Structure Refinement: LBCO, HRPT¶

This example demonstrates how to use the EasyDiffraction API in a simplified, user-friendly manner that closely follows the GUI workflow for a Rietveld refinement of La0.5Ba0.5CoO3 crystal structure using constant wavelength neutron powder diffraction data from HRPT at PSI.

It is intended for users with minimal programming experience who want to learn how to perform standard crystal structure fitting using diffraction data. This script covers creating a project, adding sample models and experiments, performing analysis, and refining parameters.

Only a single import of easydiffraction is required, and all operations are performed through high-level components of the project object, such as project.sample_models, project.experiments, and project.analysis. The project object is the main container for all information.

Import Library¶

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import easydiffraction as ed
import easydiffraction as ed

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

Step 1: Create a Project¶

This section explains how to create a project and define its metadata.

Create Project¶

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project = ed.Project(name='lbco_hrpt')
project = ed.Project(name='lbco_hrpt')

Set Project Metadata¶

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project.info.title = 'La0.5Ba0.5CoO3 at HRPT@PSI'
project.info.description = """This project demonstrates a standard
refinement of La0.5Ba0.5CoO3, which crystallizes in a perovskite-type
structure, using neutron powder diffraction data collected in constant
wavelength mode at the HRPT diffractometer (PSI)."""
project.info.title = 'La0.5Ba0.5CoO3 at HRPT@PSI'
project.info.description = """This project demonstrates a standard
refinement of La0.5Ba0.5CoO3, which crystallizes in a perovskite-type
structure, using neutron powder diffraction data collected in constant
wavelength mode at the HRPT diffractometer (PSI)."""

Show Project Metadata as CIF¶

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project.info.show_as_cif()
project.info.show_as_cif()

Project 📦 'lbco_hrpt' info as cif

_project.id lbco_hrpt

_project.title 'La0.5Ba0.5CoO3 at HRPT@PSI'

_project.description 'This project demonstrates a standard

refinement of La0.5Ba0.5CoO3, which

crystallizes in a perovskite-type structure,

using neutron powder diffraction data

collected in constant wavelength mode at the

HRPT diffractometer (PSI).'

_project.created '14 Aug 2025 13:26:19'

_project.last_modified '14 Aug 2025 13:26:19'

Save Project¶

When saving the project for the first time, you need to specify the directory path. In the example below, the project is saved to a temporary location defined by the system.

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project.save_as(dir_path='lbco_hrpt', temporary=True)
project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt
✅ project.cif
✅ analysis.cif
✅ summary.cif

Set Up Data Plotter¶

Show supported plotting engines.

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project.plotter.show_supported_engines()
project.plotter.show_supported_engines()

Supported plotter engines

Engine	Description
asciichartpy	Console ASCII line charts
plotly	Interactive browser-based graphing library

Show current plotting configuration.

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project.plotter.show_config()
project.plotter.show_config()

Current plotter configuration

Parameter	Value
Plotting engine	plotly
x-axis limits	[-inf, inf]
Chart height	9

Set plotting engine.

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

Current plotter changed to
plotly

Step 2: Define Sample Model¶

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

Add Sample Model¶

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project.sample_models.add(name='lbco')
project.sample_models.add(name='lbco')

Show Defined Sample Models¶

Show the names of the models added. These names are used to access the model using the syntax: project.sample_models['model_name']. All model parameters can be accessed via the project object.

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project.sample_models.show_names()
project.sample_models.show_names()

Defined sample models 🧩
['lbco']

Set Space Group¶

Modify the default space group parameters.

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project.sample_models['lbco'].space_group.name_h_m = 'P m -3 m'
project.sample_models['lbco'].space_group.it_coordinate_system_code = '1'
project.sample_models['lbco'].space_group.name_h_m = 'P m -3 m'
project.sample_models['lbco'].space_group.it_coordinate_system_code = '1'

Set Unit Cell¶

Modify the default unit cell parameters.

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project.sample_models['lbco'].cell.length_a = 3.88
project.sample_models['lbco'].cell.length_a = 3.88

Set Atom Sites¶

Add atom sites to the sample model.

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project.sample_models['lbco'].atom_sites.add(
    label='La',
    type_symbol='La',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    b_iso=0.5,
    occupancy=0.5,
)
project.sample_models['lbco'].atom_sites.add(
    label='Ba',
    type_symbol='Ba',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    b_iso=0.5,
    occupancy=0.5,
)
project.sample_models['lbco'].atom_sites.add(
    label='Co',
    type_symbol='Co',
    fract_x=0.5,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='b',
    b_iso=0.5,
)
project.sample_models['lbco'].atom_sites.add(
    label='O',
    type_symbol='O',
    fract_x=0,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='c',
    b_iso=0.5,
)
project.sample_models['lbco'].atom_sites.add(
    label='La',
    type_symbol='La',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    b_iso=0.5,
    occupancy=0.5,
)
project.sample_models['lbco'].atom_sites.add(
    label='Ba',
    type_symbol='Ba',
    fract_x=0,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='a',
    b_iso=0.5,
    occupancy=0.5,
)
project.sample_models['lbco'].atom_sites.add(
    label='Co',
    type_symbol='Co',
    fract_x=0.5,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='b',
    b_iso=0.5,
)
project.sample_models['lbco'].atom_sites.add(
    label='O',
    type_symbol='O',
    fract_x=0,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='c',
    b_iso=0.5,
)

Apply Symmetry Constraints¶

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project.sample_models['lbco'].apply_symmetry_constraints()
project.sample_models['lbco'].apply_symmetry_constraints()

Show Sample Model as CIF¶

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project.sample_models['lbco'].show_as_cif()
project.sample_models['lbco'].show_as_cif()

Sample model 🧩 'lbco' as cif

data_lbco

_space_group.IT_coordinate_system_code 1

_space_group.name_H-M_alt "P m -3 m"

_cell.angle_alpha 90

_cell.angle_beta 90

_cell.angle_gamma 90

_cell.length_a 3.88

_cell.length_b 3.88

_cell.length_c 3.88

loop_

_atom_site.ADP_type

_atom_site.B_iso_or_equiv

_atom_site.fract_x

_atom_site.fract_y

_atom_site.fract_z

_atom_site.label

_atom_site.occupancy

_atom_site.type_symbol

_atom_site.Wyckoff_letter

Biso 0.5 0.0 0.0 0.0 La 0.5 La a

Biso 0.5 0.0 0.0 0.0 Ba 0.5 Ba a

Biso 0.5 0.5 0.5 0.5 Co 1.0 Co b

Biso 0.5 0.0 0.5 0.5 O 1.0 O c

Show Sample Model Structure¶

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project.sample_models['lbco'].show_structure()
project.sample_models['lbco'].show_structure()

Sample model 🧩 'lbco' structure view
Not implemented yet.

Save Project State¶

Save the project state after adding the sample model. This ensures that all changes are stored and can be accessed later. The project state is saved in the directory specified during project creation.

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project.save()
project.save()

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt
✅ project.cif
✅ sample_models/lbco.cif
✅ analysis.cif
✅ summary.cif

Step 3: 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¶

Download the data file from the EasyDiffraction repository on GitHub.

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ed.download_from_repository('hrpt_lbco.xye', destination='data')
ed.download_from_repository('hrpt_lbco.xye', destination='data')

⚠️ Warning
File 'data/hrpt_lbco.xye' already exists and will not be overwritten.

