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.it_coordinate_system_code = 'h'

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

Set Unit Cell¶

In [5]:

structure.cell.length_a = 6.9
structure.cell.length_c = 14.1

structure.cell.length_a = 6.9 structure.cell.length_c = 14.1

Set Atom Sites¶

In [6]:

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

structure.atom_sites.create( label='Zn', type_symbol='Zn', fract_x=0, fract_y=0, fract_z=0.5, adp_iso=0.5, ) structure.atom_sites.create( label='Cu', type_symbol='Cu', fract_x=0.5, fract_y=0, fract_z=0, adp_iso=0.5, ) structure.atom_sites.create( label='O', type_symbol='O', fract_x=0.21, fract_y=-0.21, fract_z=0.06, adp_iso=0.5, ) structure.atom_sites.create( label='Cl', type_symbol='Cl', fract_x=0, fract_y=0, fract_z=0.197, adp_iso=0.5, ) structure.atom_sites.create( label='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(id=11, destination='data')

data_path = download_data(id=11, destination='data')

Getting data...

Data #11: HS, HRPT (PSI)

✅ Data #11 downloaded to '../../../data/ed-11.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.type = 'pseudo-voigt + empirical asymmetry'
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_x = 0.0
expt.peak.broad_lorentz_y = 0

expt.peak.show_supported() expt.peak.type = 'pseudo-voigt + empirical asymmetry' 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_x = 0.0 expt.peak.broad_lorentz_y = 0

Peak types

		Type	Description
1	*	pseudo-voigt	CWL pseudo-Voigt profile
2		pseudo-voigt + empirical asymmetry	CWL pseudo-Voigt profile with empirical asymmetry correction.

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • asym_empir_1=0.0                                                                                                             
   • asym_empir_2=0.0                                                                                                             
   • asym_empir_3=0.0                                                                                                             
   • asym_empir_4=0.0                                                                                                             

Peak profile type for experiment 'hrpt' changed to

pseudo-voigt + empirical asymmetry

Set Background¶

In [11]:

expt.background.create(id='1', x=4.4196, y=500)
expt.background.create(id='2', x=6.6207, y=500)
expt.background.create(id='3', x=10.4918, y=500)
expt.background.create(id='4', x=15.4634, y=500)
expt.background.create(id='5', x=45.6041, y=500)
expt.background.create(id='6', x=74.6844, y=500)
expt.background.create(id='7', x=103.4187, y=500)
expt.background.create(id='8', x=121.6311, y=500)
expt.background.create(id='9', x=159.4116, y=500)

expt.background.create(id='1', x=4.4196, y=500) expt.background.create(id='2', x=6.6207, y=500) expt.background.create(id='3', x=10.4918, y=500) expt.background.create(id='4', x=15.4634, y=500) expt.background.create(id='5', x=45.6041, y=500) expt.background.create(id='6', x=74.6844, y=500) expt.background.create(id='7', x=103.4187, y=500) expt.background.create(id='8', x=121.6311, y=500) expt.background.create(id='9', x=159.4116, y=500)

Set Linked Phases¶

In [12]:

expt.linked_phases.create(id='hs', scale=0.5)

expt.linked_phases.create(id='hs', scale=0.5)

📦 Define Project¶

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

Create Project¶

In [13]:

project = Project(name='hs_hrpt')

project = Project(name='hs_hrpt')

Add Structure¶

In [14]:

project.structures.add(structure)

project.structures.add(structure)

Add Experiment¶

In [15]:

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 [16]:

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 [17]:

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

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

Loading plot…

In [18]:

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 [19]:

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

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

Show free parameters after selection.

In [20]:

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	6.90000		-inf	inf	Å
2	hs	cell		length_c	14.10000		-inf	inf	Å
3	hrpt	linked_phases	hs	scale	0.50000		-inf	inf
4	hrpt	instrument		twotheta_offset	0.00000		-inf	inf	deg

Run Fitting¶

In [21]:

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	0.11	576.50
2	8	0.84	122.02	78.8% ↓
3	13	1.35	115.19	5.6% ↓
4	18	2.11	109.86	4.6% ↓
5	23	2.64	106.68	2.9% ↓
6	28	3.15	104.60	2.0% ↓
7	33	3.67	102.87	1.7% ↓
8	38	4.46	101.13	1.7% ↓
9	43	4.99	99.20	1.9% ↓
10	48	5.51	96.86	2.4% ↓
11	53	6.03	93.93	3.0% ↓
12	58	6.54	90.34	3.8% ↓
13	63	7.32	86.20	4.6% ↓
14	68	7.83	81.66	5.3% ↓
15	73	8.34	76.78	6.0% ↓
16	78	8.85	71.71	6.6% ↓
17	83	9.61	66.82	6.8% ↓
18	88	10.12	62.48	6.5% ↓
19	93	10.66	58.99	5.6% ↓
20	98	11.19	56.41	4.4% ↓
21	103	11.71	54.64	3.1% ↓
22	108	12.52	53.49	2.1% ↓
23	113	13.04	52.76	1.4% ↓
24	123	14.08	52.02	1.4% ↓
25	167	19.18	51.59
26	210	24.24	51.58
27	254	29.34	51.58
28	297	34.43	51.57
29	304	35.18	51.57

🏆 Best goodness-of-fit (reduced χ²) is 51.57 at iteration 303

✅ Fitting complete.

In [22]:

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)	35.18
4	🔁 Iterations	301
5	📏 Goodness-of-fit (reduced χ²)	51.57
6	📏 R-factor (Rf, %)	19.70
7	📏 R-factor squared (Rf², %)	30.20
8	📏 Weighted R-factor (wR, %)	30.35

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.9000	6.8623	0.0003	0.55 % ↓
2	hs	cell		length_c	Å	14.1000	14.1365	0.0008	0.26 % ↑
3	hrpt	linked_phases	hs	scale		0.5000	0.2548	0.0030	49.04 % ↓
4	hrpt	instrument		twotheta_offset	deg	0.0000	0.1271	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 [23]:

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

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

Loading plot…

In [24]:

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 [25]:

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.y.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.y.free = True

Show free parameters after selection.

In [26]:

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	6.86229	0.00029	-inf	inf	Å
2	hs	cell		length_c	14.13651	0.00084	-inf	inf	Å
3	hrpt	linked_phases	hs	scale	0.25480	0.00305	-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	0.12712	0.00515	-inf	inf	deg
9	hrpt	background	1	y	500.00000		-inf	inf
10	hrpt	background	2	y	500.00000		-inf	inf
11	hrpt	background	3	y	500.00000		-inf	inf
12	hrpt	background	4	y	500.00000		-inf	inf
13	hrpt	background	5	y	500.00000		-inf	inf
14	hrpt	background	6	y	500.00000		-inf	inf
15	hrpt	background	7	y	500.00000		-inf	inf
16	hrpt	background	8	y	500.00000		-inf	inf
17	hrpt	background	9	y	500.00000		-inf	inf

Run Fitting¶

In [27]:

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	0.15	51.78
2	21	2.85	15.91	69.3% ↓
3	39	5.28	15.07	5.3% ↓
4	57	7.68	14.17	6.0% ↓
5	75	10.12	13.42	5.3% ↓
6	115	15.20	13.39
7	152	20.26	13.39
8	191	25.43	13.39
9	220	29.20	13.39

🏆 Best goodness-of-fit (reduced χ²) is 13.39 at iteration 219

✅ Fitting complete.

In [28]:

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)	29.20
4	🔁 Iterations	217
5	📏 Goodness-of-fit (reduced χ²)	13.39
6	📏 R-factor (Rf, %)	10.13
7	📏 R-factor squared (Rf², %)	14.05
8	📏 Weighted R-factor (wR, %)	13.91

