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 SampleModelFactory
from easydiffraction import download_from_repository

from easydiffraction import ExperimentFactory from easydiffraction import Project from easydiffraction import SampleModelFactory from easydiffraction import download_from_repository

Define Sample Model¶

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

Create Sample Model¶

In [3]:

model = SampleModelFactory.create(name='hs')

model = SampleModelFactory.create(name='hs')

Set Space Group¶

In [4]:

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

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

Set Unit Cell¶

In [5]:

model.cell.length_a = 6.9
model.cell.length_c = 14.1

model.cell.length_a = 6.9 model.cell.length_c = 14.1

Set Atom Sites¶

In [6]:

model.atom_sites.add_from_args(
    label='Zn',
    type_symbol='Zn',
    fract_x=0,
    fract_y=0,
    fract_z=0.5,
    wyckoff_letter='b',
    b_iso=0.5,
)
model.atom_sites.add_from_args(
    label='Cu',
    type_symbol='Cu',
    fract_x=0.5,
    fract_y=0,
    fract_z=0,
    wyckoff_letter='e',
    b_iso=0.5,
)
model.atom_sites.add_from_args(
    label='O',
    type_symbol='O',
    fract_x=0.21,
    fract_y=-0.21,
    fract_z=0.06,
    wyckoff_letter='h',
    b_iso=0.5,
)
model.atom_sites.add_from_args(
    label='Cl',
    type_symbol='Cl',
    fract_x=0,
    fract_y=0,
    fract_z=0.197,
    wyckoff_letter='c',
    b_iso=0.5,
)
model.atom_sites.add_from_args(
    label='H',
    type_symbol='2H',
    fract_x=0.13,
    fract_y=-0.13,
    fract_z=0.08,
    wyckoff_letter='h',
    b_iso=0.5,
)

model.atom_sites.add_from_args( label='Zn', type_symbol='Zn', fract_x=0, fract_y=0, fract_z=0.5, wyckoff_letter='b', b_iso=0.5, ) model.atom_sites.add_from_args( label='Cu', type_symbol='Cu', fract_x=0.5, fract_y=0, fract_z=0, wyckoff_letter='e', b_iso=0.5, ) model.atom_sites.add_from_args( label='O', type_symbol='O', fract_x=0.21, fract_y=-0.21, fract_z=0.06, wyckoff_letter='h', b_iso=0.5, ) model.atom_sites.add_from_args( label='Cl', type_symbol='Cl', fract_x=0, fract_y=0, fract_z=0.197, wyckoff_letter='c', b_iso=0.5, ) model.atom_sites.add_from_args( label='H', type_symbol='2H', fract_x=0.13, fract_y=-0.13, fract_z=0.08, wyckoff_letter='h', b_iso=0.5, )

Symmetry constraints¶

Show CIF output before applying symmetry constraints.

In [7]:

model.show_as_cif()

model.show_as_cif()

Sample model 🧩 'hs' as cif

	CIF
1	data_hs
2
3	_cell.length_a 6.9
4	_cell.length_b 10.0
5	_cell.length_c 14.1
6	_cell.angle_alpha 90.0
7	_cell.angle_beta 90.0
8	_cell.angle_gamma 90.0
9
10	_space_group.name_H-M_alt "R -3 m"
11	_space_group.IT_coordinate_system_code h
12
13	loop_
14	_atom_site.label
15	_atom_site.type_symbol
16	_atom_site.fract_x
17	_atom_site.fract_y
18	_atom_site.fract_z
19	_atom_site.Wyckoff_letter
20	_atom_site.occupancy
21	_atom_site.B_iso_or_equiv
22	_atom_site.adp_type
23	Zn Zn 0 0 0.5 b 1.0 0.5 Biso
24	Cu Cu 0.5 0 0 e 1.0 0.5 Biso
25	O O 0.21 -0.21 0.06 h 1.0 0.5 Biso
26	Cl Cl 0 0 0.197 c 1.0 0.5 Biso
27	H 2H 0.13 -0.13 0.08 h 1.0 0.5 Biso

Apply symmetry constraints.

In [8]:

model.apply_symmetry_constraints()

model.apply_symmetry_constraints()

Show CIF output after applying symmetry constraints.

