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¶

In [2]:

Copied!

import easydiffraction as ed
import easydiffraction as ed

Step 1: Create a Project¶

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

Create Project¶

In [3]:

Copied!

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

Set Project Metadata¶

In [4]:

Copied!





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¶

In [5]:

Copied!

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

Project 📦 'lbco_hrpt' info as CIF

	CIF
1	_project.id lbco_hrpt
2	_project.title 'La0.5Ba0.5CoO3 at HRPT@PSI'
3	_project.description
4	;
5	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).
6	;
7	_project.created '23 Oct 2025 08:41:16'
8	_project.last_modified '23 Oct 2025 08:41:16'

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.

In [6]:

Copied!

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

Saving project 📦 'lbco_hrpt' to

/private/var/folders/y6/nj790rtn62lfktb1sh__79hc0000gn/T/lbco_hrpt

├── 📄 project.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Set Up Data Plotter¶

Show supported plotting engines.

In [7]:

Copied!

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

Supported engines

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

Show current plotting configuration.

In [8]:

Copied!

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

Current plotter configuration

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

Set plotting engine.

In [9]:

Copied!

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

Step 2: Define Sample Model¶

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

Add Sample Model¶

In [10]:

Copied!

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

In [11]:

Copied!

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

Defined sample models 🧩

['lbco']

Set Space Group¶

Modify the default space group parameters.

In [12]:

Copied!

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.

In [13]:

Copied!

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.

In [14]:

Copied!





project.sample_models['lbco'].atom_sites.add_from_args(
    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_from_args(
    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_from_args(
    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_from_args(
    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_from_args(
    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_from_args(
    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_from_args(
    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_from_args(
    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¶

In [15]:

Copied!

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

Show Sample Model as CIF¶

In [16]:

Copied!

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

Sample model 🧩 'lbco' as cif

	CIF
1	data_lbco
2
3	_cell.length_a 3.88
4	_cell.length_b 3.88
5	_cell.length_c 3.88
6	_cell.angle_alpha 90.0
7	_cell.angle_beta 90.0
8	_cell.angle_gamma 90.0
9
10	_space_group.name_H-M_alt "P m -3 m"
11	_space_group.IT_coordinate_system_code 1
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.B_iso_or_equiv
22	_atom_site.adp_type
23	La La 0.0 0.0 0.0 a 0.5 0.5 Biso
24	Ba Ba 0.0 0.0 0.0 a 0.5 0.5 Biso
25	Co Co 0.5 0.5 0.5 b 1.0 0.5 Biso
26	O O 0.0 0.5 0.5 c 1.0 0.5 Biso

Show Sample Model Structure¶

In [17]:

Copied!

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.

In [18]:

Copied!

project.save()
project.save()

Saving project 📦 'lbco_hrpt' to

/private/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.

In [19]:

Copied!

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

Downloading...

File 'hrpt_lbco.xye' from 'easyscience/diffraction-lib'

Add Diffraction Experiment¶

In [20]:

Copied!





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

Data loaded successfully

Experiment 🔬 'hrpt'. Number of data points: 3098

Show Defined Experiments¶

In [21]:

Copied!

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

Defined experiments 🔬

['hrpt']

Show Measured Data¶

In [22]:

Copied!

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

Set Instrument¶

Modify the default instrument parameters.

In [23]:

Copied!

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.

In [24]:

Copied!

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

Supported peak profile types

	Peak profile type	Description
1	pseudo-voigt	Pseudo-Voigt profile
2	split pseudo-voigt	Split pseudo-Voigt profile with empirical asymmetry correction.
3	thompson-cox-hastings	Thompson-Cox-Hastings profile with FCJ asymmetry correction.

Show the current peak profile type.

In [25]:

Copied!

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

Current peak profile type

PeakProfileTypeEnum.PSEUDO_VOIGT

Select the desired peak profile type.

In [26]:

Copied!

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.

In [27]:

Copied!





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.

In [28]:

Copied!

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

Supported background types

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

Show current background type.

In [29]:

Copied!

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

Current background type

BackgroundTypeEnum.LINE_SEGMENT

Select the desired background type.

