25,
    fract_z=0.985,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='Si',
    type_symbol='Si',
    fract_x=0.094,
    fract_y=0.25,
    fract_z=0.429,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='O1',
    type_symbol='O',
    fract_x=0.091,
    fract_y=0.25,
    fract_z=0.771,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='O2',
    type_symbol='O',
    fract_x=0.448,
    fract_y=0.25,
    fract_z=0.217,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='O3',
    type_symbol='O',
    fract_x=0.164,
    fract_y=0.032,
    fract_z=0.28,
    wyckoff_letter='d',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='Co1',
    type_symbol='Co',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='Co2',
    type_symbol='Co',
    fract_x=0.279,
    fract_y=0.25,
    fract_z=0.985,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='Si',
    type_symbol='Si',
    fract_x=0.094,
    fract_y=0.25,
    fract_z=0.429,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='O1',
    type_symbol='O',
    fract_x=0.091,
    fract_y=0.25,
    fract_z=0.771,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='O2',
    type_symbol='O',
    fract_x=0.448,
    fract_y=0.25,
    fract_z=0.217,
    wyckoff_letter='c',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='O3',
    type_symbol='O',
    fract_x=0.164,
    fract_y=0.032,
    fract_z=0.28,
    wyckoff_letter='d',
    adp_iso=0.5,
)

Define Experiment¶

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

Download Measured Data¶

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data_path = download_data(id=12, destination='data')
data_path = download_data(id=12, destination='data')

Getting data...

Data #12: Co2SiO4, D20 (ILL)

✅ Data #12 downloaded to 'data/ed-12.xye'

Create Experiment¶

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expt = ExperimentFactory.from_data_path(name='d20', data_path=data_path)
expt = ExperimentFactory.from_data_path(name='d20', data_path=data_path)

Set Instrument¶

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expt.instrument.setup_wavelength = 1.87
expt.instrument.calib_twotheta_offset = 0.1
expt.instrument.setup_wavelength = 1.87
expt.instrument.calib_twotheta_offset = 0.1

Set Peak Profile¶

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expt.show_current_peak_profile_type()
expt.show_supported_peak_profile_types()
expt.peak_profile_type = 'pseudo-voigt + empirical asymmetry'
expt.peak.broad_gauss_u = 0.3
expt.peak.broad_gauss_v = -0.5
expt.peak.broad_gauss_w = 0.4
expt.show_current_peak_profile_type()
expt.show_supported_peak_profile_types()
expt.peak_profile_type = 'pseudo-voigt + empirical asymmetry'
expt.peak.broad_gauss_u = 0.3
expt.peak.broad_gauss_v = -0.5
expt.peak.broad_gauss_w = 0.4

Current peak profile type

pseudo-voigt

Supported types

	Type	Description
1	pseudo-voigt	Pseudo-Voigt profile
2	pseudo-voigt + empirical asymmetry	Pseudo-Voigt with empirical asymmetry correction

⚠️ Switching peak profile type discards existing peak parameters.

Peak profile type for experiment 'd20' changed to

pseudo-voigt + empirical asymmetry

Set Background¶

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expt.show_current_background_type()
expt.show_supported_background_types()
expt.background.create(id='1', x=8, y=500)
expt.background.create(id='2', x=9, y=500)
expt.background.create(id='3', x=10, y=500)
expt.background.create(id='4', x=11, y=500)
expt.background.create(id='5', x=12, y=500)
expt.background.create(id='6', x=15, y=500)
expt.background.create(id='7', x=25, y=500)
expt.background.create(id='8', x=30, y=500)
expt.background.create(id='9', x=50, y=500)
expt.background.create(id='10', x=70, y=500)
expt.background.create(id='11', x=90, y=500)
expt.background.create(id='12', x=110, y=500)
expt.background.create(id='13', x=130, y=500)
expt.background.create(id='14', x=150, y=500)
expt.show_current_background_type()
expt.show_supported_background_types()
expt.background.create(id='1', x=8, y=500)
expt.background.create(id='2', x=9, y=500)
expt.background.create(id='3', x=10, y=500)
expt.background.create(id='4', x=11, y=500)
expt.background.create(id='5', x=12, y=500)
expt.background.create(id='6', x=15, y=500)
expt.background.create(id='7', x=25, y=500)
expt.background.create(id='8', x=30, y=500)
expt.background.create(id='9', x=50, y=500)
expt.background.create(id='10', x=70, y=500)
expt.background.create(id='11', x=90, y=500)
expt.background.create(id='12', x=110, y=500)
expt.background.create(id='13', x=130, y=500)
expt.background.create(id='14', x=150, y=500)

Current background type

line-segment

Supported types

	Type	Description
1	chebyshev	Chebyshev polynomial background
2	line-segment	Linear interpolation between points

Set Linked Phases¶

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expt.linked_phases.create(id='cosio', scale=1.0)
expt.linked_phases.create(id='cosio', scale=1.0)

Define Project¶

The project object is used to manage the structure, experiment, and analysis.

