LATP and AlPO₄ on BM01¶

Fit three phases, LATP and two AlPO₄ forms, to 73 synchrotron X-ray patterns from BM01 at ESRF, one after another, with linked displacement parameters.

The project is the catalogue case pd-xray-cwl_latp-bm01_scan, the one the command line and the app's Examples open. Al shares Ti's site, coordinate and displacement, and the impurity phase's displacements are shared, from the start.

Fitting Sequential pd xray cwl Bragg Crystal structure

import csv
from pathlib import Path

import easydiffraction as edi

Load the project¶

A sequential fit writes one row per pattern into the project's analysis/results.csv, so work on a copy of the project, saved to a folder of its own.

project_path = edi.download_data('pd-xray-cwl_latp-bm01_scan', destination='data')
project = edi.Project.load(project_path)
project.save_as('pd-xray-cwl_latp-bm01_scan')
latp = project.structures['latp']
c2221 = project.structures['alpo4_c2221']
p63mc = project.structures['alpo4_p63mc']
experiment = project.experiments['bm01']
project.display.constraints()

Data 'pd-xray-cwl_latp-bm01_scan' is at data/pd-xray-cwl_latp-bm01_scan-67292a68d53c/pd-xray-cwl_latp-bm01_scan
Saving project to 'pd-xray-cwl_latp-bm01_scan'

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

Stage the template fit¶

The template is the scan's first pattern. Fit it alone first, in stages, so the scan starts from a good model: switch the fitting mode to a single fit.

project.analysis.fitting_mode = 'single'

project.display.pattern('bm01')

Perform the analysis¶

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

Scales, 2θ zero and cells¶

The three phases' scales and cells and the zero shift.

experiment.linked_structures['latp'].scale.free = True
experiment.linked_structures['alpo4_c2221'].scale.free = True
experiment.linked_structures['alpo4_p63mc'].scale.free = True
experiment.instrument.calib_twotheta_offset.free = True
latp.cell.length_a.free = True
latp.cell.length_c.free = True
c2221.cell.length_a.free = True
c2221.cell.length_b.free = True
c2221.cell.length_c.free = True
p63mc.cell.length_a.free = True
p63mc.cell.length_c.free = True

project.display.parameters.free()

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

edi fit: project pd-xray-cwl_latp-bm01_scan, 3114 pts fitted / 3163 loaded, 11 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        4.51 140198364.17
      1      0.023      4.51 140142449.16   
      2      0.074      4.51 140112444.85   
      3      0.098      4.51 140108484.48   
      4      0.125      4.51 140107944.41   
      5      0.158      4.51 140107929.77   
  done · converged · 5 iters · reduced χ² 140107929.77 · Rwp 4.51 % · 0.18 s

project.display.pattern('bm01')

Background¶

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

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

edi fit: project pd-xray-cwl_latp-bm01_scan, 3114 pts fitted / 3163 loaded, 41 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        4.51 141475726.02
      1      0.092      4.51 141465714.66   
      2      0.147      4.51 141465291.95   
      3      0.229      4.51 141465280.04   
  done · converged · 3 iters · reduced χ² 141465280.04 · Rwp 4.51 % · 0.25 s

project.display.pattern('bm01')

Peak widths¶

experiment.peak.broad_gauss_u.free = True
experiment.peak.broad_gauss_v.free = True
experiment.peak.broad_gauss_w.free = True
experiment.peak.mixing_eta_0.free = True

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

edi fit: project pd-xray-cwl_latp-bm01_scan, 3114 pts fitted / 3163 loaded, 45 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        4.51 141649659.68
      1      0.102      4.51 141617725.69   
      2      0.167      4.51 141616397.51   
      3      0.195      4.51 141616173.71   
      4      0.229      4.51 141612847.55   
      5      0.339      4.51 141612757.46   
  done · converged · 5 iters · reduced χ² 141612757.46 · Rwp 4.51 % · 0.37 s

project.display.pattern('bm01')

Peak asymmetry¶

experiment.peak.asym_beba_a0.free = True
experiment.peak.asym_beba_b0.free = True

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

edi fit: project pd-xray-cwl_latp-bm01_scan, 3114 pts fitted / 3163 loaded, 47 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        4.51 141705103.30
      1      0.096      4.51 141704033.35   
      2      0.159      4.51 141697567.66   
      3      0.262      4.51 141697436.83   
  done · converged · 3 iters · reduced χ² 141697436.83 · Rwp 4.51 % · 0.29 s

project.display.pattern('bm01')

LATP positions¶

The main phase's free coordinates; Al's follows Ti's.

latp.atom_sites['Ti1'].fract_z.free = True
latp.atom_sites['P1'].fract_x.free = True
latp.atom_sites['O1'].fract_x.free = True
latp.atom_sites['O1'].fract_y.free = True
latp.atom_sites['O1'].fract_z.free = True
latp.atom_sites['O2'].fract_x.free = True
latp.atom_sites['O2'].fract_y.free = True
latp.atom_sites['O2'].fract_z.free = True

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

edi fit: project pd-xray-cwl_latp-bm01_scan, 3114 pts fitted / 3163 loaded, 55 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        4.51 142068008.74
      1      0.099      4.51 142054983.72   
      2      0.163      4.51 142052860.61   
      3      0.199      4.51 142052190.88   
      4      0.238      4.51 142050716.46   
      5      0.331      4.51 142050690.48   
  done · converged · 5 iters · reduced χ² 142050690.48 · Rwp 4.51 % · 0.37 s

project.display.pattern('bm01')

LATP displacements¶

latp.atom_sites['Ti1'].adp_iso.free = True
latp.atom_sites['P1'].adp_iso.free = True
latp.atom_sites['O1'].adp_iso.free = True
latp.atom_sites['O2'].adp_iso.free = True

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

edi fit: project pd-xray-cwl_latp-bm01_scan, 3114 pts fitted / 3163 loaded, 59 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                        4.51 142236681.57
      1      0.096      4.51 142234344.23   
      2      0.156      4.51 142232766.12   
      3      0.195      4.51 142229314.14   
      4      0.233      4.51 142228665.28   
      5      0.330      4.51 142228616.00   
  done · converged · 5 iters · reduced χ² 142228616.00 · Rwp 4.51 % · 0.37 s

project.display.pattern('bm01')

project.display.fit.correlations()

project.display.structure('latp')

project.display.structure('alpo4_c2221')

project.display.structure('alpo4_p63mc')

Fit the scan¶

Back to the sequential mode, with the template's free parameters. Each pattern starts from the fit before it.

project.analysis.fitting_mode = 'sequential'
fitted = []
result = project.fit_sequential(on_file_complete=lambda *args: fitted.append(args))
print(result.status.name.lower(), 'after', len(fitted), 'patterns')

done after 73 patterns

The results¶

One row per pattern, in the order they were fitted.

results = Path('pd-xray-cwl_latp-bm01_scan/analysis/results.csv')
with results.open(newline='', encoding='utf-8') as file:
    rows = list(csv.DictReader(file))
print(len(rows), 'rows; columns:', ', '.join(list(rows[0])[:6]), '...')

73 rows; columns: file_path, fit_result.reduced_chi_square, fit_result.success, fit_result.iterations, alpo4_c2221.cell.length_a, alpo4_c2221.cell.length_a.uncertainty ...

Save the report¶

project.report.save_html('pd-xray-cwl_latp-bm01_scan.html')

Saving report to 'pd-xray-cwl_latp-bm01_scan.html'