Instrument calibration: BEER at ESS¶

This example demonstrates a Rietveld refinement of a duplex steel structure using time-of-flight neutron powder diffraction data simulated with McStas.

Two datasets from two symmetrically positioned banks (S2 and N2) of the BEER instrument are analyzed in this tutorial.

Import Library¶

In [2]:

from easydiffraction import ExperimentFactory
from easydiffraction import Project
from easydiffraction import StructureFactory
from easydiffraction import download_data
from easydiffraction import extract_data_paths_from_zip
from easydiffraction import extract_metadata

from easydiffraction import ExperimentFactory from easydiffraction import Project from easydiffraction import StructureFactory from easydiffraction import download_data from easydiffraction import extract_data_paths_from_zip from easydiffraction import extract_metadata

Define Structures¶

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

Create Ferrite Structure¶

In [3]:

ferrite = StructureFactory.from_scratch(name='ferrite')

ferrite.space_group.name_h_m = 'I m -3 m'
ferrite.space_group.it_coordinate_system_code = '1'

ferrite.cell.length_a = 2.886

ferrite.atom_sites.create(
    label='Fe',
    type_symbol='Fe',
    fract_x=0.0,
    fract_y=0.0,
    fract_z=0.0,
    wyckoff_letter='a',
    adp_type='Biso',
    adp_iso=1.0,
)

ferrite = StructureFactory.from_scratch(name='ferrite') ferrite.space_group.name_h_m = 'I m -3 m' ferrite.space_group.it_coordinate_system_code = '1' ferrite.cell.length_a = 2.886 ferrite.atom_sites.create( label='Fe', type_symbol='Fe', fract_x=0.0, fract_y=0.0, fract_z=0.0, wyckoff_letter='a', adp_type='Biso', adp_iso=1.0, )

Create Austenite Structure¶

In [4]:

austenite = StructureFactory.from_scratch(name='austenite')

austenite.space_group.name_h_m = 'F m -3 m'
austenite.space_group.it_coordinate_system_code = '1'

austenite.cell.length_a = 3.6468

austenite.atom_sites.create(
    label='Fe',
    type_symbol='Fe',
    fract_x=0.0,
    fract_y=0.0,
    fract_z=0.0,
    wyckoff_letter='a',
    adp_type='Biso',
    adp_iso=1.0,
)

austenite = StructureFactory.from_scratch(name='austenite') austenite.space_group.name_h_m = 'F m -3 m' austenite.space_group.it_coordinate_system_code = '1' austenite.cell.length_a = 3.6468 austenite.atom_sites.create( label='Fe', type_symbol='Fe', fract_x=0.0, fract_y=0.0, fract_z=0.0, wyckoff_letter='a', adp_type='Biso', adp_iso=1.0, )

Define Experiments¶

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

Download Measured Data¶

In [5]:

zip_path = download_data(id=33, destination='data')
data_paths = extract_data_paths_from_zip(zip_path, destination='data/ed-20')

data_path_s2 = data_paths[1]  # 'Duplex_in_HR_for_IRF_S2.dat'
data_path_n2 = data_paths[0]  # 'Duplex_in_HR_for_IRF_N2.dat'

zip_path = download_data(id=33, destination='data') data_paths = extract_data_paths_from_zip(zip_path, destination='data/ed-20') data_path_s2 = data_paths[1] # 'Duplex_in_HR_for_IRF_S2.dat' data_path_n2 = data_paths[0] # 'Duplex_in_HR_for_IRF_N2.dat'

Getting data...

Data #33: ferrite + austenite, BEER (ESS), S2 and N2 detector bank datasets

✅ Data #33 downloaded to 'data/ed-33.zip'

Create Experiment¶

In [6]:

expt_s2 = ExperimentFactory.from_data_path(
    name='expt_s2',
    data_path=data_path_s2,
    beam_mode='time-of-flight',
)

expt_s2 = ExperimentFactory.from_data_path( name='expt_s2', data_path=data_path_s2, beam_mode='time-of-flight', )

In [7]:

expt_n2 = ExperimentFactory.from_data_path(
    name='expt_n2',
    data_path=data_path_n2,
    beam_mode='time-of-flight',
)

expt_n2 = ExperimentFactory.from_data_path( name='expt_n2', data_path=data_path_n2, beam_mode='time-of-flight', )