Add Diffraction Experiment¶

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project.experiments.add(
    name='hrpt',
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
    data_path='data/hrpt_lbco.xye',
)
project.experiments.add(
    name='hrpt',
    sample_form='powder',
    beam_mode='constant wavelength',
    radiation_probe='neutron',
    data_path='data/hrpt_lbco.xye',
)

Loading measured data from ASCII file
/Users/runner/work/diffraction-lib/diffraction-lib/docs/tutorials/data/hrpt_lbco.xye

Data loaded successfully
Experiment 🔬 'hrpt'. Number of data points: 3098

Show Defined Experiments¶

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project.experiments.show_names()
project.experiments.show_names()

Defined experiments 🔬
['hrpt']

Show Measured Data¶

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project.plot_meas(expt_name='hrpt')
project.plot_meas(expt_name='hrpt')

Set Instrument¶

Modify the default instrument parameters.

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project.experiments['hrpt'].instrument.setup_wavelength = 1.494
project.experiments['hrpt'].instrument.calib_twotheta_offset = 0.6
project.experiments['hrpt'].instrument.setup_wavelength = 1.494
project.experiments['hrpt'].instrument.calib_twotheta_offset = 0.6

Set Peak Profile¶

Show supported peak profile types.

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project.experiments['hrpt'].show_supported_peak_profile_types()
project.experiments['hrpt'].show_supported_peak_profile_types()

Supported peak profile types

Peak profile type	Description
pseudo-voigt	Pseudo-Voigt profile
split pseudo-voigt	Split pseudo-Voigt profile
thompson-cox-hastings	Thompson-Cox-Hastings profile

Show the current peak profile type.

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project.experiments['hrpt'].show_current_peak_profile_type()
project.experiments['hrpt'].show_current_peak_profile_type()

Current peak profile type
pseudo-voigt

Select the desired peak profile type.

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project.experiments['hrpt'].peak_profile_type = 'pseudo-voigt'
project.experiments['hrpt'].peak_profile_type = 'pseudo-voigt'

Peak profile type for experiment 'hrpt' changed to
pseudo-voigt

Modify default peak profile parameters.

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project.experiments['hrpt'].peak.broad_gauss_u = 0.1
project.experiments['hrpt'].peak.broad_gauss_v = -0.1
project.experiments['hrpt'].peak.broad_gauss_w = 0.1
project.experiments['hrpt'].peak.broad_lorentz_x = 0
project.experiments['hrpt'].peak.broad_lorentz_y = 0.1
project.experiments['hrpt'].peak.broad_gauss_u = 0.1
project.experiments['hrpt'].peak.broad_gauss_v = -0.1
project.experiments['hrpt'].peak.broad_gauss_w = 0.1
project.experiments['hrpt'].peak.broad_lorentz_x = 0
project.experiments['hrpt'].peak.broad_lorentz_y = 0.1

Set Background¶

Show supported background types.

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project.experiments['hrpt'].show_supported_background_types()
project.experiments['hrpt'].show_supported_background_types()

Supported background types

Background type	Description
line-segment	Linear interpolation between points
chebyshev polynomial	Chebyshev polynomial background

Show current background type.

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project.experiments['hrpt'].show_current_background_type()
project.experiments['hrpt'].show_current_background_type()

Current background type
line-segment

Select the desired background type.

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project.experiments['hrpt'].background_type = 'line-segment'
project.experiments['hrpt'].background_type = 'line-segment'

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

Add background points.

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project.experiments['hrpt'].background.add(x=10, y=170)
project.experiments['hrpt'].background.add(x=30, y=170)
project.experiments['hrpt'].background.add(x=50, y=170)
project.experiments['hrpt'].background.add(x=110, y=170)
project.experiments['hrpt'].background.add(x=165, y=170)
project.experiments['hrpt'].background.add(x=10, y=170)
project.experiments['hrpt'].background.add(x=30, y=170)
project.experiments['hrpt'].background.add(x=50, y=170)
project.experiments['hrpt'].background.add(x=110, y=170)
project.experiments['hrpt'].background.add(x=165, y=170)

Show current background points.

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project.experiments['hrpt'].background.show()
project.experiments['hrpt'].background.show()

Line-segment background points

X	Intensity
10	170
30	170
50	170
110	170
165	170

Set Linked Phases¶

Link the sample model defined in the previous step to the experiment.

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project.experiments['hrpt'].linked_phases.add(id='lbco', scale=10.0)
project.experiments['hrpt'].linked_phases.add(id='lbco', scale=10.0)

Show Experiment as CIF¶

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project.experiments['hrpt'].show_as_cif()
project.experiments['hrpt'].show_as_cif()

Experiment 🔬 'hrpt' as cif

data_hrpt

_expt_type.beam_mode "constant wavelength"
_expt_type.radiation_probe neutron
_expt_type.sample_form powder
_expt_type.scattering_type bragg

_instr.2theta_offset 0.6
_instr.wavelength 1.494

_peak.broad_gauss_u 0.1
_peak.broad_gauss_v -0.1
_peak.broad_gauss_w 0.1
_peak.broad_lorentz_x 0
_peak.broad_lorentz_y 0.1

loop_
_pd_phase_block.id
_pd_phase_block.scale
lbco 10.0

loop_
_pd_background.line_segment_X
_pd_background.line_segment_intensity
10 170
30 170
50 170
110 170
165 170

loop_
_pd_meas.2theta_scan
_pd_meas.intensity_total
_pd_meas.intensity_total_su
10.0 167.0 12.6
10.05 157.0 12.5
10.1 187.0 13.3
10.15 197.0 14.0
10.2 164.0 12.5
...
164.65 173.0 30.1
164.7 187.0 27.9
164.75 175.0 38.2
164.8 168.0 30.9
164.85 109.0 41.2

Save Project State¶

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project.save()
project.save()

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt

✅ project.cif
✅ sample_models/lbco.cif
✅ experiments/hrpt.cif
✅ analysis.cif
✅ summary.cif

Step 4: Perform Analysis¶

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

Set Calculator¶

Show supported calculation engines.

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project.analysis.show_supported_calculators()
project.analysis.show_supported_calculators()

Supported calculators

Calculator	Description
cryspy	CrysPy library for crystallographic calculations
pdffit	PDFfit2 library for pair distribution function calculations

Show current calculation engine.

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project.analysis.show_current_calculator()
project.analysis.show_current_calculator()

Current calculator
cryspy

Select the desired calculation engine.

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

Current calculator changed to
cryspy

Show Calculated Data¶

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project.plot_calc(expt_name='hrpt')
project.plot_calc(expt_name='hrpt')

Plot Measured vs Calculated¶

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

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project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)
project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)

Show Parameters¶

Show all parameters of the project.

