Fitting pd-neut-tof Si-SEPD¶

This example shows how to refine the crystal structure parameters of Si from neutron diffraction data in a time-of-flight experiment performed on SEPD diffractometer at Argonne.

Import EasyDiffraction¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

Create a job¶

Create a job — the main object to store all the information

In [3]:

job = ed.Job(type='tof')
print(job.type)

job = ed.Job(type='tof') print(job.type)

Job type: pd-tof-unp-1d-neut

Define a model¶

Create a phase object

In [4]:

phase = ed.Phase(name='si')

phase = ed.Phase(name='si')

Set space group

In [5]:

phase.space_group.name_hm_alt = 'F d -3 m'

phase.space_group.name_hm_alt = 'F d -3 m'

Set cell parameters

In [6]:

phase.cell.length_a = 5.43146

phase.cell.length_a = 5.43146

Add atoms

In [7]:

phase.atom_sites.append(label='Si',
                        type_symbol='Si',
                        fract_x=0,
                        fract_y=0,
                        fract_z=0,
                        occupancy=1,
                        b_iso_or_equiv=0.529)

phase.atom_sites.append(label='Si', type_symbol='Si', fract_x=0, fract_y=0, fract_z=0, occupancy=1, b_iso_or_equiv=0.529)

Add phase to the job object

In [8]:

job.add_phase(phase=phase)
print(job.phases)

job.add_phase(phase=phase) print(job.phases)

Several values of it_coordinate_system_code have been defined:
2, 1
The default value has been choosen:'2'.
Several values of it_coordinate_system_code have been defined:
2, 1
The default value has been choosen:'2'.
Collection of 1 phases: ['si']

Show phase info in CIF format

In [9]:

phase = job.phases['si']
print(phase.cif)

phase = job.phases['si'] print(phase.cif)

data_si
_cell_length_a 5.43146
_cell_length_b 5.43146
_cell_length_c 5.43146
_cell_angle_alpha 90.00000000
_cell_angle_beta 90.00000000
_cell_angle_gamma 90.00000000
_space_group_name_H-M_ref 'F d -3 m'
_space_group_IT_coordinate_system_code 1

loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
_atom_site_adp_type
_atom_site_B_iso_or_equiv
Si Si 0.00000000 0.00000000 0.00000000 1.00000000 Biso 0.529

Display the crystal structure of a given model

In [10]:

job.show_crystal_structure(id='si')

job.show_crystal_structure(id='si')

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Define an experiment¶

Download the data file from the EasyDiffraction repository on GitHub

In [11]:

ed.download_from_repository('sepd.xye', destination='data')

ed.download_from_repository('sepd.xye', destination='data')

Show content of the downloaded file (first 5 lines)

In [12]:

with open('data/sepd.xye') as f:
    print(''.join(f.readlines()[:5]))

with open('data/sepd.xye') as f: print(''.join(f.readlines()[:5]))

2000.0 213.8 3.3
2005.0 213.8 3.3
2010.0 210.1 3.3
2015.0 213.3 3.3
2020.0 211.9 3.3

Load experimentally measured data from a file in XYE format

In [13]:

job.add_experiment_from_file('data/sepd.xye')

job.add_experiment_from_file('data/sepd.xye')

Display the experimentally measured data

In [14]:

job.show_experiment_chart(show_legend=False)

job.show_experiment_chart(show_legend=False)

Define a point background

In [15]:

background_points = [(x, 200) for x in range(0, 35000, 5000)]
print(background_points)

background_points = [(x, 200) for x in range(0, 35000, 5000)] print(background_points)

[(0, 200), (5000, 200), (10000, 200), (15000, 200), (20000, 200), (25000, 200), (30000, 200)]

In [16]:

job.set_background(background_points)

job.set_background(background_points)

Display the experiment chart after setting the background

In [17]:

job.show_experiment_chart()

job.show_experiment_chart()

Perform an analysis¶

Display the analysis chart before setting initial parameter values

In [18]:

job.show_analysis_chart()

job.show_analysis_chart()

Create aliases for the two types of experimental parameters

In [19]:

pattern_params = job.pattern
experiment_params = job.parameters

pattern_params = job.pattern experiment_params = job.parameters

Change the default value of some instrumental parameters and display the analysis chart again

In [20]:

experiment_params.dtt1 = 7476.91
experiment_params.dtt2 = -1.54
experiment_params.ttheta_bank = 144.845
job.show_analysis_chart()

experiment_params.dtt1 = 7476.91 experiment_params.dtt2 = -1.54 experiment_params.ttheta_bank = 144.845 job.show_analysis_chart()

Change the scale and display the analysis chart again

In [21]:

phase.scale = 10
job.show_analysis_chart()

phase.scale = 10 job.show_analysis_chart()

Change the default values of the peak profile related parameters and display the analysis chart again