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8623	6.8631	0.0003	0.01 % ↑
2	hs	cell		length_c	Å	14.1365	14.1397	0.0009	0.02 % ↑
3	hrpt	linked_phases	hs	scale		0.2548	0.4270	0.0039	67.58 % ↑
4	hrpt	peak		broad_gauss_u	deg²	0.1000	0.3338	0.0270	233.82 % ↑
5	hrpt	peak		broad_gauss_v	deg²	-0.2000	-0.2705	0.0498	35.27 % ↑
6	hrpt	peak		broad_gauss_w	deg²	0.2000	0.2067	0.0214	3.37 % ↑
7	hrpt	peak		broad_lorentz_y	deg	0.0000	0.1859	0.0103	N/A
8	hrpt	instrument		twotheta_offset	deg	0.1271	0.1316	0.0040	3.49 % ↑
9	hrpt	background	1	y		500.0000	595.4716	24.8884	19.09 % ↑
10	hrpt	background	2	y		500.0000	500.0658	14.1957	0.01 % ↑
11	hrpt	background	3	y		500.0000	446.7961	10.8562	10.64 % ↓
12	hrpt	background	4	y		500.0000	423.0736	5.6094	15.39 % ↓
13	hrpt	background	5	y		500.0000	469.5233	6.1230	6.10 % ↓
14	hrpt	background	6	y		500.0000	473.3416	5.9675	5.33 % ↓
15	hrpt	background	7	y		500.0000	431.9294	5.7359	13.61 % ↓
16	hrpt	background	8	y		500.0000	388.9936	6.0673	22.20 % ↓
17	hrpt	background	9	y		500.0000	501.8443	5.6961	0.37 % ↑

• 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 [29]:

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

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

Loading plot…

In [30]:

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 [31]:

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 [32]:

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	6.86308	0.00035	-inf	inf	Å
2	hs	cell		length_c	14.13974	0.00094	-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_phases	hs	scale	0.42699	0.00386	-inf	inf
9	hrpt	peak		broad_gauss_u	0.33382	0.02703	-inf	inf	deg²
10	hrpt	peak		broad_gauss_v	-0.27053	0.04977	-inf	inf	deg²
11	hrpt	peak		broad_gauss_w	0.20675	0.02144	-inf	inf	deg²
12	hrpt	peak		broad_lorentz_y	0.18589	0.01026	-inf	inf	deg
13	hrpt	instrument		twotheta_offset	0.13156	0.00402	-inf	inf	deg
14	hrpt	background	1	y	595.47160	24.88844	-inf	inf
15	hrpt	background	2	y	500.06584	14.19569	-inf	inf
16	hrpt	background	3	y	446.79606	10.85617	-inf	inf
17	hrpt	background	4	y	423.07355	5.60941	-inf	inf
18	hrpt	background	5	y	469.52331	6.12295	-inf	inf
19	hrpt	background	6	y	473.34159	5.96754	-inf	inf
20	hrpt	background	7	y	431.92940	5.73592	-inf	inf
21	hrpt	background	8	y	388.99361	6.06730	-inf	inf
22	hrpt	background	9	y	501.84432	5.69613	-inf	inf

Run Fitting¶

In [33]:

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	0.14	13.41
2	26	3.33	5.76	57.1% ↓
3	49	6.30	5.48	4.7% ↓
4	88	11.35	5.47
5	130	16.70	5.47
6	172	21.81	5.47
7	211	26.96	5.47

🏆 Best goodness-of-fit (reduced χ²) is 5.47 at iteration 210

✅ Fitting complete.

In [34]:

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)	26.96
4	🔁 Iterations	208
5	📏 Goodness-of-fit (reduced χ²)	5.47
6	📏 R-factor (Rf, %)	6.71
7	📏 R-factor squared (Rf², %)	9.26
8	📏 Weighted R-factor (wR, %)	9.33

