Structure Refinement: HS, HRPT¶

This example demonstrates a Rietveld refinement of HS crystal structure using constant wavelength neutron powder diffraction data from HRPT at PSI.

🛠️ Import Library¶

In [2]:

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

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

🧩 Define Structure¶

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

Create Structure¶

In [3]:

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

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

Set Space Group¶

In [4]:

structure.space_group.name_h_m = 'R -3 m'
structure.space_group.coord_system_code = 'h'

structure.space_group.name_h_m = 'R -3 m' structure.space_group.coord_system_code = 'h'

Set Unit Cell¶

In [5]:

structure.cell.length_a = 6.85
structure.cell.length_c = 14.1

structure.cell.length_a = 6.85 structure.cell.length_c = 14.1

Set Atom Sites¶

In [6]:

structure.atom_sites.create(
    id='Zn',
    type_symbol='Zn',
    fract_x=0,
    fract_y=0,
    fract_z=0.5,
    adp_iso=0.5,
)
structure.atom_sites.create(
    id='Cu',
    type_symbol='Cu',
    fract_x=0.5,
    fract_y=0,
    fract_z=0,
    adp_iso=0.5,
)
structure.atom_sites.create(
    id='O',
    type_symbol='O',
    fract_x=0.21,
    fract_y=-0.21,
    fract_z=0.06,
    adp_iso=0.5,
)
structure.atom_sites.create(
    id='Cl',
    type_symbol='Cl',
    fract_x=0,
    fract_y=0,
    fract_z=0.197,
    adp_iso=0.5,
)
structure.atom_sites.create(
    id='H',
    type_symbol='2H',
    fract_x=0.13,
    fract_y=-0.13,
    fract_z=0.08,
    adp_iso=0.5,
)

structure.atom_sites.create( id='Zn', type_symbol='Zn', fract_x=0, fract_y=0, fract_z=0.5, adp_iso=0.5, ) structure.atom_sites.create( id='Cu', type_symbol='Cu', fract_x=0.5, fract_y=0, fract_z=0, adp_iso=0.5, ) structure.atom_sites.create( id='O', type_symbol='O', fract_x=0.21, fract_y=-0.21, fract_z=0.06, adp_iso=0.5, ) structure.atom_sites.create( id='Cl', type_symbol='Cl', fract_x=0, fract_y=0, fract_z=0.197, adp_iso=0.5, ) structure.atom_sites.create( id='H', type_symbol='2H', fract_x=0.13, fract_y=-0.13, fract_z=0.08, adp_iso=0.5, )

🔬 Define Experiment¶

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

Download Data¶

In [7]:

data_path = download_data('meas-hs-hrpt', destination='data')

data_path = download_data('meas-hs-hrpt', destination='data')

Getting data...

Data 'meas-hs-hrpt': HS, HRPT (PSI)

✅ Data 'meas-hs-hrpt' downloaded to '../../../data/meas-hs-hrpt.xye'

Create Experiment¶

In [8]:

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

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

Set Instrument¶

In [9]:

expt.instrument.setup_wavelength = 1.89
expt.instrument.calib_twotheta_offset = 0.0

expt.instrument.setup_wavelength = 1.89 expt.instrument.calib_twotheta_offset = 0.0

Set Peak Profile¶

In [10]:

expt.peak.show_supported()

expt.peak.show_supported()

Peak types

		Type	Description
1	*	pseudo-voigt	CWL pseudo-Voigt profile
2		pseudo-voigt + berar-baldinozzi asymmetry	CWL pseudo-Voigt profile with Berar-Baldinozzi asymmetry correction.

