{
"nbformat": 4,
"nbformat_minor": 5,
"metadata": {
"jupytext": {
"main_language": "python",
"notebook_metadata_filter": "-all",
"cell_metadata_filter": "-all",
"text_representation": {
"extension": ".py",
"format_name": "percent"
}
}
},
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"tags": [
"hide-in-docs"
],
"execution": {
"iopub.status.busy": "2026-11-12T16:09:36.888960Z",
"iopub.execute_input": "2026-11-12T16:09:36.889128Z",
"shell.execute_reply": "2026-11-12T16:09:36.891648Z",
"iopub.status.idle": "2026-11-12T16:09:36.892019Z"
}
},
"outputs": [],
"source": "# Check whether easydiffraction is installed; install it if needed.\n# Required for remote environments such as Google Colab.\nimport importlib.util\n\nif importlib.util.find_spec('easydiffraction') is None:\n %pip install easydiffraction==2026.11.13 --extra-index-url https://download.easydiffraction.org/pypi/simple/\n",
"id": "0"
},
{
"id": "1",
"cell_type": "markdown",
"source": "# Co₂SiO₄ on D20 at 2.3 K",
"metadata": {}
},
{
"cell_type": "markdown",
"metadata": {},
"source": "![\"Fitting\"](\"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NyIgaGVpZ2h0PSIyMiIgdmlld0JveD0iMCAwIDY3IDIyIj48cmVjdCB3aWR0aD0iNjciIGhlaWdodD0iMjIiIHJ4PSI0IiBmaWxsPSIjMzk4NjQ4IiBmaWxsLW9wYWNpdHk9IjAuMTMiLz48c3ZnIHg9IjciIHk9IjUuMCIgd2lkdGg9IjEyIiBoZWlnaHQ9IjEyIiB2aWV3Qm94PSIwIDAgNDk2IDUxMiIgZmlsbD0iIzM5ODY0OCI+PHBhdGggZD0iTTI0OCA4QzExMS4wMzAyNzM0Mzc1IDguMCAwLjAgMTE5LjAzMDI3MzQzNzUgMC4wIDI1Ni4wQzAuMCAzOTIuOTY5NzI2NTYyNSAxMTEuMDMwMjczNDM3NSA1MDQuMCAyNDguMCA1MDQuMEMzODQuOTY5NzI2NTYyNSA1MDQuMCA0OTYuMCAzOTIuOTY5NzI2NTYyNSA0OTYuMCAyNTYuMEM0OTYuMCAxMTkuMDMwMjczNDM3NSAzODQuOTY5NzI2NTYyNSA4LjAgMjQ4LjAgOC4wWk0yNDguMCA0NDAuMEMxNDYuMzA5NTcwMzEyNSA0NDAuMCA2NC4wIDM1Ny43MDk5NjA5Mzc1IDY0LjAgMjU2LjBDNjQuMCAxNTQuMzA5NTcwMzEyNSAxNDYuMjkwMDM5MDYyNSA3Mi4wIDI0OC4wIDcyLjBDMzQ5LjY5MDQyOTY4NzUgNzIuMCA0MzIuMCAxNTQuMjkwMDM5MDYyNSA0MzIuMCAyNTYuMEM0MzIuMCAzNTcuNjkwNDI5Njg3NSAzNDkuNzA5OTYwOTM3NSA0NDAuMCAyNDguMCA0NDAuMFpNMjQ4LjAgMTI4LjBDMTc3LjMwOTU3MDMxMjUgMTI4LjAgMTIwLjAgMTg1LjMwOTU3MDMxMjUgMTIwLjAgMjU2LjBDMTIwLjAgMzI2LjY5MDQyOTY4NzUgMTc3LjMwOTU3MDMxMjUgMzg0LjAgMjQ4LjAgMzg0LjBDMzE4LjY5MDQyOTY4NzUgMzg0LjAgMzc2LjAgMzI2LjY5MDQyOTY4NzUgMzc2LjAgMjU2LjBDMzc2LjAgMTg1LjMwOTU3MDMxMjUgMzE4LjY5MDQyOTY4NzUgMTI4LjAgMjQ4LjAgMTI4LjBaTTI0OC4wIDMyMC4wQzIxMi43MDk5NjA5Mzc1IDMyMC4wIDE4NC4wIDI5MS4yOTAwMzkwNjI1IDE4NC4wIDI1Ni4wQzE4NC4wIDIyMC43MDk5NjA5Mzc1IDIxMi43MDk5NjA5Mzc1IDE5Mi4wIDI0OC4wIDE5Mi4wQzI4My4yOTAwMzkwNjI1IDE5Mi4wIDMxMi4wIDIyMC43MDk5NjA5Mzc1IDMxMi4wIDI1Ni4wQzMxMi4wIDI5MS4yOTAwMzkwNjI1IDI4My4yOTAwMzkwNjI1IDMyMC4wIDI0OC4wIDMyMC4wWiIvPjwvc3ZnPjx0ZXh0IHg9IjIzIiB5PSIxNS4zIiBmb250LWZhbWlseT0iTm90byBTYW5zLCBTZWdvZSBVSSwgSGVsdmV0aWNhLCBBcmlhbCwgc2Fucy1zZXJpZiIgZm9udC1zaXplPSIxMiIgZmlsbD0iIzM5ODY0OCI+Rml0dGluZzwvdGV4dD48L3N2Zz4=\")
![\"Single\"](\"data:image/svg+xml;base64,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\")
![\"pd\"](\"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNyIgaGVpZ2h0PSIyMiIgdmlld0JveD0iMCAwIDI3IDIyIj48cmVjdCB3aWR0aD0iMjciIGhlaWdodD0iMjIiIHJ4PSI0IiBmaWxsPSIjMDA4NGM3IiBmaWxsLW9wYWNpdHk9IjAuMTMiLz48dGV4dCB4PSI3IiB5PSIxNS4zIiBmb250LWZhbWlseT0iTm90byBTYW5zLCBTZWdvZSBVSSwgSGVsdmV0aWNhLCBBcmlhbCwgc2Fucy1zZXJpZiIgZm9udC1zaXplPSIxMiIgZmlsbD0iIzAwODRjNyI+cGQ8L3RleHQ+PC9zdmc+\")
