La₀.₅Ba₀.₅CoO₃ on HRPT¶
The same staged fit as the Python tutorial, on the command line. The command line fits whatever the project marks free with () after a value, so each stage marks its parameters in the project's files with a text editor and runs edi fit, which writes the fitted values back into the project for the next stage. The Python tutorial builds this project by hand; here the command line starts from its starting project instead, since building a project by hand on the command line is planned for a later release.
Get the project¶
edi download-data pd-neut-cwl_lbco-hrpt
python -m edi download-data pd-neut-cwl_lbco-hrpt
Start with nothing free¶
The project marks what its finished fit frees. Remove every (), so the stages below free one group at a time.
In experiments/hrpt.edi, remove the () from every value; they now read:
_instrument.calib_twotheta_offset 0.3
_peak.broad_gauss_u 0.08
_peak.broad_gauss_v -0.1
_peak.broad_gauss_w 0.1
_peak.broad_lorentz_y 0.08
1 10 160
2 30 160The same for every other row (4 more).
In structures/lbco.edi, remove the () from every value; they now read:
_cell.length_a 3.88
La La 0 0 0 a 1 0.5 0.5 Biso
Co Co 0.5 0.5 0.5 b 1 1 0.5 BisoThe same for every other row (1 more).
Scale, 2θ zero and cell¶
The scale sets the overall height of the pattern, and the zero shift and the cell length put the peaks where they are measured, so they come first.
In experiments/hrpt.edi, add () after the values the stage frees:
_instrument.calib_twotheta_offset 0.3()
lbco 9() 1.0In structures/lbco.edi, add () after the values the stage frees:
_cell.length_a 3.88()edi fit pd-neut-cwl_lbco-hrpt --verbosity full
python -m edi fit pd-neut-cwl_lbco-hrpt --verbosity full
edi fit: project pd-neut-cwl_lbco-hrpt, 3098 pts fitted / 3098 loaded, 3 free
iter time (s) Rwp (%) reduced χ² change
53.67 71.20
1 0.015 26.76 17.70 75.1% ↓
2 0.021 14.06 4.89 72.4% ↓
3 0.025 12.52 3.87 20.7% ↓
4 0.030 12.52 3.87
5 0.040 12.52 3.87
done · converged · 5 iters · reduced χ² 3.87 · Rwp 12.52 % · 0.05 s
refined parameters (3 free):
name parameter start value s.u. change
2θ offset, deg experiment.instrument.calib_twotheta_offset 0.3000 0.6209 0.0019 107.0% ↑
scale experiment.linked_structures[lbco].scale 9 7.259 0.037 19.3% ↓
a, Å structure.cell.length_a 3.8800 3.890816 0.000061 0.3% ↑
- start the value before the fit
- value the fitted value
- s.u. its standard uncertainty
- change how far the fit moved it, in % of the start: ↑ up, ↓ down
Background¶
With the peaks in place, the five background points follow the level between them.
In experiments/hrpt.edi, add () after the values the stage frees:
1 10 160()
2 30 160()The same for every other row (3 more).
edi fit pd-neut-cwl_lbco-hrpt --verbosity full
python -m edi fit pd-neut-cwl_lbco-hrpt --verbosity full
edi fit: project pd-neut-cwl_lbco-hrpt, 3098 pts fitted / 3098 loaded, 8 free
iter time (s) Rwp (%) reduced χ² change
12.52 3.88
1 0.015 10.91 2.95 24.0% ↓
2 0.024 10.91 2.95
done · converged · 2 iters · reduced χ² 2.95 · Rwp 10.91 % · 0.03 s
refined parameters (8 free):
name parameter start value s.u. change
intensity experiment.background[1].intensity 160 168.1 2.1 5.1% ↑
intensity experiment.background[2].intensity 160 168.2 1.5 5.1% ↑
intensity experiment.background[3].intensity 160 172.0 1.1 7.5% ↑
intensity experiment.background[4].intensity 160 174.14 0.95 8.8% ↑
intensity experiment.background[5].intensity 160 176.4 1.3 10.2% ↑
2θ offset, deg experiment.instrument.calib_twotheta_offset 0.6209 0.6213 0.0017 0.1% ↑
scale experiment.linked_structures[lbco].scale 7.259 7.083 0.033 2.4% ↓
a, Å structure.cell.length_a 3.8908 3.890834 0.000055
- start the value before the fit
- value the fitted value
- s.u. its standard uncertainty
- change how far the fit moved it, in % of the start: ↑ up, ↓ down
Peak widths¶
The profile terms now fit the widths and shapes of the peaks.