In [11]:

expt.peak.type = 'pseudo-voigt + berar-baldinozzi asymmetry'

expt.peak.type = 'pseudo-voigt + berar-baldinozzi asymmetry'

⚠️ Switching peak profile type adds these settings with defaults:
• asym_beba_a0=0.0
• asym_beba_a1=0.0
• asym_beba_b0=0.0
• asym_beba_b1=0.0

Peak profile type for experiment 'hrpt' changed to

pseudo-voigt + berar-baldinozzi asymmetry

In [12]:

expt.peak.broad_gauss_u = 0.1
expt.peak.broad_gauss_v = -0.2
expt.peak.broad_gauss_w = 0.2
expt.peak.broad_lorentz_y = 0

expt.peak.broad_gauss_u = 0.1 expt.peak.broad_gauss_v = -0.2 expt.peak.broad_gauss_w = 0.2 expt.peak.broad_lorentz_y = 0

In [13]:

expt.peak.cutoff_fwhm = 8

expt.peak.cutoff_fwhm = 8

Set Background¶

In [14]:

expt.background.auto_estimate()

expt.background.auto_estimate()

Set Linked Structures¶

In [15]:

expt.linked_structures.create(structure_id='hs', scale=0.5)

expt.linked_structures.create(structure_id='hs', scale=0.5)

📦 Define Project¶

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

Create Project¶

In [16]:

project = Project(name='hs_hrpt')

project = Project(name='hs_hrpt')

Add Structure¶

In [17]:

project.structures.add(structure)

project.structures.add(structure)

Add Experiment¶

In [18]:

project.experiments.add(expt)

project.experiments.add(expt)

🚀 Perform Analysis¶

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

Display Structure¶

In [19]:

project.display.structure(struct_name='hs')

project.display.structure(struct_name='hs')

Structure 🧩 'hs' (Atom view type: 'covalent')

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

Display Pattern¶

In [20]:

project.display.pattern(expt_name='hrpt')

project.display.pattern(expt_name='hrpt')

Loading plot…

In [21]:

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

Loading plot…

Perform Fit 1/4¶

Set parameters to be refined.

In [22]:

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

expt.linked_structures['hs'].scale.free = True
expt.instrument.calib_twotheta_offset.free = True

structure.cell.length_a.free = True structure.cell.length_c.free = True expt.linked_structures['hs'].scale.free = True expt.instrument.calib_twotheta_offset.free = True

Show free parameters after selection.

In [23]:

project.display.parameters.free()

project.display.parameters.free()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	hs	cell		length_a	6.85000		-inf	inf	Å
2	hs	cell		length_c	14.10000		-inf	inf	Å
3	hrpt	linked_structure	hs	scale	0.50000		-inf	inf
4	hrpt	instrument		twotheta_offset	0.00000		-inf	inf	deg

Run Fitting¶

In [24]:

project.analysis.minimizer.chi_square_change_tolerance = 1e-2

project.analysis.minimizer.chi_square_change_tolerance = 1e-2

In [25]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.05	210.23
2	8	0.40	60.12	71.4% ↓
3	13	0.87	55.45	7.8% ↓
4	18	1.09	51.96	6.3% ↓
5	23	1.32	49.78	4.2% ↓
6	28	1.54	48.53	2.5% ↓
7	33	2.04	47.85	1.4% ↓
8	39	2.32	47.49

🏆 Best goodness-of-fit (reduced χ²) is 47.49 at iteration 38

✅ Fitting complete.

In [26]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.
2	chi_square_change_tolerance	0.01	Relative change in the objective (chi-square) used to stop fitting.
3	parameter_change_tolerance	1e-08	Relative change in fitted parameters used to stop fitting.
4	gradient_tolerance	0.0	Gradient orthogonality used to stop fitting; zero disables it.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	2.32
4	🔁 Iterations	36
5	📏 Goodness-of-fit (reduced χ²)	47.49
6	📏 R-factor (Rf, %)	17.81
7	📏 R-factor squared (Rf², %)	30.41
8	📏 Weighted R-factor (wR, %)	25.01

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8500	6.8604	0.0003	0.15 % ↑
2	hs	cell		length_c	Å	14.1000	14.1312	0.0008	0.22 % ↑
3	hrpt	linked_structure	hs	scale		0.5000	0.2432	0.0029	51.36 % ↓
4	hrpt	instrument		twotheta_offset	deg	0.0000	0.1092	0.0052	N/A

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

Display Pattern¶

In [27]:

project.display.pattern(expt_name='hrpt')

project.display.pattern(expt_name='hrpt')

Loading plot…

In [28]:

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

Loading plot…

Perform Fit 2/4¶

Set more parameters to be refined.