![\"neut\"](\"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzOCIgaGVpZ2h0PSIyMiIgdmlld0JveD0iMCAwIDM4IDIyIj48cmVjdCB3aWR0aD0iMzgiIGhlaWdodD0iMjIiIHJ4PSI0IiBmaWxsPSIjMDA4NGM3IiBmaWxsLW9wYWNpdHk9IjAuMTMiLz48dGV4dCB4PSI3IiB5PSIxNS4zIiBmb250LWZhbWlseT0iTm90byBTYW5zLCBTZWdvZSBVSSwgSGVsdmV0aWNhLCBBcmlhbCwgc2Fucy1zZXJpZiIgZm9udC1zaXplPSIxMiIgZmlsbD0iIzAwODRjNyI+bmV1dDwvdGV4dD48L3N2Zz4=\")
![\"cwl\"](\"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzNSIgaGVpZ2h0PSIyMiIgdmlld0JveD0iMCAwIDM1IDIyIj48cmVjdCB3aWR0aD0iMzUiIGhlaWdodD0iMjIiIHJ4PSI0IiBmaWxsPSIjNDI0MjQyIiBmaWxsLW9wYWNpdHk9IjAuMTMiLz48dGV4dCB4PSI3IiB5PSIxNS4zIiBmb250LWZhbWlseT0iTm90byBTYW5zLCBTZWdvZSBVSSwgSGVsdmV0aWNhLCBBcmlhbCwgc2Fucy1zZXJpZiIgZm9udC1zaXplPSIxMiIgZmlsbD0iIzQyNDI0MiI+Y3dsPC90ZXh0Pjwvc3ZnPg==\")
![\"Bragg\"](\"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0NiIgaGVpZ2h0PSIyMiIgdmlld0JveD0iMCAwIDQ2IDIyIj48cmVjdCB3aWR0aD0iNDYiIGhlaWdodD0iMjIiIHJ4PSI0IiBmaWxsPSIjMDA4NGM3IiBmaWxsLW9wYWNpdHk9IjAuMTMiLz48dGV4dCB4PSI3IiB5PSIxNS4zIiBmb250LWZhbWlseT0iTm90byBTYW5zLCBTZWdvZSBVSSwgSGVsdmV0aWNhLCBBcmlhbCwgc2Fucy1zZXJpZiIgZm9udC1zaXplPSIxMiIgZmlsbD0iIzAwODRjNyI+QnJhZ2c8L3RleHQ+PC9zdmc+\")
![\"Crystal](\"data:image/svg+xml;base64,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\")
![\"Magnetic](\"data:image/svg+xml;base64,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\")
",
"id": "2"
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Fit the magnetic structure of the olivine Co₂SiO₄ to constant-wavelength neutron powder data\nfrom D20 at ILL, measured at 2.3 K, below its ordering temperature. The cobalt moments order with\nk = 0 in the magnetic space group Pnma.1: Co1 may point in any direction, Co2 only along b.\n\nThe project is the catalogue case `pd-neut-cwl_cosio-d20_2k`, the one the command line and the\napp's Examples open. Its two Co sites share one displacement, and the two FCJ asymmetry terms are\ntied, from the start.",
"id": "3"
},
{
"id": "4",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:36.893010Z",
"iopub.execute_input": "2026-11-12T16:09:36.893127Z",
"shell.execute_reply": "2026-11-12T16:09:36.901609Z",
"iopub.status.idle": "2026-11-12T16:09:36.901920Z"
}
},
"execution_count": 2,
"source": "import easydiffraction as edi",
"outputs": []
},
{
"id": "5",
"cell_type": "markdown",
"source": "## Load the project",
"metadata": {}
},
{
"id": "6",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:36.902902Z",
"iopub.execute_input": "2026-11-12T16:09:36.903023Z",
"shell.execute_reply": "2026-11-12T16:09:37.121592Z",
"iopub.status.idle": "2026-11-12T16:09:37.122007Z"
}
},
"execution_count": 3,
"source": "project_path = edi.download_data('pd-neut-cwl_cosio-d20_2k', destination='data')\nproject = edi.Project.load(project_path)\nstructure = project.structures['cosio']\nexperiment = project.experiments['d20']\nproject.display.constraints()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "Data 'pd-neut-cwl_cosio-d20_2k' is at data/pd-neut-cwl_cosio-d20_2k-84d4534215e5/pd-neut-cwl_cosio-d20_2k\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<78,814 characters>, height=264)",
"text/html": ""
}
}
]
},
{
"id": "7",
"cell_type": "markdown",