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project.analysis.show_all_params()
project.analysis.show_all_params()

All parameters for all sample models (🧩 data blocks)

	datablock	category	entry	parameter	value	fittable
1	lbco	atom_sites	La	adp_type	Biso	False
2	lbco	atom_sites	La	b_iso	0.5000	True
3	lbco	atom_sites	La	fract_x	0.0000	True
4	lbco	atom_sites	La	fract_y	0.0000	True
5	lbco	atom_sites	La	fract_z	0.0000	True
6	lbco	atom_sites	La	label	La	False
7	lbco	atom_sites	La	occupancy	0.5000	True
8	lbco	atom_sites	La	type_symbol	La	False
9	lbco	atom_sites	La	wyckoff_letter	a	False
10	lbco	atom_sites	Ba	adp_type	Biso	False
11	lbco	atom_sites	Ba	b_iso	0.5000	True
12	lbco	atom_sites	Ba	fract_x	0.0000	True
13	lbco	atom_sites	Ba	fract_y	0.0000	True
14	lbco	atom_sites	Ba	fract_z	0.0000	True
15	lbco	atom_sites	Ba	label	Ba	False
16	lbco	atom_sites	Ba	occupancy	0.5000	True
17	lbco	atom_sites	Ba	type_symbol	Ba	False
18	lbco	atom_sites	Ba	wyckoff_letter	a	False
19	lbco	atom_sites	Co	adp_type	Biso	False
20	lbco	atom_sites	Co	b_iso	0.5000	True
21	lbco	atom_sites	Co	fract_x	0.5000	True
22	lbco	atom_sites	Co	fract_y	0.5000	True
23	lbco	atom_sites	Co	fract_z	0.5000	True
24	lbco	atom_sites	Co	label	Co	False
25	lbco	atom_sites	Co	occupancy	1.0000	True
26	lbco	atom_sites	Co	type_symbol	Co	False
27	lbco	atom_sites	Co	wyckoff_letter	b	False
28	lbco	atom_sites	O	adp_type	Biso	False
29	lbco	atom_sites	O	b_iso	0.5000	True
30	lbco	atom_sites	O	fract_x	0.0000	True
31	lbco	atom_sites	O	fract_y	0.5000	True
32	lbco	atom_sites	O	fract_z	0.5000	True
33	lbco	atom_sites	O	label	O	False
34	lbco	atom_sites	O	occupancy	1.0000	True
35	lbco	atom_sites	O	type_symbol	O	False
36	lbco	atom_sites	O	wyckoff_letter	c	False
37	lbco	cell		angle_alpha	90.0000	True
38	lbco	cell		angle_beta	90.0000	True
39	lbco	cell		angle_gamma	90.0000	True
40	lbco	cell		length_a	3.8800	True
41	lbco	cell		length_b	3.8800	True
42	lbco	cell		length_c	3.8800	True
43	lbco	space_group		it_coordinate_system_code	1	False
44	lbco	space_group		name_h_m	P m -3 m	False

All parameters for all experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	fittable
1	hrpt	background	10	x	10	False
2	hrpt	background	10	y	170.0000	True
3	hrpt	background	30	x	30	False
4	hrpt	background	30	y	170.0000	True
5	hrpt	background	50	x	50	False
6	hrpt	background	50	y	170.0000	True
7	hrpt	background	110	x	110	False
8	hrpt	background	110	y	170.0000	True
9	hrpt	background	165	x	165	False
10	hrpt	background	165	y	170.0000	True
11	hrpt	instrument		twotheta_offset	0.6000	True
12	hrpt	instrument		wavelength	1.4940	True
13	hrpt	linked_phases	lbco	id	lbco	False
14	hrpt	linked_phases	lbco	scale	10.0000	True
15	hrpt	peak		broad_gauss_u	0.1000	True
16	hrpt	peak		broad_gauss_v	-0.1000	True
17	hrpt	peak		broad_gauss_w	0.1000	True
18	hrpt	peak		broad_lorentz_x	0.0000	True
19	hrpt	peak		broad_lorentz_y	0.1000	True
20	hrpt	expt_type		beam_mode	constant wavelength	False
21	hrpt	expt_type		radiation_probe	neutron	False
22	hrpt	expt_type		sample_form	powder	False
23	hrpt	expt_type		scattering_type	bragg	False

Show all fittable parameters.

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project.analysis.show_fittable_params()
project.analysis.show_fittable_params()

Fittable parameters for all sample models (🧩 data blocks)

	datablock	category	entry	parameter	value	units	free
1	lbco	atom_sites	La	b_iso	0.5000	Å²	False
2	lbco	atom_sites	La	fract_x	0.0000		False
3	lbco	atom_sites	La	fract_y	0.0000		False
4	lbco	atom_sites	La	fract_z	0.0000		False
5	lbco	atom_sites	La	occupancy	0.5000		False
6	lbco	atom_sites	Ba	b_iso	0.5000	Å²	False
7	lbco	atom_sites	Ba	fract_x	0.0000		False
8	lbco	atom_sites	Ba	fract_y	0.0000		False
9	lbco	atom_sites	Ba	fract_z	0.0000		False
10	lbco	atom_sites	Ba	occupancy	0.5000		False
11	lbco	atom_sites	Co	b_iso	0.5000	Å²	False
12	lbco	atom_sites	Co	fract_x	0.5000		False
13	lbco	atom_sites	Co	fract_y	0.5000		False
14	lbco	atom_sites	Co	fract_z	0.5000		False
15	lbco	atom_sites	Co	occupancy	1.0000		False
16	lbco	atom_sites	O	b_iso	0.5000	Å²	False
17	lbco	atom_sites	O	fract_x	0.0000		False
18	lbco	atom_sites	O	fract_y	0.5000		False
19	lbco	atom_sites	O	fract_z	0.5000		False
20	lbco	atom_sites	O	occupancy	1.0000		False
21	lbco	cell		angle_alpha	90.0000	deg	False
22	lbco	cell		angle_beta	90.0000	deg	False
23	lbco	cell		angle_gamma	90.0000	deg	False
24	lbco	cell		length_a	3.8800	Å	False
25	lbco	cell		length_b	3.8800	Å	False
26	lbco	cell		length_c	3.8800	Å	False

Fittable parameters for all experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	units	free
1	hrpt	background	10	y	170.0000		False
2	hrpt	background	30	y	170.0000		False
3	hrpt	background	50	y	170.0000		False
4	hrpt	background	110	y	170.0000		False
5	hrpt	background	165	y	170.0000		False
6	hrpt	instrument		twotheta_offset	0.6000	deg	False
7	hrpt	instrument		wavelength	1.4940	Å	False
8	hrpt	linked_phases	lbco	scale	10.0000		False
9	hrpt	peak		broad_gauss_u	0.1000	deg²	False
10	hrpt	peak		broad_gauss_v	-0.1000	deg²	False
11	hrpt	peak		broad_gauss_w	0.1000	deg²	False
12	hrpt	peak		broad_lorentz_x	0.0000	deg	False
13	hrpt	peak		broad_lorentz_y	0.1000	deg	False

Show only free parameters.

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project.analysis.show_free_params()
project.analysis.show_free_params()

⚠️ Warning
No free parameters found.

Show how to access parameters in the code.