Create Project¶

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project = Project()
project = Project()

Add Structure¶

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project.structures.add(structure)
project.structures.add(structure)

Add Experiment¶

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project.experiments.add(expt)
project.experiments.add(expt)

Perform Analysis¶

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

Plot Measured vs Calculated¶

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project.plotter.plot_meas_vs_calc(expt_name='d20', show_residual=True)
project.plotter.plot_meas_vs_calc(expt_name='d20', show_residual=True)

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project.plotter.plot_meas_vs_calc(expt_name='d20', x_min=41, x_max=54, show_residual=True)
project.plotter.plot_meas_vs_calc(expt_name='d20', x_min=41, x_max=54, show_residual=True)

Set Free Parameters¶

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structure.cell.length_a.free = True
structure.cell.length_b.free = True
structure.cell.length_c.free = True

structure.atom_sites['Co2'].fract_x.free = True
structure.atom_sites['Co2'].fract_z.free = True
structure.atom_sites['Si'].fract_x.free = True
structure.atom_sites['Si'].fract_z.free = True
structure.atom_sites['O1'].fract_x.free = True
structure.atom_sites['O1'].fract_z.free = True
structure.atom_sites['O2'].fract_x.free = True
structure.atom_sites['O2'].fract_z.free = True
structure.atom_sites['O3'].fract_x.free = True
structure.atom_sites['O3'].fract_y.free = True
structure.atom_sites['O3'].fract_z.free = True

structure.atom_sites['Co1'].adp_iso.free = True
structure.atom_sites['Co2'].adp_iso.free = True
structure.atom_sites['Si'].adp_iso.free = True
structure.atom_sites['O1'].adp_iso.free = True
structure.atom_sites['O2'].adp_iso.free = True
structure.atom_sites['O3'].adp_iso.free = True
structure.cell.length_a.free = True
structure.cell.length_b.free = True
structure.cell.length_c.free = True

structure.atom_sites['Co2'].fract_x.free = True
structure.atom_sites['Co2'].fract_z.free = True
structure.atom_sites['Si'].fract_x.free = True
structure.atom_sites['Si'].fract_z.free = True
structure.atom_sites['O1'].fract_x.free = True
structure.atom_sites['O1'].fract_z.free = True
structure.atom_sites['O2'].fract_x.free = True
structure.atom_sites['O2'].fract_z.free = True
structure.atom_sites['O3'].fract_x.free = True
structure.atom_sites['O3'].fract_y.free = True
structure.atom_sites['O3'].fract_z.free = True

structure.atom_sites['Co1'].adp_iso.free = True
structure.atom_sites['Co2'].adp_iso.free = True
structure.atom_sites['Si'].adp_iso.free = True
structure.atom_sites['O1'].adp_iso.free = True
structure.atom_sites['O2'].adp_iso.free = True
structure.atom_sites['O3'].adp_iso.free = True

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expt.linked_phases['cosio'].scale.free = True

expt.instrument.calib_twotheta_offset.free = True

expt.peak.broad_gauss_u.free = True
expt.peak.broad_gauss_v.free = True
expt.peak.broad_gauss_w.free = True
expt.peak.broad_lorentz_y.free = True

expt.peak.asym_empir_2.free = True

for point in expt.background:
    point.y.free = True
expt.linked_phases['cosio'].scale.free = True

expt.instrument.calib_twotheta_offset.free = True

expt.peak.broad_gauss_u.free = True
expt.peak.broad_gauss_v.free = True
expt.peak.broad_gauss_w.free = True
expt.peak.broad_lorentz_y.free = True

expt.peak.asym_empir_2.free = True

for point in expt.background:
    point.y.free = True

Set Constraints¶

Set aliases for parameters.

