Si on SEPD¶

Fit silicon to time-of-flight neutron powder data from SEPD at Argonne, with the Jorgensen-Von Dreele profile.

The project is the catalogue case pd-neut-tof_si-sepd, the one the command line and the app's Examples open.

import easydiffraction as edi

Load the project¶

project_path = edi.download_data('pd-neut-tof_si-sepd', destination='data')
project = edi.Project.load(project_path)
structure = project.structures['si']
experiment = project.experiments['sepd']

Data 'pd-neut-tof_si-sepd' is at data/pd-neut-tof_si-sepd-e03f8b070e27/pd-neut-tof_si-sepd

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

Estimate the background¶

Start the background from an automatic estimate. The default method, arPLS, fits a smooth curve under the pattern that ignores the peaks, and places 14 points along it.

experiment.background.auto_estimate(n_points=14)

project.display.pattern('sepd')

Perform the analysis¶

The fit follows diffraction-lib's four cycles for this case, then frees the background once more so it ends with the case's free set.

Cell, scale and time-of-flight calibration¶

structure.cell.length_a.free = True
experiment.linked_structures['si'].scale.free = True
experiment.instrument.calib_d_to_tof_offset.free = True

project.display.parameters.free()

project.analysis.fit()
project.display.fit.results()

edi fit: project pd-neut-tof_si-sepd, 5600 pts fitted / 5600 loaded, 3 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       52.36       204.71
      1      0.103     10.45         8.16   96.0% ↓
      2      0.129     10.45         8.16   
  done · converged · 2 iters · reduced χ² 8.16 · Rwp 10.45 % · 0.14 s

project.display.pattern('sepd')

Background¶

The estimated points are a starting point; fit them now that the peaks are in place.

for point in experiment.background:
    point.intensity.free = True

project.analysis.fit()
project.display.fit.results()

edi fit: project pd-neut-tof_si-sepd, 5600 pts fitted / 5600 loaded, 17 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       10.45         8.18
      1      0.113      7.45         4.16   49.1% ↓
  done · converged · 1 iters · reduced χ² 4.16 · Rwp 7.45 % · 0.13 s

project.display.pattern('sepd')

Gaussian widths¶

The background stays free while the widths join. diffraction-lib fixes it for this step and leaves it fixed; here the fit reaches the same result with it free, as every other case does. The Gaussian terms come first.

experiment.peak.broad_gauss_sigma_0.free = True
experiment.peak.broad_gauss_sigma_1.free = True

project.analysis.fit()
project.display.fit.results()

edi fit: project pd-neut-tof_si-sepd, 5600 pts fitted / 5600 loaded, 19 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        7.45         4.16
      1      0.145      7.42         4.13   0.8% ↓
  done · converged · 1 iters · reduced χ² 4.13 · Rwp 7.42 % · 0.16 s

project.display.pattern('sepd')

Lorentzian width¶

Then the Lorentzian term.

experiment.peak.broad_lorentz_gamma_1.free = True

project.analysis.fit()
project.display.fit.results()

edi fit: project pd-neut-tof_si-sepd, 5600 pts fitted / 5600 loaded, 20 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        7.42         4.13
      1      0.149      7.28         3.97   3.7% ↓
  done · converged · 1 iters · reduced χ² 3.97 · Rwp 7.28 % · 0.17 s

project.display.pattern('sepd')

Displacement¶

structure.atom_sites['Si'].adp_iso.free = True

project.analysis.fit()
project.display.fit.results()

edi fit: project pd-neut-tof_si-sepd, 5600 pts fitted / 5600 loaded, 21 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        7.28         3.98
      1      0.149      7.28         3.97   0.2% ↓
  done · converged · 1 iters · reduced χ² 3.97 · Rwp 7.28 % · 0.17 s

project.display.pattern('sepd')

Peak decay¶

The back-to-back exponential decay terms β₀ and β₁.

experiment.peak.decay_beta_0.free = True
experiment.peak.decay_beta_1.free = True

project.analysis.fit()
project.display.fit.results()

edi fit: project pd-neut-tof_si-sepd, 5600 pts fitted / 5600 loaded, 23 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        7.28         3.97
      1      0.137      7.18         3.86   2.7% ↓
      2      0.170      7.18         3.86   
  done · converged · 2 iters · reduced χ² 3.86 · Rwp 7.18 % · 0.19 s

project.display.pattern('sepd')

project.display.fit.correlations()

project.display.structure('si')

Save the project¶

project.save_as('pd-neut-tof_si-sepd')
project.report.save_html('pd-neut-tof_si-sepd.html')

Saving project to 'pd-neut-tof_si-sepd'
Saving report to 'pd-neut-tof_si-sepd.html'

Your own measured data¶

Measured data can also come from a file on your own disk. add_from_data_path reads a file of time-of-flight, intensity and uncertainty columns into a new experiment, here in a project of its own; the experiment then needs its instrument, profile and linked structure, as above. The file here is SEPD's pattern from the collection, saved to disk first.

data_path = edi.download_data('pd-neut-tof_si-sepd-sepd-data', destination='data')
own = edi.Project(name='own_sepd')
own.experiments.add_from_data_path(
    name='mine',
    data_path=data_path,
    sample_form='powder',
    beam_mode='time-of-flight',
    radiation_probe='neutron',
)
own.display.pattern('mine')

Data 'pd-neut-tof_si-sepd-sepd-data' is at data/pd-neut-tof_si-sepd-sepd.xye