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8631	6.8623	0.0002	0.01 % ↓
2	hs	cell		length_c	Å	14.1397	14.1357	0.0005	0.03 % ↓
3	hs	atom_site	O	fract_x		0.2100	0.2059	0.0002	1.96 % ↓
4	hs	atom_site	O	fract_z		0.0600	0.0627	0.0002	4.53 % ↑
5	hs	atom_site	Cl	fract_z		0.1970	0.1979	0.0002	0.46 % ↑
6	hs	atom_site	H	fract_x		0.1300	0.1336	0.0002	2.75 % ↑
7	hs	atom_site	H	fract_z		0.0800	0.0870	0.0001	8.72 % ↑
8	hrpt	linked_phases	hs	scale		0.4270	0.3988	0.0023	6.59 % ↓
9	hrpt	peak		broad_gauss_u	deg²	0.3338	0.3426	0.0146	2.64 % ↑
10	hrpt	peak		broad_gauss_v	deg²	-0.2705	-0.3774	0.0280	39.51 % ↑
11	hrpt	peak		broad_gauss_w	deg²	0.2067	0.2762	0.0132	33.57 % ↑
12	hrpt	peak		broad_lorentz_y	deg	0.1859	0.1516	0.0062	18.46 % ↓
13	hrpt	instrument		twotheta_offset	deg	0.1316	0.1182	0.0025	10.15 % ↓
14	hrpt	background	1	y		595.4716	606.8549	15.8977	1.91 % ↑
15	hrpt	background	2	y		500.0658	506.3937	9.0721	1.27 % ↑
16	hrpt	background	3	y		446.7961	446.6115	6.9412	0.04 % ↓
17	hrpt	background	4	y		423.0736	433.4635	3.6117	2.46 % ↑
18	hrpt	background	5	y		469.5233	480.8266	3.8602	2.41 % ↑
19	hrpt	background	6	y		473.3416	504.1347	3.7880	6.51 % ↑
20	hrpt	background	7	y		431.9294	465.0255	3.6648	7.66 % ↑
21	hrpt	background	8	y		388.9936	446.8489	3.9092	14.87 % ↑
22	hrpt	background	9	y		501.8443	457.5213	3.8978	8.83 % ↓

• 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 [35]:

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

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

Loading plot…

In [36]:

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 [37]:

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_empir_1.free = True
expt.peak.asym_empir_2.free = True
expt.peak.asym_empir_3.free = True
expt.peak.asym_empir_4.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_empir_1.free = True expt.peak.asym_empir_2.free = True expt.peak.asym_empir_3.free = True expt.peak.asym_empir_4.free = True

Show free parameters after selection.

In [38]:

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	6.86227	0.00023	-inf	inf	Å
2	hs	cell		length_c	14.13575	0.00055	-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	0.20588	0.00024	-inf	inf
6	hs	atom_site	O	fract_z	0.06272	0.00018	-inf	inf
7	hs	atom_site	O	adp_iso	0.50000		-inf	inf	Ų
8	hs	atom_site	Cl	fract_z	0.19790	0.00018	-inf	inf
9	hs	atom_site	Cl	adp_iso	0.50000		-inf	inf	Ų
10	hs	atom_site	H	fract_x	0.13357	0.00018	-inf	inf
11	hs	atom_site	H	fract_z	0.08697	0.00013	-inf	inf
12	hs	atom_site	H	adp_iso	0.50000		-inf	inf	Ų
13	hrpt	linked_phases	hs	scale	0.39885	0.00233	-inf	inf
14	hrpt	peak		asym_empir_1	0.00000		-inf	inf
15	hrpt	peak		asym_empir_2	0.00000		-inf	inf
16	hrpt	peak		asym_empir_3	0.00000		-inf	inf
17	hrpt	peak		asym_empir_4	0.00000		-inf	inf
18	hrpt	peak		broad_gauss_u	0.34262	0.01459	-inf	inf	deg²
19	hrpt	peak		broad_gauss_v	-0.37742	0.02800	-inf	inf	deg²
20	hrpt	peak		broad_gauss_w	0.27616	0.01316	-inf	inf	deg²
21	hrpt	peak		broad_lorentz_y	0.15157	0.00624	-inf	inf	deg
22	hrpt	instrument		twotheta_offset	0.11821	0.00248	-inf	inf	deg
23	hrpt	background	1	y	606.85492	15.89775	-inf	inf
24	hrpt	background	2	y	506.39367	9.07212	-inf	inf
25	hrpt	background	3	y	446.61148	6.94119	-inf	inf
26	hrpt	background	4	y	433.46347	3.61166	-inf	inf
27	hrpt	background	5	y	480.82660	3.86016	-inf	inf
28	hrpt	background	6	y	504.13466	3.78801	-inf	inf
29	hrpt	background	7	y	465.02545	3.66479	-inf	inf
30	hrpt	background	8	y	446.84887	3.90918	-inf	inf
31	hrpt	background	9	y	457.52127	3.89777	-inf	inf

Run Fitting¶

In [39]:

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	0.14	5.49
2	35	4.63	2.19	60.1% ↓
3	67	8.64	1.97	9.8% ↓
4	106	13.73	1.97
5	145	18.84	1.97
6	186	23.92	1.97
7	224	28.92	1.97
8	260	34.03	1.97

🏆 Best goodness-of-fit (reduced χ²) is 1.97 at iteration 259

✅ Fitting complete.