In experiments/hrpt.edi, add () after the values the stage frees:
_peak.broad_gauss_u 0.08()
_peak.broad_gauss_v -0.1()
_peak.broad_gauss_w 0.1()
_peak.broad_lorentz_y 0.08()edi fit pd-neut-cwl_lbco-hrpt --verbosity full
python -m edi fit pd-neut-cwl_lbco-hrpt --verbosity full
edi fit: project pd-neut-cwl_lbco-hrpt, 3098 pts fitted / 3098 loaded, 12 free
iter time (s) Rwp (%) reduced χ² change
10.91 2.95
1 0.016 10.74 2.86 3.2% ↓
2 0.020 10.73 2.86
3 0.028 10.73 2.86
done · converged · 3 iters · reduced χ² 2.86 · Rwp 10.73 % · 0.03 s
refined parameters (12 free):
name parameter start value s.u. change
intensity experiment.background[1].intensity 168.1 168.5 2.1 0.2% ↑
intensity experiment.background[2].intensity 168.2 167.5 1.5 0.4% ↓
intensity experiment.background[3].intensity 172 170.8 1.1 0.7% ↓
intensity experiment.background[4].intensity 174.14 173.05 0.97 0.6% ↓
intensity experiment.background[5].intensity 176.4 175.4 1.4 0.6% ↓
2θ offset, deg experiment.instrument.calib_twotheta_offset 0.6213 0.6211 0.0017
scale experiment.linked_structures[lbco].scale 7.083 7.207 0.041 1.7% ↑
U, deg² experiment.peak.broad_gauss_u 0.08 0.0818 0.0048 2.3% ↑
V, deg² experiment.peak.broad_gauss_v -0.1 -0.105 0.011 5.5% ↓
W, deg² experiment.peak.broad_gauss_w 0.1 0.1090 0.0052 9.0% ↑
Y, deg experiment.peak.broad_lorentz_y 0.08 0.0884 0.0033 10.5% ↑
a, Å structure.cell.length_a 3.8908 3.890841 0.000056
- start the value before the fit
- value the fitted value
- s.u. its standard uncertainty
- change how far the fit moved it, in % of the start: ↑ up, ↓ down
Displacements¶
Every atom sits on a special position of P m -3 m, so there are no coordinates to fit. The displacements change the peak intensities with angle and come last.
In structures/lbco.edi, add () after the values the stage frees:
La La 0 0 0 a 1 0.5 0.5() Biso
Ba Ba 0 0 0 a 1 0.5 0.5() BisoThe same for every other row (2 more).
