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 crystal structures 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.structures, project.experiments, and project.analysis. The project object is the main container for all information.

Import Library¶

In [2]:

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]:

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

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

Set Project Metadata¶

In [4]:

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]:

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 '31 Mar 2026 21:25:54'
8	_project.last_modified '31 Mar 2026 21:25:54'

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]:

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

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

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

├── 📁 experiments/

├── 📄 analysis.cif

└── 📄 summary.cif

Set Up Data Plotter¶

Show supported plotting engines.

In [7]:

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]:

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	25

Set plotting engine.

In [9]:

# Keep the auto-selected engine. Alternatively, you can uncomment the
# line below to explicitly set the engine to the required one.
# project.plotter.engine = 'plotly'

# Keep the auto-selected engine. Alternatively, you can uncomment the # line below to explicitly set the engine to the required one. # project.plotter.engine = 'plotly'

Step 2: Define Structure¶

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

Add Structure¶

In [10]:

project.structures.create(name='lbco')

project.structures.create(name='lbco')

Show Defined Structures¶

Show the names of the crystal structures added. These names are used to access the structure using the syntax: project.structures[name]. All structure parameters can be accessed via the project object.

In [11]:

project.structures.show_names()

project.structures.show_names()

Defined structures 🧩

['lbco']

Set Space Group¶

Modify the default space group parameters.

In [12]:

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

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

Set Unit Cell¶

Modify the default unit cell parameters.

In [13]:

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

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

Set Atom Sites¶

Add atom sites to the structure.

In [14]:

project.structures['lbco'].atom_sites.create(
    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.structures['lbco'].atom_sites.create(
    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.structures['lbco'].atom_sites.create(
    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.structures['lbco'].atom_sites.create(
    label='O',
    type_symbol='O',
    fract_x=0,
    fract_y=0.5,
    fract_z=0.5,
    wyckoff_letter='c',
    b_iso=0.5,
)

project.structures['lbco'].atom_sites.create( 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.structures['lbco'].atom_sites.create( 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.structures['lbco'].atom_sites.create( 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.structures['lbco'].atom_sites.create( label='O', type_symbol='O', fract_x=0, fract_y=0.5, fract_z=0.5, wyckoff_letter='c', b_iso=0.5, )

Show Structure as CIF¶

In [15]:

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

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

Structure 🧩 'lbco' as cif

	CIF
1	data_lbco
2
3	_cell.length_a 3.88000000
4	_cell.length_b 3.88000000
5	_cell.length_c 3.88000000
6	_cell.angle_alpha 90.00000000
7	_cell.angle_beta 90.00000000
8	_cell.angle_gamma 90.00000000
9
10	_space_group.name_H-M_alt "P 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 0.00000000 0.00000000 0.00000000 a 0.50000000 0.50000000 Biso
24	Ba Ba 0.00000000 0.00000000 0.00000000 a 0.50000000 0.50000000 Biso
25	Co Co 0.50000000 0.50000000 0.50000000 b 1.00000000 0.50000000 Biso
26	O O 0.00000000 0.50000000 0.50000000 c 1.00000000 0.50000000 Biso

Show Structure Structure¶

In [16]:

project.structures['lbco'].show()

project.structures['lbco'].show()

Structure 🧩 'lbco'

Not implemented yet.

Save Project State¶

Save the project state after adding the structure. 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 [17]:

project.save()

project.save()

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

├── 📄 analysis.cif

└── 📄 summary.cif

Step 3: Define Experiment¶

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

Download Measured Data¶

Download the data file from the EasyDiffraction repository on GitHub.

In [18]:

data_path = ed.download_data(id=3, destination='data')

data_path = ed.download_data(id=3, destination='data')

Getting data...

Data #3: La0.5Ba0.5CoO3, HRPT (PSI), 300 K

✅ Data #3 already present at 'data/ed-3.xye'. Keeping existing file.

Add Diffraction Experiment¶

In [19]:

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

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

Data loaded successfully

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

Show Defined Experiments¶

In [20]:

project.experiments.show_names()

project.experiments.show_names()

Defined experiments 🔬

['hrpt']

Show Measured Data¶

In [21]:

project.plot_meas(expt_name='hrpt')

project.plot_meas(expt_name='hrpt')

Warning: No linked phases defined. Returning empty pattern.

Set Instrument¶

Modify the default instrument parameters.

