YAlO₃ and Al₂O₃ on SPODI¶
Fit two phases, YAlO₃ and corundum Al₂O₃, in one constant-wavelength neutron pattern from SPODI at FRM II, measured at 3 K, with a shared Bérar-Baldinozzi profile and cylinder absorption.
The project is the catalogue case pd-neut-cwl_yalo3-al2o3-spodi, the one the command line and
the app's Examples open.
Fitting 
Single pd neut cwl Bragg 
Crystal structure
import easydiffraction as edi
Load the project¶
project_path = edi.download_data('pd-neut-cwl_yalo3-al2o3-spodi', destination='data')
project = edi.Project.load(project_path)
yalo3 = project.structures['YAlO3']
alumina = project.structures['Al2O3']
experiment = project.experiments['spodi']
Data 'pd-neut-cwl_yalo3-al2o3-spodi' is at data/pd-neut-cwl_yalo3-al2o3-spodi-5ae8d5ec72da/pd-neut-cwl_yalo3-al2o3-spodi
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('spodi')
Perform the analysis¶
The fit follows diffraction-lib's three cycles for this case (its YAP tutorial). diffraction-lib frees the Lorentzian Y and two asymmetry terms where this profile has the mixing η₀ and four.
Cells, scales and 2θ zero¶
Both phases' cells and scales, and the zero shift, put the peaks of both phases in place.
yalo3.cell.length_a.free = True
yalo3.cell.length_b.free = True
yalo3.cell.length_c.free = True
alumina.cell.length_a.free = True
alumina.cell.length_c.free = True
experiment.linked_structures['YAlO3'].scale.free = True
experiment.linked_structures['Al2O3'].scale.free = True
experiment.instrument.calib_twotheta_offset.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: project pd-neut-cwl_yalo3-al2o3-spodi, 2959 pts fitted / 2959 loaded, 8 free
iter time (s) Rwp (%) reduced χ² change
18.59 201.52
1 0.008 13.43 105.14 47.8% ↓
2 0.015 13.38 104.44 0.7% ↓
3 0.022 13.38 104.43
4 0.029 13.38 104.43
5 0.036 13.38 104.42
6 0.042 13.38 104.42
7 0.049 13.38 104.42
8 0.059 13.38 104.42
done · converged · 8 iters · reduced χ² 104.42 · Rwp 13.38 % · 0.07 s
project.display.pattern('spodi')
Background¶
for point in experiment.background:
point.intensity.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: project pd-neut-cwl_yalo3-al2o3-spodi, 2959 pts fitted / 2959 loaded, 33 free
iter time (s) Rwp (%) reduced χ² change
13.38 105.32
1 0.038 11.96 84.08 20.2% ↓
2 0.054 11.96 84.08
3 0.064 11.96 84.07
4 0.073 11.96 84.07
5 0.084 11.96 84.06
6 0.092 11.96 84.06
7 0.102 11.96 84.06
8 0.110 11.96 84.06
9 0.120 11.96 84.06
10 0.157 11.96 84.06
done · converged · 10 iters · reduced χ² 84.06 · Rwp 11.96 % · 0.17 s
project.display.pattern('spodi')
Peak widths¶
The Gaussian widths and the mixing η₀.
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-neut-cwl_yalo3-al2o3-spodi, 2959 pts fitted / 2959 loaded, 37 free
iter time (s) Rwp (%) reduced χ² change
11.96 84.18
1 0.038 11.47 77.42 8.0% ↓
2 0.047 11.46 77.33 0.1% ↓
3 0.057 11.46 77.33
4 0.074 11.46 77.33
5 0.082 11.46 77.33
6 0.093 11.46 77.33
7 0.102 11.46 77.32
8 0.140 11.46 77.32
done · converged · 8 iters · reduced χ² 77.32 · Rwp 11.46 % · 0.15 s
project.display.pattern('spodi')
Asymmetry¶
The four Bérar-Baldinozzi asymmetry terms.