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project.analysis.how_to_access_parameters()
project.analysis.how_to_access_parameters()

How to access parameters

	datablock	category	entry	parameter	How to Access in Python Code	Unique Identifier for CIF Constraints
1	lbco	atom_sites	La	adp_type	project.sample_models['lbco'].atom_sites['La'].adp_type	lbco.atom_site.La.ADP_type
2	lbco	atom_sites	La	b_iso	project.sample_models['lbco'].atom_sites['La'].b_iso	lbco.atom_site.La.B_iso_or_equiv
3	lbco	atom_sites	La	fract_x	project.sample_models['lbco'].atom_sites['La'].fract_x	lbco.atom_site.La.fract_x
4	lbco	atom_sites	La	fract_y	project.sample_models['lbco'].atom_sites['La'].fract_y	lbco.atom_site.La.fract_y
5	lbco	atom_sites	La	fract_z	project.sample_models['lbco'].atom_sites['La'].fract_z	lbco.atom_site.La.fract_z
6	lbco	atom_sites	La	label	project.sample_models['lbco'].atom_sites['La'].label	lbco.atom_site.La.label
7	lbco	atom_sites	La	occupancy	project.sample_models['lbco'].atom_sites['La'].occupancy	lbco.atom_site.La.occupancy
8	lbco	atom_sites	La	type_symbol	project.sample_models['lbco'].atom_sites['La'].type_symbol	lbco.atom_site.La.type_symbol
9	lbco	atom_sites	La	wyckoff_letter	project.sample_models['lbco'].atom_sites['La'].wyckoff_letter	lbco.atom_site.La.Wyckoff_letter
10	lbco	atom_sites	Ba	adp_type	project.sample_models['lbco'].atom_sites['Ba'].adp_type	lbco.atom_site.Ba.ADP_type
11	lbco	atom_sites	Ba	b_iso	project.sample_models['lbco'].atom_sites['Ba'].b_iso	lbco.atom_site.Ba.B_iso_or_equiv
12	lbco	atom_sites	Ba	fract_x	project.sample_models['lbco'].atom_sites['Ba'].fract_x	lbco.atom_site.Ba.fract_x
13	lbco	atom_sites	Ba	fract_y	project.sample_models['lbco'].atom_sites['Ba'].fract_y	lbco.atom_site.Ba.fract_y
14	lbco	atom_sites	Ba	fract_z	project.sample_models['lbco'].atom_sites['Ba'].fract_z	lbco.atom_site.Ba.fract_z
15	lbco	atom_sites	Ba	label	project.sample_models['lbco'].atom_sites['Ba'].label	lbco.atom_site.Ba.label
16	lbco	atom_sites	Ba	occupancy	project.sample_models['lbco'].atom_sites['Ba'].occupancy	lbco.atom_site.Ba.occupancy
17	lbco	atom_sites	Ba	type_symbol	project.sample_models['lbco'].atom_sites['Ba'].type_symbol	lbco.atom_site.Ba.type_symbol
18	lbco	atom_sites	Ba	wyckoff_letter	project.sample_models['lbco'].atom_sites['Ba'].wyckoff_letter	lbco.atom_site.Ba.Wyckoff_letter
19	lbco	atom_sites	Co	adp_type	project.sample_models['lbco'].atom_sites['Co'].adp_type	lbco.atom_site.Co.ADP_type
20	lbco	atom_sites	Co	b_iso	project.sample_models['lbco'].atom_sites['Co'].b_iso	lbco.atom_site.Co.B_iso_or_equiv
21	lbco	atom_sites	Co	fract_x	project.sample_models['lbco'].atom_sites['Co'].fract_x	lbco.atom_site.Co.fract_x
22	lbco	atom_sites	Co	fract_y	project.sample_models['lbco'].atom_sites['Co'].fract_y	lbco.atom_site.Co.fract_y
23	lbco	atom_sites	Co	fract_z	project.sample_models['lbco'].atom_sites['Co'].fract_z	lbco.atom_site.Co.fract_z
24	lbco	atom_sites	Co	label	project.sample_models['lbco'].atom_sites['Co'].label	lbco.atom_site.Co.label
25	lbco	atom_sites	Co	occupancy	project.sample_models['lbco'].atom_sites['Co'].occupancy	lbco.atom_site.Co.occupancy
26	lbco	atom_sites	Co	type_symbol	project.sample_models['lbco'].atom_sites['Co'].type_symbol	lbco.atom_site.Co.type_symbol
27	lbco	atom_sites	Co	wyckoff_letter	project.sample_models['lbco'].atom_sites['Co'].wyckoff_letter	lbco.atom_site.Co.Wyckoff_letter
28	lbco	atom_sites	O	adp_type	project.sample_models['lbco'].atom_sites['O'].adp_type	lbco.atom_site.O.ADP_type
29	lbco	atom_sites	O	b_iso	project.sample_models['lbco'].atom_sites['O'].b_iso	lbco.atom_site.O.B_iso_or_equiv
30	lbco	atom_sites	O	fract_x	project.sample_models['lbco'].atom_sites['O'].fract_x	lbco.atom_site.O.fract_x
31	lbco	atom_sites	O	fract_y	project.sample_models['lbco'].atom_sites['O'].fract_y	lbco.atom_site.O.fract_y
32	lbco	atom_sites	O	fract_z	project.sample_models['lbco'].atom_sites['O'].fract_z	lbco.atom_site.O.fract_z
33	lbco	atom_sites	O	label	project.sample_models['lbco'].atom_sites['O'].label	lbco.atom_site.O.label
34	lbco	atom_sites	O	occupancy	project.sample_models['lbco'].atom_sites['O'].occupancy	lbco.atom_site.O.occupancy
35	lbco	atom_sites	O	type_symbol	project.sample_models['lbco'].atom_sites['O'].type_symbol	lbco.atom_site.O.type_symbol
36	lbco	atom_sites	O	wyckoff_letter	project.sample_models['lbco'].atom_sites['O'].wyckoff_letter	lbco.atom_site.O.Wyckoff_letter
37	lbco	cell		angle_alpha	project.sample_models['lbco'].cell.angle_alpha	lbco.cell.angle_alpha
38	lbco	cell		angle_beta	project.sample_models['lbco'].cell.angle_beta	lbco.cell.angle_beta
39	lbco	cell		angle_gamma	project.sample_models['lbco'].cell.angle_gamma	lbco.cell.angle_gamma
40	lbco	cell		length_a	project.sample_models['lbco'].cell.length_a	lbco.cell.length_a
41	lbco	cell		length_b	project.sample_models['lbco'].cell.length_b	lbco.cell.length_b
42	lbco	cell		length_c	project.sample_models['lbco'].cell.length_c	lbco.cell.length_c
43	lbco	space_group		it_coordinate_system_code	project.sample_models['lbco'].space_group.it_coordinate_system_code	lbco.space_group.IT_coordinate_system_code
44	lbco	space_group		name_h_m	project.sample_models['lbco'].space_group.name_h_m	lbco.space_group.name_H-M_alt
45	hrpt	background	10	x	project.experiments['hrpt'].background['10'].x	hrpt.pd_background.10.line_segment_X
46	hrpt	background	10	y	project.experiments['hrpt'].background['10'].y	hrpt.pd_background.10.line_segment_intensity
47	hrpt	background	30	x	project.experiments['hrpt'].background['30'].x	hrpt.pd_background.30.line_segment_X
48	hrpt	background	30	y	project.experiments['hrpt'].background['30'].y	hrpt.pd_background.30.line_segment_intensity
49	hrpt	background	50	x	project.experiments['hrpt'].background['50'].x	hrpt.pd_background.50.line_segment_X
50	hrpt	background	50	y	project.experiments['hrpt'].background['50'].y	hrpt.pd_background.50.line_segment_intensity
51	hrpt	background	110	x	project.experiments['hrpt'].background['110'].x	hrpt.pd_background.110.line_segment_X
52	hrpt	background	110	y	project.experiments['hrpt'].background['110'].y	hrpt.pd_background.110.line_segment_intensity
53	hrpt	background	165	x	project.experiments['hrpt'].background['165'].x	hrpt.pd_background.165.line_segment_X
54	hrpt	background	165	y	project.experiments['hrpt'].background['165'].y	hrpt.pd_background.165.line_segment_intensity
55	hrpt	instrument		twotheta_offset	project.experiments['hrpt'].instrument.twotheta_offset	hrpt.instr.2theta_offset
56	hrpt	instrument		wavelength	project.experiments['hrpt'].instrument.wavelength	hrpt.instr.wavelength
57	hrpt	linked_phases	lbco	id	project.experiments['hrpt'].linked_phases['lbco'].id	hrpt.pd_phase_block.lbco.id
58	hrpt	linked_phases	lbco	scale	project.experiments['hrpt'].linked_phases['lbco'].scale	hrpt.pd_phase_block.lbco.scale
59	hrpt	peak		broad_gauss_u	project.experiments['hrpt'].peak.broad_gauss_u	hrpt.peak.broad_gauss_u
60	hrpt	peak		broad_gauss_v	project.experiments['hrpt'].peak.broad_gauss_v	hrpt.peak.broad_gauss_v
61	hrpt	peak		broad_gauss_w	project.experiments['hrpt'].peak.broad_gauss_w	hrpt.peak.broad_gauss_w
62	hrpt	peak		broad_lorentz_x	project.experiments['hrpt'].peak.broad_lorentz_x	hrpt.peak.broad_lorentz_x
63	hrpt	peak		broad_lorentz_y	project.experiments['hrpt'].peak.broad_lorentz_y	hrpt.peak.broad_lorentz_y
64	hrpt	expt_type		beam_mode	project.experiments['hrpt'].expt_type.beam_mode	hrpt.expt_type.beam_mode
65	hrpt	expt_type		radiation_probe	project.experiments['hrpt'].expt_type.radiation_probe	hrpt.expt_type.radiation_probe
66	hrpt	expt_type		sample_form	project.experiments['hrpt'].expt_type.sample_form	hrpt.expt_type.sample_form
67	hrpt	expt_type		scattering_type	project.experiments['hrpt'].expt_type.scattering_type	hrpt.expt_type.scattering_type