Set Instrument¶

In [8]:

expt_s2.instrument.setup_twotheta_bank = extract_metadata(
    data_path_s2, r'two_theta\s*=\s*(\d*\.?\d+)'
)
expt_s2.instrument.calib_d_to_tof_linear = extract_metadata(
    data_path_s2, r'DIFC\s*=\s*(\d*\.?\d+)'
)

expt_s2.instrument.setup_twotheta_bank = extract_metadata( data_path_s2, r'two_theta\s*=\s*(\d*\.?\d+)' ) expt_s2.instrument.calib_d_to_tof_linear = extract_metadata( data_path_s2, r'DIFC\s*=\s*(\d*\.?\d+)' )

In [9]:

expt_n2.instrument.setup_twotheta_bank = extract_metadata(
    data_path_n2, r'two_theta\s*=\s*(\d*\.?\d+)'
)
expt_n2.instrument.calib_d_to_tof_linear = extract_metadata(
    data_path_n2, r'DIFC\s*=\s*(\d*\.?\d+)'
)

expt_n2.instrument.setup_twotheta_bank = extract_metadata( data_path_n2, r'two_theta\s*=\s*(\d*\.?\d+)' ) expt_n2.instrument.calib_d_to_tof_linear = extract_metadata( data_path_n2, r'DIFC\s*=\s*(\d*\.?\d+)' )

Set Peak Profile¶

In [10]:

expt_s2.show_peak_profile_types()

expt_s2.show_peak_profile_types()

Peak profile types

		Type	Description
1		pseudo-voigt	TOF non-convoluted pseudo-Voigt profile
2	*	jorgensen	TOF Jorgensen profile: back-to-back exponentials ⊗ Gaussian
3		jorgensen-von-dreele	TOF Jorgensen-Von Dreele profile: back-to-back exponentials ⊗ pseudo-Voigt
4		double-jorgensen-von-dreele	TOF Double-Jorgensen-Von Dreele profile: double back-to-back exponentials ⊗ pseudo-Voigt (Z-Rietveld type0m)

In [11]:

expt_s2.peak_profile_type = 'pseudo-voigt'

expt_s2.peak_profile_type = 'pseudo-voigt'

⚠️ Switching peak profile type discards existing peak parameters.                                                                 

Peak profile type for experiment 'expt_s2' changed to

pseudo-voigt

In [12]:

expt_s2.peak.broad_gauss_sigma_0 = 300
expt_s2.peak.broad_gauss_sigma_1 = 1200
expt_s2.peak.broad_gauss_sigma_2 = 900

expt_s2.peak.broad_gauss_sigma_0 = 300 expt_s2.peak.broad_gauss_sigma_1 = 1200 expt_s2.peak.broad_gauss_sigma_2 = 900

In [13]:

expt_n2.peak_profile_type = 'pseudo-voigt'

expt_n2.peak_profile_type = 'pseudo-voigt'

⚠️ Switching peak profile type discards existing peak parameters.                                                                 

Peak profile type for experiment 'expt_n2' changed to

pseudo-voigt

In [14]:

expt_n2.peak.broad_gauss_sigma_0 = 300
expt_n2.peak.broad_gauss_sigma_1 = 1200
expt_n2.peak.broad_gauss_sigma_2 = 900

expt_n2.peak.broad_gauss_sigma_0 = 300 expt_n2.peak.broad_gauss_sigma_1 = 1200 expt_n2.peak.broad_gauss_sigma_2 = 900

Set Background¶

In [15]:

expt_s2.show_background_types()

expt_s2.show_background_types()

Background types

		Type	Description
1		chebyshev	Chebyshev polynomial background
2	*	line-segment	Linear interpolation between points

In [16]:

# expt_s2.background_type = 'line-segment'

# expt_s2.background_type = 'line-segment'

In [17]:

for idx, (x, y) in enumerate(
    [
        (40111.8789, 0.0170),
        (41193.5664, 0.1484),
        (42041.3750, 0.1848),
        (42713.7734, 0.1975),
        (44409.3945, 0.1891),
        (45198.7344, 0.2147),
        (46251.1875, 0.1887),
        (49350.0742, 0.2194),
        (51289.6836, 0.1991),
        (55245.1992, 0.1981),
        (55679.7070, 0.2276),
        (56383.9102, 0.2439),
        (58956.1797, 0.2907),
        (61536.4570, 0.3067),
        (63768.0469, 0.3242),
        (65581.2109, 0.2973),
        (70183.8516, 0.2575),
        (71787.8203, 0.2321),
        (78343.1094, 0.2158),
        (80016.8047, 0.1694),
        (98141.8516, 0.2400),
        (99262.2344, 0.4335),
        (100985.8516, 0.4375),
        (101933.8516, 0.3427),
        (108656.0312, 0.5339),
        (110896.7500, 0.9537),
        (113137.4844, 1.1668),
        (114430.2031, 1.1164),
        (116929.4844, 0.9161),
        (119428.7422, 0.6885),
        (134506.3438, 0.0692),
    ],
    start=1,
):
    expt_s2.background.create(id=str(idx), x=x, y=y)

for idx, (x, y) in enumerate( [ (40111.8789, 0.0170), (41193.5664, 0.1484), (42041.3750, 0.1848), (42713.7734, 0.1975), (44409.3945, 0.1891), (45198.7344, 0.2147), (46251.1875, 0.1887), (49350.0742, 0.2194), (51289.6836, 0.1991), (55245.1992, 0.1981), (55679.7070, 0.2276), (56383.9102, 0.2439), (58956.1797, 0.2907), (61536.4570, 0.3067), (63768.0469, 0.3242), (65581.2109, 0.2973), (70183.8516, 0.2575), (71787.8203, 0.2321), (78343.1094, 0.2158), (80016.8047, 0.1694), (98141.8516, 0.2400), (99262.2344, 0.4335), (100985.8516, 0.4375), (101933.8516, 0.3427), (108656.0312, 0.5339), (110896.7500, 0.9537), (113137.4844, 1.1668), (114430.2031, 1.1164), (116929.4844, 0.9161), (119428.7422, 0.6885), (134506.3438, 0.0692), ], start=1, ): expt_s2.background.create(id=str(idx), x=x, y=y)

In [18]:

for point in expt_s2.background:
    expt_n2.background.create(id=point.id.value, x=point.x.value, y=point.y.value)

for point in expt_s2.background: expt_n2.background.create(id=point.id.value, x=point.x.value, y=point.y.value)

Set Linked Phases¶

In [19]:

expt_s2.linked_phases.create(id='ferrite', scale=10)
expt_s2.linked_phases.create(id='austenite', scale=10)

expt_s2.linked_phases.create(id='ferrite', scale=10) expt_s2.linked_phases.create(id='austenite', scale=10)

In [20]:

expt_n2.linked_phases.create(id='ferrite', scale=10)
expt_n2.linked_phases.create(id='austenite', scale=10)

expt_n2.linked_phases.create(id='ferrite', scale=10) expt_n2.linked_phases.create(id='austenite', scale=10)

Set Excluded Regions¶

In [21]:

expt_s2.excluded_regions.create(id='1', start=0, end=40500)
expt_s2.excluded_regions.create(id='2', start=130000, end=180000)

expt_s2.excluded_regions.create(id='1', start=0, end=40500) expt_s2.excluded_regions.create(id='2', start=130000, end=180000)

In [22]:

expt_n2.excluded_regions.create(id='1', start=0, end=40500)
expt_n2.excluded_regions.create(id='2', start=130000, end=180000)

expt_n2.excluded_regions.create(id='1', start=0, end=40500) expt_n2.excluded_regions.create(id='2', start=130000, end=180000)

Define Project¶

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

Create Project¶

In [23]:

project = Project(name='beer')
project.save_as(dir_path='beer_mcstas')

project = Project(name='beer') project.save_as(dir_path='beer_mcstas')

Saving project 📦 'beer' to

/home/runner/work/diffraction-lib/diffraction-lib/docs/docs/tutorials/beer_mcstas

├── 📄 project.cif

├── 📁 structures/

├── 📁 experiments/

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Add Structures¶

In [24]:

project.structures.add(ferrite)
project.structures.add(austenite)

project.structures.add(ferrite) project.structures.add(austenite)

Add Experiments¶

In [25]:

project.experiments.add(expt_s2)
project.experiments.add(expt_n2)

project.experiments.add(expt_s2) project.experiments.add(expt_n2)

