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.coord_system_code = '1'

ferrite.cell.length_a = 2.886

ferrite.atom_sites.create(
    id='Fe',
    type_symbol='Fe',
    fract_x=0.0,
    fract_y=0.0,
    fract_z=0.0,
    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.coord_system_code = '1' ferrite.cell.length_a = 2.886 ferrite.atom_sites.create( id='Fe', type_symbol='Fe', fract_x=0.0, fract_y=0.0, fract_z=0.0, 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.coord_system_code = '1'

austenite.cell.length_a = 3.6468

austenite.atom_sites.create(
    id='Fe',
    type_symbol='Fe',
    fract_x=0.0,
    fract_y=0.0,
    fract_z=0.0,
    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.coord_system_code = '1' austenite.cell.length_a = 3.6468 austenite.atom_sites.create( id='Fe', type_symbol='Fe', fract_x=0.0, fract_y=0.0, fract_z=0.0, 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 Data¶

In [5]:

zip_path = download_data('meas-ferrite-austenite-beer', destination='data')
data_paths = extract_data_paths_from_zip(zip_path, destination='data/calibrate-beer-ess')

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('meas-ferrite-austenite-beer', destination='data') data_paths = extract_data_paths_from_zip(zip_path, destination='data/calibrate-beer-ess') 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 'meas-ferrite-austenite-beer': ferrite + austenite, BEER (ESS), S2 and N2 detector bank datasets

✅ Data 'meas-ferrite-austenite-beer' downloaded to '../../../data/meas-ferrite-austenite-beer.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.peak.show_supported()

expt_s2.peak.show_supported()

Peak 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.type = 'pseudo-voigt'

expt_s2.peak.type = 'pseudo-voigt'

⚠️ Switching peak profile type removes these settings:                                                                            
   • decay_beta_0                                                                                                                 
   • decay_beta_1                                                                                                                 
   • rise_alpha_0                                                                                                                 
   • rise_alpha_1                                                                                                                 

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • broad_lorentz_gamma_0=0.0                                                                                                    
   • broad_lorentz_gamma_1=0.0                                                                                                    
   • broad_lorentz_gamma_2=0.0                                                                                                    
   • broad_lorentz_size_l=0.0                                                                                                     
   • broad_lorentz_strain_l=0.0                                                                                                   

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.type = 'pseudo-voigt'

expt_n2.peak.type = 'pseudo-voigt'

⚠️ Switching peak profile type removes these settings:                                                                            
   • decay_beta_0                                                                                                                 
   • decay_beta_1                                                                                                                 
   • rise_alpha_0                                                                                                                 
   • rise_alpha_1                                                                                                                 

⚠️ Switching peak profile type adds these settings with defaults:                                                                 
   • broad_lorentz_gamma_0=0.0                                                                                                    
   • broad_lorentz_gamma_1=0.0                                                                                                    
   • broad_lorentz_gamma_2=0.0                                                                                                    
   • broad_lorentz_size_l=0.0                                                                                                     
   • broad_lorentz_strain_l=0.0                                                                                                   

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.background.show_supported()

expt_s2.background.show_supported()

Background types

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

In [16]:

expt_s2.background.auto_estimate()

expt_s2.background.auto_estimate()

In [17]:

expt_s2.background.show()

expt_s2.background.show()

Line-segment background points

	Position	Intensity
1	40094.52340	0.00154
2	48089.84890	0.16817
3	51976.02300	0.18318
4	54301.35670	0.17817
5	58729.04700	0.29095
6	62710.78280	0.30387
7	67711.84290	0.25310
8	73158.85750	0.22573
9	76439.80780	0.20324
10	81249.74460	0.19453
11	85263.33430	0.17297
12	96157.36350	0.24903
13	98132.30440	0.34182
14	102368.87130	0.39039
15	104248.25060	0.36120
16	108771.50250	0.62067
17	111606.49840	1.22400
18	112721.38440	1.32442
19	115715.64970	1.12711
20	135592.47480	0.00952

In [18]:

for point in expt_s2.background:
    expt_n2.background.create(
        id=point.id.value, position=point.position.value, intensity=point.intensity.value
    )

for point in expt_s2.background: expt_n2.background.create( id=point.id.value, position=point.position.value, intensity=point.intensity.value )

Set Linked Structures¶

In [19]:

expt_s2.linked_structures.create(structure_id='ferrite', scale=285)
expt_s2.linked_structures.create(structure_id='austenite', scale=68)

expt_s2.linked_structures.create(structure_id='ferrite', scale=285) expt_s2.linked_structures.create(structure_id='austenite', scale=68)