Set Fit Mode¶

Show supported fit modes.

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project.analysis.show_available_fit_modes()
project.analysis.show_available_fit_modes()

Available fit modes

Strategy	Description
single	Independent fitting of each experiment; no shared parameters
joint	Simultaneous fitting of all experiments; some parameters are shared

Show current fit mode.

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project.analysis.show_current_fit_mode()
project.analysis.show_current_fit_mode()

Current fit mode
single

Select desired fit mode.

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project.analysis.fit_mode = 'single'
project.analysis.fit_mode = 'single'

Current fit mode changed to
single

Set Minimizer¶

Show supported fitting engines.

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project.analysis.show_available_minimizers()
project.analysis.show_available_minimizers()

Supported minimizers

Minimizer	Description
lmfit	LMFIT library using the default Levenberg-Marquardt least squares method
lmfit (leastsq)	LMFIT library with Levenberg-Marquardt least squares method
lmfit (least_squares)	LMFIT library with SciPy’s trust region reflective algorithm
dfols	DFO-LS library for derivative-free least-squares optimization

Show current fitting engine.

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project.analysis.show_current_minimizer()
project.analysis.show_current_minimizer()

Current minimizer
lmfit (leastsq)

Select desired fitting engine.

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

Current minimizer changed to
lmfit (leastsq)

Perform Fit 1/5¶

Set sample model parameters to be refined.

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project.sample_models['lbco'].cell.length_a.free = True
project.sample_models['lbco'].cell.length_a.free = True

Set experiment parameters to be refined.

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project.experiments['hrpt'].linked_phases['lbco'].scale.free = True
project.experiments['hrpt'].instrument.calib_twotheta_offset.free = True
project.experiments['hrpt'].background['10'].y.free = True
project.experiments['hrpt'].background['30'].y.free = True
project.experiments['hrpt'].background['50'].y.free = True
project.experiments['hrpt'].background['110'].y.free = True
project.experiments['hrpt'].background['165'].y.free = True
project.experiments['hrpt'].linked_phases['lbco'].scale.free = True
project.experiments['hrpt'].instrument.calib_twotheta_offset.free = True
project.experiments['hrpt'].background['10'].y.free = True
project.experiments['hrpt'].background['30'].y.free = True
project.experiments['hrpt'].background['50'].y.free = True
project.experiments['hrpt'].background['110'].y.free = True
project.experiments['hrpt'].background['165'].y.free = True

Show free parameters after selection.

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project.analysis.show_free_params()
project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	units
1	lbco	cell		length_a	3.8800	Å
2	hrpt	background	10	y	170.0000
3	hrpt	background	30	y	170.0000
4	hrpt	background	50	y	170.0000
5	hrpt	background	110	y	170.0000
6	hrpt	background	165	y	170.0000
7	hrpt	instrument		twotheta_offset	0.6000	deg
8	hrpt	linked_phases	lbco	scale	10.0000

Run Fitting¶

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

Using experiment 🔬 'hrpt' for 'single' fitting
🚀 Starting fit process with 'lmfit (leastsq)'...
📈 Goodness-of-fit (reduced χ²) change:

iteration	χ²	improvement [%]
1	164.59
12	33.43	79.7% ↓
21	13.22	60.4% ↓
30	5.78	56.3% ↓
39	3.15	45.6% ↓
77	3.14

🏆 Best goodness-of-fit (reduced χ²) is 3.14 at iteration 73
✅ Fitting complete.

Fit results
✅ Success: True
⏱️ Fitting time: 0.68 seconds
📏 Goodness-of-fit (reduced χ²): 3.14
📏 R-factor (Rf): 8.42%
📏 R-factor squared (Rf²): 11.79%
📏 Weighted R-factor (wR): 11.62%
📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8800	3.8910	0.0001	Å	0.28 % ↑
2	hrpt	background	10	y	170.0000	167.7066	2.1300		1.35 % ↓
3	hrpt	background	30	y	170.0000	166.0338	1.5404		2.33 % ↓
4	hrpt	background	50	y	170.0000	169.9495	1.1025		0.03 % ↓
5	hrpt	background	110	y	170.0000	170.0802	0.9788		0.05 % ↑
6	hrpt	background	165	y	170.0000	179.6656	1.3289		5.69 % ↑
7	hrpt	instrument		twotheta_offset	0.6000	0.6243	0.0018	deg	4.05 % ↑
8	hrpt	linked_phases	lbco	scale	10.0000	7.3409	0.0350		26.59 % ↓

Plot Measured vs Calculated¶

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

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project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)
project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)

Save Project State¶

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project.save_as(dir_path='lbco_hrpt', temporary=True)
project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt
✅ project.cif
✅ sample_models/lbco.cif
✅ experiments/hrpt.cif
✅ analysis.cif
✅ summary.cif

Perform Fit 2/5¶

Set more parameters to be refined.