In [22]:

experiment_params.alpha0 = 0.024
experiment_params.alpha1 = 0.204
experiment_params.beta0 = 0.038
experiment_params.beta1 = 0.011
experiment_params.sigma0 = 0.0
experiment_params.sigma1 = 0.0
experiment_params.sigma2 = 0.0
job.show_analysis_chart()

experiment_params.alpha0 = 0.024 experiment_params.alpha1 = 0.204 experiment_params.beta0 = 0.038 experiment_params.beta1 = 0.011 experiment_params.sigma0 = 0.0 experiment_params.sigma1 = 0.0 experiment_params.sigma2 = 0.0 job.show_analysis_chart()

Select parameters to be refined in the first round

In [23]:

phase.scale.free = True
pattern_params.zero_shift.free = True

phase.scale.free = True pattern_params.zero_shift.free = True

Print parameters to be refined (free parameters) before fitting

In [24]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['si'].scale	10.0		0.0

Start Least-Squares minimization to refine the selected parameters

In [25]:

job.fit()

job.fit()

Fitting result
Status: 🥳 Success
Duration: ⌛ 7.87 s
Reduced χ²: 👍 36.80

Print the refined parameters after fitting

In [26]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['si'].scale	12.810954		0.112699
2	.pattern.zero_shift	-4.166396	µs	0.052262

Display the analysis chart after the first fitting

In [27]:

job.show_analysis_chart()

job.show_analysis_chart()

Allow background parameters to be refined

In [28]:

for background_point in pattern_params.backgrounds[0]:
    background_point.y.free = True

for background_point in pattern_params.backgrounds[0]: background_point.y.free = True

Print free parameters before the second fitting

In [29]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['si'].scale	12.810954		0.112699
2	.pattern.zero_shift	-4.166396	µs	0.052262
3	.pattern.backgrounds[0]['0,0_deg'].intensity	200.000000		0.000000
4	.pattern.backgrounds[0]['5000,0_deg'].intensity	200.000000		0.000000
5	.pattern.backgrounds[0]['10000,0_deg'].intensity	200.000000		0.000000
6	.pattern.backgrounds[0]['15000,0_deg'].intensity	200.000000		0.000000
7	.pattern.backgrounds[0]['20000,0_deg'].intensity	200.000000		0.000000
8	.pattern.backgrounds[0]['25000,0_deg'].intensity	200.000000		0.000000
9	.pattern.backgrounds[0]['30000,0_deg'].intensity	200.000000		0.000000

Start second round of minimization

In [30]:

job.fit()

job.fit()

Fitting result
Status: 🥳 Success
Duration: ⌛ 5.49 s
Reduced χ²: 👍 16.18

Print free parameters after the second fitting

In [31]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['si'].scale	13.169738		0.075010
2	.pattern.zero_shift	-4.165397	µs	0.033715
3	.pattern.backgrounds[0]['0,0_deg'].intensity	269.666225		7.992930
4	.pattern.backgrounds[0]['5000,0_deg'].intensity	150.600340		2.523188
5	.pattern.backgrounds[0]['10000,0_deg'].intensity	121.156660		1.990883
6	.pattern.backgrounds[0]['15000,0_deg'].intensity	136.251201		1.988307
7	.pattern.backgrounds[0]['20000,0_deg'].intensity	133.911792		1.974323
8	.pattern.backgrounds[0]['25000,0_deg'].intensity	175.057849		2.293309
9	.pattern.backgrounds[0]['30000,0_deg'].intensity	183.334800		3.224987

Display the analysis chart after the second fitting

In [32]:

job.show_analysis_chart()

job.show_analysis_chart()

Select more parameters to be refined in the third round

In [33]:

experiment_params.sigma0.free = True
experiment_params.sigma1.free = True
experiment_params.sigma2.free = True

experiment_params.sigma0.free = True experiment_params.sigma1.free = True experiment_params.sigma2.free = True

Disable refinement of background parameters

In [34]:

for background_point in pattern_params.backgrounds[0]:
    background_point.y.free = False

for background_point in pattern_params.backgrounds[0]: background_point.y.free = False

Print free parameters before the third fitting

In [35]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['si'].scale	13.169738		0.075010
2	.instrument.sigma0	0.000000	µs²	0.000000
3	.instrument.sigma1	0.000000	µs²/Ų	0.000000
4	.instrument.sigma2	0.000000	µs²/Å⁴	0.000000
5	.pattern.zero_shift	-4.165397	µs	0.033715

Start third round of minimization

In [36]:

job.fit()

job.fit()

Fitting result
Status: 🥳 Success
Duration: ⌛ 13.52 s
Reduced χ²: 👍 5.57

Print free parameters after the third fitting

In [37]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['si'].scale	14.846289		0.046806
2	.instrument.sigma0	-4.968327	µs²	0.923895
3	.instrument.sigma1	66.704832	µs²/Ų	1.503366
4	.instrument.sigma2	-10.512966	µs²/Å⁴	0.172826
5	.pattern.zero_shift	-3.357013	µs	0.034452

Display the analysis chart after the third fitting

In [38]:

job.show_analysis_chart()

job.show_analysis_chart()