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]:

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 '24 Dec 2025 21:55:48'
8	_project.last_modified '24 Dec 2025 21:55:48'

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

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/T/lbco_hrpt

├── 📄 project.cif

├── 📄 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	9

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 Sample Model¶

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

Add Sample Model¶

In [10]:

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

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

Show Defined Sample Models¶

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

In [11]:

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]:

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]:

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]:

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

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

Show Sample Model as CIF¶

In [15]:

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 3.8800
4	_cell.length_b 3.8800
5	_cell.length_c 3.8800
6	_cell.angle_alpha 90.0000
7	_cell.angle_beta 90.0000
8	_cell.angle_gamma 90.0000
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 0.0000 0.0000 0.0000 a 0.5000 0.5000 Biso
24	Ba Ba 0.0000 0.0000 0.0000 a 0.5000 0.5000 Biso
25	Co Co 0.5000 0.5000 0.5000 b 1.0000 0.5000 Biso
26	O O 0.0000 0.5000 0.5000 c 1.0000 0.5000 Biso

Show Sample Model Structure¶

In [16]:

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 [17]:

project.save()

project.save()

Saving project 📦 'lbco_hrpt' to

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/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 [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 downloaded to 'data/ed-3.xye'

Add Diffraction Experiment¶

In [19]:

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

project.experiments.add( 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 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 [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'

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 background types

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

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' changed to

line-segment

Add background points.

In [30]:

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

project.experiments['hrpt'].background.add(id='10', x=10, y=170) project.experiments['hrpt'].background.add(id='30', x=30, y=170) project.experiments['hrpt'].background.add(id='50', x=50, y=170) project.experiments['hrpt'].background.add(id='110', x=110, y=170) project.experiments['hrpt'].background.add(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 sample model defined in the previous step to the experiment.

In [32]:

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

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

Show Experiment as CIF¶

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	_peak.broad_gauss_u 0.1000
9	_peak.broad_gauss_v -0.1000
10	_peak.broad_gauss_w 0.1000
11	_peak.broad_lorentz_x 0.0000
12	_peak.broad_lorentz_y 0.1000
13
14	_instr.wavelength 1.4940
15	_instr.2theta_offset 0.6000
16
17	loop_
18	_pd_phase_block.id
19	_pd_phase_block.scale
20	lbco 10.0000
21
22
23
24	loop_
25	_pd_proc.2theta_scan
26	_pd_data.point_id
27	_pd_proc.d_spacing
28	_pd_meas.intensity_total
29	_pd_meas.intensity_total_su
30	_pd_calc.intensity_total
31	_pd_calc.intensity_bkg
32	_pd_data.refinement_status
33	10.0000 1 8.5709 167.0000 12.6000 172.3278 170.0000 incl
34	10.0500 2 8.5283 157.0000 12.5000 172.3086 170.0000 incl
35	10.1000 3 8.4862 187.0000 13.3000 172.2897 170.0000 incl
36	10.1500 4 8.4445 197.0000 14.0000 172.2711 170.0000 incl
37	10.2000 5 8.4032 164.0000 12.5000 172.2528 170.0000 incl
38	10.2500 6 8.3624 171.0000 13.0000 172.2347 170.0000 incl
39	10.3000 7 8.3219 190.0000 13.4000 172.2169 170.0000 incl
40	10.3500 8 8.2818 182.0000 13.5000 172.1994 170.0000 incl
41	10.4000 9 8.2421 166.0000 12.6000 172.1822 170.0000 incl
42	10.4500 10 8.2027 203.0000 14.3000 172.1652 170.0000 incl
43	...
44	164.4000 3089 0.7540 202.0000 18.5000 172.6004 170.0000 incl
45	164.4500 3090 0.7539 178.0000 20.4000 172.5970 170.0000 incl
46	164.5000 3091 0.7539 153.0000 18.0000 172.5938 170.0000 incl
47	164.5500 3092 0.7538 197.0000 25.3000 172.5909 170.0000 incl
48	164.6000 3093 0.7538 153.0000 20.7000 172.5883 170.0000 incl
49	164.6500 3094 0.7538 173.0000 30.1000 172.5859 170.0000 incl
50	164.7000 3095 0.7537 187.0000 27.9000 172.5838 170.0000 incl
51	164.7500 3096 0.7537 175.0000 38.2000 172.5819 170.0000 incl
52	164.8000 3097 0.7536 168.0000 30.9000 172.5803 170.0000 incl
53	164.8500 3098 0.7536 109.0000 41.2000 172.5789 170.0000 incl
54
55	loop_
56	_pd_background.id
57	_pd_background.line_segment_X
58	_pd_background.line_segment_intensity
59	10 10.0000 170.0000
60	30 30.0000 170.0000
61	50 50.0000 170.0000
62	110 110.0000 170.0000
63	165 165.0000 170.0000