"source": "The project marks what its fit frees. The fit below frees it in stages, so start with all of it\nfixed.",
"metadata": {}
},
{
"id": "8",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.123067Z",
"iopub.execute_input": "2026-11-12T16:09:37.123185Z",
"shell.execute_reply": "2026-11-12T16:09:37.183490Z",
"iopub.status.idle": "2026-11-12T16:09:37.183838Z"
}
},
"execution_count": 4,
"source": "for parameter in project.free_parameters:\n parameter.free = False",
"outputs": []
},
{
"id": "9",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.184993Z",
"iopub.execute_input": "2026-11-12T16:09:37.185111Z",
"iopub.status.idle": "2026-11-12T16:09:37.210382Z",
"shell.execute_reply": "2026-11-12T16:09:37.209982Z"
}
},
"execution_count": 5,
"source": "project.display.pattern('d20')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<308,745 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "10",
"cell_type": "markdown",
"source": "## Perform the analysis\n\nEverything starts fixed, and five stages each free one more group, keeping the earlier ones free:\nthe scale, cell and moments, then the background, the atoms, the peak widths and last the peak\nasymmetry.\n\n### Scale, 2θ zero, cell and magnetic moments\n\nThe first stage frees the phase scale, the 2θ zero shift, the three cell lengths and the magnetic\nmodel: the moment components the magnetic space group allows (Co1 in any direction, Co2 only\nalong b) and the j2 term of the Co²⁺ form factor, which sets how the magnetic intensities fall\nwith angle.",
"metadata": {}
},
{
"id": "11",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.213599Z",
"iopub.execute_input": "2026-11-12T16:09:37.213730Z",
"iopub.status.idle": "2026-11-12T16:09:37.229732Z",
"shell.execute_reply": "2026-11-12T16:09:37.229349Z"
}
},
"execution_count": 6,
"source": "experiment.linked_structures['cosio'].scale.free = True\nexperiment.instrument.calib_twotheta_offset.free = True\nstructure.cell.length_a.free = True\nstructure.cell.length_b.free = True\nstructure.cell.length_c.free = True\nstructure.atom_site_moment['Co1'].crystalaxis_x.free = True\nstructure.atom_site_moment['Co1'].crystalaxis_y.free = True\nstructure.atom_site_moment['Co1'].crystalaxis_z.free = True\nstructure.atom_site_moment['Co2'].crystalaxis_y.free = True\nstructure.magnetic_form_factor['Co'].j2_coefficient.free = True",
"outputs": []
},
{
"id": "12",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.230775Z",
"iopub.execute_input": "2026-11-12T16:09:37.230916Z",
"iopub.status.idle": "2026-11-12T16:09:37.245449Z",
"shell.execute_reply": "2026-11-12T16:09:37.245075Z"
}
},
"execution_count": 7,
"source": "project.display.parameters.free()",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<84,988 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "13",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.246415Z",
"iopub.execute_input": "2026-11-12T16:09:37.246524Z",
"shell.execute_reply": "2026-11-12T16:09:37.317564Z",
"iopub.status.idle": "2026-11-12T16:09:37.317979Z"
}
},