In [30]:

Copied!

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.

In [31]:

Copied!





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

Show current background points.

In [32]:

Copied!

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

Line-segment background points

	X	Intensity
1	10	170
2	30	170
3	50	170
4	110	170
5	165	170

Set Linked Phases¶

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

In [33]:

Copied!

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

Show Experiment as CIF¶

In [34]:

Copied!

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

Experiment 🔬 'hrpt' as cif

	CIF
1	data_hrpt
2
3	_expt_type.sample_form powder
4	_expt_type.beam_mode "constant wavelength"
5	_expt_type.radiation_probe neutron
6	_expt_type.scattering_type bragg
7
8	_peak.broad_gauss_u 0.1
9	_peak.broad_gauss_v -0.1
10	_peak.broad_gauss_w 0.1
11	_peak.broad_lorentz_x 0
12	_peak.broad_lorentz_y 0.1
13
14	_instr.wavelength 1.494
15	_instr.2theta_offset 0.6
16
17	loop_
18	_pd_phase_block.id
19	_pd_phase_block.scale
20	lbco 10.0
21
22
23
24	loop_
25	_pd_background.line_segment_X
26	_pd_background.line_segment_intensity
27	10 170
28	30 170
29	50 170
30	110 170
31	165 170
32
33	loop_
34	_pd_meas.2theta_scan
35	_pd_meas.intensity_total
36	_pd_meas.intensity_total_su
37	10.0 167.0 12.6
38	10.05 157.0 12.5
39	10.1 187.0 13.3
40	10.15 197.0 14.0
41	10.2 164.0 12.5
42	...
43	164.65 173.0 30.1
44	164.7 187.0 27.9
45	164.75 175.0 38.2
46	164.8 168.0 30.9
47	164.85 109.0 41.2

Save Project State¶

In [35]:

Copied!

project.save()
project.save()

Saving project 📦 'lbco_hrpt' to

/private/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.

In [36]:

Copied!

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

Supported calculators

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

Show current calculation engine.

In [37]:

Copied!

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

Current calculator

cryspy

Select the desired calculation engine.

In [38]:

Copied!

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

Current calculator changed to

cryspy

Show Calculated Data¶

In [39]:

Copied!

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

Plot Measured vs Calculated¶

In [40]:

Copied!

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

In [41]:

Copied!

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.

In [42]:

Copied!

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	cell		length_a	3.88000	True
2	lbco	cell		length_b	3.88000	True
3	lbco	cell		length_c	3.88000	True
4	lbco	cell		angle_alpha	90.00000	True
5	lbco	cell		angle_beta	90.00000	True
6	lbco	cell		angle_gamma	90.00000	True
7	lbco	space_group		name_h_m	P m -3 m	False
8	lbco	space_group		it_coordinate_system_code	1	False
9	lbco	atom_site	La	label	La	False
10	lbco	atom_site	La	type_symbol	La	False
11	lbco	atom_site	La	fract_x	0.00000	True
12	lbco	atom_site	La	fract_y	0.00000	True
13	lbco	atom_site	La	fract_z	0.00000	True
14	lbco	atom_site	La	wyckoff_letter	a	False
15	lbco	atom_site	La	occupancy	0.50000	True
16	lbco	atom_site	La	b_iso	0.50000	True
17	lbco	atom_site	La	adp_type	Biso	False
18	lbco	atom_site	Ba	label	Ba	False
19	lbco	atom_site	Ba	type_symbol	Ba	False
20	lbco	atom_site	Ba	fract_x	0.00000	True
21	lbco	atom_site	Ba	fract_y	0.00000	True
22	lbco	atom_site	Ba	fract_z	0.00000	True
23	lbco	atom_site	Ba	wyckoff_letter	a	False
24	lbco	atom_site	Ba	occupancy	0.50000	True
25	lbco	atom_site	Ba	b_iso	0.50000	True
26	lbco	atom_site	Ba	adp_type	Biso	False
27	lbco	atom_site	Co	label	Co	False
28	lbco	atom_site	Co	type_symbol	Co	False
29	lbco	atom_site	Co	fract_x	0.50000	True
30	lbco	atom_site	Co	fract_y	0.50000	True
31	lbco	atom_site	Co	fract_z	0.50000	True
32	lbco	atom_site	Co	wyckoff_letter	b	False
33	lbco	atom_site	Co	occupancy	1.00000	True
34	lbco	atom_site	Co	b_iso	0.50000	True
35	lbco	atom_site	Co	adp_type	Biso	False
36	lbco	atom_site	O	label	O	False
37	lbco	atom_site	O	type_symbol	O	False
38	lbco	atom_site	O	fract_x	0.00000	True
39	lbco	atom_site	O	fract_y	0.50000	True
40	lbco	atom_site	O	fract_z	0.50000	True
41	lbco	atom_site	O	wyckoff_letter	c	False
42	lbco	atom_site	O	occupancy	1.00000	True
43	lbco	atom_site	O	b_iso	0.50000	True
44	lbco	atom_site	O	adp_type	Biso	False