In [29]:

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

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

expt.peak.broad_gauss_u.free = True expt.peak.broad_gauss_v.free = True expt.peak.broad_gauss_w.free = True expt.peak.broad_lorentz_y.free = True for point in expt.background: point.intensity.free = True

Show free parameters after selection.

In [30]:

project.display.parameters.free()

project.display.parameters.free()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	hs	cell		length_a	6.86041	0.00030	-inf	inf	Å
2	hs	cell		length_c	14.13115	0.00085	-inf	inf	Å
3	hrpt	linked_structure	hs	scale	0.24321	0.00292	-inf	inf
4	hrpt	peak		broad_gauss_u	0.10000		-inf	inf	deg²
5	hrpt	peak		broad_gauss_v	-0.20000		-inf	inf	deg²
6	hrpt	peak		broad_gauss_w	0.20000		-inf	inf	deg²
7	hrpt	peak		broad_lorentz_y	0.00000		-inf	inf	deg
8	hrpt	instrument		twotheta_offset	0.10920	0.00519	-inf	inf	deg
9	hrpt	background	1	intensity	645.00000		-inf	inf
10	hrpt	background	2	intensity	460.00000		-inf	inf
11	hrpt	background	3	intensity	451.00000		-inf	inf
12	hrpt	background	4	intensity	616.75182		-inf	inf
13	hrpt	background	5	intensity	451.00000		-inf	inf
14	hrpt	background	6	intensity	522.48916		-inf	inf
15	hrpt	background	7	intensity	497.01720		-inf	inf
16	hrpt	background	8	intensity	613.15327		-inf	inf
17	hrpt	background	9	intensity	657.13723		-inf	inf
18	hrpt	background	10	intensity	573.00000		-inf	inf
19	hrpt	background	11	intensity	514.00000		-inf	inf
20	hrpt	background	12	intensity	538.17307		-inf	inf

Run Fitting¶

In [31]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.07	47.73
2	24	1.43	16.34	65.8% ↓
3	45	2.72	15.68	4.0% ↓
4	66	4.02	13.04	16.8% ↓
5	88	5.46	12.92

🏆 Best goodness-of-fit (reduced χ²) is 12.92 at iteration 87

✅ Fitting complete.

In [32]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.
2	chi_square_change_tolerance	0.01	Relative change in the objective (chi-square) used to stop fitting.
3	parameter_change_tolerance	1e-08	Relative change in fitted parameters used to stop fitting.
4	gradient_tolerance	0.0	Gradient orthogonality used to stop fitting; zero disables it.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	5.46
4	🔁 Iterations	85
5	📏 Goodness-of-fit (reduced χ²)	12.92
6	📏 R-factor (Rf, %)	9.89
7	📏 R-factor squared (Rf², %)	13.84
8	📏 Weighted R-factor (wR, %)	13.01

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8604	6.8626	0.0003	0.03 % ↑
2	hs	cell		length_c	Å	14.1312	14.1392	0.0009	0.06 % ↑
3	hrpt	linked_structure	hs	scale		0.2432	0.4173	0.0039	71.58 % ↑
4	hrpt	peak		broad_gauss_u	deg²	0.1000	0.3637	0.0271	263.67 % ↑
5	hrpt	peak		broad_gauss_v	deg²	-0.2000	-0.2912	0.0483	45.62 % ↑
6	hrpt	peak		broad_gauss_w	deg²	0.2000	0.2240	0.0204	11.98 % ↑
7	hrpt	peak		broad_lorentz_y	deg	0.0000	0.1621	0.0099	N/A
8	hrpt	instrument		twotheta_offset	deg	0.1092	0.1282	0.0039	17.40 % ↑
9	hrpt	background	1	intensity		645.0000	673.1456	20.0373	4.36 % ↑
10	hrpt	background	2	intensity		460.0000	454.8721	6.2706	1.11 % ↓
11	hrpt	background	3	intensity		451.0000	436.5026	6.1284	3.21 % ↓
12	hrpt	background	4	intensity		616.7518	559.5748	13.5653	9.27 % ↓
13	hrpt	background	5	intensity		451.0000	472.3101	7.6401	4.73 % ↑
14	hrpt	background	6	intensity		522.4892	495.7019	5.4444	5.13 % ↓
15	hrpt	background	7	intensity		497.0172	404.0516	5.2688	18.70 % ↓
16	hrpt	background	8	intensity		613.1533	439.4066	10.4649	28.34 % ↓
17	hrpt	background	9	intensity		657.1372	393.7549	11.4582	40.08 % ↓
18	hrpt	background	10	intensity		573.0000	537.5813	8.9592	6.18 % ↓
19	hrpt	background	11	intensity		514.0000	454.6474	8.3857	11.55 % ↓
20	hrpt	background	12	intensity		538.1731	551.7281	14.7072	2.52 % ↑

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

Display Pattern¶

In [33]:

project.display.pattern(expt_name='hrpt')

project.display.pattern(expt_name='hrpt')

Loading plot…

In [34]:

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

Loading plot…

Perform Fit 3/4¶

Set more parameters to be refined.

In [35]:

structure.atom_sites['O'].fract_x.free = True
structure.atom_sites['O'].fract_z.free = True
structure.atom_sites['Cl'].fract_z.free = True
structure.atom_sites['H'].fract_x.free = True
structure.atom_sites['H'].fract_z.free = True

structure.atom_sites['O'].fract_x.free = True structure.atom_sites['O'].fract_z.free = True structure.atom_sites['Cl'].fract_z.free = True structure.atom_sites['H'].fract_x.free = True structure.atom_sites['H'].fract_z.free = True

Show free parameters after selection.

In [36]:

project.display.parameters.free()

project.display.parameters.free()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	hs	cell		length_a	6.86265	0.00034	-inf	inf	Å
2	hs	cell		length_c	14.13920	0.00092	-inf	inf	Å
3	hs	atom_site	O	fract_x	0.21000		-inf	inf
4	hs	atom_site	O	fract_z	0.06000		-inf	inf
5	hs	atom_site	Cl	fract_z	0.19700		-inf	inf
6	hs	atom_site	H	fract_x	0.13000		-inf	inf
7	hs	atom_site	H	fract_z	0.08000		-inf	inf
8	hrpt	linked_structure	hs	scale	0.41730	0.00391	-inf	inf
9	hrpt	peak		broad_gauss_u	0.36367	0.02709	-inf	inf	deg²
10	hrpt	peak		broad_gauss_v	-0.29125	0.04827	-inf	inf	deg²
11	hrpt	peak		broad_gauss_w	0.22397	0.02035	-inf	inf	deg²
12	hrpt	peak		broad_lorentz_y	0.16208	0.00989	-inf	inf	deg
13	hrpt	instrument		twotheta_offset	0.12820	0.00391	-inf	inf	deg
14	hrpt	background	1	intensity	673.14564	20.03728	-inf	inf
15	hrpt	background	2	intensity	454.87212	6.27064	-inf	inf
16	hrpt	background	3	intensity	436.50257	6.12836	-inf	inf
17	hrpt	background	4	intensity	559.57484	13.56527	-inf	inf
18	hrpt	background	5	intensity	472.31015	7.64012	-inf	inf
19	hrpt	background	6	intensity	495.70195	5.44440	-inf	inf
20	hrpt	background	7	intensity	404.05160	5.26882	-inf	inf
21	hrpt	background	8	intensity	439.40658	10.46488	-inf	inf
22	hrpt	background	9	intensity	393.75491	11.45819	-inf	inf
23	hrpt	background	10	intensity	537.58135	8.95915	-inf	inf
24	hrpt	background	11	intensity	454.64740	8.38570	-inf	inf
25	hrpt	background	12	intensity	551.72808	14.70719	-inf	inf

Run Fitting¶

In [37]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.06	12.94
2	29	1.74	5.19	59.9% ↓
3	55	3.34	4.95	4.6% ↓
4	82	5.57	4.95

🏆 Best goodness-of-fit (reduced χ²) is 4.95 at iteration 81

✅ Fitting complete.

In [38]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.
2	chi_square_change_tolerance	0.01	Relative change in the objective (chi-square) used to stop fitting.
3	parameter_change_tolerance	1e-08	Relative change in fitted parameters used to stop fitting.
4	gradient_tolerance	0.0	Gradient orthogonality used to stop fitting; zero disables it.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	5.57
4	🔁 Iterations	79
5	📏 Goodness-of-fit (reduced χ²)	4.95
6	📏 R-factor (Rf, %)	6.42
7	📏 R-factor squared (Rf², %)	8.75
8	📏 Weighted R-factor (wR, %)	8.05

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8626	6.8620	0.0002	0.01 % ↓
2	hs	cell		length_c	Å	14.1392	14.1349	0.0005	0.03 % ↓
3	hs	atom_site	O	fract_x		0.2100	0.2059	0.0002	1.95 % ↓
4	hs	atom_site	O	fract_z		0.0600	0.0629	0.0002	4.80 % ↑
5	hs	atom_site	Cl	fract_z		0.1970	0.1974	0.0002	0.20 % ↑
6	hs	atom_site	H	fract_x		0.1300	0.1339	0.0002	2.99 % ↑
7	hs	atom_site	H	fract_z		0.0800	0.0871	0.0001	8.86 % ↑
8	hrpt	linked_structure	hs	scale		0.4173	0.3950	0.0023	5.34 % ↓
9	hrpt	peak		broad_gauss_u	deg²	0.3637	0.3600	0.0143	1.01 % ↓
10	hrpt	peak		broad_gauss_v	deg²	-0.2912	-0.3846	0.0271	32.06 % ↑
11	hrpt	peak		broad_gauss_w	deg²	0.2240	0.2837	0.0126	26.68 % ↑
12	hrpt	peak		broad_lorentz_y	deg	0.1621	0.1385	0.0062	14.55 % ↓
13	hrpt	instrument		twotheta_offset	deg	0.1282	0.1150	0.0024	10.33 % ↓
14	hrpt	background	1	intensity		673.1456	672.1280	12.3975	0.15 % ↓
15	hrpt	background	2	intensity		454.8721	456.2864	3.8837	0.31 % ↑
16	hrpt	background	3	intensity		436.5026	448.0908	3.7966	2.65 % ↑
17	hrpt	background	4	intensity		559.5748	564.5114	8.4315	0.88 % ↑
18	hrpt	background	5	intensity		472.3101	464.7541	4.7981	1.60 % ↓
19	hrpt	background	6	intensity		495.7019	517.9317	3.3706	4.48 % ↑
20	hrpt	background	7	intensity		404.0516	449.7735	3.2345	11.32 % ↑
21	hrpt	background	8	intensity		439.4066	473.4162	6.7673	7.74 % ↑
22	hrpt	background	9	intensity		393.7549	476.4911	8.0702	21.01 % ↑
23	hrpt	background	10	intensity		537.5813	455.3346	6.0913	15.30 % ↓
24	hrpt	background	11	intensity		454.6474	405.2356	5.6053	10.87 % ↓
25	hrpt	background	12	intensity		551.7281	589.7602	9.2067	6.89 % ↑

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

Display Pattern¶

In [39]:

project.display.pattern(expt_name='hrpt')

project.display.pattern(expt_name='hrpt')

Loading plot…

In [40]:

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

Loading plot…

Perform Fit 4/4¶

Set more parameters to be refined.

In [41]:

structure.atom_sites['Zn'].adp_iso.free = True
structure.atom_sites['Cu'].adp_iso.free = True
structure.atom_sites['O'].adp_iso.free = True
structure.atom_sites['Cl'].adp_iso.free = True
structure.atom_sites['H'].adp_iso.free = True

expt.peak.asym_beba_a0.free = True
expt.peak.asym_beba_b0.free = True
expt.peak.asym_beba_a1.free = True
expt.peak.asym_beba_b1.free = True

structure.atom_sites['Zn'].adp_iso.free = True structure.atom_sites['Cu'].adp_iso.free = True structure.atom_sites['O'].adp_iso.free = True structure.atom_sites['Cl'].adp_iso.free = True structure.atom_sites['H'].adp_iso.free = True expt.peak.asym_beba_a0.free = True expt.peak.asym_beba_b0.free = True expt.peak.asym_beba_a1.free = True expt.peak.asym_beba_b1.free = True

Show free parameters after selection.

In [42]:

project.display.parameters.free()

project.display.parameters.free()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	hs	cell		length_a	6.86205	0.00022	-inf	inf	Å
2	hs	cell		length_c	14.13486	0.00053	-inf	inf	Å
3	hs	atom_site	Zn	adp_iso	0.50000		-inf	inf	Ų
4	hs	atom_site	Cu	adp_iso	0.50000		-inf	inf	Ų
5	hs	atom_site	O	fract_x	0.20591	0.00024	-inf	inf
6	hs	atom_site	O	fract_z	0.06288	0.00018	-inf	inf
7	hs	atom_site	O	adp_iso	0.50000		-inf	inf	Ų
8	hs	atom_site	Cl	fract_z	0.19740	0.00018	-inf	inf
9	hs	atom_site	Cl	adp_iso	0.50000		-inf	inf	Ų
10	hs	atom_site	H	fract_x	0.13389	0.00018	-inf	inf
11	hs	atom_site	H	fract_z	0.08709	0.00013	-inf	inf
12	hs	atom_site	H	adp_iso	0.50000		-inf	inf	Ų
13	hrpt	linked_structure	hs	scale	0.39500	0.00234	-inf	inf
14	hrpt	peak		asym_beba_a0	0.00000		-inf	inf
15	hrpt	peak		asym_beba_b0	0.00000		-inf	inf
16	hrpt	peak		asym_beba_a1	0.00000		-inf	inf
17	hrpt	peak		asym_beba_b1	0.00000		-inf	inf
18	hrpt	peak		broad_gauss_u	0.36000	0.01431	-inf	inf	deg²
19	hrpt	peak		broad_gauss_v	-0.38461	0.02713	-inf	inf	deg²
20	hrpt	peak		broad_gauss_w	0.28371	0.01259	-inf	inf	deg²
21	hrpt	peak		broad_lorentz_y	0.13850	0.00618	-inf	inf	deg
22	hrpt	instrument		twotheta_offset	0.11496	0.00239	-inf	inf	deg
23	hrpt	background	1	intensity	672.12803	12.39752	-inf	inf
24	hrpt	background	2	intensity	456.28643	3.88365	-inf	inf
25	hrpt	background	3	intensity	448.09079	3.79655	-inf	inf
26	hrpt	background	4	intensity	564.51138	8.43152	-inf	inf
27	hrpt	background	5	intensity	464.75410	4.79810	-inf	inf
28	hrpt	background	6	intensity	517.93168	3.37063	-inf	inf
29	hrpt	background	7	intensity	449.77350	3.23455	-inf	inf
30	hrpt	background	8	intensity	473.41616	6.76726	-inf	inf
31	hrpt	background	9	intensity	476.49106	8.07021	-inf	inf
32	hrpt	background	10	intensity	455.33458	6.09127	-inf	inf
33	hrpt	background	11	intensity	405.23560	5.60530	-inf	inf
34	hrpt	background	12	intensity	589.76017	9.20666	-inf	inf

Run Fitting¶

In [43]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit progress:

	iteration	time (s)	χ²	change / status
1	1	0.05	4.96
2	38	2.18	2.15	56.6% ↓
3	73	4.48	1.95	9.2% ↓
4	109	7.41	1.95

🏆 Best goodness-of-fit (reduced χ²) is 1.95 at iteration 108

✅ Fitting complete.

In [44]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.
2	chi_square_change_tolerance	0.01	Relative change in the objective (chi-square) used to stop fitting.
3	parameter_change_tolerance	1e-08	Relative change in fitted parameters used to stop fitting.
4	gradient_tolerance	0.0	Gradient orthogonality used to stop fitting; zero disables it.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	7.41
4	🔁 Iterations	106
5	📏 Goodness-of-fit (reduced χ²)	1.95
6	📏 R-factor (Rf, %)	3.99
7	📏 R-factor squared (Rf², %)	4.64
8	📏 Weighted R-factor (wR, %)	5.05

