CeO₂ on PEARL¶

Fit the CeO₂ standard to time-of-flight neutron powder data from PEARL at ISIS: the calibration and the profile, with a polynomial background.

The project is the catalogue case pd-neut-tof_ceo2-pearl, the one the command line and the app's Examples open.

Fitting Single pd neut tof Bragg Crystal structure

import easydiffraction as edi

Load the project¶

project_path = edi.download_data('pd-neut-tof_ceo2-pearl', destination='data')
project = edi.Project.load(project_path)
structure = project.structures['ceo2']
experiment = project.experiments['pearl']

Data 'pd-neut-tof_ceo2-pearl' is at data/pd-neut-tof_ceo2-pearl-d212831a55d0/pd-neut-tof_ceo2-pearl

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('pearl')

Perform the analysis¶

The fit goes in stages, freeing one group of parameters at a time.

Scale and time-of-flight calibration¶

CeO₂ is the calibration standard, so its cell stays fixed and the DIFC terms put the peaks in place.

experiment.linked_structures['ceo2'].scale.free = True
experiment.instrument.calib_d_to_tof_offset.free = True
experiment.instrument.calib_d_to_tof_linear.free = True
experiment.instrument.calib_d_to_tof_quadratic.free = True

project.display.parameters.free()

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

edi fit: project pd-neut-tof_ceo2-pearl, 2237 pts fitted / 2524 loaded, 4 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       14.21        27.74
      1      0.008     13.04        23.36   15.8% ↓
      2      0.015     13.03        23.34   0.1% ↓
      3      0.024     13.03        23.34   
      4      0.037     13.03        23.34   
  done · converged · 4 iters · reduced χ² 23.34 · Rwp 13.03 % · 0.05 s

project.display.pattern('pearl')

Background¶

The six polynomial terms follow the level between the peaks.

for term in experiment.background_terms:
    term.coef.free = True

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

edi fit: project pd-neut-tof_ceo2-pearl, 2237 pts fitted / 2524 loaded, 10 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       13.03        23.41
      1      0.016      6.73         6.24   73.4% ↓
      2      0.026      6.73         6.24   
      3      0.041      6.73         6.24   
  done · converged · 3 iters · reduced χ² 6.24 · Rwp 6.73 % · 0.05 s

project.display.pattern('pearl')

Gaussian widths¶

The Gaussian terms that grow with d spacing.

experiment.peak.broad_gauss_sigma_1.free = True
experiment.peak.broad_gauss_sigma_2.free = True

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

edi fit: project pd-neut-tof_ceo2-pearl, 2237 pts fitted / 2524 loaded, 12 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        6.73         6.24
      1      0.014      6.28         5.44   12.9% ↓
      2      0.020      6.27         5.43   0.1% ↓
      3      0.036      6.27         5.43   
  done · converged · 3 iters · reduced χ² 5.43 · Rwp 6.27 % · 0.05 s

project.display.pattern('pearl')

Lorentzian width¶

The Lorentzian term that grows with d spacing.

experiment.peak.broad_lorentz_gamma_1.free = True

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

edi fit: project pd-neut-tof_ceo2-pearl, 2237 pts fitted / 2524 loaded, 13 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        6.27         5.43
      1      0.017      6.19         5.30   2.5% ↓
      2      0.028      6.19         5.30   
      3      0.043      6.19         5.30   
  done · converged · 3 iters · reduced χ² 5.30 · Rwp 6.19 % · 0.05 s

project.display.pattern('pearl')

Rise and decay¶

The back-to-back exponentials that shape each time-of-flight peak.

experiment.peak.rise_alpha_1.free = True
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_ceo2-pearl, 2237 pts fitted / 2524 loaded, 16 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        6.19         5.30
      1      0.018      6.02         5.01   5.4% ↓
      2      0.028      5.67         4.45   11.3% ↓
      3      0.037      5.67         4.44   0.3% ↓
      4      0.052      5.67         4.44   
  done · converged · 4 iters · reduced χ² 4.44 · Rwp 5.67 % · 0.06 s

project.display.pattern('pearl')

Displacements¶

structure.atom_sites['Ce'].adp_iso.free = True
structure.atom_sites['O'].adp_iso.free = True

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

edi fit: project pd-neut-tof_ceo2-pearl, 2237 pts fitted / 2524 loaded, 18 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        5.67         4.44
      1      0.015      5.30         3.88   12.5% ↓
      2      0.022      5.29         3.88   0.2% ↓
      3      0.032      5.29         3.88   
      4      0.047      5.29         3.88   
  done · converged · 4 iters · reduced χ² 3.88 · Rwp 5.29 % · 0.06 s

project.display.pattern('pearl')

Absorption¶

Absorption weakens the intensities with time of flight, as the displacements do, so it comes after them, on its own.

experiment.absorption.abscor1.free = True

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

edi fit: project pd-neut-tof_ceo2-pearl, 2237 pts fitted / 2524 loaded, 19 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        5.29         3.88
      1      0.018      5.29         3.88   
      2      0.032      5.29         3.88   
  done · converged · 2 iters · reduced χ² 3.88 · Rwp 5.29 % · 0.04 s

project.display.pattern('pearl')

project.display.fit.correlations()

project.display.structure('ceo2')

Save the project¶

project.save_as('pd-neut-tof_ceo2-pearl')
project.report.save_html('pd-neut-tof_ceo2-pearl.html')

Saving project to 'pd-neut-tof_ceo2-pearl'
Saving report to 'pd-neut-tof_ceo2-pearl.html'