All parameters for all experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	fittable
1	hrpt	expt_type		sample_form	powder	False
2	hrpt	expt_type		beam_mode	constant wavelength	False
3	hrpt	expt_type		radiation_probe	neutron	False
4	hrpt	expt_type		scattering_type	bragg	False
5	hrpt	peak		broad_gauss_u	0.10000	True
6	hrpt	peak		broad_gauss_v	-0.10000	True
7	hrpt	peak		broad_gauss_w	0.10000	True
8	hrpt	peak		broad_lorentz_x	0	True
9	hrpt	peak		broad_lorentz_y	0.10000	True
10	hrpt	linked_phases	lbco	id	lbco	False
11	hrpt	linked_phases	lbco	scale	10.00000	True
12	hrpt	instrument		wavelength	1.49400	True
13	hrpt	instrument		twotheta_offset	0.60000	True
14	hrpt	background	10	x	10	False
15	hrpt	background	10	y	170	True
16	hrpt	background	30	x	30	False
17	hrpt	background	30	y	170	True
18	hrpt	background	50	x	50	False
19	hrpt	background	50	y	170	True
20	hrpt	background	110	x	110	False
21	hrpt	background	110	y	170	True
22	hrpt	background	165	x	165	False
23	hrpt	background	165	y	170	True

Show all fittable parameters.

In [43]:

Copied!

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	cell		length_a	3.88000	Å	False
2	lbco	cell		length_b	3.88000	Å	False
3	lbco	cell		length_c	3.88000	Å	False
4	lbco	cell		angle_alpha	90.00000	deg	False
5	lbco	cell		angle_beta	90.00000	deg	False
6	lbco	cell		angle_gamma	90.00000	deg	False
7	lbco	atom_site	La	fract_x	0.00000		False
8	lbco	atom_site	La	fract_y	0.00000		False
9	lbco	atom_site	La	fract_z	0.00000		False
10	lbco	atom_site	La	occupancy	0.50000		False
11	lbco	atom_site	La	b_iso	0.50000	Å²	False
12	lbco	atom_site	Ba	fract_x	0.00000		False
13	lbco	atom_site	Ba	fract_y	0.00000		False
14	lbco	atom_site	Ba	fract_z	0.00000		False
15	lbco	atom_site	Ba	occupancy	0.50000		False
16	lbco	atom_site	Ba	b_iso	0.50000	Å²	False
17	lbco	atom_site	Co	fract_x	0.50000		False
18	lbco	atom_site	Co	fract_y	0.50000		False
19	lbco	atom_site	Co	fract_z	0.50000		False
20	lbco	atom_site	Co	occupancy	1.00000		False
21	lbco	atom_site	Co	b_iso	0.50000	Å²	False
22	lbco	atom_site	O	fract_x	0.00000		False
23	lbco	atom_site	O	fract_y	0.50000		False
24	lbco	atom_site	O	fract_z	0.50000		False
25	lbco	atom_site	O	occupancy	1.00000		False
26	lbco	atom_site	O	b_iso	0.50000	Å²	False