Plot Measured vs Calculated¶

In [26]:

project.display.plotter.plot_meas_vs_calc(expt_name='expt_s2')

project.display.plotter.plot_meas_vs_calc(expt_name='expt_s2')

In [27]:

project.display.plotter.plot_meas_vs_calc(expt_name='expt_n2')

project.display.plotter.plot_meas_vs_calc(expt_name='expt_n2')

Perform Analysis¶

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

Set Fit Mode¶

In [28]:

project.analysis.fit.show_modes()

project.analysis.fit.show_modes()

Fit modes

		Type	Description
1	*	single	Independent fitting of each experiment
2		joint	Simultaneous fitting of all experiments with weights
3		sequential	Sequential fitting over data files in a directory

In [29]:

project.analysis.fit.mode = 'joint'

project.analysis.fit.mode = 'joint'

Set Free Parameters¶

In [30]:

project.analysis.display.fittable_params()

project.analysis.display.fittable_params()

Fittable parameters for all structures (🧩 data blocks)

	datablock	category	entry	parameter	value	uncertainty	units	free
1	ferrite	cell		length_a	2.88600		Å	False
2	ferrite	cell		length_b	2.88600		Å	False
3	ferrite	cell		length_c	2.88600		Å	False
4	ferrite	cell		angle_alpha	90.00000		deg	False
5	ferrite	cell		angle_beta	90.00000		deg	False
6	ferrite	cell		angle_gamma	90.00000		deg	False
7	ferrite	atom_site	Fe	fract_x	0.00000			False
8	ferrite	atom_site	Fe	fract_y	0.00000			False
9	ferrite	atom_site	Fe	fract_z	0.00000			False
10	ferrite	atom_site	Fe	occupancy	1.00000			False
11	ferrite	atom_site	Fe	adp_iso	1.00000		Ų	False
12	austenite	cell		length_a	3.64680		Å	False
13	austenite	cell		length_b	3.64680		Å	False
14	austenite	cell		length_c	3.64680		Å	False
15	austenite	cell		angle_alpha	90.00000		deg	False
16	austenite	cell		angle_beta	90.00000		deg	False
17	austenite	cell		angle_gamma	90.00000		deg	False
18	austenite	atom_site	Fe	fract_x	0.00000			False
19	austenite	atom_site	Fe	fract_y	0.00000			False
20	austenite	atom_site	Fe	fract_z	0.00000			False
21	austenite	atom_site	Fe	occupancy	1.00000			False
22	austenite	atom_site	Fe	adp_iso	1.00000		Ų	False

Fittable parameters for all experiments (🔬 data blocks)