In [22]:

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 [23]:

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

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

Supported types

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

Show the current peak profile type.

In [24]:

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 [25]:

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

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

⚠️ Switching peak profile type discards existing peak parameters.                                                                 

Peak profile type for experiment 'hrpt' changed to

pseudo-voigt

Modify default peak profile parameters.

In [26]:

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 [27]:

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

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

Supported types

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

Show current background type.

In [28]:

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 [29]:

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

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

Background type for experiment 'hrpt' already set to

line-segment

Add background points.

In [30]:

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

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

Show current background points.

In [31]:

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 structure defined in the previous step to the experiment.

In [32]:

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

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

Show Experiment as CIF¶

In [33]:

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	_diffrn.ambient_temperature None
9	_diffrn.ambient_pressure None
10	_diffrn.ambient_magnetic_field None
11	_diffrn.ambient_electric_field None
12
13	_peak.broad_gauss_u 0.10000000
14	_peak.broad_gauss_v -0.10000000
15	_peak.broad_gauss_w 0.10000000
16	_peak.broad_lorentz_x 0.00000000
17	_peak.broad_lorentz_y 0.10000000
18
19	_instr.wavelength 1.49400000
20	_instr.2theta_offset 0.60000000
21
22	loop_
23	_pd_phase_block.id
24	_pd_phase_block.scale
25	lbco 10.00000000
26
27
28
29	loop_
30	_pd_proc.2theta_scan
31	_pd_data.point_id
32	_pd_proc.d_spacing
33	_pd_meas.intensity_total
34	_pd_meas.intensity_total_su
35	_pd_calc.intensity_total
36	_pd_calc.intensity_bkg
37	_pd_data.refinement_status
38	10.00000000 1 8.57086379 167.00000000 12.60000000 172.32780248 170.00000000 incl
39	10.05000000 2 8.52833125 157.00000000 12.50000000 172.30859914 170.00000000 incl
40	10.10000000 3 8.48622036 187.00000000 13.30000000 172.28969336 170.00000000 incl
41	10.15000000 4 8.44452490 197.00000000 14.00000000 172.27107915 170.00000000 incl
42	10.20000000 5 8.40323875 164.00000000 12.50000000 172.25275064 170.00000000 incl
43	10.25000000 6 8.36235592 171.00000000 13.00000000 172.23470212 170.00000000 incl
44	10.30000000 7 8.32187055 190.00000000 13.40000000 172.21692803 170.00000000 incl
45	10.35000000 8 8.28177687 182.00000000 13.50000000 172.19942295 170.00000000 incl
46	10.40000000 9 8.24206922 166.00000000 12.60000000 172.18218159 170.00000000 incl
47	10.45000000 10 8.20274208 203.00000000 14.30000000 172.16519880 170.00000000 incl
48	...
49	164.40000000 3089 0.75397591 202.00000000 18.50000000 172.60037118 170.00000000 incl
50	164.45000000 3090 0.75393091 178.00000000 20.40000000 172.59695823 170.00000000 incl
51	164.50000000 3091 0.75388607 153.00000000 18.00000000 172.59381336 170.00000000 incl
52	164.55000000 3092 0.75384138 197.00000000 25.30000000 172.59093099 170.00000000 incl
53	164.60000000 3093 0.75379684 153.00000000 20.70000000 172.58830579 170.00000000 incl
54	164.65000000 3094 0.75375244 173.00000000 30.10000000 172.58593268 170.00000000 incl
55	164.70000000 3095 0.75370819 187.00000000 27.90000000 172.58380680 170.00000000 incl
56	164.75000000 3096 0.75366410 175.00000000 38.20000000 172.58192354 170.00000000 incl
57	164.80000000 3097 0.75362015 168.00000000 30.90000000 172.58027848 170.00000000 incl
58	164.85000000 3098 0.75357634 109.00000000 41.20000000 172.57886743 170.00000000 incl
59
60	loop_
61	_pd_background.id
62	_pd_background.line_segment_X
63	_pd_background.line_segment_intensity
64	10 10.00000000 170.00000000
65	30 30.00000000 170.00000000
66	50 50.00000000 170.00000000
67	110 110.00000000 170.00000000
68	165 165.00000000 170.00000000

Save Project State¶

In [34]:

project.save()

project.save()

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 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 for this experiment.

