Na₂Ca₃Al₂F₁₄ on WISH¶
Fit Na₂Ca₃Al₂F₁₄ to time-of-flight neutron powder data from WISH at ISIS, all five detector bank pairs at once. Each bank has its own calibration and profile; the structure is shared.
The project is the catalogue case pd-neut-tof_ncaf-wish, the one the command line and the
app's Examples open.
Fitting 
Joint pd neut tof Bragg 
Crystal structure
import easydiffraction as edi
Load the project¶
project_path = edi.download_data('pd-neut-tof_ncaf-wish', destination='data')
project = edi.Project.load(project_path)
structure = project.structures['ncaf']
wish_1_10 = project.experiments['wish_1_10']
wish_2_9 = project.experiments['wish_2_9']
wish_3_8 = project.experiments['wish_3_8']
wish_4_7 = project.experiments['wish_4_7']
wish_5_6 = project.experiments['wish_5_6']
Data 'pd-neut-tof_ncaf-wish' is at data/pd-neut-tof_ncaf-wish-b954a41f79ce/pd-neut-tof_ncaf-wish
The project marks what its fit frees. The fit below frees it in stages, so start with all of it fixed.
for parameter in project.free_parameters:
parameter.free = False
project.display.pattern('wish_1_10')
Perform the analysis¶
Five banks fit together. diffraction-lib's tutorial of this case fits two banks at once with everything free; this one has five, so it stages them.
Scales and time-of-flight calibration¶
Each bank's scale and DIFC offset and linear term put its peaks in place and at the right height.
wish_1_10.linked_structures['ncaf'].scale.free = True
wish_1_10.instrument.calib_d_to_tof_offset.free = True
wish_1_10.instrument.calib_d_to_tof_linear.free = True
wish_2_9.linked_structures['ncaf'].scale.free = True
wish_2_9.instrument.calib_d_to_tof_offset.free = True
wish_2_9.instrument.calib_d_to_tof_linear.free = True
wish_3_8.linked_structures['ncaf'].scale.free = True
wish_3_8.instrument.calib_d_to_tof_offset.free = True
wish_3_8.instrument.calib_d_to_tof_linear.free = True
wish_4_7.linked_structures['ncaf'].scale.free = True
wish_4_7.instrument.calib_d_to_tof_offset.free = True
wish_4_7.instrument.calib_d_to_tof_linear.free = True
wish_5_6.linked_structures['ncaf'].scale.free = True
wish_5_6.instrument.calib_d_to_tof_offset.free = True
wish_5_6.instrument.calib_d_to_tof_linear.free = True
project.display.parameters.free()
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 15 free
iter time (s) Rwp (%) reduced χ² change
29.70 140.21
1 0.153 21.43 73.01 47.9% ↓
2 0.284 20.12 64.34 11.9% ↓
3 0.414 19.93 63.15 1.8% ↓
4 0.546 19.91 62.98 0.3% ↓
5 0.683 19.90 62.95
6 0.840 19.90 62.95
7 0.995 19.90 62.95
8 1.154 19.90 62.95
9 1.377 19.90 62.95
done · converged · 9 iters · reduced χ² 62.95 · Rwp 19.90 % · 1.53 s
project.display.pattern('wish_1_10')
project.display.pattern('wish_2_9')
project.display.pattern('wish_3_8')
project.display.pattern('wish_4_7')
project.display.pattern('wish_5_6')
Background¶
Each bank's background points; bank 1-10's first and last stay fixed, as its source has them.
for point in wish_1_10.background:
point.intensity.free = True
for point in wish_2_9.background:
point.intensity.free = True
for point in wish_3_8.background:
point.intensity.free = True
for point in wish_4_7.background:
point.intensity.free = True
for point in wish_5_6.background:
point.intensity.free = True
wish_1_10.background[0].intensity.free = False
wish_1_10.background[35].intensity.free = False
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 149 free
iter time (s) Rwp (%) reduced χ² change
19.90 63.39
1 0.318 13.97 31.22 50.8% ↓
2 0.554 13.97 31.22
3 0.854 13.97 31.21
done · converged · 3 iters · reduced χ² 31.21 · Rwp 13.97 % · 1.11 s
project.display.pattern('wish_1_10')
project.display.pattern('wish_2_9')
project.display.pattern('wish_3_8')
project.display.pattern('wish_4_7')
project.display.pattern('wish_5_6')
Peak asymmetry¶
Each bank's back-to-back exponentials, the terms its data determine; bank 1-10 keeps its instrument values.
wish_2_9.peak.rise_alpha_0.free = True
wish_2_9.peak.rise_alpha_1.free = True
wish_2_9.peak.decay_beta_0.free = True
wish_2_9.peak.decay_beta_1.free = True
wish_3_8.peak.rise_alpha_0.free = True
wish_3_8.peak.rise_alpha_1.free = True
wish_3_8.peak.decay_beta_0.free = True
wish_3_8.peak.decay_beta_1.free = True
wish_4_7.peak.rise_alpha_0.free = True
wish_4_7.peak.rise_alpha_1.free = True
wish_4_7.peak.decay_beta_0.free = True
wish_4_7.peak.decay_beta_1.free = True
wish_5_6.peak.rise_alpha_0.free = True
wish_5_6.peak.rise_alpha_1.free = True
wish_5_6.peak.decay_beta_0.free = True
wish_5_6.peak.decay_beta_1.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 165 free
iter time (s) Rwp (%) reduced χ² change
13.97 31.24
1 0.334 11.96 22.90 26.7% ↓
2 0.562 11.20 20.09 12.3% ↓
3 0.807 10.85 18.85 6.1% ↓
4 1.047 10.62 18.05 4.2% ↓
5 1.301 10.44 17.45 3.3% ↓
6 1.536 10.34 17.11 1.9% ↓
7 1.769 10.29 16.95 0.9% ↓
8 2.004 10.26 16.86 0.6% ↓
9 2.246 10.24 16.80 0.3% ↓
10 2.496 10.24 16.78 0.1% ↓
11 2.732 10.23 16.77 0.1% ↓
12 2.961 10.23 16.77
13 3.227 10.23 16.77
14 3.500 10.23 16.77
15 3.779 10.23 16.77
16 4.063 10.23 16.77
17 4.441 10.23 16.77
done · converged · 17 iters · reduced χ² 16.77 · Rwp 10.23 % · 4.73 s
project.display.pattern('wish_2_9')
Gaussian widths¶
The Gaussian width terms the banks' data determine.