	datablock	category	entry	parameter	value	uncertainty	units	free
1	expt_s2	linked_phases	ferrite	scale	10.00000			False
2	expt_s2	linked_phases	austenite	scale	10.00000			False
3	expt_s2	peak		lorentz_gamma_0	0.00000		μs	False
4	expt_s2	peak		lorentz_gamma_1	0.00000		μs/Å	False
5	expt_s2	peak		lorentz_gamma_2	0.00000		μs²/Ų	False
6	expt_s2	peak		gauss_sigma_0	300.00000		μs²	False
7	expt_s2	peak		gauss_sigma_1	1200.00000		μs/Å	False
8	expt_s2	peak		gauss_sigma_2	900.00000		μs²/Ų	False
9	expt_s2	instrument		twotheta_bank	90.00000		deg	False
10	expt_s2	instrument		d_to_tof_offset	0.00000		μs	False
11	expt_s2	instrument		d_to_tof_linear	54902.18695		μs/Å	False
12	expt_s2	instrument		d_to_tof_quad	0.00000		μs/Ų	False
13	expt_s2	instrument		d_to_tof_recip	0.00000		μs·Å	False
14	expt_s2	background	1	y	0.01700			False
15	expt_s2	background	2	y	0.14840			False
16	expt_s2	background	3	y	0.18480			False
17	expt_s2	background	4	y	0.19750			False
18	expt_s2	background	5	y	0.18910			False
19	expt_s2	background	6	y	0.21470			False
20	expt_s2	background	7	y	0.18870			False
21	expt_s2	background	8	y	0.21940			False
22	expt_s2	background	9	y	0.19910			False
23	expt_s2	background	10	y	0.19810			False
24	expt_s2	background	11	y	0.22760			False
25	expt_s2	background	12	y	0.24390			False
26	expt_s2	background	13	y	0.29070			False
27	expt_s2	background	14	y	0.30670			False
28	expt_s2	background	15	y	0.32420			False
29	expt_s2	background	16	y	0.29730			False
30	expt_s2	background	17	y	0.25750			False
31	expt_s2	background	18	y	0.23210			False
32	expt_s2	background	19	y	0.21580			False
33	expt_s2	background	20	y	0.16940			False
34	expt_s2	background	21	y	0.24000			False
35	expt_s2	background	22	y	0.43350			False
36	expt_s2	background	23	y	0.43750			False
37	expt_s2	background	24	y	0.34270			False
38	expt_s2	background	25	y	0.53390			False
39	expt_s2	background	26	y	0.95370			False
40	expt_s2	background	27	y	1.16680			False
41	expt_s2	background	28	y	1.11640			False
42	expt_s2	background	29	y	0.91610			False
43	expt_s2	background	30	y	0.68850			False
44	expt_s2	background	31	y	0.06920			False
45	expt_n2	linked_phases	ferrite	scale	10.00000			False
46	expt_n2	linked_phases	austenite	scale	10.00000			False
47	expt_n2	peak		lorentz_gamma_0	0.00000		μs	False
48	expt_n2	peak		lorentz_gamma_1	0.00000		μs/Å	False
49	expt_n2	peak		lorentz_gamma_2	0.00000		μs²/Ų	False
50	expt_n2	peak		gauss_sigma_0	300.00000		μs²	False
51	expt_n2	peak		gauss_sigma_1	1200.00000		μs/Å	False
52	expt_n2	peak		gauss_sigma_2	900.00000		μs²/Ų	False
53	expt_n2	instrument		twotheta_bank	90.00000		deg	False
54	expt_n2	instrument		d_to_tof_offset	0.00000		μs	False
55	expt_n2	instrument		d_to_tof_linear	54902.18695		μs/Å	False
56	expt_n2	instrument		d_to_tof_quad	0.00000		μs/Ų	False
57	expt_n2	instrument		d_to_tof_recip	0.00000		μs·Å	False
58	expt_n2	background	1	y	0.01700			False
59	expt_n2	background	2	y	0.14840			False
60	expt_n2	background	3	y	0.18480			False
61	expt_n2	background	4	y	0.19750			False
62	expt_n2	background	5	y	0.18910			False
63	expt_n2	background	6	y	0.21470			False
64	expt_n2	background	7	y	0.18870			False
65	expt_n2	background	8	y	0.21940			False
66	expt_n2	background	9	y	0.19910			False
67	expt_n2	background	10	y	0.19810			False
68	expt_n2	background	11	y	0.22760			False
69	expt_n2	background	12	y	0.24390			False
70	expt_n2	background	13	y	0.29070			False
71	expt_n2	background	14	y	0.30670			False
72	expt_n2	background	15	y	0.32420			False
73	expt_n2	background	16	y	0.29730			False
74	expt_n2	background	17	y	0.25750			False
75	expt_n2	background	18	y	0.23210			False
76	expt_n2	background	19	y	0.21580			False
77	expt_n2	background	20	y	0.16940			False
78	expt_n2	background	21	y	0.24000			False
79	expt_n2	background	22	y	0.43350			False
80	expt_n2	background	23	y	0.43750			False
81	expt_n2	background	24	y	0.34270			False
82	expt_n2	background	25	y	0.53390			False
83	expt_n2	background	26	y	0.95370			False
84	expt_n2	background	27	y	1.16680			False
85	expt_n2	background	28	y	1.11640			False
86	expt_n2	background	29	y	0.91610			False
87	expt_n2	background	30	y	0.68850			False
88	expt_n2	background	31	y	0.06920			False

In [31]:

ferrite.atom_sites['Fe'].adp_iso.free = True
austenite.atom_sites['Fe'].adp_iso.free = True

ferrite.atom_sites['Fe'].adp_iso.free = True austenite.atom_sites['Fe'].adp_iso.free = True

In [32]:

expt_s2.linked_phases['ferrite'].scale.free = True
expt_s2.linked_phases['austenite'].scale.free = True

expt_s2.peak.broad_gauss_sigma_0.free = True
expt_s2.peak.broad_gauss_sigma_1.free = True
expt_s2.peak.broad_gauss_sigma_2.free = True
expt_s2.peak.broad_lorentz_gamma_0.free = True

expt_s2.instrument.calib_d_to_tof_offset.free = True

for segment in expt_s2.background:
    segment.y.free = True

expt_s2.linked_phases['ferrite'].scale.free = True expt_s2.linked_phases['austenite'].scale.free = True expt_s2.peak.broad_gauss_sigma_0.free = True expt_s2.peak.broad_gauss_sigma_1.free = True expt_s2.peak.broad_gauss_sigma_2.free = True expt_s2.peak.broad_lorentz_gamma_0.free = True expt_s2.instrument.calib_d_to_tof_offset.free = True for segment in expt_s2.background: segment.y.free = True

In [33]:

expt_n2.linked_phases['ferrite'].scale.free = True
expt_n2.linked_phases['austenite'].scale.free = True

expt_n2.peak.broad_gauss_sigma_0.free = True
expt_n2.peak.broad_gauss_sigma_1.free = True
expt_n2.peak.broad_gauss_sigma_2.free = True
expt_n2.peak.broad_lorentz_gamma_0.free = True

expt_n2.instrument.calib_d_to_tof_offset.free = True

for segment in expt_n2.background:
    segment.y.free = True

expt_n2.linked_phases['ferrite'].scale.free = True expt_n2.linked_phases['austenite'].scale.free = True expt_n2.peak.broad_gauss_sigma_0.free = True expt_n2.peak.broad_gauss_sigma_1.free = True expt_n2.peak.broad_gauss_sigma_2.free = True expt_n2.peak.broad_lorentz_gamma_0.free = True expt_n2.instrument.calib_d_to_tof_offset.free = True for segment in expt_n2.background: segment.y.free = True

Add Constraints¶

In [34]:

project.analysis.aliases.create(
    label='s2_ferrite_scale', param=expt_s2.linked_phases['ferrite'].scale
)
project.analysis.aliases.create(
    label='s2_austenite_scale', param=expt_s2.linked_phases['austenite'].scale
)

project.analysis.aliases.create(
    label='n2_ferrite_scale', param=expt_n2.linked_phases['ferrite'].scale
)
project.analysis.aliases.create(
    label='n2_austenite_scale', param=expt_n2.linked_phases['austenite'].scale
)

project.analysis.constraints.create(expression='n2_ferrite_scale = s2_ferrite_scale')
project.analysis.constraints.create(expression='n2_austenite_scale = s2_austenite_scale')

project.analysis.aliases.create( label='s2_ferrite_scale', param=expt_s2.linked_phases['ferrite'].scale ) project.analysis.aliases.create( label='s2_austenite_scale', param=expt_s2.linked_phases['austenite'].scale ) project.analysis.aliases.create( label='n2_ferrite_scale', param=expt_n2.linked_phases['ferrite'].scale ) project.analysis.aliases.create( label='n2_austenite_scale', param=expt_n2.linked_phases['austenite'].scale ) project.analysis.constraints.create(expression='n2_ferrite_scale = s2_ferrite_scale') project.analysis.constraints.create(expression='n2_austenite_scale = s2_austenite_scale')

Run Fitting¶

Run full fitting with all free parameters.

In [35]:

project.analysis.fit()

project.analysis.fit()

Using all experiments 🔬 ['expt_s2', 'expt_n2'] for 'joint' fitting

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

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

	iteration	χ²	improvement [%]
1	1	843.64
2	80	89.69	89.4% ↓
3	157	15.07	83.2% ↓
4	234	13.82	8.3% ↓
5	543	13.81

🏆 Best goodness-of-fit (reduced χ²) is 13.81 at iteration 542

✅ Fitting complete.

Saving project 📦 'beer' to

/home/runner/work/diffraction-lib/diffraction-lib/docs/docs/tutorials/beer_mcstas

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 ferrite.cif

│   └── 📄 austenite.cif

├── 📁 experiments/

│   └── 📄 expt_s2.cif

│   └── 📄 expt_n2.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Fix background and run fitting again.