In [35]:

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

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

Supported calculator types

	Type	Description
1	cryspy	CrysPy library for crystallographic calculations

Show current calculation engine for this experiment.

In [36]:

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

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

Current calculator type

CalculatorEnum.CRYSPY

Select the desired calculation engine.

In [37]:

project.experiments['hrpt'].calculator_type = 'cryspy'

project.experiments['hrpt'].calculator_type = 'cryspy'

Calculator for experiment 'hrpt' changed to

cryspy

Show Calculated Data¶

In [38]:

project.plot_calc(expt_name='hrpt')

project.plot_calc(expt_name='hrpt')

Plot Measured vs Calculated¶

In [39]:

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

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

In [40]:

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 [41]:

# project.analysis.show_all_params()

# project.analysis.show_all_params()

Show all fittable parameters.

In [42]:

project.analysis.show_fittable_params()

project.analysis.show_fittable_params()

Fittable parameters for all structures (🧩 data blocks)

	datablock	category	entry	parameter	value	uncertainty	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		Ų	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		Ų	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		Ų	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		Ų	False

Fittable parameters for all experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	units	free
1	hrpt	linked_phases	lbco	scale	10.00000			False
2	hrpt	peak		broad_gauss_u	0.10000		deg²	False
3	hrpt	peak		broad_gauss_v	-0.10000		deg²	False
4	hrpt	peak		broad_gauss_w	0.10000		deg²	False
5	hrpt	peak		broad_lorentz_x	0.00000		deg	False
6	hrpt	peak		broad_lorentz_y	0.10000		deg	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 [43]:

project.analysis.show_free_params()

project.analysis.show_free_params()

⚠️ No free parameters found.                                                                                                      

Show how to access parameters in the code.

In [44]:

# project.analysis.how_to_access_parameters()

# project.analysis.how_to_access_parameters()

Set Fit Mode¶

Show supported fit modes.

In [45]:

project.analysis.show_supported_fit_mode_types()

project.analysis.show_supported_fit_mode_types()

Supported types

	Type	Description
1	default	Fit-mode category

Show current fit mode.

In [46]:

project.analysis.show_current_fit_mode_type()

project.analysis.show_current_fit_mode_type()

Current fit-mode type

default

Select desired fit mode.

In [47]:

project.analysis.fit_mode.mode = 'single'

project.analysis.fit_mode.mode = 'single'

Set Minimizer¶

Show supported fitting engines.

In [48]:

project.analysis.show_available_minimizers()

project.analysis.show_available_minimizers()

Supported types

	Type	Description
1	dfols	DFO-LS derivative-free least-squares optimization
2	lmfit	LMFIT with Levenberg-Marquardt least squares

Show current fitting engine.

In [49]:

project.analysis.show_current_minimizer()

project.analysis.show_current_minimizer()

Current minimizer

lmfit

Select desired fitting engine.

In [50]:

project.analysis.current_minimizer = 'lmfit'

project.analysis.current_minimizer = 'lmfit'

Current minimizer changed to

lmfit

Perform Fit 1/5¶

Set structure parameters to be refined.

In [51]:

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

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

Set experiment parameters to be refined.

In [52]:

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 [53]:

project.analysis.show_free_params()

project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	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 [54]:

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

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

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.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 4.12 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	linked_phases	lbco	scale	10.0000	7.3409	0.0350		26.59 % ↓
3	hrpt	instrument		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 [55]:

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

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

In [56]:

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 [57]:

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

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

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 2/5¶

Set more parameters to be refined.

In [58]:

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 [59]:

project.analysis.show_free_params()

project.analysis.show_free_params()

Free parameters for both structures (🧩 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	linked_phases	lbco	scale	7.34088	0.03496	-inf	inf
3	hrpt	peak		broad_gauss_u	0.10000		-inf	inf	deg²
4	hrpt	peak		broad_gauss_v	-0.10000		-inf	inf	deg²
5	hrpt	peak		broad_gauss_w	0.10000		-inf	inf	deg²
6	hrpt	peak		broad_lorentz_y	0.10000		-inf	inf	deg
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 [60]:

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

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

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.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 2.96 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	linked_phases	lbco	scale	7.3409	7.2120	0.0406		1.76 % ↓
3	hrpt	peak		broad_gauss_u	0.1000	0.0803	0.0047	deg²	19.74 % ↓
4	hrpt	peak		broad_gauss_v	-0.1000	-0.1029	0.0104	deg²	2.93 % ↑
5	hrpt	peak		broad_gauss_w	0.1000	0.1077	0.0051	deg²	7.66 % ↑
6	hrpt	peak		broad_lorentz_y	0.1000	0.0893	0.0032	deg	10.67 % ↓
7	hrpt	instrument		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 [61]:

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

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

In [62]:

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 [63]:

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

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

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 3/5¶

Set more parameters to be refined.