In [40]:

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)	34.03
4	🔁 Iterations	257
5	📏 Goodness-of-fit (reduced χ²)	1.97
6	📏 R-factor (Rf, %)	4.03
7	📏 R-factor squared (Rf², %)	4.68
8	📏 Weighted R-factor (wR, %)	4.19

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	hs	cell		length_a	Å	6.8623	6.8643	0.0004	0.03 % ↑
2	hs	cell		length_c	Å	14.1357	14.1424	0.0010	0.05 % ↑
3	hs	atom_site	Zn	adp_iso	Ų	0.5000	0.2297	0.0611	54.05 % ↓
4	hs	atom_site	Cu	adp_iso	Ų	0.5000	1.4700	0.0379	193.99 % ↑
5	hs	atom_site	O	fract_x		0.2059	0.2064	0.0002	0.24 % ↑
6	hs	atom_site	O	fract_z		0.0627	0.0610	0.0001	2.76 % ↓
7	hs	atom_site	O	adp_iso	Ų	0.5000	0.9782	0.0347	95.65 % ↑
8	hs	atom_site	Cl	fract_z		0.1979	0.1966	0.0001	0.63 % ↓
9	hs	atom_site	Cl	adp_iso	Ų	0.5000	1.3926	0.0369	178.53 % ↑
10	hs	atom_site	H	fract_x		0.1336	0.1325	0.0001	0.79 % ↓
11	hs	atom_site	H	fract_z		0.0870	0.0898	0.0001	3.27 % ↑
12	hs	atom_site	H	adp_iso	Ų	0.5000	2.5006	0.0393	400.11 % ↑
13	hrpt	linked_phases	hs	scale		0.3988	0.5138	0.0025	28.83 % ↑
14	hrpt	peak		asym_empir_1		0.0000	-0.2145	0.0248	N/A
15	hrpt	peak		asym_empir_2		0.0000	-0.0506	0.0040	N/A
16	hrpt	peak		asym_empir_3		0.0000	0.1504	0.0553	N/A
17	hrpt	peak		asym_empir_4		0.0000	0.0644	0.0089	N/A
18	hrpt	peak		broad_gauss_u	deg²	0.3426	0.2371	0.0095	30.81 % ↓
19	hrpt	peak		broad_gauss_v	deg²	-0.3774	-0.3015	0.0172	20.11 % ↓
20	hrpt	peak		broad_gauss_w	deg²	0.2762	0.2705	0.0078	2.04 % ↓
21	hrpt	peak		broad_lorentz_y	deg	0.1516	0.1616	0.0036	6.61 % ↑
22	hrpt	instrument		twotheta_offset	deg	0.1182	0.1512	0.0071	27.93 % ↑
23	hrpt	background	1	y		606.8549	601.1574	9.5418	0.94 % ↓
24	hrpt	background	2	y		506.3937	503.9188	5.4442	0.49 % ↓
25	hrpt	background	3	y		446.6115	445.2163	4.1651	0.31 % ↓
26	hrpt	background	4	y		433.4635	432.9735	2.1783	0.11 % ↓
27	hrpt	background	5	y		480.8266	455.6484	2.3910	5.24 % ↓
28	hrpt	background	6	y		504.1347	492.5767	2.3061	2.29 % ↓
29	hrpt	background	7	y		465.0255	480.8476	2.2145	3.40 % ↑
30	hrpt	background	8	y		446.8489	510.1369	2.4165	14.16 % ↑
31	hrpt	background	9	y		457.5213	498.7801	2.5676	9.02 % ↑

• 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 [41]:

project.display.fit.correlations()

project.display.fit.correlations()

Loading plot…

Display Pattern¶

In [42]:

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

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

Loading plot…

In [43]:

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 [44]:

project.save_as(dir_path='projects/ed_6_hs_hrpt')

project.save_as(dir_path='projects/ed_6_hs_hrpt')

Saving project 📦 'hs_hrpt' to '../../../projects/ed_6_hs_hrpt'

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 hs.cif

├── 📁 experiments/

│   └── 📄 hrpt.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📁 reports/

    └── 📄 hs_hrpt.html