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project.analysis.aliases.create(
    label='biso_Co1',
    param=project.structures['cosio'].atom_sites['Co1'].adp_iso,
)
project.analysis.aliases.create(
    label='biso_Co2',
    param=project.structures['cosio'].atom_sites['Co2'].adp_iso,
)
project.analysis.aliases.create(
    label='biso_Co1',
    param=project.structures['cosio'].atom_sites['Co1'].adp_iso,
)
project.analysis.aliases.create(
    label='biso_Co2',
    param=project.structures['cosio'].atom_sites['Co2'].adp_iso,
)

Set constraints.

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project.analysis.constraints.create(expression='biso_Co2 = biso_Co1')
project.analysis.constraints.create(expression='biso_Co2 = biso_Co1')

Run Fitting¶

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

Standard fitting

📋 Using experiment 🔬 'd20' for 'single' fitting

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

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	423.51
2	44	73.62	82.6% ↓
3	85	38.63	47.5% ↓
4	127	18.79	51.4% ↓
5	168	15.79	16.0% ↓
6	209	10.43	34.0% ↓
7	250	7.95	23.8% ↓
8	291	4.82	39.4% ↓
9	332	4.50	6.6% ↓
10	538	4.50

🏆 Best goodness-of-fit (reduced χ²) is 4.50 at iteration 521

✅ Fitting complete.

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project.analysis.display.fit_results()
project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 30.19 seconds

📏 Goodness-of-fit (reduced χ²): 4.50

📏 R-factor (Rf): 3.02%

📏 R-factor squared (Rf²): 4.50%

📏 Weighted R-factor (wR): 4.82%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	cosio	cell		length_a	10.3000	10.3084	0.0003	Å	0.08 % ↑
2	cosio	cell		length_b	6.0000	6.0036	0.0002	Å	0.06 % ↑
3	cosio	cell		length_c	4.8000	4.7865	0.0001	Å	0.28 % ↓
4	cosio	atom_site	Co1	adp_iso	0.5000	0.2832	0.0795	Å²	43.37 % ↓
5	cosio	atom_site	Co2	fract_x	0.2790	0.2793	0.0007		0.11 % ↑
6	cosio	atom_site	Co2	fract_z	0.9850	0.9851	0.0014		0.01 % ↑
7	cosio	atom_site	Si	fract_x	0.0940	0.0936	0.0004		0.43 % ↓
8	cosio	atom_site	Si	fract_z	0.4290	0.4289	0.0008		0.01 % ↓
9	cosio	atom_site	Si	adp_iso	0.5000	0.3653	0.0622	Å²	26.93 % ↓
10	cosio	atom_site	O1	fract_x	0.0910	0.0911	0.0003		0.13 % ↑
11	cosio	atom_site	O1	fract_z	0.7710	0.7714	0.0006		0.05 % ↑
12	cosio	atom_site	O1	adp_iso	0.5000	0.6564	0.0577	Å²	31.29 % ↑
13	cosio	atom_site	O2	fract_x	0.4480	0.4482	0.0003		0.05 % ↑
14	cosio	atom_site	O2	fract_z	0.2170	0.2168	0.0007		0.08 % ↓
15	cosio	atom_site	O2	adp_iso	0.5000	0.5898	0.0578	Å²	17.96 % ↑
16	cosio	atom_site	O3	fract_x	0.1640	0.1636	0.0002		0.25 % ↓
17	cosio	atom_site	O3	fract_y	0.0320	0.0317	0.0003		1.09 % ↓
18	cosio	atom_site	O3	fract_z	0.2800	0.2801	0.0005		0.05 % ↑
19	cosio	atom_site	O3	adp_iso	0.5000	0.8357	0.0481	Å²	67.14 % ↑
20	d20	linked_phases	cosio	scale	1.0000	1.1971	0.0106		19.71 % ↑
21	d20	peak		asym_empir_2	0.0000	-0.0088	0.0019		N/A
22	d20	peak		broad_gauss_u	0.3000	0.2434	0.0067	deg²	18.85 % ↓
23	d20	peak		broad_gauss_v	-0.5000	-0.5316	0.0145	deg²	6.32 % ↑
24	d20	peak		broad_gauss_w	0.4000	0.3863	0.0090	deg²	3.43 % ↓
25	d20	peak		broad_lorentz_y	0.0000	0.0151	0.0044	deg	N/A
26	d20	instrument		twotheta_offset	0.1000	0.2766	0.0033	deg	176.58 % ↑
27	d20	background	1	y	500.0000	608.6687	14.4339		21.73 % ↑
28	d20	background	2	y	500.0000	580.6521	9.6559		16.13 % ↑
29	d20	background	3	y	500.0000	562.9262	9.1738		12.59 % ↑
30	d20	background	4	y	500.0000	540.3070	8.7047		8.06 % ↑
31	d20	background	5	y	500.0000	519.8761	6.0048		3.98 % ↑
32	d20	background	6	y	500.0000	507.3630	3.4588		1.47 % ↑
33	d20	background	7	y	500.0000	463.2907	3.1664		7.34 % ↓
34	d20	background	8	y	500.0000	434.2065	2.3727		13.16 % ↓
35	d20	background	9	y	500.0000	450.8811	2.2342		9.82 % ↓
36	d20	background	10	y	500.0000	430.4276	2.0102		13.91 % ↓
37	d20	background	11	y	500.0000	413.9130	2.2431		17.22 % ↓
38	d20	background	12	y	500.0000	361.4064	2.0763		27.72 % ↓
39	d20	background	13	y	500.0000	291.1902	1.9518		41.76 % ↓
40	d20	background	14	y	500.0000	238.9220	2.9516		52.22 % ↓