"execution_count": 8,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: project pd-neut-cwl_cosio-d20_2k, 1438 pts fitted / 1506 loaded, 10 free\n iter time (s) Rwp (%) reduced χ² change\n 11.38 35.86\n 1 0.024 5.97 9.88 72.5% ↓\n 2 0.028 5.97 9.88 \n 3 0.032 5.97 9.88 \n 4 0.037 5.97 9.88 \n done · converged · 4 iters · reduced χ² 9.88 · Rwp 5.97 % · 0.04 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<93,283 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "14",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.318979Z",
"iopub.execute_input": "2026-11-12T16:09:37.319095Z",
"iopub.status.idle": "2026-11-12T16:09:37.342664Z",
"shell.execute_reply": "2026-11-12T16:09:37.342272Z"
}
},
"execution_count": 9,
"source": "project.display.pattern('d20')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<309,619 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "15",
"cell_type": "markdown",
"source": "### Background\n\nThe second stage frees the sixteen background points, which follow the level between the peaks.",
"metadata": {}
},
{
"id": "16",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.345233Z",
"iopub.execute_input": "2026-11-12T16:09:37.345358Z",
"shell.execute_reply": "2026-11-12T16:09:37.367845Z",
"iopub.status.idle": "2026-11-12T16:09:37.368162Z"
}
},
"execution_count": 10,
"source": "for point in experiment.background:\n point.intensity.free = True",
"outputs": []
},
{
"id": "17",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.369172Z",
"iopub.execute_input": "2026-11-12T16:09:37.369297Z",
"iopub.status.idle": "2026-11-12T16:09:37.443047Z",
"shell.execute_reply": "2026-11-12T16:09:37.442673Z"
}
},
"execution_count": 11,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: project pd-neut-cwl_cosio-d20_2k, 1438 pts fitted / 1506 loaded, 26 free\n iter time (s) Rwp (%) reduced χ² change\n 5.97 9.99\n 1 0.026 5.65 8.93 10.6% ↓\n 2 0.031 5.65 8.93 \n 3 0.037 5.65 8.93 \n done · converged · 3 iters · reduced χ² 8.93 · Rwp 5.65 % · 0.04 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<114,042 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "18",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.444357Z",
"iopub.execute_input": "2026-11-12T16:09:37.444480Z",
"iopub.status.idle": "2026-11-12T16:09:37.468418Z",
"shell.execute_reply": "2026-11-12T16:09:37.468028Z"
}
},
"execution_count": 12,
"source": "project.display.pattern('d20')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<309,449 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "19",
"cell_type": "markdown",
"source": "### Atomic displacements and positions\n\nThe third stage frees the atoms: each site's isotropic displacement (Co2's follows Co1's by the\nproject's constraint) and the coordinates the symmetry leaves free. Co1 sits on a centre of\nsymmetry, so it has none; the other sites lie on the mirror plane, except O3.",
"metadata": {}
},
{
"id": "20",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.471135Z",
"iopub.execute_input": "2026-11-12T16:09:37.471258Z",
"iopub.status.idle": "2026-11-12T16:09:37.516232Z",
"shell.execute_reply": "2026-11-12T16:09:37.515830Z"
}
},
"execution_count": 13,
"source": "for site in structure.atom_sites:\n site.adp_iso.free = not site.adp_iso.user_constrained\n for coordinate in (site.fract_x, site.fract_y, site.fract_z):\n coordinate.free = not coordinate.symmetry_constrained",
"outputs": []
},
{
"id": "21",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.517399Z",
"iopub.execute_input": "2026-11-12T16:09:37.517527Z",