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project.experiments['hrpt'].peak.broad_gauss_u.free = True
project.experiments['hrpt'].peak.broad_gauss_v.free = True
project.experiments['hrpt'].peak.broad_gauss_w.free = True
project.experiments['hrpt'].peak.broad_lorentz_y.free = True
project.experiments['hrpt'].peak.broad_gauss_u.free = True
project.experiments['hrpt'].peak.broad_gauss_v.free = True
project.experiments['hrpt'].peak.broad_gauss_w.free = True
project.experiments['hrpt'].peak.broad_lorentz_y.free = True

Show free parameters after selection.

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project.analysis.show_free_params()
project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	units
1	lbco	cell		length_a	3.8910	0.0001	Å
2	hrpt	background	10	y	167.7066	2.1300
3	hrpt	background	30	y	166.0338	1.5404
4	hrpt	background	50	y	169.9495	1.1025
5	hrpt	background	110	y	170.0802	0.9788
6	hrpt	background	165	y	179.6656	1.3289
7	hrpt	instrument		twotheta_offset	0.6243	0.0018	deg
8	hrpt	linked_phases	lbco	scale	7.3409	0.0350
9	hrpt	peak		broad_gauss_u	0.1000		deg²
10	hrpt	peak		broad_gauss_v	-0.1000		deg²
11	hrpt	peak		broad_gauss_w	0.1000		deg²
12	hrpt	peak		broad_lorentz_y	0.1000		deg

Run Fitting¶

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

Using experiment 🔬 'hrpt' for 'single' fitting
🚀 Starting fit process with 'lmfit (leastsq)'...
📈 Goodness-of-fit (reduced χ²) change:

iteration	χ²	improvement [%]
1	3.14
16	2.85	9.1% ↓
69	2.85

🏆 Best goodness-of-fit (reduced χ²) is 2.85 at iteration 68
✅ Fitting complete.

Fit results
✅ Success: True
⏱️ Fitting time: 0.58 seconds
📏 Goodness-of-fit (reduced χ²): 2.85
📏 R-factor (Rf): 8.30%
📏 R-factor squared (Rf²): 11.85%
📏 Weighted R-factor (wR): 11.91%
📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	cell		length_a	3.8910	3.8909	0.0001	Å	0.00 % ↓
2	hrpt	background	10	y	167.7066	167.5167	2.0311		0.11 % ↓
3	hrpt	background	30	y	166.0338	166.7627	1.4794		0.44 % ↑
4	hrpt	background	50	y	169.9495	170.8330	1.0808		0.52 % ↑
5	hrpt	background	110	y	170.0802	172.2546	0.9660		1.28 % ↑
6	hrpt	background	165	y	179.6656	180.6405	1.2737		0.54 % ↑
7	hrpt	instrument		twotheta_offset	0.6243	0.6231	0.0017	deg	0.19 % ↓
8	hrpt	linked_phases	lbco	scale	7.3409	7.2120	0.0406		1.76 % ↓
9	hrpt	peak		broad_gauss_u	0.1000	0.0803	0.0047	deg²	19.74 % ↓
10	hrpt	peak		broad_gauss_v	-0.1000	-0.1029	0.0104	deg²	2.93 % ↑
11	hrpt	peak		broad_gauss_w	0.1000	0.1077	0.0051	deg²	7.66 % ↑
12	hrpt	peak		broad_lorentz_y	0.1000	0.0893	0.0032	deg	10.67 % ↓

Plot Measured vs Calculated¶

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

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project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)
project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)

Save Project State¶

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project.save_as(dir_path='lbco_hrpt', temporary=True)
project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt
✅ project.cif
✅ sample_models/lbco.cif
✅ experiments/hrpt.cif
✅ analysis.cif
✅ summary.cif

Perform Fit 3/5¶

Set more parameters to be refined.

In [65]:

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project.sample_models['lbco'].atom_sites['La'].b_iso.free = True
project.sample_models['lbco'].atom_sites['Ba'].b_iso.free = True
project.sample_models['lbco'].atom_sites['Co'].b_iso.free = True
project.sample_models['lbco'].atom_sites['O'].b_iso.free = True
project.sample_models['lbco'].atom_sites['La'].b_iso.free = True
project.sample_models['lbco'].atom_sites['Ba'].b_iso.free = True
project.sample_models['lbco'].atom_sites['Co'].b_iso.free = True
project.sample_models['lbco'].atom_sites['O'].b_iso.free = True

Show free parameters after selection.

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project.analysis.show_free_params()
project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	units
1	lbco	atom_sites	La	b_iso	0.5000		Å²
2	lbco	atom_sites	Ba	b_iso	0.5000		Å²
3	lbco	atom_sites	Co	b_iso	0.5000		Å²
4	lbco	atom_sites	O	b_iso	0.5000		Å²
5	lbco	cell		length_a	3.8909	0.0001	Å
6	hrpt	background	10	y	167.5167	2.0311
7	hrpt	background	30	y	166.7627	1.4794
8	hrpt	background	50	y	170.8330	1.0808
9	hrpt	background	110	y	172.2546	0.9660
10	hrpt	background	165	y	180.6405	1.2737
11	hrpt	instrument		twotheta_offset	0.6231	0.0017	deg
12	hrpt	linked_phases	lbco	scale	7.2120	0.0406
13	hrpt	peak		broad_gauss_u	0.0803	0.0047	deg²
14	hrpt	peak		broad_gauss_v	-0.1029	0.0104	deg²
15	hrpt	peak		broad_gauss_w	0.1077	0.0051	deg²
16	hrpt	peak		broad_lorentz_y	0.0893	0.0032	deg

Run Fitting¶

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

Using experiment 🔬 'hrpt' for 'single' fitting
🚀 Starting fit process with 'lmfit (leastsq)'...
📈 Goodness-of-fit (reduced χ²) change:

iteration	χ²	improvement [%]
1	2.85
28	2.28	19.9% ↓
45	1.62	28.9% ↓
62	1.47	9.6% ↓
79	1.36	7.0% ↓
97	1.29	5.4% ↓
204	1.29

🏆 Best goodness-of-fit (reduced χ²) is 1.29 at iteration 186
✅ Fitting complete.

Fit results
✅ Success: True
⏱️ Fitting time: 1.69 seconds
📏 Goodness-of-fit (reduced χ²): 1.29
📏 R-factor (Rf): 5.63%
📏 R-factor squared (Rf²): 5.27%
📏 Weighted R-factor (wR): 4.41%
📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	atom_sites	La	b_iso	0.5000	0.5051	1216.0297	Å²	1.02 % ↑
2	lbco	atom_sites	Ba	b_iso	0.5000	0.5048	1976.1470	Å²	0.96 % ↑
3	lbco	atom_sites	Co	b_iso	0.5000	0.2371	0.0612	Å²	52.59 % ↓
4	lbco	atom_sites	O	b_iso	0.5000	1.3935	0.0167	Å²	178.71 % ↑
5	lbco	cell		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↓
6	hrpt	background	10	y	167.5167	168.5585	1.3671		0.62 % ↑
7	hrpt	background	30	y	166.7627	164.3357	0.9992		1.46 % ↓
8	hrpt	background	50	y	170.8330	166.8881	0.7388		2.31 % ↓
9	hrpt	background	110	y	172.2546	175.4004	0.6571		1.83 % ↑
10	hrpt	background	165	y	180.6405	174.2811	0.9113		3.52 % ↓
11	hrpt	instrument		twotheta_offset	0.6231	0.6226	0.0010	deg	0.09 % ↓
12	hrpt	linked_phases	lbco	scale	7.2120	9.1350	0.0641		26.66 % ↑
13	hrpt	peak		broad_gauss_u	0.0803	0.0816	0.0031	deg²	1.63 % ↑
14	hrpt	peak		broad_gauss_v	-0.1029	-0.1159	0.0067	deg²	12.62 % ↑
15	hrpt	peak		broad_gauss_w	0.1077	0.1204	0.0033	deg²	11.88 % ↑
16	hrpt	peak		broad_lorentz_y	0.0893	0.0844	0.0021	deg	5.47 % ↓

