Ferrite and austenite on BEER¶

Calibrate the BEER instrument at ESS with two McStas-simulated banks of a ferrite and austenite duplex steel, fitted together: each bank has its own zero and resolution.

The project is the catalogue case pd-neut-tof_ferrite-austenite-beer, the one the command line and the app's Examples open. Austenite's displacement follows ferrite's, and each phase's scale in bank n2 follows bank s2, from the start.

Fitting Joint pd neut tof Bragg Crystal structure

import easydiffraction as edi

Load the project¶

project_path = edi.download_data('pd-neut-tof_ferrite-austenite-beer', destination='data')
project = edi.Project.load(project_path)
ferrite = project.structures['ferrite']
austenite = project.structures['austenite']
bank_s2 = project.experiments['expt_s2']
bank_n2 = project.experiments['expt_n2']
project.display.constraints()

Data 'pd-neut-tof_ferrite-austenite-beer' is at data/pd-neut-tof_ferrite-austenite-beer-eccc89de8995/pd-neut-tof_ferrite-austenite-beer

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('expt_s2')

Perform the analysis¶

The cells stay fixed: this is a calibration, and the two phases are the standards.

Scales and time-of-flight calibration¶

Both phases' scales and each bank's DIFC offset put the peaks in place and at the right height.

bank_s2.linked_structures['ferrite'].scale.free = True
bank_s2.linked_structures['austenite'].scale.free = True
bank_s2.instrument.calib_d_to_tof_offset.free = True
bank_n2.instrument.calib_d_to_tof_offset.free = True

project.display.parameters.free()

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

edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 4 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       41.43       229.76
      1      0.002     23.98        76.97   66.5% ↓
      2      0.005     23.84        76.05   1.2% ↓
      3      0.007     23.83        76.04   
      4      0.009     23.83        76.04   
  done · converged · 4 iters · reduced χ² 76.04 · Rwp 23.83 % · 0.01 s

project.display.pattern('expt_s2')

project.display.pattern('expt_n2')

Background¶

Each bank's background points; the last, past the end of the data, stays fixed.

for point in bank_s2.background:
    point.intensity.free = True
for point in bank_n2.background:
    point.intensity.free = True
bank_s2.background[30].intensity.free = False
bank_n2.background[30].intensity.free = False

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

edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 64 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       23.83        76.86
      1      0.061     18.05        44.10   42.6% ↓
      2      0.123     18.05        44.10   
  done · converged · 2 iters · reduced χ² 44.10 · Rwp 18.05 % · 0.14 s

project.display.pattern('expt_s2')

project.display.pattern('expt_n2')

Peak widths¶

Each bank's widths.

bank_s2.peak.broad_gauss_sigma_0.free = True
bank_s2.peak.broad_gauss_sigma_1.free = True
bank_s2.peak.broad_gauss_sigma_2.free = True
bank_s2.peak.broad_lorentz_gamma_0.free = True
bank_n2.peak.broad_gauss_sigma_0.free = True
bank_n2.peak.broad_gauss_sigma_1.free = True
bank_n2.peak.broad_gauss_sigma_2.free = True
bank_n2.peak.broad_lorentz_gamma_0.free = True

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

edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 72 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       18.05        44.16
      1      0.059     16.39        36.39   17.6% ↓
      2      0.069     16.38        36.35   0.1% ↓
      3      0.127     16.38        36.35   
  done · converged · 3 iters · reduced χ² 36.35 · Rwp 16.38 % · 0.15 s

project.display.pattern('expt_s2')

project.display.pattern('expt_n2')

Displacement¶

Last, ferrite's displacement; austenite's follows it.

ferrite.atom_sites['Fe'].adp_iso.free = True

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

edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 73 free
   iter   time (s)   Rwp (%)  reduced χ²   change
                       16.38        36.36
      1      0.055      7.73         8.10   77.7% ↓
      2      0.065      7.14         6.91   14.7% ↓
      3      0.076      7.13         6.89   0.3% ↓
      4      0.087      7.13         6.89   
      5      0.142      7.13         6.89   
  done · converged · 5 iters · reduced χ² 6.89 · Rwp 7.13 % · 0.16 s

project.display.pattern('expt_s2')

project.display.pattern('expt_n2')

project.display.fit.correlations()

project.display.structure('ferrite')

project.display.structure('austenite')

Save the project¶

project.save_as('pd-neut-tof_ferrite-austenite-beer')
project.report.save_html('pd-neut-tof_ferrite-austenite-beer.html')

Saving project to 'pd-neut-tof_ferrite-austenite-beer'
Saving report to 'pd-neut-tof_ferrite-austenite-beer.html'