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project.plotter.plot_param_correlations()
project.plotter.plot_param_correlations()

Plot Measured vs Calculated¶

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project.plotter.plot_meas_vs_calc(expt_name='d20', show_residual=True)
project.plotter.plot_meas_vs_calc(expt_name='d20', show_residual=True)

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project.plotter.plot_meas_vs_calc(expt_name='d20', x_min=42, x_max=52, show_residual=True)
project.plotter.plot_meas_vs_calc(expt_name='d20', x_min=42, x_max=52, show_residual=True)

Perform Analysis (ADP aniso)¶

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for label in ('O1', 'O2', 'O3'):
    atom_site = structure.atom_sites[label]
    atom_site.occupancy.free = True
for label in ('O1', 'O2', 'O3'):
    atom_site = structure.atom_sites[label]
    atom_site.occupancy.free = True

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for label in ('O1', 'O2', 'O3'):
    atom_site = structure.atom_sites[label]
    atom_site.adp_type = 'Uani'
    atom_site_aniso = structure.atom_site_aniso[label]
    for component in ('adp_11', 'adp_22', 'adp_33', 'adp_12', 'adp_13', 'adp_23'):
        getattr(atom_site_aniso, component).free = True
for label in ('O1', 'O2', 'O3'):
    atom_site = structure.atom_sites[label]
    atom_site.adp_type = 'Uani'
    atom_site_aniso = structure.atom_site_aniso[label]
    for component in ('adp_11', 'adp_22', 'adp_33', 'adp_12', 'adp_13', 'adp_23'):
        getattr(atom_site_aniso, component).free = True

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structure.show_as_cif()
structure.show_as_cif()

Structure 🧩 'cosio' as cif

	CIF
1	data_cosio
2
3	_cell.length_a 10.30842232(28061)
4	_cell.length_b 6.00362684(16423)
5	_cell.length_c 4.78645786(13344)
6	_cell.angle_alpha 90.00000000
7	_cell.angle_beta 90.00000000
8	_cell.angle_gamma 90.00000000
9
10	_space_group.name_H-M_alt "P n m a"
11	_space_group.IT_coordinate_system_code abc
12
13	loop_
14	_atom_site.label
15	_atom_site.type_symbol
16	_atom_site.fract_x
17	_atom_site.fract_y
18	_atom_site.fract_z
19	_atom_site.Wyckoff_letter
20	_atom_site.occupancy
21	_atom_site.U_iso_or_equiv
22	_atom_site.adp_type
23	Co1 Co 0.00000000 0.00000000 0.00000000 a 1.00000000 0.00358633(7951018) Uiso
24	Co2 Co 0.27930486(68947) 0.25000000 0.98507511(144478) c 1.00000000 0.00358633 Uiso
25	Si Si 0.09359828(38646) 0.25000000 0.42894964(82698) c 1.00000000 0.00462694(6224821) Uiso
26	O1 O 0.09112237(29571) 0.25000000 0.77140447(64155) c 1.00000000() 0.00831378 Uani
27	O2 O 0.44824292(25137) 0.25000000 0.21682903(67726) c 1.00000000() 0.00747013 Uani
28	O3 O 0.16358488(22865) 0.03165250(32597) 0.28012709(48825) d 1.00000000() 0.01058419 Uani
29
30	loop_
31	_atom_site_aniso.label
32	_atom_site_aniso.U_11
33	_atom_site_aniso.U_22
34	_atom_site_aniso.U_33
35	_atom_site_aniso.U_12
36	_atom_site_aniso.U_13
37	_atom_site_aniso.U_23
38	Co1 ? ? ? ? ? ?
39	Co2 ? ? ? ? ? ?
40	Si ? ? ? ? ? ?
41	O1 0.00831378() 0.00831378() 0.00831378() 0.00000000 0.00000000() 0.00000000
42	O2 0.00747013() 0.00747013() 0.00747013() 0.00000000 0.00000000() 0.00000000
43	O3 0.01058419() 0.01058419() 0.01058419() 0.00000000() 0.00000000() 0.00000000()