Fittable parameters for all experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	units	free
1	hrpt	peak		broad_gauss_u	0.10000	deg²	False
2	hrpt	peak		broad_gauss_v	-0.10000	deg²	False
3	hrpt	peak		broad_gauss_w	0.10000	deg²	False
4	hrpt	peak		broad_lorentz_x	0.00000	deg	False
5	hrpt	peak		broad_lorentz_y	0.10000	deg	False
6	hrpt	linked_phases	lbco	scale	10.00000		False
7	hrpt	instrument		wavelength	1.49400	Å	False
8	hrpt	instrument		twotheta_offset	0.60000	deg	False
9	hrpt	background	10	y	170.00000		False
10	hrpt	background	30	y	170.00000		False
11	hrpt	background	50	y	170.00000		False
12	hrpt	background	110	y	170.00000		False
13	hrpt	background	165	y	170.00000		False

Show only free parameters.

In [44]:

Copied!

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

⚠️ No free parameters found.

Show how to access parameters in the code.

In [45]:

Copied!

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

Set Fit Mode¶

Show supported fit modes.

In [46]:

Copied!

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

Available fit modes

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

Show current fit mode.

In [47]:

Copied!

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

Current fit mode

single

Select desired fit mode.

In [48]:

Copied!

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

Current fit mode changed to

single

Set Minimizer¶

Show supported fitting engines.

In [49]:

Copied!

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

Supported minimizers

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

Show current fitting engine.

In [50]:

Copied!

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

Current minimizer

lmfit (leastsq)

Select desired fitting engine.

In [51]:

Copied!

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.

In [52]:

Copied!

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

Set experiment parameters to be refined.

In [53]:

Copied!





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.

In [54]:

Copied!

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	min	max	units
1	lbco	cell		length_a	3.88000	-inf	inf	Å
2	hrpt	linked_phases	lbco	scale	10.00000	-inf	inf
3	hrpt	instrument		twotheta_offset	0.60000	-inf	inf	deg
4	hrpt	background	10	y	170.00000	-inf	inf
5	hrpt	background	30	y	170.00000	-inf	inf
6	hrpt	background	50	y	170.00000	-inf	inf
7	hrpt	background	110	y	170.00000	-inf	inf
8	hrpt	background	165	y	170.00000	-inf	inf

Run Fitting¶

In [55]:

Copied!

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	164.59
2	12	33.43	79.7% ↓
3	21	13.22	60.4% ↓
4	30	5.78	56.3% ↓
5	39	3.15	45.6% ↓
6	77	3.14

🏆 Best goodness-of-fit (reduced χ²) is 3.14 at iteration 69

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 2.71 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	None	length_a	3.8800	3.8910	0.0001	Å	0.28 % ↑
2	hrpt	linked_phases	lbco	scale	10.0000	7.3409	0.0350		26.59 % ↓
3	hrpt	instrument	None	twotheta_offset	0.6000	0.6243	0.0018	deg	4.05 % ↑
4	hrpt	background	10	y	170.0000	167.7066	2.1300		1.35 % ↓
5	hrpt	background	30	y	170.0000	166.0338	1.5404		2.33 % ↓
6	hrpt	background	50	y	170.0000	169.9495	1.1025		0.03 % ↓
7	hrpt	background	110	y	170.0000	170.0802	0.9788		0.05 % ↑
8	hrpt	background	165	y	170.0000	179.6656	1.3289		5.69 % ↑

Plot Measured vs Calculated¶

In [56]:

Copied!

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

In [57]:

Copied!

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 [58]:

Copied!

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

Saving project 📦 'lbco_hrpt' to

/private/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.

In [59]:

Copied!





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.

In [60]:

Copied!