In [64]:

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

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

Show free parameters after selection.

In [65]:

project.analysis.show_free_params()

project.analysis.show_free_params()

Free parameters for both structures (🧩 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	Ų
3	lbco	atom_site	Ba	b_iso	0.50000		-inf	inf	Ų
4	lbco	atom_site	Co	b_iso	0.50000		-inf	inf	Ų
5	lbco	atom_site	O	b_iso	0.50000		-inf	inf	Ų
6	hrpt	linked_phases	lbco	scale	7.21199	0.04057	-inf	inf
7	hrpt	peak		broad_gauss_u	0.08026	0.00472	-inf	inf	deg²
8	hrpt	peak		broad_gauss_v	-0.10293	0.01036	-inf	inf	deg²
9	hrpt	peak		broad_gauss_w	0.10766	0.00515	-inf	inf	deg²
10	hrpt	peak		broad_lorentz_y	0.08933	0.00320	-inf	inf	deg
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 [66]:

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

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

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.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 8.80 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		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↓
2	lbco	atom_site	La	b_iso	0.5000	0.5051	1216.7409	Ų	1.02 % ↑
3	lbco	atom_site	Ba	b_iso	0.5000	0.5048	1977.3028	Ų	0.96 % ↑
4	lbco	atom_site	Co	b_iso	0.5000	0.2371	0.0612	Ų	52.59 % ↓
5	lbco	atom_site	O	b_iso	0.5000	1.3935	0.0167	Ų	178.71 % ↑
6	hrpt	linked_phases	lbco	scale	7.2120	9.1350	0.0641		26.66 % ↑
7	hrpt	peak		broad_gauss_u	0.0803	0.0816	0.0031	deg²	1.63 % ↑
8	hrpt	peak		broad_gauss_v	-0.1029	-0.1159	0.0067	deg²	12.62 % ↑
9	hrpt	peak		broad_gauss_w	0.1077	0.1204	0.0033	deg²	11.88 % ↑
10	hrpt	peak		broad_lorentz_y	0.0893	0.0844	0.0021	deg	5.47 % ↓
11	hrpt	instrument		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 [67]:

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

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

In [68]:

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 [69]:

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

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

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 4/5¶

Set Constraints¶

Set aliases for parameters.

In [70]:

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

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

Set constraints.

In [71]:

project.analysis.constraints.create(expression='biso_Ba = biso_La')

project.analysis.constraints.create(expression='biso_Ba = biso_La')

Show defined constraints.

In [72]:

project.analysis.show_constraints()

project.analysis.show_constraints()

User defined constraints

	expression
1	biso_Ba = biso_La

Show free parameters before applying constraints.

In [73]:

project.analysis.show_free_params()

project.analysis.show_free_params()

Free parameters for both structures (🧩 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	1216.74090	-inf	inf	Ų
3	lbco	atom_site	Ba	b_iso	0.50481	1977.30283	-inf	inf	Ų
4	lbco	atom_site	Co	b_iso	0.23707	0.06119	-inf	inf	Ų
5	lbco	atom_site	O	b_iso	1.39354	0.01668	-inf	inf	Ų
6	hrpt	linked_phases	lbco	scale	9.13503	0.06407	-inf	inf
7	hrpt	peak		broad_gauss_u	0.08157	0.00314	-inf	inf	deg²
8	hrpt	peak		broad_gauss_v	-0.11592	0.00672	-inf	inf	deg²
9	hrpt	peak		broad_gauss_w	0.12045	0.00328	-inf	inf	deg²
10	hrpt	peak		broad_lorentz_y	0.08445	0.00215	-inf	inf	deg
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 [74]:

project.analysis.apply_constraints()

project.analysis.apply_constraints()

Show free parameters after applying constraints.

