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,
    wyckoff_letter='b',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='Cu',
    type_symbol='Cu',
    fract_x=0.5,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='e',
    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,
    wyckoff_letter='h',
    adp_iso=0.5,
)
structure.atom_sites.create(
    label='Cl',
    type_symbol='Cl',
    fract_x=0,
    fract_y=0,
    fract_z=0.197,
    wyckoff_letter='c',
    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,
    wyckoff_letter='h',
    adp_iso=0.5,
)

structure.atom_sites.create( label='Zn', type_symbol='Zn', fract_x=0, fract_y=0, fract_z=0.5, wyckoff_letter='b', adp_iso=0.5, ) structure.atom_sites.create( label='Cu', type_symbol='Cu', fract_x=0.5, fract_y=0, fract_z=0, wyckoff_letter='e', 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, wyckoff_letter='h', adp_iso=0.5, ) structure.atom_sites.create( label='Cl', type_symbol='Cl', fract_x=0, fract_y=0, fract_z=0.197, wyckoff_letter='c', 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, wyckoff_letter='h', 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 Measured 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.show_supported_peak_profile_types()
expt.show_current_peak_profile_type()
expt.peak_profile_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.show_supported_peak_profile_types() expt.show_current_peak_profile_type() expt.peak_profile_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

Supported types

	Type	Description
1	pseudo-voigt	Pseudo-Voigt profile
2	pseudo-voigt + empirical asymmetry	Pseudo-Voigt with empirical asymmetry correction

Current peak profile type

pseudo-voigt

⚠️ Switching peak profile type discards existing peak parameters.                                                                 

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()

project = Project()

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.

Plot Measured vs Calculated¶

In [16]:

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

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

In [17]:

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

Perform Fit 1/4¶

Set parameters to be refined.

In [18]:

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 [19]:

project.analysis.display.free_params()

project.analysis.display.free_params()

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 [20]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	576.50
2	8	122.02	78.8% ↓
3	13	115.19	5.6% ↓
4	18	109.86	4.6% ↓
5	23	106.68	2.9% ↓
6	28	104.60	2.0% ↓
7	33	102.87	1.7% ↓
8	38	101.13	1.7% ↓
9	43	99.20	1.9% ↓
10	48	96.86	2.4% ↓
11	53	93.93	3.0% ↓
12	58	90.34	3.8% ↓
13	63	86.20	4.6% ↓
14	68	81.66	5.3% ↓
15	73	76.78	6.0% ↓
16	78	71.71	6.6% ↓
17	83	66.82	6.8% ↓
18	88	62.48	6.5% ↓
19	93	58.99	5.6% ↓
20	98	56.41	4.4% ↓
21	103	54.64	3.1% ↓
22	108	53.49	2.1% ↓
23	113	52.76	1.4% ↓
24	123	52.02	1.4% ↓
25	304	51.57

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

✅ Fitting complete.

In [21]:

project.analysis.display.fit_results()

project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 25.53 seconds

📏 Goodness-of-fit (reduced χ²): 51.57

📏 R-factor (Rf): 19.70%

📏 R-factor squared (Rf²): 30.20%

📏 Weighted R-factor (wR): 30.35%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	hs	cell		length_a	6.9000	6.8623	0.0003	Å	0.55 % ↓
2	hs	cell		length_c	14.1000	14.1365	0.0008	Å	0.26 % ↑
3	hrpt	linked_phases	hs	scale	0.5000	0.2548	0.0030		49.04 % ↓
4	hrpt	instrument		twotheta_offset	0.0000	0.1271	0.0051	deg	N/A

Plot Measured vs Calculated¶

In [22]:

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

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

In [23]:

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

Perform Fit 2/4¶

Set more parameters to be refined.

In [24]:

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 [25]:

project.analysis.display.free_params()

project.analysis.display.free_params()

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 [26]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	51.78
2	21	15.91	69.3% ↓
3	39	15.07	5.3% ↓
4	57	14.17	6.0% ↓
5	75	13.42	5.3% ↓
6	220	13.39

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

✅ Fitting complete.

In [27]:

project.analysis.display.fit_results()

project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 19.30 seconds

📏 Goodness-of-fit (reduced χ²): 13.39

📏 R-factor (Rf): 10.13%

📏 R-factor squared (Rf²): 14.05%

📏 Weighted R-factor (wR): 13.91%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	hs	cell		length_a	6.8623	6.8631	0.0003	Å	0.01 % ↑
2	hs	cell		length_c	14.1365	14.1397	0.0009	Å	0.02 % ↑
3	hrpt	linked_phases	hs	scale	0.2548	0.4270	0.0039		67.58 % ↑
4	hrpt	peak		broad_gauss_u	0.1000	0.3338	0.0270	deg²	233.82 % ↑
5	hrpt	peak		broad_gauss_v	-0.2000	-0.2705	0.0498	deg²	35.27 % ↑
6	hrpt	peak		broad_gauss_w	0.2000	0.2067	0.0214	deg²	3.37 % ↑
7	hrpt	peak		broad_lorentz_y	0.0000	0.1859	0.0103	deg	N/A
8	hrpt	instrument		twotheta_offset	0.1271	0.1316	0.0040	deg	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 % ↑

Plot Measured vs Calculated¶

In [28]:

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

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

In [29]:

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

Perform Fit 3/4¶

Set more parameters to be refined.

In [30]:

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 [31]:

project.analysis.display.free_params()

project.analysis.display.free_params()

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 [32]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	13.41
2	26	5.76	57.1% ↓
3	49	5.48	4.7% ↓
4	211	5.47

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

✅ Fitting complete.