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	min	max	units
1	lbco	cell		length_a	3.89099	0.00006	-inf	inf	Å
2	hrpt	peak		broad_gauss_u	0.10000		-inf	inf	deg²
3	hrpt	peak		broad_gauss_v	-0.10000		-inf	inf	deg²
4	hrpt	peak		broad_gauss_w	0.10000		-inf	inf	deg²
5	hrpt	peak		broad_lorentz_y	0.10000		-inf	inf	deg
6	hrpt	linked_phases	lbco	scale	7.34088	0.03496	-inf	inf
7	hrpt	instrument		twotheta_offset	0.62432	0.00181	-inf	inf	deg
8	hrpt	background	10	y	167.70662	2.13004	-inf	inf
9	hrpt	background	30	y	166.03383	1.54041	-inf	inf
10	hrpt	background	50	y	169.94949	1.10249	-inf	inf
11	hrpt	background	110	y	170.08023	0.97879	-inf	inf
12	hrpt	background	165	y	179.66557	1.32895	-inf	inf

Run Fitting¶

In [61]:

Copied!

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	3.14
2	16	2.85	9.1% ↓
3	69	2.85

🏆 Best goodness-of-fit (reduced χ²) is 2.85 at iteration 68

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 1.48 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	None	length_a	3.8910	3.8909	0.0001	Å	0.00 % ↓
2	hrpt	peak	None	broad_gauss_u	0.1000	0.0803	0.0047	deg²	19.74 % ↓
3	hrpt	peak	None	broad_gauss_v	-0.1000	-0.1029	0.0104	deg²	2.93 % ↑
4	hrpt	peak	None	broad_gauss_w	0.1000	0.1077	0.0051	deg²	7.66 % ↑
5	hrpt	peak	None	broad_lorentz_y	0.1000	0.0893	0.0032	deg	10.67 % ↓
6	hrpt	linked_phases	lbco	scale	7.3409	7.2120	0.0406		1.76 % ↓
7	hrpt	instrument	None	twotheta_offset	0.6243	0.6231	0.0017	deg	0.19 % ↓
8	hrpt	background	10	y	167.7066	167.5167	2.0311		0.11 % ↓
9	hrpt	background	30	y	166.0338	166.7627	1.4794		0.44 % ↑
10	hrpt	background	50	y	169.9495	170.8330	1.0808		0.52 % ↑
11	hrpt	background	110	y	170.0802	172.2546	0.9660		1.28 % ↑
12	hrpt	background	165	y	179.6656	180.6405	1.2737		0.54 % ↑

Plot Measured vs Calculated¶

In [62]:

Copied!

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

In [63]:

Copied!

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 [64]:

Copied!

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

Saving project 📦 'lbco_hrpt' to

/private/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]:

Copied!





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.

In [66]:

Copied!

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	min	max	units
1	lbco	cell		length_a	3.89091	0.00005	-inf	inf	Å
2	lbco	atom_site	La	b_iso	0.50000		-inf	inf	Å²
3	lbco	atom_site	Ba	b_iso	0.50000		-inf	inf	Å²
4	lbco	atom_site	Co	b_iso	0.50000		-inf	inf	Å²
5	lbco	atom_site	O	b_iso	0.50000		-inf	inf	Å²
6	hrpt	peak		broad_gauss_u	0.08026	0.00472	-inf	inf	deg²
7	hrpt	peak		broad_gauss_v	-0.10293	0.01036	-inf	inf	deg²
8	hrpt	peak		broad_gauss_w	0.10766	0.00515	-inf	inf	deg²
9	hrpt	peak		broad_lorentz_y	0.08933	0.00320	-inf	inf	deg
10	hrpt	linked_phases	lbco	scale	7.21199	0.04057	-inf	inf
11	hrpt	instrument		twotheta_offset	0.62314	0.00167	-inf	inf	deg
12	hrpt	background	10	y	167.51669	2.03112	-inf	inf
13	hrpt	background	30	y	166.76268	1.47937	-inf	inf
14	hrpt	background	50	y	170.83305	1.08080	-inf	inf
15	hrpt	background	110	y	172.25458	0.96599	-inf	inf
16	hrpt	background	165	y	180.64054	1.27368	-inf	inf

Run Fitting¶

In [67]:

Copied!