In [75]:

project.analysis.show_free_params()

project.analysis.show_free_params()

Free parameters for both structures (🧩 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	1216.74090	-inf	inf	Ų
3	lbco	atom_site	Co	b_iso	0.23707	0.06119	-inf	inf	Ų
4	lbco	atom_site	O	b_iso	1.39354	0.01668	-inf	inf	Ų
5	hrpt	linked_phases	lbco	scale	9.13503	0.06407	-inf	inf
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	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 [76]:

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

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

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.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 0.96 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		length_a	3.8909	3.8909	0.0000	Å	0.00 % ↑
2	lbco	atom_site	La	b_iso	0.5051	0.5051	0.0278	Ų	0.00 % ↓
3	lbco	atom_site	Co	b_iso	0.2371	0.2370	0.0564	Ų	0.03 % ↓
4	lbco	atom_site	O	b_iso	1.3935	1.3935	0.0160	Ų	0.00 % ↑
5	hrpt	linked_phases	lbco	scale	9.1350	9.1351	0.0538		0.00 % ↑
6	hrpt	peak		broad_gauss_u	0.0816	0.0816	0.0031	deg²	0.00 % ↑
7	hrpt	peak		broad_gauss_v	-0.1159	-0.1159	0.0066	deg²	0.00 % ↑
8	hrpt	peak		broad_gauss_w	0.1204	0.1204	0.0032	deg²	0.00 % ↑
9	hrpt	peak		broad_lorentz_y	0.0844	0.0844	0.0021	deg	0.00 % ↓
10	hrpt	instrument		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 [77]:

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

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

In [78]:

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 [79]:

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

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

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Perform Fit 5/5¶

Set Constraints¶

Set more aliases for parameters.

In [80]:

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

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

Set more constraints.

In [81]:

project.analysis.constraints.create(
    expression='occ_Ba = 1 - occ_La',
)

project.analysis.constraints.create( expression='occ_Ba = 1 - occ_La', )

Show defined constraints.

In [82]:

project.analysis.show_constraints()

project.analysis.show_constraints()

User defined constraints

	expression
1	biso_Ba = biso_La
2	occ_Ba = 1 - occ_La

Apply constraints.

In [83]:

project.analysis.apply_constraints()

project.analysis.apply_constraints()

Set structure parameters to be refined.

In [84]:

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

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

Show free parameters after selection.

In [85]:

project.analysis.show_free_params()

project.analysis.show_free_params()

Free parameters for both structures (🧩 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	Ų
4	lbco	atom_site	Co	b_iso	0.23699	0.05643	-inf	inf	Ų
5	lbco	atom_site	O	b_iso	1.39355	0.01599	-inf	inf	Ų
6	hrpt	linked_phases	lbco	scale	9.13509	0.05380	-inf	inf
7	hrpt	peak		broad_gauss_u	0.08157	0.00310	-inf	inf	deg²
8	hrpt	peak		broad_gauss_v	-0.11593	0.00664	-inf	inf	deg²
9	hrpt	peak		broad_gauss_w	0.12045	0.00325	-inf	inf	deg²
10	hrpt	peak		broad_lorentz_y	0.08445	0.00214	-inf	inf	deg
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 [86]:

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

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

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.

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 lbco.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📄 analysis.cif

└── 📄 summary.cif

Fit results

✅ Success: True

⏱️ Fitting time: 2.15 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		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	Ų	18.46 % ↑
4	lbco	atom_site	Co	b_iso	0.2370	0.1665	0.0580	Ų	29.74 % ↓
5	lbco	atom_site	O	b_iso	1.3935	1.3491	0.0192	Ų	3.19 % ↓
6	hrpt	linked_phases	lbco	scale	9.1351	8.9057	0.0761		2.51 % ↓
7	hrpt	peak		broad_gauss_u	0.0816	0.0812	0.0031	deg²	0.43 % ↓
8	hrpt	peak		broad_gauss_v	-0.1159	-0.1154	0.0066	deg²	0.48 % ↓
9	hrpt	peak		broad_gauss_w	0.1204	0.1203	0.0032	deg²	0.14 % ↓
10	hrpt	peak		broad_lorentz_y	0.0844	0.0846	0.0021	deg	0.18 % ↑
11	hrpt	instrument		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 [87]:

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

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

In [88]:

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 [89]:

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

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

Saving project 📦 'lbco_hrpt' to

/tmp/lbco_hrpt

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 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 [90]:

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

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

  hrpt: cryspy

Minimization engine

lmfit

Fit quality

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

In [ ]: