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.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	0.41	60.12	71.4% ↓
3	13	0.88	55.45	7.8% ↓
4	18	1.12	51.96	6.3% ↓
5	23	1.37	49.78	4.2% ↓
6	28	1.62	48.53	2.5% ↓
7	33	2.10	47.85	1.4% ↓
8	43	2.61	47.31	1.1% ↓
9	110	6.71	47.11

🏆 Best goodness-of-fit (reduced χ²) is 47.11 at iteration 80

✅ Fitting complete.

In [25]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	6.71
4	🔁 Iterations	107
5	📏 Goodness-of-fit (reduced χ²)	47.11
6	📏 R-factor (Rf, %)	17.69
7	📏 R-factor squared (Rf², %)	30.23
8	📏 Weighted R-factor (wR, %)	31.10

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8500	6.8622	0.0003	0.18 % ↑
2	hs	cell		length_c	Å	14.1000	14.1363	0.0008	0.26 % ↑
3	hrpt	linked_structure	hs	scale		0.5000	0.2442	0.0029	51.16 % ↓
4	hrpt	instrument		twotheta_offset	deg	0.0000	0.1258	0.0051	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 [26]:

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

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

Loading plot…

In [27]:

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 [28]:

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 [29]:

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	6.86216	0.00029	-inf	inf	Å
2	hs	cell		length_c	14.13634	0.00084	-inf	inf	Å
3	hrpt	linked_structure	hs	scale	0.24422	0.00291	-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	0.12575	0.00513	-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 [30]:

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	47.35
2	24	1.45	16.05	66.1% ↓
3	46	2.85	14.94	6.9% ↓
4	67	4.23	13.01	12.9% ↓
5	145	9.23	12.92
6	219	14.25	12.92
7	224	14.61	12.92

🏆 Best goodness-of-fit (reduced χ²) is 12.92 at iteration 202

✅ Fitting complete.

In [31]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	14.61
4	🔁 Iterations	221
5	📏 Goodness-of-fit (reduced χ²)	12.92
6	📏 R-factor (Rf, %)	9.89
7	📏 R-factor squared (Rf², %)	13.86
8	📏 Weighted R-factor (wR, %)	13.80

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8622	6.8626	0.0003	0.01 % ↑
2	hs	cell		length_c	Å	14.1363	14.1392	0.0009	0.02 % ↑
3	hrpt	linked_structure	hs	scale		0.2442	0.4162	0.0040	70.42 % ↑
4	hrpt	peak		broad_gauss_u	deg²	0.1000	0.3458	0.0267	245.76 % ↑
5	hrpt	peak		broad_gauss_v	deg²	-0.2000	-0.2479	0.0493	23.94 % ↑
6	hrpt	peak		broad_gauss_w	deg²	0.2000	0.2127	0.0211	6.34 % ↑
7	hrpt	peak		broad_lorentz_y	deg	0.0000	0.1574	0.0106	N/A
8	hrpt	instrument		twotheta_offset	deg	0.1258	0.1272	0.0040	1.14 % ↑
9	hrpt	background	1	intensity		645.0000	673.1075	20.0334	4.36 % ↑
10	hrpt	background	2	intensity		460.0000	454.9251	6.2694	1.10 % ↓
11	hrpt	background	3	intensity		451.0000	436.5423	6.1275	3.21 % ↓
12	hrpt	background	4	intensity		616.7518	562.0722	13.6510	8.87 % ↓
13	hrpt	background	5	intensity		451.0000	472.8034	7.6853	4.83 % ↑
14	hrpt	background	6	intensity		522.4892	495.6934	5.4898	5.13 % ↓
15	hrpt	background	7	intensity		497.0172	404.5708	5.2875	18.60 % ↓
16	hrpt	background	8	intensity		613.1533	440.4542	10.4755	28.17 % ↓
17	hrpt	background	9	intensity		657.1372	394.8575	11.4790	39.91 % ↓
18	hrpt	background	10	intensity		573.0000	538.7733	8.9774	5.97 % ↓
19	hrpt	background	11	intensity		514.0000	456.0360	8.4105	11.28 % ↓
20	hrpt	background	12	intensity		538.1731	552.2311	14.7053	2.61 % ↑

• 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 [32]:

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

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

Loading plot…

In [33]:

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 [34]:

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 [35]:

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	6.86260	0.00035	-inf	inf	Å
2	hs	cell		length_c	14.13920	0.00093	-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	0.41619	0.00400	-inf	inf
9	hrpt	peak		broad_gauss_u	0.34576	0.02672	-inf	inf	deg²
10	hrpt	peak		broad_gauss_v	-0.24788	0.04934	-inf	inf	deg²
11	hrpt	peak		broad_gauss_w	0.21267	0.02110	-inf	inf	deg²
12	hrpt	peak		broad_lorentz_y	0.15740	0.01058	-inf	inf	deg
13	hrpt	instrument		twotheta_offset	0.12718	0.00396	-inf	inf	deg
14	hrpt	background	1	intensity	673.10753	20.03337	-inf	inf
15	hrpt	background	2	intensity	454.92508	6.26943	-inf	inf
16	hrpt	background	3	intensity	436.54232	6.12751	-inf	inf
17	hrpt	background	4	intensity	562.07220	13.65100	-inf	inf
18	hrpt	background	5	intensity	472.80337	7.68533	-inf	inf
19	hrpt	background	6	intensity	495.69338	5.48976	-inf	inf
20	hrpt	background	7	intensity	404.57081	5.28747	-inf	inf
21	hrpt	background	8	intensity	440.45421	10.47549	-inf	inf
22	hrpt	background	9	intensity	394.85751	11.47903	-inf	inf
23	hrpt	background	10	intensity	538.77335	8.97740	-inf	inf
24	hrpt	background	11	intensity	456.03599	8.41055	-inf	inf
25	hrpt	background	12	intensity	552.23109	14.70527	-inf	inf

Run Fitting¶

In [36]:

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	1.82	5.20	59.8% ↓
3	55	3.40	4.95	4.7% ↓
4	131	8.41	4.95
5	211	13.43	4.95
6	246	15.93	4.95

🏆 Best goodness-of-fit (reduced χ²) is 4.95 at iteration 178

✅ Fitting complete.

In [37]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	15.93
4	🔁 Iterations	243
5	📏 Goodness-of-fit (reduced χ²)	4.95
6	📏 R-factor (Rf, %)	6.43
7	📏 R-factor squared (Rf², %)	8.76
8	📏 Weighted R-factor (wR, %)	8.89

📈 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	14.1348	0.0005	0.03 % ↓
3	hs	atom_site	O	fract_x		0.2100	0.2059	0.0002	1.94 % ↓
4	hs	atom_site	O	fract_z		0.0600	0.0629	0.0002	4.75 % ↑
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	3.01 % ↑
7	hs	atom_site	H	fract_z		0.0800	0.0871	0.0001	8.89 % ↑
8	hrpt	linked_structure	hs	scale		0.4162	0.3950	0.0023	5.09 % ↓
9	hrpt	peak		broad_gauss_u	deg²	0.3458	0.3572	0.0140	3.30 % ↑
10	hrpt	peak		broad_gauss_v	deg²	-0.2479	-0.3818	0.0268	54.01 % ↑
11	hrpt	peak		broad_gauss_w	deg²	0.2127	0.2825	0.0125	32.86 % ↑
12	hrpt	peak		broad_lorentz_y	deg	0.1574	0.1390	0.0062	11.68 % ↓
13	hrpt	instrument		twotheta_offset	deg	0.1272	0.1148	0.0024	9.71 % ↓
14	hrpt	background	1	intensity		673.1075	672.1313	12.3974	0.15 % ↓
15	hrpt	background	2	intensity		454.9251	456.2819	3.8836	0.30 % ↑
16	hrpt	background	3	intensity		436.5423	448.0780	3.7964	2.64 % ↑
17	hrpt	background	4	intensity		562.0722	564.3133	8.4295	0.40 % ↑
18	hrpt	background	5	intensity		472.8034	464.7443	4.7938	1.70 % ↓
19	hrpt	background	6	intensity		495.6934	517.8974	3.3679	4.48 % ↑
20	hrpt	background	7	intensity		404.5708	449.9013	3.2316	11.20 % ↑
21	hrpt	background	8	intensity		440.4542	473.3742	6.7661	7.47 % ↑
22	hrpt	background	9	intensity		394.8575	477.2343	8.0578	20.86 % ↑
23	hrpt	background	10	intensity		538.7733	454.9376	6.0965	15.56 % ↓
24	hrpt	background	11	intensity		456.0360	405.1224	5.6028	11.16 % ↓
25	hrpt	background	12	intensity		552.2311	589.7398	9.2059	6.79 % ↑

• 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 [38]:

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

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

Loading plot…

In [39]:

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 [40]:

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 [41]:

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	6.86203	0.00022	-inf	inf	Å
2	hs	cell		length_c	14.13484	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	0.20592	0.00024	-inf	inf
6	hs	atom_site	O	fract_z	0.06285	0.00018	-inf	inf
7	hs	atom_site	O	adp_iso	0.50000		-inf	inf	Ų
8	hs	atom_site	Cl	fract_z	0.19739	0.00018	-inf	inf
9	hs	atom_site	Cl	adp_iso	0.50000		-inf	inf	Ų
10	hs	atom_site	H	fract_x	0.13391	0.00018	-inf	inf
11	hs	atom_site	H	fract_z	0.08711	0.00013	-inf	inf
12	hs	atom_site	H	adp_iso	0.50000		-inf	inf	Ų
13	hrpt	linked_structure	hs	scale	0.39501	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	0.35717	0.01404	-inf	inf	deg²
19	hrpt	peak		broad_gauss_v	-0.38176	0.02676	-inf	inf	deg²
20	hrpt	peak		broad_gauss_w	0.28255	0.01248	-inf	inf	deg²
21	hrpt	peak		broad_lorentz_y	0.13901	0.00615	-inf	inf	deg
22	hrpt	instrument		twotheta_offset	0.11483	0.00237	-inf	inf	deg
23	hrpt	background	1	intensity	672.13128	12.39736	-inf	inf
24	hrpt	background	2	intensity	456.28194	3.88358	-inf	inf
25	hrpt	background	3	intensity	448.07805	3.79639	-inf	inf
26	hrpt	background	4	intensity	564.31327	8.42947	-inf	inf
27	hrpt	background	5	intensity	464.74432	4.79375	-inf	inf
28	hrpt	background	6	intensity	517.89737	3.36789	-inf	inf
29	hrpt	background	7	intensity	449.90125	3.23156	-inf	inf
30	hrpt	background	8	intensity	473.37425	6.76608	-inf	inf
31	hrpt	background	9	intensity	477.23431	8.05784	-inf	inf
32	hrpt	background	10	intensity	454.93762	6.09645	-inf	inf
33	hrpt	background	11	intensity	405.12239	5.60281	-inf	inf
34	hrpt	background	12	intensity	589.73981	9.20593	-inf	inf

Run Fitting¶

In [42]:

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	4.96
2	38	2.71	2.15	56.6% ↓
3	73	4.92	1.95	9.1% ↓
4	150	10.22	1.95
5	227	15.25	1.95
6	304	20.26	1.95
7	380	25.57	1.95
8	395	26.93	1.95

🏆 Best goodness-of-fit (reduced χ²) is 1.95 at iteration 373

✅ Fitting complete.

In [43]:

project.display.fit.results()

project.display.fit.results()

⚙️ Settings used:

	Name	Value	Description
1	max_iterations	1000	Maximum solver iterations.

📋 Least-squares fit results:

	Metric	Value
1	🧪 Minimizer	lmfit (leastsq)
2	✅ Overall status	success
3	⏱️ Fitting time (seconds)	26.93
4	🔁 Iterations	392
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, %)	4.14

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8620	6.8640	0.0004	0.03 % ↑
2	hs	cell		length_c	Å	14.1348	14.1418	0.0010	0.05 % ↑
3	hs	atom_site	Zn	adp_iso	Ų	0.5000	0.1618	0.0609	67.65 % ↓
4	hs	atom_site	Cu	adp_iso	Ų	0.5000	1.4873	0.0380	197.46 % ↑
5	hs	atom_site	O	fract_x		0.2059	0.2063	0.0002	0.16 % ↑
6	hs	atom_site	O	fract_z		0.0629	0.0611	0.0001	2.85 % ↓
7	hs	atom_site	O	adp_iso	Ų	0.5000	1.0782	0.0377	115.64 % ↑
8	hs	atom_site	Cl	fract_z		0.1974	0.1967	0.0001	0.34 % ↓
9	hs	atom_site	Cl	adp_iso	Ų	0.5000	1.4329	0.0380	186.58 % ↑
10	hs	atom_site	H	fract_x		0.1339	0.1324	0.0002	1.15 % ↓
11	hs	atom_site	H	fract_z		0.0871	0.0898	0.0001	3.12 % ↑
12	hs	atom_site	H	adp_iso	Ų	0.5000	2.4445	0.0430	388.90 % ↑
13	hrpt	linked_structure	hs	scale		0.3950	0.5110	0.0026	29.37 % ↑
14	hrpt	peak		asym_beba_a0		0.0000	-0.1969	0.0258	N/A
15	hrpt	peak		asym_beba_b0		0.0000	-0.0474	0.0041	N/A
16	hrpt	peak		asym_beba_a1		0.0000	0.1179	0.0591	N/A
17	hrpt	peak		asym_beba_b1		0.0000	0.0553	0.0093	N/A
18	hrpt	peak		broad_gauss_u	deg²	0.3572	0.2304	0.0075	35.50 % ↓
19	hrpt	peak		broad_gauss_v	deg²	-0.3818	-0.2884	0.0113	24.45 % ↓
20	hrpt	peak		broad_gauss_w	deg²	0.2825	0.2722	0.0032	3.65 % ↓
21	hrpt	peak		broad_lorentz_y	deg	0.1390	0.1528	0.0031	9.90 % ↑
22	hrpt	instrument		twotheta_offset	deg	0.1148	0.1461	0.0071	27.24 % ↑
23	hrpt	background	1	intensity		672.1313	672.1970	7.7886	0.01 % ↑
24	hrpt	background	2	intensity		456.2819	456.1904	2.4427	0.02 % ↓
25	hrpt	background	3	intensity		448.0780	444.7383	2.3898	0.75 % ↓
26	hrpt	background	4	intensity		564.3133	472.7138	5.6219	16.23 % ↓
27	hrpt	background	5	intensity		464.7443	460.8542	3.0171	0.84 % ↓
28	hrpt	background	6	intensity		517.8974	494.4704	2.0904	4.52 % ↓
29	hrpt	background	7	intensity		449.9013	492.3397	2.0718	9.43 % ↑
30	hrpt	background	8	intensity		473.3742	533.2086	4.4152	12.64 % ↑
31	hrpt	background	9	intensity		477.2343	525.1618	5.2338	10.04 % ↑
32	hrpt	background	10	intensity		454.9376	526.7387	3.9282	15.78 % ↑
33	hrpt	background	11	intensity		405.1224	492.4487	3.6512	21.56 % ↑
34	hrpt	background	12	intensity		589.7398	507.1961	6.6711	14.00 % ↓

• 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 [44]:

project.display.fit.correlations()

project.display.fit.correlations()

Loading plot…

Display Pattern¶

In [45]:

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

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

Loading plot…

In [46]:

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 [47]:

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