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project.analysis.display.free_params()
project.analysis.display.free_params()

Free parameters for both structures (🧩 data blocks) and experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	cosio	cell		length_a	10.30842	0.00028	-inf	inf	Å
2	cosio	cell		length_b	6.00363	0.00016	-inf	inf	Å
3	cosio	cell		length_c	4.78646	0.00013	-inf	inf	Å
4	cosio	atom_site	Co1	adp_iso	0.00359	0.07951	-inf	inf	Å²
5	cosio	atom_site	Co2	fract_x	0.27930	0.00069	-inf	inf
6	cosio	atom_site	Co2	fract_z	0.98508	0.00144	-inf	inf
7	cosio	atom_site	Si	fract_x	0.09360	0.00039	-inf	inf
8	cosio	atom_site	Si	fract_z	0.42895	0.00083	-inf	inf
9	cosio	atom_site	Si	adp_iso	0.00463	0.06225	-inf	inf	Å²
10	cosio	atom_site	O1	fract_x	0.09112	0.00030	-inf	inf
11	cosio	atom_site	O1	fract_z	0.77140	0.00064	-inf	inf
12	cosio	atom_site	O1	occupancy	1.00000		-inf	inf
13	cosio	atom_site	O2	fract_x	0.44824	0.00025	-inf	inf
14	cosio	atom_site	O2	fract_z	0.21683	0.00068	-inf	inf
15	cosio	atom_site	O2	occupancy	1.00000		-inf	inf
16	cosio	atom_site	O3	fract_x	0.16358	0.00023	-inf	inf
17	cosio	atom_site	O3	fract_y	0.03165	0.00033	-inf	inf
18	cosio	atom_site	O3	fract_z	0.28013	0.00049	-inf	inf
19	cosio	atom_site	O3	occupancy	1.00000		-inf	inf
20	cosio	atom_site_aniso	O1	adp_11	0.00831		-inf	inf	Å²
21	cosio	atom_site_aniso	O1	adp_22	0.00831		-inf	inf	Å²
22	cosio	atom_site_aniso	O1	adp_33	0.00831		-inf	inf	Å²
23	cosio	atom_site_aniso	O1	adp_13	0.00000		-inf	inf	Å²
24	cosio	atom_site_aniso	O2	adp_11	0.00747		-inf	inf	Å²
25	cosio	atom_site_aniso	O2	adp_22	0.00747		-inf	inf	Å²
26	cosio	atom_site_aniso	O2	adp_33	0.00747		-inf	inf	Å²
27	cosio	atom_site_aniso	O2	adp_13	0.00000		-inf	inf	Å²
28	cosio	atom_site_aniso	O3	adp_11	0.01058		-inf	inf	Å²
29	cosio	atom_site_aniso	O3	adp_22	0.01058		-inf	inf	Å²
30	cosio	atom_site_aniso	O3	adp_33	0.01058		-inf	inf	Å²
31	cosio	atom_site_aniso	O3	adp_12	0.00000		-inf	inf	Å²
32	cosio	atom_site_aniso	O3	adp_13	0.00000		-inf	inf	Å²
33	cosio	atom_site_aniso	O3	adp_23	0.00000		-inf	inf	Å²
34	d20	linked_phases	cosio	scale	1.19706	0.01058	-inf	inf
35	d20	peak		asym_empir_2	-0.00882	0.00193	-inf	inf
36	d20	peak		broad_gauss_u	0.24345	0.00675	-inf	inf	deg²
37	d20	peak		broad_gauss_v	-0.53160	0.01450	-inf	inf	deg²
38	d20	peak		broad_gauss_w	0.38630	0.00904	-inf	inf	deg²
39	d20	peak		broad_lorentz_y	0.01507	0.00443	-inf	inf	deg
40	d20	instrument		twotheta_offset	0.27658	0.00330	-inf	inf	deg
41	d20	background	1	y	608.66872	14.43393	-inf	inf
42	d20	background	2	y	580.65214	9.65593	-inf	inf
43	d20	background	3	y	562.92616	9.17384	-inf	inf
44	d20	background	4	y	540.30697	8.70473	-inf	inf
45	d20	background	5	y	519.87613	6.00484	-inf	inf
46	d20	background	6	y	507.36298	3.45877	-inf	inf
47	d20	background	7	y	463.29072	3.16643	-inf	inf
48	d20	background	8	y	434.20649	2.37275	-inf	inf
49	d20	background	9	y	450.88113	2.23420	-inf	inf
50	d20	background	10	y	430.42758	2.01023	-inf	inf
51	d20	background	11	y	413.91300	2.24310	-inf	inf
52	d20	background	12	y	361.40638	2.07632	-inf	inf
53	d20	background	13	y	291.19017	1.95181	-inf	inf
54	d20	background	14	y	238.92197	2.95161	-inf	inf