In [9]:

model.show_as_cif()

model.show_as_cif()

Sample model 🧩 'hs' as cif

	CIF
1	data_hs
2
3	_cell.length_a 6.9
4	_cell.length_b 6.9
5	_cell.length_c 14.1
6	_cell.angle_alpha 90.0
7	_cell.angle_beta 90.0
8	_cell.angle_gamma 120.0
9
10	_space_group.name_H-M_alt "R -3 m"
11	_space_group.IT_coordinate_system_code h
12
13	loop_
14	_atom_site.label
15	_atom_site.type_symbol
16	_atom_site.fract_x
17	_atom_site.fract_y
18	_atom_site.fract_z
19	_atom_site.Wyckoff_letter
20	_atom_site.occupancy
21	_atom_site.B_iso_or_equiv
22	_atom_site.adp_type
23	Zn Zn 0.0 0.0 0.5 b 1.0 0.5 Biso
24	Cu Cu 0.5 0.0 0.0 e 1.0 0.5 Biso
25	O O 0.21 -0.21 0.06 h 1.0 0.5 Biso
26	Cl Cl 0.0 0.0 0.197 c 1.0 0.5 Biso
27	H 2H 0.13 -0.13 0.08 h 1.0 0.5 Biso

Define Experiment¶

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

Download Measured Data¶

In [10]:

download_from_repository('hrpt_hs.xye', destination='data')

download_from_repository('hrpt_hs.xye', destination='data')

Downloading...

File 'hrpt_hs.xye' from 'easyscience/diffraction-lib'

Create Experiment¶

In [11]:

expt = ExperimentFactory.create(name='hrpt', data_path='data/hrpt_hs.xye')

expt = ExperimentFactory.create(name='hrpt', data_path='data/hrpt_hs.xye')

Data loaded successfully

Experiment 🔬 'hrpt'. Number of data points: 3220

Set Instrument¶

In [12]:

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 [13]:

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.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

Set Background¶

In [14]:

expt.background.add_from_args(x=4.4196, y=500)
expt.background.add_from_args(x=6.6207, y=500)
expt.background.add_from_args(x=10.4918, y=500)
expt.background.add_from_args(x=15.4634, y=500)
expt.background.add_from_args(x=45.6041, y=500)
expt.background.add_from_args(x=74.6844, y=500)
expt.background.add_from_args(x=103.4187, y=500)
expt.background.add_from_args(x=121.6311, y=500)
expt.background.add_from_args(x=159.4116, y=500)

expt.background.add_from_args(x=4.4196, y=500) expt.background.add_from_args(x=6.6207, y=500) expt.background.add_from_args(x=10.4918, y=500) expt.background.add_from_args(x=15.4634, y=500) expt.background.add_from_args(x=45.6041, y=500) expt.background.add_from_args(x=74.6844, y=500) expt.background.add_from_args(x=103.4187, y=500) expt.background.add_from_args(x=121.6311, y=500) expt.background.add_from_args(x=159.4116, y=500)

Set Linked Phases¶

In [15]:

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

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

Define Project¶

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

Create Project¶

In [16]:

project = Project()

project = Project()

Set Plotting Engine¶

In [17]:

project.plotter.engine = 'plotly'

project.plotter.engine = 'plotly'

Add Sample Model¶

In [18]:

project.sample_models.add(model)

project.sample_models.add(model)

Add Experiment¶

In [19]:

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.

Set Calculator¶

In [20]:

project.analysis.current_calculator = 'cryspy'

project.analysis.current_calculator = 'cryspy'

Current calculator changed to

cryspy

Set Minimizer¶

In [21]:

project.analysis.current_minimizer = 'lmfit (leastsq)'

project.analysis.current_minimizer = 'lmfit (leastsq)'

Current minimizer changed to

lmfit (leastsq)

Plot Measured vs Calculated¶

In [22]:

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

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

In [23]:

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

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

Perform Fit 1/5¶

Set parameters to be refined.

In [24]:

model.cell.length_a.free = True
model.cell.length_c.free = True

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

model.cell.length_a.free = True model.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 [25]:

project.analysis.show_free_params()

project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	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 [26]:

project.analysis.fit()

project.analysis.fit()

Using experiment 🔬 'hrpt' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	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.

Fit results

✅ Success: True

⏱️ Fitting time: 16.50 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	None	length_a	6.9000	6.8623	0.0003	Å	0.55 % ↓
2	hs	cell	None	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	None	twotheta_offset	0.0000	0.1271	0.0051	deg	N/A

Plot Measured vs Calculated¶

In [27]:

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

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

In [28]:

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

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

Perform Fit 2/5¶

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_x.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_x.free = True for point in expt.background: point.y.free = True

Show free parameters after selection.