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8620	6.8639	0.0004	0.03 % ↑
2	hs	cell		length_c	Å	14.1349	14.1417	0.0009	0.05 % ↑
3	hs	atom_site	Zn	adp_iso	Ų	0.5000	0.1678	0.0604	66.43 % ↓
4	hs	atom_site	Cu	adp_iso	Ų	0.5000	1.4870	0.0380	197.40 % ↑
5	hs	atom_site	O	fract_x		0.2059	0.2062	0.0002	0.17 % ↑
6	hs	atom_site	O	fract_z		0.0629	0.0611	0.0001	2.91 % ↓
7	hs	atom_site	O	adp_iso	Ų	0.5000	1.0805	0.0374	116.10 % ↑
8	hs	atom_site	Cl	fract_z		0.1974	0.1967	0.0001	0.35 % ↓
9	hs	atom_site	Cl	adp_iso	Ų	0.5000	1.4335	0.0380	186.69 % ↑
10	hs	atom_site	H	fract_x		0.1339	0.1324	0.0002	1.14 % ↓
11	hs	atom_site	H	fract_z		0.0871	0.0898	0.0001	3.15 % ↑
12	hs	atom_site	H	adp_iso	Ų	0.5000	2.4461	0.0429	389.23 % ↑
13	hrpt	linked_structure	hs	scale		0.3950	0.5110	0.0027	29.37 % ↑
14	hrpt	peak		asym_beba_a0		0.0000	-0.1918	0.0257	N/A
15	hrpt	peak		asym_beba_b0		0.0000	-0.0462	0.0040	N/A
16	hrpt	peak		asym_beba_a1		0.0000	0.1049	0.0591	N/A
17	hrpt	peak		asym_beba_b1		0.0000	0.0521	0.0092	N/A
18	hrpt	peak		broad_gauss_u	deg²	0.3600	0.2243	0.0048	37.69 % ↓
19	hrpt	peak		broad_gauss_v	deg²	-0.3846	-0.2763	0.0056	28.15 % ↓
20	hrpt	peak		broad_gauss_w	deg²	0.2837	0.2681	0.0055	5.52 % ↓
21	hrpt	peak		broad_lorentz_y	deg	0.1385	0.1524	0.0036	10.05 % ↑
22	hrpt	instrument		twotheta_offset	deg	0.1150	0.1455	0.0064	26.59 % ↑
23	hrpt	background	1	intensity		672.1280	672.1924	7.7893	0.01 % ↑
24	hrpt	background	2	intensity		456.2864	456.1969	2.4429	0.02 % ↓
25	hrpt	background	3	intensity		448.0908	444.7640	2.3902	0.74 % ↓
26	hrpt	background	4	intensity		564.5114	473.0814	5.6505	16.20 % ↓
27	hrpt	background	5	intensity		464.7541	461.0107	3.0287	0.81 % ↓
28	hrpt	background	6	intensity		517.9317	494.4534	2.1895	4.53 % ↓
29	hrpt	background	7	intensity		449.7735	492.4306	2.0943	9.48 % ↑
30	hrpt	background	8	intensity		473.4162	533.3785	4.4364	12.67 % ↑
31	hrpt	background	9	intensity		476.4911	525.6834	5.1820	10.32 % ↑
32	hrpt	background	10	intensity		455.3346	527.1397	3.9558	15.77 % ↑
33	hrpt	background	11	intensity		405.2356	492.6152	3.6286	21.56 % ↑
34	hrpt	background	12	intensity		589.7602	507.1019	6.6529	14.02 % ↓

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

In [45]:

project.display.fit.correlations()

project.display.fit.correlations()

Loading plot…

Display Pattern¶

In [46]:

project.display.pattern(expt_name='hrpt')

project.display.pattern(expt_name='hrpt')

Loading plot…

In [47]:

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

project.display.pattern(expt_name='hrpt', x_min=48, x_max=51)

Loading plot…

📊 Report¶

The HTML report is written automatically when the project is saved; enable project.report.pdf as well for a PDF version.

💾 Save Project¶

In [48]:

project.save_as(dir_path='projects/refine-hs-hrpt')

project.save_as(dir_path='projects/refine-hs-hrpt')

Saving project 📦 'hs_hrpt' to '../../../projects/refine-hs-hrpt'

├── 📄 project.edi
├── 📁 structures/
│   └── 📄 hs.edi
├── 📁 experiments/
│   └── 📄 hrpt.edi
├── 📁 analysis/
│   └── 📄 analysis.edi
└── 📁 reports/
    └── 📄 hs_hrpt.html