wish_2_9.peak.broad_gauss_sigma_1.free = True
wish_2_9.peak.broad_gauss_sigma_2.free = True
wish_3_8.peak.broad_gauss_sigma_1.free = True
wish_3_8.peak.broad_gauss_sigma_2.free = True
wish_4_7.peak.broad_gauss_sigma_1.free = True
wish_4_7.peak.broad_gauss_sigma_2.free = True
wish_5_6.peak.broad_gauss_sigma_2.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 172 free
iter time (s) Rwp (%) reduced χ² change
10.23 16.78
1 0.374 10.02 16.09 4.1% ↓
2 0.646 10.00 16.03 0.4% ↓
3 0.941 10.00 16.02
4 1.279 10.00 16.02
5 1.616 10.00 16.02
6 1.922 10.00 16.02
7 2.219 10.00 16.02
8 2.522 10.00 16.02
9 2.835 10.00 16.02
10 3.105 10.00 16.01
11 3.383 9.99 16.00 0.1% ↓
12 3.648 9.99 15.98 0.2% ↓
13 3.918 9.98 15.96 0.1% ↓
14 4.189 9.97 15.93 0.2% ↓
15 4.508 9.97 15.93
16 4.929 9.97 15.93
done · converged · 16 iters · reduced χ² 15.93 · Rwp 9.97 % · 5.26 s
project.display.pattern('wish_2_9')
Lorentzian width¶
Bank 2-9's Lorentzian term.
wish_2_9.peak.broad_lorentz_gamma_1.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 173 free
iter time (s) Rwp (%) reduced χ² change
9.97 15.93
1 0.710 9.97 15.93
2 1.341 9.97 15.93
done · converged · 2 iters · reduced χ² 15.93 · Rwp 9.97 % · 1.82 s
project.display.pattern('wish_1_10')
project.display.pattern('wish_2_9')
project.display.pattern('wish_3_8')
project.display.pattern('wish_4_7')
project.display.pattern('wish_5_6')
Absorption¶
Banks 2-9 to 5-6 each fit their absorption.
wish_2_9.absorption.abscor1.free = True
wish_3_8.absorption.abscor1.free = True
wish_4_7.absorption.abscor1.free = True
wish_5_6.absorption.abscor1.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 177 free
iter time (s) Rwp (%) reduced χ² change
9.97 15.94
1 0.640 9.91 15.75 1.2% ↓
2 0.928 9.91 15.74
3 1.259 9.91 15.74
4 1.584 9.91 15.74
5 1.920 9.91 15.74
6 2.345 9.91 15.74
done · converged · 6 iters · reduced χ² 15.74 · Rwp 9.91 % · 2.70 s
project.display.pattern('wish_1_10')
project.display.pattern('wish_2_9')
project.display.pattern('wish_3_8')
project.display.pattern('wish_4_7')
project.display.pattern('wish_5_6')
Atom positions¶
The coordinates the cubic symmetry leaves free.
for site in structure.atom_sites:
for coordinate in (site.fract_x, site.fract_y, site.fract_z):
coordinate.free = not coordinate.symmetry_constrained
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 187 free
iter time (s) Rwp (%) reduced χ² change
9.91 15.75
1 0.712 8.11 10.56 32.9% ↓
2 0.996 8.07 10.43 1.2% ↓
3 1.292 8.07 10.43
4 1.626 8.07 10.43
5 1.957 8.07 10.43
6 2.377 8.07 10.43
done · converged · 6 iters · reduced χ² 10.43 · Rwp 8.07 % · 2.85 s
project.display.pattern('wish_1_10')
project.display.pattern('wish_2_9')
project.display.pattern('wish_3_8')
project.display.pattern('wish_4_7')
project.display.pattern('wish_5_6')
Displacements¶
for site in structure.atom_sites:
site.adp_iso.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: joint project pd-neut-tof_ncaf-wish, 5 banks (wish_1_10, wish_2_9, wish_3_8, wish_4_7, wish_5_6), 18973 pts fitted / 20475 loaded, 193 free
iter time (s) Rwp (%) reduced χ² change
8.07 10.43
1 6.315 7.77 9.68 7.3% ↓
2 7.046 7.70 9.50 1.8% ↓
3 7.756 7.69 9.50
4 8.677 7.69 9.50
5 9.549 7.69 9.50
done · converged · 5 iters · reduced χ² 9.50 · Rwp 7.69 % · 10.36 s
project.display.pattern('wish_1_10')
project.display.pattern('wish_2_9')
project.display.pattern('wish_3_8')
project.display.pattern('wish_4_7')
project.display.pattern('wish_5_6')
project.display.fit.correlations()
project.display.structure('ncaf')
Save the project¶
project.save_as('pd-neut-tof_ncaf-wish')
project.report.save_html('pd-neut-tof_ncaf-wish.html')
Saving project to 'pd-neut-tof_ncaf-wish'
Saving report to 'pd-neut-tof_ncaf-wish.html'