In [33]:

project.analysis.display.fit_results()

project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 18.25 seconds

📏 Goodness-of-fit (reduced χ²): 5.47

📏 R-factor (Rf): 6.71%

📏 R-factor squared (Rf²): 9.26%

📏 Weighted R-factor (wR): 9.33%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	hs	cell		length_a	6.8631	6.8623	0.0002	Å	0.01 % ↓
2	hs	cell		length_c	14.1397	14.1357	0.0005	Å	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	0.3338	0.3426	0.0146	deg²	2.64 % ↑
10	hrpt	peak		broad_gauss_v	-0.2705	-0.3774	0.0280	deg²	39.51 % ↑
11	hrpt	peak		broad_gauss_w	0.2067	0.2762	0.0132	deg²	33.57 % ↑
12	hrpt	peak		broad_lorentz_y	0.1859	0.1516	0.0062	deg	18.46 % ↓
13	hrpt	instrument		twotheta_offset	0.1316	0.1182	0.0025	deg	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 % ↓

Plot Measured vs Calculated¶

In [34]:

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

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

In [35]:

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

Perform Fit 4/4¶

Set more parameters to be refined.

In [36]:

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 [37]:

project.analysis.display.free_params()

project.analysis.display.free_params()

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 [38]:

project.analysis.fit()

project.analysis.fit()

Standard fitting

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

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

📈 Goodness-of-fit (reduced χ²) change:

	iteration	χ²	improvement [%]
1	1	5.49
2	35	2.19	60.1% ↓
3	67	1.97	9.8% ↓
4	260	1.97

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

✅ Fitting complete.

In [39]:

project.analysis.display.fit_results()

project.analysis.display.fit_results()

Fit results

✅ Success: True

⏱️ Fitting time: 22.62 seconds

📏 Goodness-of-fit (reduced χ²): 1.97

📏 R-factor (Rf): 4.03%

📏 R-factor squared (Rf²): 4.68%

📏 Weighted R-factor (wR): 4.19%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	hs	cell		length_a	6.8623	6.8643	0.0004	Å	0.03 % ↑
2	hs	cell		length_c	14.1357	14.1424	0.0010	Å	0.05 % ↑
3	hs	atom_site	Zn	adp_iso	0.5000	0.2297	0.0611	Ų	54.05 % ↓
4	hs	atom_site	Cu	adp_iso	0.5000	1.4700	0.0379	Ų	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	0.5000	0.9782	0.0347	Ų	95.65 % ↑
8	hs	atom_site	Cl	fract_z	0.1979	0.1966	0.0001		0.63 % ↓
9	hs	atom_site	Cl	adp_iso	0.5000	1.3926	0.0369	Ų	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	0.5000	2.5006	0.0393	Ų	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	0.3426	0.2371	0.0095	deg²	30.81 % ↓
19	hrpt	peak		broad_gauss_v	-0.3774	-0.3015	0.0172	deg²	20.11 % ↓
20	hrpt	peak		broad_gauss_w	0.2762	0.2705	0.0078	deg²	2.04 % ↓
21	hrpt	peak		broad_lorentz_y	0.1516	0.1616	0.0036	deg	6.61 % ↑
22	hrpt	instrument		twotheta_offset	0.1182	0.1512	0.0071	deg	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 % ↑

In [40]:

project.plotter.plot_param_correlations()

project.plotter.plot_param_correlations()

Plot Measured vs Calculated¶

In [41]:

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

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

In [42]:

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

project.plotter.plot_meas_vs_calc(expt_name='hrpt', x_min=48, x_max=51, show_residual=True)

Summary¶

This final section shows how to review the results of the analysis.

Show Project Summary¶

In [43]:

project.summary.show_report()

project.summary.show_report()

————————————
PROJECT INFO
————————————

Title

Untitled Project

—————————————————————
CRYSTALLOGRAPHIC DATA
—————————————————————

Phase datablock

🧩 hs

Space group

R -3 m

	Parameter	Value	Uncertainty
1	a	6.86430591	0.00043941
2	b	6.86430591	0.00043941
3	c	6.86430591	0.00043941
4	α	90.00000000
5	β	90.00000000
6	γ	120.00000000

Atom sites

	label	type	x	y	z	occ	Biso
1	Zn	Zn	0.00000000	0.00000000	0.50000000	1.00000000	0.22974071
2	Cu	Cu	0.50000000	0.00000000	0.00000000	1.00000000	1.46995633
3	O	O	0.20636507	-0.20636507	0.06098687	1.00000000	0.97823840
4	Cl	Cl	0.00000000	0.00000000	0.19664786	1.00000000	1.39263830
5	H	2H	0.13251047	-0.13251047	0.08981735	1.00000000	2.50055965

———————————
EXPERIMENTS
———————————

Experiment datablock

🔬 hrpt

Experiment type

powder, neutron, constant wavelength bragg

Calculation engine

cryspy

Wavelength

1.89000

2θ offset

0.15122

Profile type

pseudo-voigt + empirical asymmetry

Peak broadening (Gaussian)

	Parameter	Value	Uncertainty
1	U	0.23707057	0.00945812
2	V	-0.30153917	0.01721957
3	W	0.27051354	0.00780096

Peak broadening (Lorentzian)

	Parameter	Value	Uncertainty
1	X	0.00000000
2	Y	0.16158673	0.00356715

Asymmetry (Empirical)

	Parameter	Value	Uncertainty
1	p1	-0.21445483	0.02477167
2	p2	-0.05057848	0.00400889
3	p3	0.15041528	0.05532097
4	p4	0.06443360	0.00890042

———————
FITTING
———————

Minimization engine

lmfit (leastsq)

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	1.97