In [30]:

project.analysis.show_free_params()

project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	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	peak		broad_gauss_u	0.10000		-inf	inf	deg²
4	hrpt	peak		broad_gauss_v	-0.20000		-inf	inf	deg²
5	hrpt	peak		broad_gauss_w	0.20000		-inf	inf	deg²
6	hrpt	peak		broad_lorentz_x	0.00000		-inf	inf	deg
7	hrpt	linked_phases	hs	scale	0.25480	0.00305	-inf	inf
8	hrpt	instrument		twotheta_offset	0.12712	0.00515	-inf	inf	deg
9	hrpt	background	4.4196	y	500.00000		-inf	inf
10	hrpt	background	6.6207	y	500.00000		-inf	inf
11	hrpt	background	10.4918	y	500.00000		-inf	inf
12	hrpt	background	15.4634	y	500.00000		-inf	inf
13	hrpt	background	45.6041	y	500.00000		-inf	inf
14	hrpt	background	74.6844	y	500.00000		-inf	inf
15	hrpt	background	103.4187	y	500.00000		-inf	inf
16	hrpt	background	121.6311	y	500.00000		-inf	inf
17	hrpt	background	159.4116	y	500.00000		-inf	inf

Run Fitting¶

In [31]:

project.analysis.fit()

project.analysis.fit()

Using experiment 🔬 'hrpt' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	51.78
2	21	13.07	74.8% ↓
3	40	12.66	3.2% ↓
4	58	12.49	1.3% ↓
5	340	12.41

🏆 Best goodness-of-fit (reduced χ²) is 12.41 at iteration 339

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 13.50 seconds

📏 Goodness-of-fit (reduced χ²): 12.41

📏 R-factor (Rf): 9.62%

📏 R-factor squared (Rf²): 12.83%

📏 Weighted R-factor (wR): 12.21%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	hs	cell	None	length_a	6.8623	6.8628	0.0003	Å	0.01 % ↑
2	hs	cell	None	length_c	14.1365	14.1389	0.0009	Å	0.02 % ↑
3	hrpt	peak	None	broad_gauss_u	0.1000	0.1042	0.0451	deg²	4.18 % ↑
4	hrpt	peak	None	broad_gauss_v	-0.2000	-0.4977	0.0619	deg²	148.83 % ↑
5	hrpt	peak	None	broad_gauss_w	0.2000	0.3592	0.0227	deg²	79.60 % ↑
6	hrpt	peak	None	broad_lorentz_x	0.0000	0.5042	0.0075	deg	N/A
7	hrpt	linked_phases	hs	scale	0.2548	0.4570	0.0032		79.37 % ↑
8	hrpt	instrument	None	twotheta_offset	0.1271	0.1289	0.0038	deg	1.39 % ↑
9	hrpt	background	4.4196	y	500.0000	645.4830	23.7674		29.10 % ↑
10	hrpt	background	6.6207	y	500.0000	520.8595	13.6088		4.17 % ↑
11	hrpt	background	10.4918	y	500.0000	455.0036	10.4220		9.00 % ↓
12	hrpt	background	15.4634	y	500.0000	428.8639	5.4019		14.23 % ↓
13	hrpt	background	45.6041	y	500.0000	453.5008	5.2135		9.30 % ↓
14	hrpt	background	74.6844	y	500.0000	446.7592	5.4686		10.65 % ↓
15	hrpt	background	103.4187	y	500.0000	411.5620	5.4490		17.69 % ↓
16	hrpt	background	121.6311	y	500.0000	364.3828	5.6634		27.12 % ↓
17	hrpt	background	159.4116	y	500.0000	469.2837	5.4987		6.14 % ↓

Plot Measured vs Calculated¶

In [32]:

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

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

In [33]:

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

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

Perform Fit 3/5¶

Set more parameters to be refined.

In [34]:

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

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

Show free parameters after selection.