In [20]:

expt_n2.linked_structures.create(structure_id='ferrite', scale=285)
expt_n2.linked_structures.create(structure_id='austenite', scale=68)

expt_n2.linked_structures.create(structure_id='ferrite', scale=285) expt_n2.linked_structures.create(structure_id='austenite', scale=68)

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_mcstas')
project.save_as(dir_path='projects/calibrate-beer-ess')

project = Project(name='beer_mcstas') project.save_as(dir_path='projects/calibrate-beer-ess')

Saving project 📦 'beer_mcstas' to '../../../projects/calibrate-beer-ess'

├── 📄 project.edi

├── 📁 structures/

├── 📁 experiments/

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 beer_mcstas.html

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)

Display Structure¶

In [26]:

project.display.structure(struct_name='ferrite')
project.display.structure(struct_name='austenite')

project.display.structure(struct_name='ferrite') project.display.structure(struct_name='austenite')

Structure 🧩 'ferrite' (Atom view type: 'covalent')

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

Structure 🧩 'austenite' (Atom view type: 'covalent')

Loading plot…

drag = rotate
wheel = zoom
right-drag = pan

Display Pattern¶

In [27]:

project.display.pattern(expt_name='expt_s2')

project.display.pattern(expt_name='expt_s2')

Loading plot…

In [28]:

project.display.pattern(expt_name='expt_n2')

project.display.pattern(expt_name='expt_n2')

Loading plot…

🚀 Perform Analysis¶

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

Set Fit Mode¶

In [29]:

project.analysis.fitting_mode.show_supported()

project.analysis.fitting_mode.show_supported()

Fitting Mode types

		Type	Description
1		joint	Fit several experiments together with shared parameters.

In [30]:

project.analysis.fitting_mode.type = 'joint'

project.analysis.fitting_mode.type = 'joint'

Fitting mode changed to

joint

Set Free Parameters¶

In [31]:

project.display.parameters.fittable()

project.display.parameters.fittable()

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	atom_site	Fe	occupancy	1.00000			False
3	ferrite	atom_site	Fe	adp_iso	1.00000		Ų	False
4	austenite	cell		length_a	3.64680		Å	False
5	austenite	atom_site	Fe	occupancy	1.00000			False
6	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_structure	ferrite	scale	285.00000			False
2	expt_s2	linked_structure	austenite	scale	68.00000			False
3	expt_s2	peak		broad_lorentz_gamma_0	0.00000		μs	False
4	expt_s2	peak		broad_lorentz_gamma_1	0.00000		μs/Å	False
5	expt_s2	peak		broad_lorentz_gamma_2	0.00000		μs²/Ų	False
6	expt_s2	peak		broad_lorentz_size_l	0.00000		μs²/Ų	False
7	expt_s2	peak		broad_lorentz_strain_l	0.00000		μs/Å	False
8	expt_s2	peak		broad_gauss_sigma_0	300.00000		μs²	False
9	expt_s2	peak		broad_gauss_sigma_1	1200.00000		μs/Å	False
10	expt_s2	peak		broad_gauss_sigma_2	900.00000		μs²/Ų	False
11	expt_s2	peak		broad_gauss_size_g	0.00000		μs²/Ų	False
12	expt_s2	peak		broad_gauss_strain_g	0.00000		μs/Å	False
13	expt_s2	instrument		twotheta_bank	90.00000		deg	False
14	expt_s2	instrument		d_to_tof_offset	0.00000		μs	False
15	expt_s2	instrument		d_to_tof_linear	54902.18695		μs/Å	False
16	expt_s2	instrument		d_to_tof_quadratic	0.00000		μs/Ų	False
17	expt_s2	instrument		d_to_tof_reciprocal	0.00000		μs·Å	False
18	expt_s2	background	1	intensity	0.00154			False
19	expt_s2	background	2	intensity	0.16817			False
20	expt_s2	background	3	intensity	0.18318			False
21	expt_s2	background	4	intensity	0.17817			False
22	expt_s2	background	5	intensity	0.29095			False
23	expt_s2	background	6	intensity	0.30387			False
24	expt_s2	background	7	intensity	0.25310			False
25	expt_s2	background	8	intensity	0.22573			False
26	expt_s2	background	9	intensity	0.20324			False
27	expt_s2	background	10	intensity	0.19453			False
28	expt_s2	background	11	intensity	0.17297			False
29	expt_s2	background	12	intensity	0.24903			False
30	expt_s2	background	13	intensity	0.34182			False
31	expt_s2	background	14	intensity	0.39039			False
32	expt_s2	background	15	intensity	0.36120			False
33	expt_s2	background	16	intensity	0.62067			False
34	expt_s2	background	17	intensity	1.22400			False
35	expt_s2	background	18	intensity	1.32442			False
36	expt_s2	background	19	intensity	1.12711			False
37	expt_s2	background	20	intensity	0.00952			False
38	expt_n2	linked_structure	ferrite	scale	285.00000			False
39	expt_n2	linked_structure	austenite	scale	68.00000			False
40	expt_n2	peak		broad_lorentz_gamma_0	0.00000		μs	False
41	expt_n2	peak		broad_lorentz_gamma_1	0.00000		μs/Å	False
42	expt_n2	peak		broad_lorentz_gamma_2	0.00000		μs²/Ų	False
43	expt_n2	peak		broad_lorentz_size_l	0.00000		μs²/Ų	False
44	expt_n2	peak		broad_lorentz_strain_l	0.00000		μs/Å	False
45	expt_n2	peak		broad_gauss_sigma_0	300.00000		μs²	False
46	expt_n2	peak		broad_gauss_sigma_1	1200.00000		μs/Å	False
47	expt_n2	peak		broad_gauss_sigma_2	900.00000		μs²/Ų	False
48	expt_n2	peak		broad_gauss_size_g	0.00000		μs²/Ų	False
49	expt_n2	peak		broad_gauss_strain_g	0.00000		μs/Å	False
50	expt_n2	instrument		twotheta_bank	90.00000		deg	False
51	expt_n2	instrument		d_to_tof_offset	0.00000		μs	False
52	expt_n2	instrument		d_to_tof_linear	54902.18695		μs/Å	False
53	expt_n2	instrument		d_to_tof_quadratic	0.00000		μs/Ų	False
54	expt_n2	instrument		d_to_tof_reciprocal	0.00000		μs·Å	False
55	expt_n2	background	1	intensity	0.00154			False
56	expt_n2	background	2	intensity	0.16817			False
57	expt_n2	background	3	intensity	0.18318			False
58	expt_n2	background	4	intensity	0.17817			False
59	expt_n2	background	5	intensity	0.29095			False
60	expt_n2	background	6	intensity	0.30387			False
61	expt_n2	background	7	intensity	0.25310			False
62	expt_n2	background	8	intensity	0.22573			False
63	expt_n2	background	9	intensity	0.20324			False
64	expt_n2	background	10	intensity	0.19453			False
65	expt_n2	background	11	intensity	0.17297			False
66	expt_n2	background	12	intensity	0.24903			False
67	expt_n2	background	13	intensity	0.34182			False
68	expt_n2	background	14	intensity	0.39039			False
69	expt_n2	background	15	intensity	0.36120			False
70	expt_n2	background	16	intensity	0.62067			False
71	expt_n2	background	17	intensity	1.22400			False
72	expt_n2	background	18	intensity	1.32442			False
73	expt_n2	background	19	intensity	1.12711			False
74	expt_n2	background	20	intensity	0.00952			False

In [32]:

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 [33]:

expt_s2.linked_structures['ferrite'].scale.free = True
expt_s2.linked_structures['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.intensity.free = True

expt_s2.linked_structures['ferrite'].scale.free = True expt_s2.linked_structures['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.intensity.free = True

In [34]:

expt_n2.linked_structures['ferrite'].scale.free = True
expt_n2.linked_structures['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.intensity.free = True

expt_n2.linked_structures['ferrite'].scale.free = True expt_n2.linked_structures['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.intensity.free = True

Add Constraints¶

In [35]:

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

project.analysis.aliases.create(
    id='n2_ferrite_scale', param=expt_n2.linked_structures['ferrite'].scale
)
project.analysis.aliases.create(
    id='n2_austenite_scale', param=expt_n2.linked_structures['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( id='s2_ferrite_scale', param=expt_s2.linked_structures['ferrite'].scale ) project.analysis.aliases.create( id='s2_austenite_scale', param=expt_s2.linked_structures['austenite'].scale ) project.analysis.aliases.create( id='n2_ferrite_scale', param=expt_n2.linked_structures['ferrite'].scale ) project.analysis.aliases.create( id='n2_austenite_scale', param=expt_n2.linked_structures['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 [36]:

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 progress:

	iteration	time (s)	χ²	change / status
1	1	0.06	589.93
2	58	3.38	32.98	94.4% ↓
3	113	6.86	12.96	60.7% ↓
4	197	11.86	12.85
5	278	16.87	12.85
6	334	23.53	12.85

🏆 Best goodness-of-fit (reduced χ²) is 12.85 at iteration 333

✅ Fitting complete.

Saving project 📦 'beer_mcstas' to '../../../projects/calibrate-beer-ess'

├── 📄 project.edi

├── 📁 structures/

│   └── 📄 ferrite.edi

│   └── 📄 austenite.edi

├── 📁 experiments/

│   └── 📄 expt_s2.edi

│   └── 📄 expt_n2.edi

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 beer_mcstas.html

Fix background and run fitting again.

In [37]:

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

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

In [38]:

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 progress:

	iteration	time (s)	χ²	change / status
1	1	0.06	12.76
2	19	1.14	12.76

🏆 Best goodness-of-fit (reduced χ²) is 12.76 at iteration 18

✅ Fitting complete.

Saving project 📦 'beer_mcstas' to '../../../projects/calibrate-beer-ess'

├── 📄 project.edi

├── 📁 structures/

│   └── 📄 ferrite.edi

│   └── 📄 austenite.edi

├── 📁 experiments/

│   └── 📄 expt_s2.edi

│   └── 📄 expt_n2.edi

├── 📁 analysis/

│   └── 📄 analysis.edi

└── 📁 reports/

    └── 📄 beer_mcstas.html

Show fit results and parameter correlations.

In [39]:

project.display.fit.results()
project.display.fit.correlations()

project.display.fit.results() project.display.fit.correlations()

⚙️ 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)	1.14
4	🔁 Iterations	16
5	📏 Goodness-of-fit (reduced χ²)	12.76
6	📏 R-factor (Rf, %)	4.97
7	📏 R-factor squared (Rf², %)	3.89
8	📏 Weighted R-factor (wR, %)	3.40

📈 Refined parameters:

	datablock	category	entry	parameter	units	start	value	s.u.	change
1	ferrite	atom_site	Fe	adp_iso	Ų	1.7191	1.7191	0.0126	0.00 % ↑
2	austenite	atom_site	Fe	adp_iso	Ų	1.7126	1.7126	0.0118	0.00 % ↑
3	expt_s2	linked_structure	ferrite	scale		284.7197	284.7201	0.8354	0.00 % ↑
4	expt_s2	linked_structure	austenite	scale		67.9132	67.9133	0.1683	0.00 % ↑
5	expt_s2	peak		broad_lorentz_gamma_0	μs	5.2351	5.2351	0.1470	0.00 % ↑
6	expt_s2	peak		broad_gauss_sigma_0	μs²	884.3308	884.3524	56.2993	0.00 % ↑
7	expt_s2	peak		broad_gauss_sigma_1	μs/Å	1284.1657	1284.1455	56.2420	0.00 % ↓
8	expt_s2	peak		broad_gauss_sigma_2	μs²/Ų	311.1710	311.1747	11.1945	0.00 % ↑
9	expt_s2	instrument		d_to_tof_offset	μs	-10.4533	-10.4534	0.1176	0.00 % ↑
10	expt_n2	peak		broad_lorentz_gamma_0	μs	5.2429	5.2429	0.1475	0.00 % ↑
11	expt_n2	peak		broad_gauss_sigma_0	μs²	921.6972	921.7187	56.8582	0.00 % ↑
12	expt_n2	peak		broad_gauss_sigma_1	μs/Å	1226.5363	1226.5159	56.8131	0.00 % ↓
13	expt_n2	peak		broad_gauss_sigma_2	μs²/Ų	329.0370	329.0408	11.3113	0.00 % ↑
14	expt_n2	instrument		d_to_tof_offset	μs	-2.2574	-2.2574	0.1178	0.00 % ↑

• start = parameter value before refinement
• value = refined value from least-squares minimization
• s.u. = standard uncertainty (one sigma), from the covariance matrix
• change = relative change from start, in %; ↑ = increase, ↓ = decrease

Loading plot…

Display Pattern¶

Show full range in TOF.

In [40]:

project.display.pattern(expt_name='expt_s2')

project.display.pattern(expt_name='expt_s2')

Loading plot…

In [41]:

project.display.pattern(expt_name='expt_n2')

project.display.pattern(expt_name='expt_n2')

Loading plot…

Show selected peaks in d-spacing.

In [42]:

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

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

Loading plot…

In [43]:

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

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

Loading plot…