In [31]:

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

Standard fitting

📋 Using experiment 🔬 'd20' for 'single' fitting

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

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	4.54
2	58	4.15	8.7% ↓
3	444	4.11

🏆 Best goodness-of-fit (reduced χ²) is 4.11 at iteration 443

✅ Fitting complete.

⚠️ Parameter 'cosio.atom_site_aniso.O1.adp_33' (-0.00334835) is below its physical lower limit (0.0).

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project.analysis.display.fit_results()
project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 32.39 seconds

📏 Goodness-of-fit (reduced χ²): 4.11

📏 R-factor (Rf): 2.91%

📏 R-factor squared (Rf²): 4.19%

📏 Weighted R-factor (wR): 4.42%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	cosio	cell		length_a	10.3084	10.3082	0.0003	Å	0.00 % ↓
2	cosio	cell		length_b	6.0036	6.0037	0.0002	Å	0.00 % ↑
3	cosio	cell		length_c	4.7865	4.7864	0.0001	Å	0.00 % ↓
4	cosio	atom_site	Co1	adp_iso	0.0036	0.0091	0.0014	Å²	154.56 % ↑
5	cosio	atom_site	Co2	fract_x	0.2793	0.2787	0.0007		0.21 % ↓
6	cosio	atom_site	Co2	fract_z	0.9851	0.9881	0.0015		0.30 % ↑
7	cosio	atom_site	Si	fract_x	0.0936	0.0945	0.0004		0.94 % ↑
8	cosio	atom_site	Si	fract_z	0.4289	0.4294	0.0008		0.11 % ↑
9	cosio	atom_site	Si	adp_iso	0.0046	0.0077	0.0012	Å²	65.59 % ↑
10	cosio	atom_site	O1	fract_x	0.0911	0.0905	0.0003		0.65 % ↓
11	cosio	atom_site	O1	fract_z	0.7714	0.7713	0.0006		0.02 % ↓
12	cosio	atom_site	O1	occupancy	1.0000	0.9142	0.0136		8.58 % ↓
13	cosio	atom_site	O2	fract_x	0.4482	0.4475	0.0003		0.17 % ↓
14	cosio	atom_site	O2	fract_z	0.2168	0.2170	0.0007		0.09 % ↑
15	cosio	atom_site	O2	occupancy	1.0000	0.9597	0.0133		4.03 % ↓
16	cosio	atom_site	O3	fract_x	0.1636	0.1631	0.0002		0.33 % ↓
17	cosio	atom_site	O3	fract_y	0.0317	0.0312	0.0003		1.57 % ↓
18	cosio	atom_site	O3	fract_z	0.2801	0.2816	0.0005		0.52 % ↑
19	cosio	atom_site	O3	occupancy	1.0000	0.9505	0.0116		4.95 % ↓
20	cosio	atom_site_aniso	O1	adp_11	0.0083	0.0088	0.0017	Å²	6.18 % ↑
21	cosio	atom_site_aniso	O1	adp_22	0.0083	0.0070	0.0016	Å²	15.30 % ↓
22	cosio	atom_site_aniso	O1	adp_33	0.0083	-0.0033	0.0021	Å²	140.27 % ↓
23	cosio	atom_site_aniso	O1	adp_13	0.0000	0.0053	0.0017	Å²	N/A
24	cosio	atom_site_aniso	O2	adp_11	0.0075	0.0053	0.0016	Å²	28.91 % ↓
25	cosio	atom_site_aniso	O2	adp_22	0.0075	0.0144	0.0016	Å²	93.17 % ↑
26	cosio	atom_site_aniso	O2	adp_33	0.0075	0.0028	0.0020	Å²	63.03 % ↓
27	cosio	atom_site_aniso	O2	adp_13	0.0000	0.0030	0.0013	Å²	N/A