Plot Measured vs Calculated¶

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

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project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)
project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)

Save Project State¶

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project.save_as(dir_path='lbco_hrpt', temporary=True)
project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt
✅ project.cif
✅ sample_models/lbco.cif
✅ experiments/hrpt.cif
✅ analysis.cif
✅ summary.cif

Perform Fit 4/5¶

Set Constraints¶

Set aliases for parameters.

In [71]:

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project.analysis.aliases.add(label='biso_La', param_uid=project.sample_models['lbco'].atom_sites['La'].b_iso.uid)
project.analysis.aliases.add(label='biso_Ba', param_uid=project.sample_models['lbco'].atom_sites['Ba'].b_iso.uid)
project.analysis.aliases.add(label='biso_La', param_uid=project.sample_models['lbco'].atom_sites['La'].b_iso.uid)
project.analysis.aliases.add(label='biso_Ba', param_uid=project.sample_models['lbco'].atom_sites['Ba'].b_iso.uid)

Set constraints.

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project.analysis.constraints.add(lhs_alias='biso_Ba', rhs_expr='biso_La')
project.analysis.constraints.add(lhs_alias='biso_Ba', rhs_expr='biso_La')

Show defined constraints.

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project.analysis.show_constraints()
project.analysis.show_constraints()

User defined constraints

lhs_alias	rhs_expr	full expression
biso_Ba	biso_La	biso_Ba = biso_La

Show free parameters before applying constraints.

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project.analysis.show_free_params()
project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	units
1	lbco	atom_sites	La	b_iso	0.5051	1216.0297	Å²
2	lbco	atom_sites	Ba	b_iso	0.5048	1976.1470	Å²
3	lbco	atom_sites	Co	b_iso	0.2371	0.0612	Å²
4	lbco	atom_sites	O	b_iso	1.3935	0.0167	Å²
5	lbco	cell		length_a	3.8909	0.0000	Å
6	hrpt	background	10	y	168.5585	1.3671
7	hrpt	background	30	y	164.3357	0.9992
8	hrpt	background	50	y	166.8881	0.7388
9	hrpt	background	110	y	175.4004	0.6571
10	hrpt	background	165	y	174.2811	0.9113
11	hrpt	instrument		twotheta_offset	0.6226	0.0010	deg
12	hrpt	linked_phases	lbco	scale	9.1350	0.0641
13	hrpt	peak		broad_gauss_u	0.0816	0.0031	deg²
14	hrpt	peak		broad_gauss_v	-0.1159	0.0067	deg²
15	hrpt	peak		broad_gauss_w	0.1204	0.0033	deg²
16	hrpt	peak		broad_lorentz_y	0.0844	0.0021	deg

Apply constraints.

In [75]:

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project.analysis.apply_constraints()
project.analysis.apply_constraints()

Show free parameters after applying constraints.

In [76]:

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project.analysis.show_free_params()
project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	units
1	lbco	atom_sites	La	b_iso	0.5051	1216.0297	Å²
2	lbco	atom_sites	Co	b_iso	0.2371	0.0612	Å²
3	lbco	atom_sites	O	b_iso	1.3935	0.0167	Å²
4	lbco	cell		length_a	3.8909	0.0000	Å
5	hrpt	background	10	y	168.5585	1.3671
6	hrpt	background	30	y	164.3357	0.9992
7	hrpt	background	50	y	166.8881	0.7388
8	hrpt	background	110	y	175.4004	0.6571
9	hrpt	background	165	y	174.2811	0.9113
10	hrpt	instrument		twotheta_offset	0.6226	0.0010	deg
11	hrpt	linked_phases	lbco	scale	9.1350	0.0641
12	hrpt	peak		broad_gauss_u	0.0816	0.0031	deg²
13	hrpt	peak		broad_gauss_v	-0.1159	0.0067	deg²
14	hrpt	peak		broad_gauss_w	0.1204	0.0033	deg²
15	hrpt	peak		broad_lorentz_y	0.0844	0.0021	deg

Run Fitting¶

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

Using experiment 🔬 'hrpt' for 'single' fitting
🚀 Starting fit process with 'lmfit (leastsq)'...
📈 Goodness-of-fit (reduced χ²) change:

iteration	χ²	improvement [%]
1	1.29
20	1.29

🏆 Best goodness-of-fit (reduced χ²) is 1.29 at iteration 19
✅ Fitting complete.

Fit results
✅ Success: True
⏱️ Fitting time: 0.17 seconds
📏 Goodness-of-fit (reduced χ²): 1.29
📏 R-factor (Rf): 5.63%
📏 R-factor squared (Rf²): 5.27%
📏 Weighted R-factor (wR): 4.41%
📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	atom_sites	La	b_iso	0.5051	0.5051	0.0278	Å²	0.00 % ↓
2	lbco	atom_sites	Co	b_iso	0.2371	0.2370	0.0564	Å²	0.03 % ↓
3	lbco	atom_sites	O	b_iso	1.3935	1.3935	0.0160	Å²	0.00 % ↑
4	lbco	cell		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↑
5	hrpt	background	10	y	168.5585	168.5585	1.3669		0.00 % ↓
6	hrpt	background	30	y	164.3357	164.3357	0.9990		0.00 % ↓
7	hrpt	background	50	y	166.8881	166.8881	0.7386		0.00 % ↓
8	hrpt	background	110	y	175.4004	175.4006	0.6488		0.00 % ↑
9	hrpt	background	165	y	174.2811	174.2812	0.8944		0.00 % ↑
10	hrpt	instrument		twotheta_offset	0.6226	0.6226	0.0010	deg	0.00 % ↑
11	hrpt	linked_phases	lbco	scale	9.1350	9.1351	0.0538		0.00 % ↑
12	hrpt	peak		broad_gauss_u	0.0816	0.0816	0.0031	deg²	0.00 % ↑
13	hrpt	peak		broad_gauss_v	-0.1159	-0.1159	0.0066	deg²	0.00 % ↑
14	hrpt	peak		broad_gauss_w	0.1204	0.1204	0.0032	deg²	0.00 % ↑
15	hrpt	peak		broad_lorentz_y	0.0844	0.0844	0.0021	deg	0.00 % ↓

Plot Measured vs Calculated¶

In [78]:

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

In [79]:

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project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)
project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)

Save Project State¶

In [80]:

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project.save_as(dir_path='lbco_hrpt', temporary=True)
project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt
✅ project.cif
✅ sample_models/lbco.cif
✅ experiments/hrpt.cif
✅ analysis.cif
✅ summary.cif

Perform Fit 5/5¶

Set Constraints¶

Set more aliases for parameters.