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	2.85
2	28	2.28	19.9% ↓
3	45	1.62	28.9% ↓
4	62	1.47	9.6% ↓
5	79	1.36	7.0% ↓
6	97	1.29	5.4% ↓
7	204	1.29

🏆 Best goodness-of-fit (reduced χ²) is 1.29 at iteration 187

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 4.31 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	cell	None	length_a	3.8909	3.8909	0.0000	Å	0.00 % ↓
2	lbco	atom_site	La	b_iso	0.5000	0.5051	1216.0421	Å²	1.02 % ↑
3	lbco	atom_site	Ba	b_iso	0.5000	0.5048	1976.1672	Å²	0.96 % ↑
4	lbco	atom_site	Co	b_iso	0.5000	0.2371	0.0612	Å²	52.59 % ↓
5	lbco	atom_site	O	b_iso	0.5000	1.3935	0.0167	Å²	178.71 % ↑
6	hrpt	peak	None	broad_gauss_u	0.0803	0.0816	0.0031	deg²	1.63 % ↑
7	hrpt	peak	None	broad_gauss_v	-0.1029	-0.1159	0.0067	deg²	12.62 % ↑
8	hrpt	peak	None	broad_gauss_w	0.1077	0.1204	0.0033	deg²	11.88 % ↑
9	hrpt	peak	None	broad_lorentz_y	0.0893	0.0844	0.0021	deg	5.47 % ↓
10	hrpt	linked_phases	lbco	scale	7.2120	9.1350	0.0641		26.66 % ↑
11	hrpt	instrument	None	twotheta_offset	0.6231	0.6226	0.0010	deg	0.09 % ↓
12	hrpt	background	10	y	167.5167	168.5585	1.3671		0.62 % ↑
13	hrpt	background	30	y	166.7627	164.3357	0.9992		1.46 % ↓
14	hrpt	background	50	y	170.8330	166.8881	0.7388		2.31 % ↓
15	hrpt	background	110	y	172.2546	175.4004	0.6571		1.83 % ↑
16	hrpt	background	165	y	180.6405	174.2811	0.9113		3.52 % ↓

Plot Measured vs Calculated¶

In [68]:

Copied!

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

In [69]:

Copied!

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 [70]:

Copied!

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

Saving project 📦 'lbco_hrpt' to

/private/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]:

Copied!





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

Set constraints.

In [72]:

Copied!

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

Show defined constraints.

In [73]:

Copied!

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

User defined constraints

	lhs_alias	rhs_expr	full expression
1	biso_Ba	biso_La	biso_Ba = biso_La

Show free parameters before applying constraints.

In [74]:

Copied!

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	min	max	units
1	lbco	cell		length_a	3.89087	0.00004	-inf	inf	Å
2	lbco	atom_site	La	b_iso	0.50509	1216.04215	-inf	inf	Å²
3	lbco	atom_site	Ba	b_iso	0.50481	1976.16719	-inf	inf	Å²
4	lbco	atom_site	Co	b_iso	0.23707	0.06119	-inf	inf	Å²
5	lbco	atom_site	O	b_iso	1.39354	0.01668	-inf	inf	Å²
6	hrpt	peak		broad_gauss_u	0.08157	0.00314	-inf	inf	deg²
7	hrpt	peak		broad_gauss_v	-0.11592	0.00672	-inf	inf	deg²
8	hrpt	peak		broad_gauss_w	0.12045	0.00328	-inf	inf	deg²
9	hrpt	peak		broad_lorentz_y	0.08445	0.00215	-inf	inf	deg
10	hrpt	linked_phases	lbco	scale	9.13503	0.06407	-inf	inf
11	hrpt	instrument		twotheta_offset	0.62258	0.00104	-inf	inf	deg
12	hrpt	background	10	y	168.55849	1.36709	-inf	inf
13	hrpt	background	30	y	164.33571	0.99917	-inf	inf
14	hrpt	background	50	y	166.88814	0.73884	-inf	inf
15	hrpt	background	110	y	175.40040	0.65706	-inf	inf
16	hrpt	background	165	y	174.28113	0.91128	-inf	inf

Apply constraints.

In [75]:

Copied!

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

Show free parameters after applying constraints.

In [76]:

Copied!