28	cosio	atom_site_aniso	O3	adp_11	0.0106	0.0123	0.0013	Å²	16.63 % ↑
29	cosio	atom_site_aniso	O3	adp_22	0.0106	0.0068	0.0012	Å²	36.07 % ↓
30	cosio	atom_site_aniso	O3	adp_33	0.0106	0.0106	0.0014	Å²	0.43 % ↑
31	cosio	atom_site_aniso	O3	adp_12	0.0000	0.0008	0.0010	Å²	N/A
32	cosio	atom_site_aniso	O3	adp_13	0.0000	0.0014	0.0010	Å²	N/A
33	cosio	atom_site_aniso	O3	adp_23	0.0000	-0.0041	0.0012	Å²	N/A
34	d20	linked_phases	cosio	scale	1.1971	1.3271	0.0284		10.86 % ↑
35	d20	peak		asym_empir_2	-0.0088	-0.0093	0.0019		5.16 % ↑
36	d20	peak		broad_gauss_u	0.2434	0.2342	0.0065	deg²	3.78 % ↓
37	d20	peak		broad_gauss_v	-0.5316	-0.5110	0.0140	deg²	3.87 % ↓
38	d20	peak		broad_gauss_w	0.3863	0.3743	0.0087	deg²	3.11 % ↓
39	d20	peak		broad_lorentz_y	0.0151	0.0192	0.0043	deg	27.09 % ↑
40	d20	instrument		twotheta_offset	0.2766	0.2754	0.0032	deg	0.41 % ↓
41	d20	background	1	y	608.6687	608.4816	13.8046		0.03 % ↓
42	d20	background	2	y	580.6521	580.4996	9.2349		0.03 % ↓
43	d20	background	3	y	562.9262	562.7937	8.7739		0.02 % ↓
44	d20	background	4	y	540.3070	540.2054	8.3252		0.02 % ↓
45	d20	background	5	y	519.8761	519.7378	5.7433		0.03 % ↓
46	d20	background	6	y	507.3630	507.3920	3.3119		0.01 % ↑
47	d20	background	7	y	463.2907	462.3284	3.0496		0.21 % ↓
48	d20	background	8	y	434.2065	432.0829	2.3596		0.49 % ↓
49	d20	background	9	y	450.8811	451.2529	2.1642		0.08 % ↑
50	d20	background	10	y	430.4276	428.4964	1.9493		0.45 % ↓
51	d20	background	11	y	413.9130	410.1342	2.2316		0.91 % ↓
52	d20	background	12	y	361.4064	355.9475	2.1734		1.51 % ↓
53	d20	background	13	y	291.1902	292.3257	1.9417		0.39 % ↑
54	d20	background	14	y	238.9220	249.3180	3.0347		4.35 % ↑

⚠️ Red fitted value: outside expected physical limits (consider adding constraints)

⚠️ Red uncertainty: exceeds the fitted value (consider adding constraints)

In [33]:

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project.plotter.plot_param_correlations()
project.plotter.plot_param_correlations()

In [34]:

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project.plotter.plot_meas_vs_calc(expt_name='d20', show_residual=True)
project.plotter.plot_meas_vs_calc(expt_name='d20', show_residual=True)

In [35]:

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project.plotter.plot_meas_vs_calc(expt_name='d20', x_min=42, x_max=52, show_residual=True)
project.plotter.plot_meas_vs_calc(expt_name='d20', x_min=42, x_max=52, show_residual=True)

In [36]:

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structure.show_as_cif()
structure.show_as_cif()