edi fit pd-neut-cwl_lbco-hrpt --verbosity full
python -m edi fit pd-neut-cwl_lbco-hrpt --verbosity full
edi fit: project pd-neut-cwl_lbco-hrpt, 3098 pts fitted / 3098 loaded, 16 free
iter time (s) Rwp (%) reduced χ² change
10.73 2.86
1 0.017 7.76 1.49 47.8% ↓
2 0.021 7.24 1.30 13.0% ↓
3 0.030 7.23 1.30 0.2% ↓
4 0.034 7.23 1.30
5 0.047 7.23 1.30
done · converged · 5 iters · reduced χ² 1.30 · Rwp 7.23 % · 0.05 s
refined parameters (16 free):
name parameter start value s.u. change
intensity experiment.background[1].intensity 168.5 169.6 1.4 0.6% ↑
intensity experiment.background[2].intensity 167.5 165.0 1.0 1.5% ↓
intensity experiment.background[3].intensity 170.8 166.99 0.74 2.2% ↓
intensity experiment.background[4].intensity 173.05 175.89 0.66 1.6% ↑
intensity experiment.background[5].intensity 175.4 171.24 0.94 2.4% ↓
2θ offset, deg experiment.instrument.calib_twotheta_offset 0.6211 0.6204 0.0011 0.1% ↓
scale experiment.linked_structures[lbco].scale 7.207 9.132 0.065 26.7% ↑
U, deg² experiment.peak.broad_gauss_u 0.0818 0.0826 0.0032 1.0% ↑
V, deg² experiment.peak.broad_gauss_v -0.105 -0.1176 0.0068 12.0% ↓
W, deg² experiment.peak.broad_gauss_w 0.109 0.1213 0.0033 11.3% ↑
Y, deg experiment.peak.broad_lorentz_y 0.0884 0.0839 0.0022 5.1% ↓
B iso, Ų structure.atom_sites[Ba].adp_iso 0.500 1 43 4.6% ↑
B iso, Ų structure.atom_sites[Co].adp_iso 0.500 0.211 0.061 57.8% ↓
B iso, Ų structure.atom_sites[La].adp_iso 0.500 1 27 2.0% ↑
B iso, Ų structure.atom_sites[O].adp_iso 0.500 1.392 0.017 178.3% ↑
a, Å structure.cell.length_a 3.8908 3.890791 0.000039
- start the value before the fit
- value the fitted value
- s.u. its standard uncertainty
- change how far the fit moved it, in % of the start: ↑ up, ↓ down
Constrain La and Ba¶
The correlations show the displacements of La and Ba moving together almost exactly, with opposite signs: they share one site and scatter neutrons similarly, so the pattern cannot tell them apart, and their s.u. are large. Give each an alias and constrain Ba's to follow La's, then fit again. Ba's displacement is no longer fitted on its own.
In analysis/analysis.edi, add these rows to its alias and constraint loops:
biso_La lbco.atom_site.La.adp_iso
biso_Ba lbco.atom_site.Ba.adp_isoThe same for every other row (1 more).
edi fit pd-neut-cwl_lbco-hrpt --verbosity full
python -m edi fit pd-neut-cwl_lbco-hrpt --verbosity full
edi fit: project pd-neut-cwl_lbco-hrpt, 3098 pts fitted / 3098 loaded, 15 free
iter time (s) Rwp (%) reduced χ² change
8.28 1.70
1 0.019 7.28 1.31 22.7% ↓
2 0.023 7.23 1.30 1.3% ↓
3 0.027 7.23 1.30
4 0.035 7.23 1.30
done · converged · 4 iters · reduced χ² 1.30 · Rwp 7.23 % · 0.04 s
refined parameters (15 free):
name parameter start value s.u. change
intensity experiment.background[1].intensity 169.6 169.6 1.4
intensity experiment.background[2].intensity 165 165.0 1.0
intensity experiment.background[3].intensity 166.99 166.99 0.74
intensity experiment.background[4].intensity 175.89 175.89 0.65
intensity experiment.background[5].intensity 171.24 171.24 0.92
2θ offset, deg experiment.instrument.calib_twotheta_offset 0.6204 0.6204 0.0011
scale experiment.linked_structures[lbco].scale 9.132 9.132 0.054
U, deg² experiment.peak.broad_gauss_u 0.0826 0.0826 0.0032
V, deg² experiment.peak.broad_gauss_v -0.1176 -0.1176 0.0067
W, deg² experiment.peak.broad_gauss_w 0.1213 0.1213 0.0033
Y, deg experiment.peak.broad_lorentz_y 0.0839 0.0839 0.0022
B iso, Ų structure.atom_sites[Co].adp_iso 0.211 0.211 0.056 0.1% ↑
B iso, Ų structure.atom_sites[La].adp_iso 1.000 0.515 0.028 48.5% ↓
B iso, Ų structure.atom_sites[O].adp_iso 1.392 1.392 0.017
a, Å structure.cell.length_a 3.8908 3.890791 0.000039
- start the value before the fit
- value the fitted value
- s.u. its standard uncertainty
- change how far the fit moved it, in % of the start: ↑ up, ↓ down
Report¶
Write the HTML report of the fitted project and open it in a browser.
The standalone executable has no report; use the Python package.
python -m edi report pd-neut-cwl_lbco-hrpt --output pd-neut-cwl_lbco-hrpt.html