In [35]:

project.analysis.show_free_params()

project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	hs	cell		length_a	6.86276	0.00033	-inf	inf	Å
2	hs	cell		length_c	14.13889	0.00088	-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	peak		broad_gauss_u	0.10418	0.04510	-inf	inf	deg²
9	hrpt	peak		broad_gauss_v	-0.49766	0.06188	-inf	inf	deg²
10	hrpt	peak		broad_gauss_w	0.35919	0.02266	-inf	inf	deg²
11	hrpt	peak		broad_lorentz_x	0.50419	0.00753	-inf	inf	deg
12	hrpt	linked_phases	hs	scale	0.45704	0.00318	-inf	inf
13	hrpt	instrument		twotheta_offset	0.12889	0.00379	-inf	inf	deg
14	hrpt	background	4.4196	y	645.48303	23.76745	-inf	inf
15	hrpt	background	6.6207	y	520.85952	13.60879	-inf	inf
16	hrpt	background	10.4918	y	455.00355	10.42197	-inf	inf
17	hrpt	background	15.4634	y	428.86390	5.40186	-inf	inf
18	hrpt	background	45.6041	y	453.50084	5.21353	-inf	inf
19	hrpt	background	74.6844	y	446.75916	5.46856	-inf	inf
20	hrpt	background	103.4187	y	411.56202	5.44902	-inf	inf
21	hrpt	background	121.6311	y	364.38279	5.66340	-inf	inf
22	hrpt	background	159.4116	y	469.28374	5.49874	-inf	inf

Run Fitting¶

In [36]:

project.analysis.fit()

project.analysis.fit()

Using experiment 🔬 'hrpt' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	12.43
2	26	5.11	58.9% ↓
3	49	4.40	13.9% ↓
4	72	4.35	1.3% ↓
5	188	4.34

🏆 Best goodness-of-fit (reduced χ²) is 4.34 at iteration 187

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 7.80 seconds

📏 Goodness-of-fit (reduced χ²): 4.34

📏 R-factor (Rf): 6.01%

📏 R-factor squared (Rf²): 7.74%

📏 Weighted R-factor (wR): 7.51%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	hs	cell	None	length_a	6.8628	6.8621	0.0002	Å	0.01 % ↓
2	hs	cell	None	length_c	14.1389	14.1356	0.0005	Å	0.02 % ↓
3	hs	atom_site	O	fract_x	0.2100	0.2059	0.0002		1.96 % ↓
4	hs	atom_site	O	fract_z	0.0600	0.0625	0.0002		4.14 % ↑
5	hs	atom_site	Cl	fract_z	0.1970	0.1977	0.0002		0.36 % ↑
6	hs	atom_site	H	fract_x	0.1300	0.1330	0.0002		2.33 % ↑
7	hs	atom_site	H	fract_z	0.0800	0.0877	0.0001		9.59 % ↑
8	hrpt	peak	None	broad_gauss_u	0.1042	0.1789	0.0119	deg²	71.71 % ↑
9	hrpt	peak	None	broad_gauss_v	-0.4977	-0.3964	0.0222	deg²	20.35 % ↓
10	hrpt	peak	None	broad_gauss_w	0.3592	0.3272	0.0100	deg²	8.92 % ↓
11	hrpt	peak	None	broad_lorentz_x	0.5042	0.3601	0.0089	deg	28.57 % ↓
12	hrpt	linked_phases	hs	scale	0.4570	0.4176	0.0021		8.63 % ↓
13	hrpt	instrument	None	twotheta_offset	0.1289	0.1167	0.0021	deg	9.43 % ↓
14	hrpt	background	4.4196	y	645.4830	647.4024	14.0610		0.30 % ↑
15	hrpt	background	6.6207	y	520.8595	523.4725	8.0510		0.50 % ↑
16	hrpt	background	10.4918	y	455.0036	453.7545	6.1678		0.27 % ↓
17	hrpt	background	15.4634	y	428.8639	437.9479	3.2221		2.12 % ↑
18	hrpt	background	45.6041	y	453.5008	477.4863	3.2261		5.29 % ↑
19	hrpt	background	74.6844	y	446.7592	485.0177	3.4007		8.56 % ↑
20	hrpt	background	103.4187	y	411.5620	452.4338	3.2894		9.93 % ↑
21	hrpt	background	121.6311	y	364.3828	435.3732	3.5007		19.48 % ↑
22	hrpt	background	159.4116	y	469.2837	427.3883	3.6274		8.93 % ↓

Plot Measured vs Calculated¶

In [37]:

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

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

In [38]:

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

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

Perform Fit 4/5¶

Set more parameters to be refined.