Structure 🧩 'cosio' as cif

	CIF
1	data_cosio
2
3	_cell.length_a 10.30818445(28090)
4	_cell.length_b 6.00366390(16124)
5	_cell.length_c 4.78642176(12809)
6	_cell.angle_alpha 90.00000000
7	_cell.angle_beta 90.00000000
8	_cell.angle_gamma 90.00000000
9
10	_space_group.name_H-M_alt "P n m a"
11	_space_group.IT_coordinate_system_code abc
12
13	loop_
14	_atom_site.label
15	_atom_site.type_symbol
16	_atom_site.fract_x
17	_atom_site.fract_y
18	_atom_site.fract_z
19	_atom_site.Wyckoff_letter
20	_atom_site.occupancy
21	_atom_site.U_iso_or_equiv
22	_atom_site.adp_type
23	Co1 Co 0.00000000 0.00000000 0.00000000 a 1.00000000 0.00912929(141124) Uiso
24	Co2 Co 0.27871933(71268) 0.25000000 0.98807812(151327) c 1.00000000 0.00912929 Uiso
25	Si Si 0.09447953(39330) 0.25000000 0.42943797(80938) c 1.00000000 0.00766171(117633) Uiso
26	O1 O 0.09052637(30161) 0.25000000 0.77125812(61367) c 0.91421444(1359209) 0.00417369 Uani
27	O2 O 0.44746798(26342) 0.25000000 0.21702885(66468) c 0.95968887(1325764) 0.00750094 Uani
28	O3 O 0.16305125(22544) 0.03115682(33663) 0.28159153(48958) d 0.95053728(1161225) 0.00991363 Uani
29
30	loop_
31	_atom_site_aniso.label
32	_atom_site_aniso.U_11
33	_atom_site_aniso.U_22
34	_atom_site_aniso.U_33
35	_atom_site_aniso.U_12
36	_atom_site_aniso.U_13
37	_atom_site_aniso.U_23
38	Co1 ? ? ? ? ? ?
39	Co2 ? ? ? ? ? ?
40	Si ? ? ? ? ? ?
41	O1 0.00882757(166530) 0.00704186(160366) -0.00334835(207383) 0.00000000 0.00528321(173289) 0.00000000
42	O2 0.00531076(158344) 0.01443034(163140) 0.00276172(195302) 0.00000000 0.00296717(130017) 0.00000000
43	O3 0.01234440(131286) 0.00676666(115951) 0.01062983(136916) 0.00082005(95937) 0.00137755(104719) -0.00410052(122531)

Summary¶

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

Show Project Summary¶

In [37]:

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

————————————
PROJECT INFO
————————————

Title

Untitled Project

—————————————————————
CRYSTALLOGRAPHIC DATA
—————————————————————

Phase datablock

🧩 cosio

Space group

P n m a

	Parameter	Value	Uncertainty
1	a	10.30818445	0.00028090
2	b	10.30818445	0.00028090
3	c	10.30818445	0.00028090
4	α	90.00000000
5	β	90.00000000
6	γ	90.00000000

Atom sites

	label	type	x	y	z	occ	Biso
1	Co1	Co	0.00000000	0.00000000	0.00000000	1.00000000	0.00912929
2	Co2	Co	0.27871933	0.25000000	0.98807812	1.00000000	0.00912929
3	Si	Si	0.09447953	0.25000000	0.42943797	1.00000000	0.00766171
4	O1	O	0.09052637	0.25000000	0.77125812	0.91421444	0.00417369
5	O2	O	0.44746798	0.25000000	0.21702885	0.95968887	0.00750094
6	O3	O	0.16305125	0.03115682	0.28159153	0.95053728	0.00991363

———————————
EXPERIMENTS
———————————

Experiment datablock

🔬 d20

Experiment type

powder, neutron, constant wavelength bragg

Calculation engine

cryspy

Wavelength

1.87000

2θ offset

0.27544

Profile type

pseudo-voigt + empirical asymmetry

Peak broadening (Gaussian)

	Parameter	Value	Uncertainty
1	U	0.23424314	0.00646947
2	V	-0.51103015	0.01397355
3	W	0.37428983	0.00872317

Peak broadening (Lorentzian)

	Parameter	Value	Uncertainty
1	X	0.00000000
2	Y	0.01915666	0.00431367

Asymmetry (Empirical)

	Parameter	Value	Uncertainty
1	p1	0.00000000
2	p2	-0.00927290	0.00187080
3	p3	0.00000000
4	p4	0.00000000

———————
FITTING
———————

Minimization engine

lmfit (leastsq)

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	4.11