"iopub.status.idle": "2026-11-12T16:09:37.604715Z",
"shell.execute_reply": "2026-11-12T16:09:37.604282Z"
}
},
"execution_count": 14,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: project pd-neut-cwl_cosio-d20_2k, 1438 pts fitted / 1506 loaded, 42 free\n iter time (s) Rwp (%) reduced χ² change\n 5.65 9.03\n 1 0.026 5.60 8.87 1.8% ↓\n 2 0.031 5.59 8.87 \n 3 0.035 5.59 8.87 \n 4 0.039 5.59 8.86 \n 5 0.043 5.59 8.86 \n 6 0.048 5.59 8.86 \n done · converged · 6 iters · reduced χ² 8.86 · Rwp 5.59 % · 0.05 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<133,575 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "22",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.606084Z",
"iopub.execute_input": "2026-11-12T16:09:37.606199Z",
"iopub.status.idle": "2026-11-12T16:09:37.631509Z",
"shell.execute_reply": "2026-11-12T16:09:37.631113Z"
}
},
"execution_count": 15,
"source": "project.display.pattern('d20')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<309,601 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "23",
"cell_type": "markdown",
"source": "### Peak widths\n\nThe fourth stage frees the peak profile: the Gaussian widths U, V and W and the Lorentzian Y.",
"metadata": {}
},
{
"id": "24",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.634026Z",
"iopub.execute_input": "2026-11-12T16:09:37.634152Z",
"shell.execute_reply": "2026-11-12T16:09:37.641418Z",
"iopub.status.idle": "2026-11-12T16:09:37.641782Z"
}
},
"execution_count": 16,
"source": "experiment.peak.broad_gauss_u.free = True\nexperiment.peak.broad_gauss_v.free = True\nexperiment.peak.broad_gauss_w.free = True\nexperiment.peak.broad_lorentz_y.free = True",
"outputs": []
},
{
"id": "25",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.642845Z",
"iopub.execute_input": "2026-11-12T16:09:37.642967Z",
"iopub.status.idle": "2026-11-12T16:09:37.755251Z",
"shell.execute_reply": "2026-11-12T16:09:37.754954Z"
}
},
"execution_count": 17,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: project pd-neut-cwl_cosio-d20_2k, 1438 pts fitted / 1506 loaded, 46 free\n iter time (s) Rwp (%) reduced χ² change\n 5.59 8.89\n 1 0.031 5.58 8.86 0.3% ↓\n 2 0.036 5.58 8.86 \n 3 0.041 5.58 8.86 \n 4 0.046 5.58 8.86 \n 5 0.051 5.58 8.86 \n 6 0.056 5.58 8.86 \n 7 0.061 5.58 8.86 \n 8 0.065 5.58 8.86 \n 9 0.071 5.58 8.86 \n done · converged · 9 iters · reduced χ² 8.86 · Rwp 5.58 % · 0.08 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<136,443 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "26",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.756888Z",
"iopub.execute_input": "2026-11-12T16:09:37.757013Z",
"iopub.status.idle": "2026-11-12T16:09:37.781521Z",
"shell.execute_reply": "2026-11-12T16:09:37.781176Z"
}
},
"execution_count": 18,
"source": "project.display.pattern('d20')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<309,654 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "27",
"cell_type": "markdown",
"source": "### Peak asymmetry\n\nThe last stage frees the asymmetry: the low-angle peaks lean towards low angle. One FCJ term is\nfreed; the other follows it by the project's constraint.",
"metadata": {}
},
{
"id": "28",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.784790Z",
"iopub.execute_input": "2026-11-12T16:09:37.784939Z",
"shell.execute_reply": "2026-11-12T16:09:37.788046Z",
"iopub.status.idle": "2026-11-12T16:09:37.788386Z"
}
},
"execution_count": 19,
"source": "experiment.peak.asym_fcj_1.free = True",
"outputs": []
},
{
"id": "29",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:37.789328Z",
"iopub.execute_input": "2026-11-12T16:09:37.789439Z",
"iopub.status.idle": "2026-11-12T16:09:38.158135Z",
"shell.execute_reply": "2026-11-12T16:09:38.157703Z"
}
},
"execution_count": 20,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: project pd-neut-cwl_cosio-d20_2k, 1438 pts fitted / 1506 loaded, 47 free\n iter time (s) Rwp (%) reduced χ² change\n 5.58 8.87\n 1 0.185 5.51 8.62 2.8% ↓\n 2 0.191 5.44 8.41 2.4% ↓\n 3 0.197 5.36 8.16 3.0% ↓\n 4 0.202 5.21 7.71 5.5% ↓\n 5 0.208 5.06 7.28 5.6% ↓\n 6 0.214 4.74 6.39 12.1% ↓\n 7 0.220 4.72 6.33 1.0% ↓\n 8 0.226 4.70 6.27 1.0% ↓\n 9 0.234 4.69 6.26 0.1% ↓\n 10 0.241 4.69 6.26 \n 11 0.249 4.69 6.26 \n 12 0.257 4.69 6.26 \n 13 0.264 4.69 6.25 0.1% ↓\n 14 0.271 4.69 6.25 \n 15 0.279 4.69 6.25 \n 16 0.287 4.69 6.25 \n 17 0.295 4.69 6.25 \n 18 0.303 4.69 6.25 \n 19 0.311 4.69 6.25 \n 20 0.322 4.69 6.25 \n done · converged · 20 iters · reduced χ² 6.25 · Rwp 4.69 % · 0.33 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<142,630 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "30",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:38.159554Z",
"iopub.execute_input": "2026-11-12T16:09:38.159685Z",
"iopub.status.idle": "2026-11-12T16:09:38.185681Z",
"shell.execute_reply": "2026-11-12T16:09:38.185283Z"
}
},
"execution_count": 21,
"source": "project.display.pattern('d20')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<309,908 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "31",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:38.188552Z",
"iopub.execute_input": "2026-11-12T16:09:38.188679Z",
"iopub.status.idle": "2026-11-12T16:09:38.206354Z",
"shell.execute_reply": "2026-11-12T16:09:38.205991Z"
}
},
"execution_count": 22,
"source": "project.display.fit.correlations()",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<80,180 characters>, height=560)",
"text/html": ""
}
}
]
},
{
"id": "32",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:38.207432Z",
"iopub.execute_input": "2026-11-12T16:09:38.207560Z",
"iopub.status.idle": "2026-11-12T16:09:38.231956Z",
"shell.execute_reply": "2026-11-12T16:09:38.231589Z"
}
},
"execution_count": 23,
"source": "project.display.structure('cosio')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<340,630 characters>, height=660)",
"text/html": ""
}
}
]
},
{
"id": "33",
"cell_type": "markdown",
"source": "## Save the project",
"metadata": {}
},
{
"id": "34",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:09:38.235065Z",
"iopub.execute_input": "2026-11-12T16:09:38.235184Z",
"shell.execute_reply": "2026-11-12T16:09:38.400636Z",
"iopub.status.idle": "2026-11-12T16:09:38.401032Z"
}
},
"execution_count": 24,
"source": "project.save_as('pd-neut-cwl_cosio-d20_2k')\nproject.report.save_html('pd-neut-cwl_cosio-d20_2k.html')",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "Saving project to 'pd-neut-cwl_cosio-d20_2k'\nSaving report to 'pd-neut-cwl_cosio-d20_2k.html'\n"
}
]
}
]
}