In [39]:

model.atom_sites['Zn'].b_iso.free = True
model.atom_sites['Cu'].b_iso.free = True
model.atom_sites['O'].b_iso.free = True
model.atom_sites['Cl'].b_iso.free = True
model.atom_sites['H'].b_iso.free = True

model.atom_sites['Zn'].b_iso.free = True model.atom_sites['Cu'].b_iso.free = True model.atom_sites['O'].b_iso.free = True model.atom_sites['Cl'].b_iso.free = True model.atom_sites['H'].b_iso.free = True

Show free parameters after selection.

In [40]:

project.analysis.show_free_params()

project.analysis.show_free_params()

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

	datablock	category	entry	parameter	value	uncertainty	min	max	units
1	hs	cell		length_a	6.86205	0.00020	-inf	inf	Å
2	hs	cell		length_c	14.13560	0.00049	-inf	inf	Å
3	hs	atom_site	Zn	b_iso	0.50000		-inf	inf	Ų
4	hs	atom_site	Cu	b_iso	0.50000		-inf	inf	Ų
5	hs	atom_site	O	fract_x	0.20589	0.00022	-inf	inf
6	hs	atom_site	O	fract_z	0.06248	0.00016	-inf	inf
7	hs	atom_site	O	b_iso	0.50000		-inf	inf	Ų
8	hs	atom_site	Cl	fract_z	0.19771	0.00016	-inf	inf
9	hs	atom_site	Cl	b_iso	0.50000		-inf	inf	Ų
10	hs	atom_site	H	fract_x	0.13303	0.00017	-inf	inf
11	hs	atom_site	H	fract_z	0.08767	0.00012	-inf	inf
12	hs	atom_site	H	b_iso	0.50000		-inf	inf	Ų
13	hrpt	peak		broad_gauss_u	0.17888	0.01187	-inf	inf	deg²
14	hrpt	peak		broad_gauss_v	-0.39638	0.02219	-inf	inf	deg²
15	hrpt	peak		broad_gauss_w	0.32715	0.00999	-inf	inf	deg²
16	hrpt	peak		broad_lorentz_x	0.36012	0.00888	-inf	inf	deg
17	hrpt	linked_phases	hs	scale	0.41758	0.00208	-inf	inf
18	hrpt	instrument		twotheta_offset	0.11674	0.00215	-inf	inf	deg
19	hrpt	background	4.4196	y	647.40242	14.06098	-inf	inf
20	hrpt	background	6.6207	y	523.47254	8.05103	-inf	inf
21	hrpt	background	10.4918	y	453.75449	6.16778	-inf	inf
22	hrpt	background	15.4634	y	437.94787	3.22213	-inf	inf
23	hrpt	background	45.6041	y	477.48627	3.22612	-inf	inf
24	hrpt	background	74.6844	y	485.01766	3.40075	-inf	inf
25	hrpt	background	103.4187	y	452.43379	3.28943	-inf	inf
26	hrpt	background	121.6311	y	435.37321	3.50066	-inf	inf
27	hrpt	background	159.4116	y	427.38825	3.62743	-inf	inf

Run Fitting¶

In [41]:

project.analysis.fit()

project.analysis.fit()

Using experiment 🔬 'hrpt' for 'single' fitting

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

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

	iteration	χ²	improvement [%]
1	1	4.35
2	31	2.30	47.1% ↓
3	59	2.11	8.3% ↓
4	144	2.11

🏆 Best goodness-of-fit (reduced χ²) is 2.11 at iteration 118

✅ Fitting complete.