experiment.peak.asym_beba_a0.free = True
experiment.peak.asym_beba_b0.free = True
experiment.peak.asym_beba_a1.free = True
experiment.peak.asym_beba_b1.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: project pd-neut-cwl_yalo3-al2o3-spodi, 2959 pts fitted / 2959 loaded, 41 free
iter time (s) Rwp (%) reduced χ² change
11.46 77.43
1 0.036 11.30 75.33 2.7% ↓
2 0.045 11.28 75.05 0.4% ↓
3 0.055 11.28 74.99 0.1% ↓
4 0.064 11.28 74.99
5 0.072 11.28 74.99
6 0.106 11.28 74.99
done · converged · 6 iters · reduced χ² 74.99 · Rwp 11.28 % · 0.12 s
project.display.pattern('spodi')
Atom positions¶
The coordinates the symmetry leaves free in both phases.
yalo3.atom_sites['Y'].fract_x.free = True
yalo3.atom_sites['Y'].fract_y.free = True
yalo3.atom_sites['O1'].fract_x.free = True
yalo3.atom_sites['O1'].fract_y.free = True
yalo3.atom_sites['O2'].fract_x.free = True
yalo3.atom_sites['O2'].fract_y.free = True
yalo3.atom_sites['O2'].fract_z.free = True
alumina.atom_sites['Al1'].fract_z.free = True
alumina.atom_sites['O1'].fract_x.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: project pd-neut-cwl_yalo3-al2o3-spodi, 2959 pts fitted / 2959 loaded, 50 free
iter time (s) Rwp (%) reduced χ² change
11.28 75.22
1 0.043 6.52 25.17 66.5% ↓
2 0.056 6.46 24.71 1.8% ↓
3 0.077 6.46 24.70
4 0.091 6.46 24.69
5 0.104 6.46 24.69
6 0.117 6.46 24.69
7 0.130 6.46 24.69
8 0.144 6.46 24.69
9 0.156 6.46 24.69
10 0.169 6.46 24.69
11 0.182 6.46 24.69
12 0.195 6.46 24.69
13 0.207 6.46 24.69
14 0.224 6.46 24.69
15 0.262 6.46 24.69
done · converged · 15 iters · reduced χ² 24.69 · Rwp 6.46 % · 0.28 s
project.display.pattern('spodi')
Displacements¶
Every site's displacement in both phases.
for structure in (yalo3, alumina):
for site in structure.atom_sites:
site.adp_iso.free = True
project.analysis.fit()
project.display.fit.results()
edi fit: project pd-neut-cwl_yalo3-al2o3-spodi, 2959 pts fitted / 2959 loaded, 56 free
iter time (s) Rwp (%) reduced χ² change
6.46 24.74
1 0.045 4.13 10.13 59.0% ↓
2 0.060 4.06 9.79 3.4% ↓
3 0.075 4.06 9.77 0.1% ↓
4 0.089 4.06 9.77
5 0.103 4.06 9.77
6 0.118 4.06 9.77
7 0.132 4.06 9.76
8 0.146 4.06 9.76 0.1% ↓
9 0.159 4.05 9.74 0.1% ↓
10 0.171 4.05 9.73 0.1% ↓
11 0.185 4.05 9.73
12 0.198 4.05 9.73
13 0.211 4.05 9.73
14 0.223 4.05 9.73
15 0.266 4.05 9.73
done · converged · 15 iters · reduced χ² 9.73 · Rwp 4.05 % · 0.28 s
project.display.pattern('spodi')
project.display.fit.correlations()
project.display.structure('YAlO3')
project.display.structure('Al2O3')
Save the project¶
project.save_as('pd-neut-cwl_yalo3-al2o3-spodi')
project.report.save_html('pd-neut-cwl_yalo3-al2o3-spodi.html')
Saving project to 'pd-neut-cwl_yalo3-al2o3-spodi'
Saving report to 'pd-neut-cwl_yalo3-al2o3-spodi.html'