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	min	max	units
1	lbco	cell		length_a	3.89087	0.00004	-inf	inf	Å
2	lbco	atom_site	La	b_iso	0.50509	1216.04215	-inf	inf	Å²
3	lbco	atom_site	Co	b_iso	0.23707	0.06119	-inf	inf	Å²
4	lbco	atom_site	O	b_iso	1.39354	0.01668	-inf	inf	Å²
5	hrpt	peak		broad_gauss_u	0.08157	0.00314	-inf	inf	deg²
6	hrpt	peak		broad_gauss_v	-0.11592	0.00672	-inf	inf	deg²
7	hrpt	peak		broad_gauss_w	0.12045	0.00328	-inf	inf	deg²
8	hrpt	peak		broad_lorentz_y	0.08445	0.00215	-inf	inf	deg
9	hrpt	linked_phases	lbco	scale	9.13503	0.06407	-inf	inf
10	hrpt	instrument		twotheta_offset	0.62258	0.00104	-inf	inf	deg
11	hrpt	background	10	y	168.55849	1.36709	-inf	inf
12	hrpt	background	30	y	164.33571	0.99917	-inf	inf
13	hrpt	background	50	y	166.88814	0.73884	-inf	inf
14	hrpt	background	110	y	175.40040	0.65706	-inf	inf
15	hrpt	background	165	y	174.28113	0.91128	-inf	inf

Run Fitting¶

In [77]:

Copied!

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	1.29
2	20	1.29

🏆 Best goodness-of-fit (reduced χ²) is 1.29 at iteration 19

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 0.82 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	cell	None	length_a	3.8909	3.8909	0.0000	Å	0.00 % ↑
2	lbco	atom_site	La	b_iso	0.5051	0.5051	0.0278	Å²	0.00 % ↓
3	lbco	atom_site	Co	b_iso	0.2371	0.2370	0.0564	Å²	0.03 % ↓
4	lbco	atom_site	O	b_iso	1.3935	1.3935	0.0160	Å²	0.00 % ↑
5	hrpt	peak	None	broad_gauss_u	0.0816	0.0816	0.0031	deg²	0.00 % ↑
6	hrpt	peak	None	broad_gauss_v	-0.1159	-0.1159	0.0066	deg²	0.00 % ↑
7	hrpt	peak	None	broad_gauss_w	0.1204	0.1204	0.0032	deg²	0.00 % ↑
8	hrpt	peak	None	broad_lorentz_y	0.0844	0.0844	0.0021	deg	0.00 % ↓
9	hrpt	linked_phases	lbco	scale	9.1350	9.1351	0.0538		0.00 % ↑
10	hrpt	instrument	None	twotheta_offset	0.6226	0.6226	0.0010	deg	0.00 % ↑
11	hrpt	background	10	y	168.5585	168.5585	1.3669		0.00 % ↓
12	hrpt	background	30	y	164.3357	164.3357	0.9990		0.00 % ↓
13	hrpt	background	50	y	166.8881	166.8881	0.7386		0.00 % ↓
14	hrpt	background	110	y	175.4004	175.4006	0.6488		0.00 % ↑
15	hrpt	background	165	y	174.2811	174.2812	0.8944		0.00 % ↑

Plot Measured vs Calculated¶

In [78]:

Copied!

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

In [79]:

Copied!

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]:

Copied!

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

Saving project 📦 'lbco_hrpt' to

/private/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]:

Copied!





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

Set more constraints.

In [82]:

Copied!





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

Show defined constraints.

In [83]:

Copied!

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

User defined constraints

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

Apply constraints.

In [84]:

Copied!

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

Set sample model parameters to be refined.

In [85]:

Copied!

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]:

Copied!