In [36]:

for segment in expt_s2.background:
    segment.y.free = False
for segment in expt_n2.background:
    segment.y.free = False

for segment in expt_s2.background: segment.y.free = False for segment in expt_n2.background: segment.y.free = False

In [37]:

project.analysis.fit()

project.analysis.fit()

Using all experiments 🔬 ['expt_s2', 'expt_n2'] for 'joint' fitting

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

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

	iteration	χ²	improvement [%]
1	1	13.66
2	19	13.66

🏆 Best goodness-of-fit (reduced χ²) is 13.66 at iteration 18

✅ Fitting complete.

Saving project 📦 'beer' to

/home/runner/work/diffraction-lib/diffraction-lib/docs/docs/tutorials/beer_mcstas

├── 📄 project.cif

├── 📁 structures/

│   └── 📄 ferrite.cif

│   └── 📄 austenite.cif

├── 📁 experiments/

│   └── 📄 expt_s2.cif

│   └── 📄 expt_n2.cif

├── 📁 analysis/

│   └── 📄 analysis.cif

└── 📄 summary.cif

Show fit results and parameter correlations.

In [38]:

project.analysis.display.fit_results()
project.display.plotter.plot_param_correlations()

project.analysis.display.fit_results() project.display.plotter.plot_param_correlations()

Fit results

✅ Success: True

⏱️ Fitting time: 1.39 seconds

📏 Goodness-of-fit (reduced χ²): 13.66

📏 R-factor (Rf): 4.96%

📏 R-factor squared (Rf²): 3.86%

📏 Weighted R-factor (wR): 3.36%

📈 Fitted parameters:

	datablock	category	entry	parameter	start	fitted	uncertainty	units	change
1	ferrite	atom_site	Fe	adp_iso	1.7213	1.7213	0.0131	Ų	0.00 % ↑
2	austenite	atom_site	Fe	adp_iso	1.7092	1.7092	0.0122	Ų	0.00 % ↑
3	expt_s2	linked_phases	ferrite	scale	50.3587	50.3587	0.1529		0.00 % ↑
4	expt_s2	linked_phases	austenite	scale	11.9852	11.9852	0.0308		0.00 % ↑
5	expt_s2	peak		lorentz_gamma_0	5.0196	5.0196	0.1521	μs	0.00 % ↑
6	expt_s2	peak		gauss_sigma_0	881.0993	881.1030	58.2232	μs²	0.00 % ↑
7	expt_s2	peak		gauss_sigma_1	1298.8025	1298.7991	58.1755	μs/Å	0.00 % ↓
8	expt_s2	peak		gauss_sigma_2	308.1175	308.1181	11.5800	μs²/Ų	0.00 % ↑
9	expt_s2	instrument		d_to_tof_offset	-10.4444	-10.4444	0.1217	μs	0.00 % ↑
10	expt_n2	peak		lorentz_gamma_0	5.0134	5.0134	0.1527	μs	0.00 % ↑
11	expt_n2	peak		gauss_sigma_0	915.4872	915.4909	58.7904	μs²	0.00 % ↑
12	expt_n2	peak		gauss_sigma_1	1243.9300	1243.9265	58.7590	μs/Å	0.00 % ↓
13	expt_n2	peak		gauss_sigma_2	325.5845	325.5851	11.6997	μs²/Ų	0.00 % ↑
14	expt_n2	instrument		d_to_tof_offset	-2.2502	-2.2502	0.1219	μs	0.00 % ↑

Plot Measured vs Calculated¶

Show full range in TOF.

In [39]:

project.display.plotter.plot_meas_vs_calc(expt_name='expt_s2')

project.display.plotter.plot_meas_vs_calc(expt_name='expt_s2')

In [40]:

project.display.plotter.plot_meas_vs_calc(expt_name='expt_n2')

project.display.plotter.plot_meas_vs_calc(expt_name='expt_n2')

Show selected peaks in d-spacing.

In [41]:

project.display.plotter.plot_meas_vs_calc(
    expt_name='expt_s2',
    x='d_spacing',
    x_min=2.08,
    x_max=2.13,
)

project.display.plotter.plot_meas_vs_calc( expt_name='expt_s2', x='d_spacing', x_min=2.08, x_max=2.13, )

In [42]:

project.display.plotter.plot_meas_vs_calc(
    expt_name='expt_n2',
    x='d_spacing',
    x_min=2.08,
    x_max=2.13,
)

project.display.plotter.plot_meas_vs_calc( expt_name='expt_n2', x='d_spacing', x_min=2.08, x_max=2.13, )