In [81]:

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project.analysis.aliases.add(
    label='occ_La',
    param_uid=project.sample_models['lbco'].atom_sites['La'].occupancy.uid,
)
project.analysis.aliases.add(
    label='occ_Ba',
    param_uid=project.sample_models['lbco'].atom_sites['Ba'].occupancy.uid,
)
project.analysis.aliases.add(
    label='occ_La',
    param_uid=project.sample_models['lbco'].atom_sites['La'].occupancy.uid,
)
project.analysis.aliases.add(
    label='occ_Ba',
    param_uid=project.sample_models['lbco'].atom_sites['Ba'].occupancy.uid,
)

Set more constraints.

In [82]:

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project.analysis.constraints.add(
    lhs_alias='occ_Ba',
    rhs_expr='1 - occ_La',
)
project.analysis.constraints.add(
    lhs_alias='occ_Ba',
    rhs_expr='1 - occ_La',
)

Show defined constraints.

In [83]:

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project.analysis.show_constraints()
project.analysis.show_constraints()

User defined constraints

lhs_alias	rhs_expr	full expression
biso_Ba	biso_La	biso_Ba = biso_La
occ_Ba	1 - occ_La	occ_Ba = 1 - occ_La

Apply constraints.

In [84]:

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project.analysis.apply_constraints()
project.analysis.apply_constraints()

Set sample model parameters to be refined.

In [85]:

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project.sample_models['lbco'].atom_sites['La'].occupancy.free = True
project.sample_models['lbco'].atom_sites['La'].occupancy.free = True

Show free parameters after selection.

In [86]:

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project.analysis.show_free_params()
project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	units
1	lbco	atom_sites	La	b_iso	0.5051	0.0278	Å²
2	lbco	atom_sites	La	occupancy	0.5000
3	lbco	atom_sites	Co	b_iso	0.2370	0.0564	Å²
4	lbco	atom_sites	O	b_iso	1.3935	0.0160	Å²
5	lbco	cell		length_a	3.8909	0.0000	Å
6	hrpt	background	10	y	168.5585	1.3669
7	hrpt	background	30	y	164.3357	0.9990
8	hrpt	background	50	y	166.8881	0.7386
9	hrpt	background	110	y	175.4006	0.6488
10	hrpt	background	165	y	174.2812	0.8944
11	hrpt	instrument		twotheta_offset	0.6226	0.0010	deg
12	hrpt	linked_phases	lbco	scale	9.1351	0.0538
13	hrpt	peak		broad_gauss_u	0.0816	0.0031	deg²
14	hrpt	peak		broad_gauss_v	-0.1159	0.0066	deg²
15	hrpt	peak		broad_gauss_w	0.1204	0.0032	deg²
16	hrpt	peak		broad_lorentz_y	0.0844	0.0021	deg

Run Fitting¶

In [87]:

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

Using experiment 🔬 'hrpt' for 'single' fitting
🚀 Starting fit process with 'lmfit (leastsq)'...
📈 Goodness-of-fit (reduced χ²) change:

iteration	χ²	improvement [%]
1	1.29
55	1.28

🏆 Best goodness-of-fit (reduced χ²) is 1.28 at iteration 54
✅ Fitting complete.

Fit results
✅ Success: True
⏱️ Fitting time: 0.47 seconds
📏 Goodness-of-fit (reduced χ²): 1.28
📏 R-factor (Rf): 5.61%
📏 R-factor squared (Rf²): 5.25%
📏 Weighted R-factor (wR): 4.39%
📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	lbco	atom_sites	La	b_iso	0.5051	0.5983	0.0355	Å²	18.46 % ↑
2	lbco	atom_sites	La	occupancy	0.5000	0.5840	0.0203		16.81 % ↑
3	lbco	atom_sites	Co	b_iso	0.2370	0.1665	0.0580	Å²	29.74 % ↓
4	lbco	atom_sites	O	b_iso	1.3935	1.3491	0.0192	Å²	3.19 % ↓
5	lbco	cell		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↑
6	hrpt	background	10	y	168.5585	168.9780	1.3666		0.25 % ↑
7	hrpt	background	30	y	164.3357	164.0535	0.9992		0.17 % ↓
8	hrpt	background	50	y	166.8881	166.9125	0.7364		0.01 % ↑
9	hrpt	background	110	y	175.4006	175.2699	0.6479		0.07 % ↓
10	hrpt	background	165	y	174.2812	174.5580	0.8935		0.16 % ↑
11	hrpt	instrument		twotheta_offset	0.6226	0.6226	0.0010	deg	0.00 % ↑
12	hrpt	linked_phases	lbco	scale	9.1351	8.9057	0.0761		2.51 % ↓
13	hrpt	peak		broad_gauss_u	0.0816	0.0812	0.0031	deg²	0.43 % ↓
14	hrpt	peak		broad_gauss_v	-0.1159	-0.1154	0.0066	deg²	0.48 % ↓
15	hrpt	peak		broad_gauss_w	0.1204	0.1203	0.0032	deg²	0.14 % ↓
16	hrpt	peak		broad_lorentz_y	0.0844	0.0846	0.0021	deg	0.18 % ↑

Plot Measured vs Calculated¶

In [88]:

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

In [89]:

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project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)
project.plot_meas_vs_calc(expt_name='hrpt', x_min=38, x_max=41, show_residual=True)

Save Project State¶

In [90]:

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project.save_as(dir_path='lbco_hrpt', temporary=True)
project.save_as(dir_path='lbco_hrpt', temporary=True)

Saving project 📦 'lbco_hrpt' to
/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt
✅ project.cif
✅ sample_models/lbco.cif
✅ experiments/hrpt.cif
✅ analysis.cif
✅ summary.cif

Step 5: 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
La0.5Ba0.5CoO3 at HRPT@PSI

Description
This project demonstrates a standard refinement of
La0.5Ba0.5CoO3, which crystallizes in a perovskite-type
structure, using neutron powder diffraction data collected
in constant wavelength mode at the HRPT diffractometer
(PSI).

*** CRYSTALLOGRAPHIC DATA ***

Phase datablock
🧩 lbco

Space group
P m -3 m

Cell parameters

alpha	90.00000
beta	90.00000
gamma	90.00000
a	3.89087
b	3.89087
c	3.89087

Atom sites

Label	Type	fract_x	fract_y	fract_z	Occupancy	B_iso
La	La	0.00000	0.00000	0.00000	0.58403	0.59832
Ba	Ba	0.00000	0.00000	0.00000	0.41597	0.59832
Co	Co	0.50000	0.50000	0.50000	1.00000	0.16651
O	O	0.00000	0.50000	0.50000	1.00000	1.34914

*** EXPERIMENTS ***

Experiment datablock
🔬 hrpt

Experiment type
powder, neutron, constant wavelength

Wavelength
1.49400

2θ offset
0.62261

Profile type
pseudo-voigt

Peak broadening (Gaussian)

U	0.08122
V	-0.11537
W	0.12028

Peak broadening (Lorentzian)

X	0.00000
Y	0.08460

*** FITTING ***

Calculation engine
cryspy

Minimization engine
lmfit (leastsq)

Fit quality

Goodness-of-fit (reduced χ²)

1.28