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	min	max	units
1	lbco	cell		length_a	3.89087	0.00004	-inf	inf	Å
2	lbco	atom_site	La	occupancy	0.50000		-inf	inf
3	lbco	atom_site	La	b_iso	0.50508	0.02777	-inf	inf	Å²
4	lbco	atom_site	Co	b_iso	0.23699	0.05643	-inf	inf	Å²
5	lbco	atom_site	O	b_iso	1.39355	0.01599	-inf	inf	Å²
6	hrpt	peak		broad_gauss_u	0.08157	0.00310	-inf	inf	deg²
7	hrpt	peak		broad_gauss_v	-0.11593	0.00664	-inf	inf	deg²
8	hrpt	peak		broad_gauss_w	0.12045	0.00325	-inf	inf	deg²
9	hrpt	peak		broad_lorentz_y	0.08445	0.00214	-inf	inf	deg
10	hrpt	linked_phases	lbco	scale	9.13509	0.05380	-inf	inf
11	hrpt	instrument		twotheta_offset	0.62258	0.00103	-inf	inf	deg
12	hrpt	background	10	y	168.55849	1.36685	-inf	inf
13	hrpt	background	30	y	164.33569	0.99900	-inf	inf
14	hrpt	background	50	y	166.88808	0.73857	-inf	inf
15	hrpt	background	110	y	175.40056	0.64879	-inf	inf
16	hrpt	background	165	y	174.28124	0.89439	-inf	inf

Run Fitting¶

In [87]:

Copied!

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	1.29
2	55	1.28

🏆 Best goodness-of-fit (reduced χ²) is 1.28 at iteration 54

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 1.10 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	cell	None	length_a	3.8909	3.8909	0.0000	Å	0.00 % ↑
2	lbco	atom_site	La	occupancy	0.5000	0.5840	0.0203		16.81 % ↑
3	lbco	atom_site	La	b_iso	0.5051	0.5983	0.0355	Å²	18.46 % ↑
4	lbco	atom_site	Co	b_iso	0.2370	0.1665	0.0580	Å²	29.74 % ↓
5	lbco	atom_site	O	b_iso	1.3935	1.3491	0.0192	Å²	3.19 % ↓
6	hrpt	peak	None	broad_gauss_u	0.0816	0.0812	0.0031	deg²	0.43 % ↓
7	hrpt	peak	None	broad_gauss_v	-0.1159	-0.1154	0.0066	deg²	0.48 % ↓
8	hrpt	peak	None	broad_gauss_w	0.1204	0.1203	0.0032	deg²	0.14 % ↓
9	hrpt	peak	None	broad_lorentz_y	0.0844	0.0846	0.0021	deg	0.18 % ↑
10	hrpt	linked_phases	lbco	scale	9.1351	8.9057	0.0761		2.51 % ↓
11	hrpt	instrument	None	twotheta_offset	0.6226	0.6226	0.0010	deg	0.00 % ↑
12	hrpt	background	10	y	168.5585	168.9780	1.3666		0.25 % ↑
13	hrpt	background	30	y	164.3357	164.0535	0.9992		0.17 % ↓
14	hrpt	background	50	y	166.8881	166.9125	0.7364		0.01 % ↑
15	hrpt	background	110	y	175.4006	175.2699	0.6479		0.07 % ↓
16	hrpt	background	165	y	174.2812	174.5580	0.8935		0.16 % ↑

Plot Measured vs Calculated¶

In [88]:

Copied!

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

In [89]:

Copied!

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]:

Copied!

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

Saving project 📦 'lbco_hrpt' to

/private/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¶

In [91]:

Copied!

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

	Parameter	Value
1	a	3.89087
2	b	3.89087
3	c	3.89087
4	alpha	90.00000
5	beta	90.00000
6	gamma	90.00000

Atom sites

	label	type	x	y	z	occ	Biso
1	La	La	0.00000	0.00000	0.00000	0.58403	0.59832
2	Ba	Ba	0.00000	0.00000	0.00000	0.41597	0.59832
3	Co	Co	0.50000	0.50000	0.50000	1.00000	0.16651
4	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

PeakProfileTypeEnum.PSEUDO_VOIGT

Peak broadening (Gaussian)

	Parameter	Value
1	U	0.08122
2	V	-0.11537
3	W	0.12028

Peak broadening (Lorentzian)

	Parameter	Value
1	X	0.00000
2	Y	0.08460

FITTING
━━━━━━━

Calculation engine

cryspy

Minimization engine

lmfit (leastsq)

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	1.28