Fit results

✅ Success: True

⏱️ Fitting time: 6.75 seconds

📏 Goodness-of-fit (reduced χ²): 2.11

📏 R-factor (Rf): 4.17%

📏 R-factor squared (Rf²): 5.05%

📏 Weighted R-factor (wR): 4.73%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	hs	cell	None	length_a	6.8621	6.8615	0.0001	Å	0.01 % ↓
2	hs	cell	None	length_c	14.1356	14.1360	0.0004	Å	0.00 % ↑
3	hs	atom_site	Zn	b_iso	0.5000	0.0855	0.0630	Ų	82.91 % ↓
4	hs	atom_site	Cu	b_iso	0.5000	1.1937	0.0399	Ų	138.74 % ↑
5	hs	atom_site	O	fract_x	0.2059	0.2060	0.0002		0.06 % ↑
6	hs	atom_site	O	fract_z	0.0625	0.0609	0.0001		2.53 % ↓
7	hs	atom_site	O	b_iso	0.5000	0.7001	0.0360	Ų	40.02 % ↑
8	hs	atom_site	Cl	fract_z	0.1977	0.1968	0.0001		0.49 % ↓
9	hs	atom_site	Cl	b_iso	0.5000	1.1129	0.0385	Ų	122.58 % ↑
10	hs	atom_site	H	fract_x	0.1330	0.1322	0.0002		0.62 % ↓
11	hs	atom_site	H	fract_z	0.0877	0.0900	0.0001		2.63 % ↑
12	hs	atom_site	H	b_iso	0.5000	2.3404	0.0401	Ų	368.08 % ↑
13	hrpt	peak	None	broad_gauss_u	0.1789	0.1579	0.0076	deg²	11.70 % ↓
14	hrpt	peak	None	broad_gauss_v	-0.3964	-0.3571	0.0147	deg²	9.91 % ↓
15	hrpt	peak	None	broad_gauss_w	0.3272	0.3498	0.0067	deg²	6.92 % ↑
16	hrpt	peak	None	broad_lorentz_x	0.3601	0.2927	0.0065	deg	18.73 % ↓
17	hrpt	linked_phases	hs	scale	0.4176	0.4918	0.0022		17.76 % ↑
18	hrpt	instrument	None	twotheta_offset	0.1167	0.1137	0.0015	deg	2.62 % ↓
19	hrpt	background	4.4196	y	647.4024	648.4125	9.7968		0.16 % ↑
20	hrpt	background	6.6207	y	523.4725	523.7880	5.6095		0.06 % ↑
21	hrpt	background	10.4918	y	453.7545	454.9375	4.2976		0.26 % ↑
22	hrpt	background	15.4634	y	437.9479	435.9131	2.2512		0.46 % ↓
23	hrpt	background	45.6041	y	477.4863	472.9718	2.2759		0.95 % ↓
24	hrpt	background	74.6844	y	485.0177	486.6064	2.4356		0.33 % ↑
25	hrpt	background	103.4187	y	452.4338	472.4095	2.3483		4.42 % ↑
26	hrpt	background	121.6311	y	435.3732	496.7338	2.6211		14.09 % ↑
27	hrpt	background	159.4116	y	427.3883	473.1457	2.9361		10.71 % ↑

Plot Measured vs Calculated¶

In [42]:

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

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

In [43]:

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

project.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 [44]:

project.summary.show_report()

project.summary.show_report()

PROJECT INFO
━━━━━━━━━━━━

Title

Untitled Project

CRYSTALLOGRAPHIC DATA
━━━━━━━━━━━━━━━━━━━━━

Phase datablock

🧩 hs

Space group

R -3 m

Cell parameters

	Parameter	Value
1	a	6.86149
2	b	6.86149
3	c	14.13604
4	alpha	90.00000
5	beta	90.00000
6	gamma	120.00000

Atom sites

	label	type	x	y	z	occ	Biso
1	Zn	Zn	0.00000	0.00000	0.50000	1.00000	0.08546
2	Cu	Cu	0.50000	0.00000	0.00000	1.00000	1.19372
3	O	O	0.20601	-0.20601	0.06090	1.00000	0.70009
4	Cl	Cl	0.00000	0.00000	0.19675	1.00000	1.11288
5	H	2H	0.13220	-0.13220	0.08998	1.00000	2.34039

EXPERIMENTS
━━━━━━━━━━━

Experiment datablock

🔬 hrpt

Experiment type

SampleFormEnum.POWDER, RadiationProbeEnum.NEUTRON, BeamModeEnum.CONSTANT_WAVELENGTH

Wavelength

1.89000

2θ offset

0.11368

Profile type

PeakProfileTypeEnum.PSEUDO_VOIGT

Peak broadening (Gaussian)

	Parameter	Value
1	U	0.15795
2	V	-0.35708
3	W	0.34978

Peak broadening (Lorentzian)

	Parameter	Value
1	X	0.29266
2	Y	0.00000

FITTING
━━━━━━━

Calculation engine

cryspy

Minimization engine

lmfit (leastsq)

Fit quality

	metric	value
1	Goodness-of-fit (reduced χ²)	2.11