Save Project State¶

In [34]:

project.save()

project.save()

Saving project 📦 'lbco_hrpt' to

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/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 [35]:

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 [36]:

project.analysis.show_current_calculator()

project.analysis.show_current_calculator()

Current calculator

cryspy

Select the desired calculation engine.

In [37]:

project.analysis.current_calculator = 'cryspy'

project.analysis.current_calculator = 'cryspy'

Current calculator 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 sample models (🧩 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_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 [46]:

project.analysis.show_current_fit_mode()

project.analysis.show_current_fit_mode()

Current fit mode

single

Select desired fit mode.

In [47]:

project.analysis.fit_mode = 'single'

project.analysis.fit_mode = 'single'

Current fit mode changed to

single

Set Minimizer¶

Show supported fitting engines.

In [48]:

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 [49]:

project.analysis.show_current_minimizer()

project.analysis.show_current_minimizer()

Current minimizer

lmfit (leastsq)

Select desired fitting engine.

In [50]:

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 [51]:

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 [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 sample models (🧩 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.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: 6.11 seconds

📏 Goodness-of-fit (reduced χ²): 3.14

📏 R-factor (Rf): 8.42%

📏 R-factor squared (Rf²): 11.79%

📏 Weighted R-factor (wR): 11.63%

📈 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

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/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 [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 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	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.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: 2.90 seconds

📏 Goodness-of-fit (reduced χ²): 2.85

📏 R-factor (Rf): 8.30%

📏 R-factor squared (Rf²): 11.85%

📏 Weighted R-factor (wR): 11.90%

📈 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

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/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 [64]:

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 [65]:

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	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.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: 11.98 seconds

📏 Goodness-of-fit (reduced χ²): 1.29

📏 R-factor (Rf): 5.65%

📏 R-factor squared (Rf²): 5.30%

📏 Weighted R-factor (wR): 4.47%

📈 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	1216.0511	Ų	1.02 % ↑
3	lbco	atom_site	Ba	b_iso	0.5000	0.5048	1976.1818	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

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/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 [70]:

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

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

Set constraints.

In [71]:

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

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

Show defined constraints.

In [72]:

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 [73]:

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	1216.05113	-inf	inf	Ų
3	lbco	atom_site	Ba	b_iso	0.50481	1976.18178	-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 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	1216.05113	-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.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: 1.24 seconds

📏 Goodness-of-fit (reduced χ²): 1.29

📏 R-factor (Rf): 5.65%

📏 R-factor squared (Rf²): 5.30%

📏 Weighted R-factor (wR): 4.47%

📈 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

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/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 [80]:

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

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

Set more constraints.

In [81]:

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

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

Show defined constraints.

In [82]:

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 [83]:

project.analysis.apply_constraints()

project.analysis.apply_constraints()

Set sample model parameters to be refined.

In [84]:

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 [85]:

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	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.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: 3.09 seconds

📏 Goodness-of-fit (reduced χ²): 1.28

📏 R-factor (Rf): 5.63%

📏 R-factor squared (Rf²): 5.28%

📏 Weighted R-factor (wR): 4.44%

📈 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

/private/var/folders/sm/xrr7tmqj20s7hrsh1qhfl1d40000gn/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 [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

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

In [ ]: