{
"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": "2026-11-12T16:10:26.880307Z",
"iopub.execute_input": "2026-11-12T16:10:26.880421Z",
"iopub.status.idle": "2026-11-12T16:10:26.883403Z",
"shell.execute_reply": "2026-11-12T16:10:26.883154Z"
}
},
"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": "# Ferrite and austenite on BEER",
"metadata": {}
},
{
"cell_type": "markdown",
"metadata": {},
"source": "![\"Fitting\"](\"data:image/svg+xml;base64,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\")
![\"Joint\"](\"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=\")
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![\"Bragg\"](\"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0NiIgaGVpZ2h0PSIyMiIgdmlld0JveD0iMCAwIDQ2IDIyIj48cmVjdCB3aWR0aD0iNDYiIGhlaWdodD0iMjIiIHJ4PSI0IiBmaWxsPSIjMDA4NGM3IiBmaWxsLW9wYWNpdHk9IjAuMTMiLz48dGV4dCB4PSI3IiB5PSIxNS4zIiBmb250LWZhbWlseT0iTm90byBTYW5zLCBTZWdvZSBVSSwgSGVsdmV0aWNhLCBBcmlhbCwgc2Fucy1zZXJpZiIgZm9udC1zaXplPSIxMiIgZmlsbD0iIzAwODRjNyI+QnJhZ2c8L3RleHQ+PC9zdmc+\")
![\"Crystal](\"data:image/svg+xml;base64,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\")
",
"id": "2"
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Calibrate the BEER instrument at ESS with two McStas-simulated banks of a ferrite and austenite\nduplex steel, fitted together: each bank has its own zero and resolution.\n\nThe project is the catalogue case `pd-neut-tof_ferrite-austenite-beer`, the one the command line\nand the app's Examples open. Austenite's displacement follows ferrite's, and each phase's scale\nin bank n2 follows bank s2, from the start.",
"id": "3"
},
{
"id": "4",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:26.884378Z",
"iopub.execute_input": "2026-11-12T16:10:26.884495Z",
"shell.execute_reply": "2026-11-12T16:10:26.893037Z",
"iopub.status.idle": "2026-11-12T16:10:26.893335Z"
}
},
"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": "2026-11-12T16:10:26.894301Z",
"iopub.execute_input": "2026-11-12T16:10:26.894410Z",
"iopub.status.idle": "2026-11-12T16:10:27.157833Z",
"shell.execute_reply": "2026-11-12T16:10:27.157464Z"
}
},
"execution_count": 3,
"source": "project_path = edi.download_data('pd-neut-tof_ferrite-austenite-beer', destination='data')\nproject = edi.Project.load(project_path)\nferrite = project.structures['ferrite']\naustenite = project.structures['austenite']\nbank_s2 = project.experiments['expt_s2']\nbank_n2 = project.experiments['expt_n2']\nproject.display.constraints()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "Data 'pd-neut-tof_ferrite-austenite-beer' is at data/pd-neut-tof_ferrite-austenite-beer-764611d2acc1/pd-neut-tof_ferrite-austenite-beer\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<85,205 characters>, height=348)",
"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": "2026-11-12T16:10:27.158990Z",
"iopub.execute_input": "2026-11-12T16:10:27.159117Z",
"shell.execute_reply": "2026-11-12T16:10:27.324842Z",
"iopub.status.idle": "2026-11-12T16:10:27.325324Z"
}
},
"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": "2026-11-12T16:10:27.326781Z",
"iopub.execute_input": "2026-11-12T16:10:27.326947Z",
"iopub.status.idle": "2026-11-12T16:10:27.377760Z",
"shell.execute_reply": "2026-11-12T16:10:27.377358Z"
}
},
"execution_count": 5,
"source": "project.display.pattern('expt_s2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<485,376 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "10",
"cell_type": "markdown",
"source": "## Perform the analysis\n\nThe cells stay fixed: this is a calibration, and the two phases are the standards.",
"metadata": {}
},
{
"id": "11",
"cell_type": "markdown",
"source": "### Scales and time-of-flight calibration\n\nBoth phases' scales and each bank's DIFC offset put the peaks in place and at the right height.",
"metadata": {}
},
{
"id": "12",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.382277Z",
"iopub.execute_input": "2026-11-12T16:10:27.382429Z",
"shell.execute_reply": "2026-11-12T16:10:27.394112Z",
"iopub.status.idle": "2026-11-12T16:10:27.394441Z"
}
},
"execution_count": 6,
"source": "bank_s2.linked_structures['ferrite'].scale.free = True\nbank_s2.linked_structures['austenite'].scale.free = True\nbank_s2.instrument.calib_d_to_tof_offset.free = True\nbank_n2.instrument.calib_d_to_tof_offset.free = True",
"outputs": []
},
{
"id": "13",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.395562Z",
"iopub.execute_input": "2026-11-12T16:10:27.395693Z",
"iopub.status.idle": "2026-11-12T16:10:27.428232Z",
"shell.execute_reply": "2026-11-12T16:10:27.427802Z"
}
},
"execution_count": 7,
"source": "project.display.parameters.free()",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<86,632 characters>, height=208)",
"text/html": ""
}
}
]
},
{
"id": "14",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.429428Z",
"iopub.execute_input": "2026-11-12T16:10:27.429548Z",
"iopub.status.idle": "2026-11-12T16:10:27.510879Z",
"shell.execute_reply": "2026-11-12T16:10:27.510448Z"
}
},
"execution_count": 8,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 4 free\n iter time (s) Rwp (%) reduced χ² change\n 41.43 229.76\n 1 0.010 23.83 76.04 66.9% ↓\n 2 0.012 23.83 76.04 \n done · converged · 2 iters · reduced χ² 76.04 · Rwp 23.83 % · 0.01 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<91,077 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "15",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.512090Z",
"iopub.execute_input": "2026-11-12T16:10:27.512225Z",
"iopub.status.idle": "2026-11-12T16:10:27.561154Z",
"shell.execute_reply": "2026-11-12T16:10:27.560697Z"
}
},
"execution_count": 9,
"source": "project.display.pattern('expt_s2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<485,748 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "16",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.565329Z",
"iopub.execute_input": "2026-11-12T16:10:27.565480Z",
"iopub.status.idle": "2026-11-12T16:10:27.616102Z",
"shell.execute_reply": "2026-11-12T16:10:27.615569Z"
}
},
"execution_count": 10,
"source": "project.display.pattern('expt_n2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<486,125 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "17",
"cell_type": "markdown",
"source": "### Background\n\nEach bank's background points; the last, past the end of the data, stays fixed.",
"metadata": {}
},
{
"id": "18",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.620218Z",
"iopub.execute_input": "2026-11-12T16:10:27.620348Z",
"shell.execute_reply": "2026-11-12T16:10:27.768634Z",
"iopub.status.idle": "2026-11-12T16:10:27.768994Z"
}
},
"execution_count": 11,
"source": "for point in bank_s2.background:\n point.intensity.free = True\nfor point in bank_n2.background:\n point.intensity.free = True\nbank_s2.background[30].intensity.free = False\nbank_n2.background[30].intensity.free = False",
"outputs": []
},
{
"id": "19",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.770434Z",
"iopub.execute_input": "2026-11-12T16:10:27.770587Z",
"shell.execute_reply": "2026-11-12T16:10:27.967592Z",
"iopub.status.idle": "2026-11-12T16:10:27.967964Z"
}
},
"execution_count": 12,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 64 free\n iter time (s) Rwp (%) reduced χ² change\n 23.83 76.86\n 1 0.107 18.05 44.10 42.6% ↓\n done · converged · 1 iters · reduced χ² 44.10 · Rwp 18.05 % · 0.12 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<174,472 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "20",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:27.969057Z",
"iopub.execute_input": "2026-11-12T16:10:27.969174Z",
"iopub.status.idle": "2026-11-12T16:10:28.022005Z",
"shell.execute_reply": "2026-11-12T16:10:28.021509Z"
}
},
"execution_count": 13,
"source": "project.display.pattern('expt_s2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<548,453 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "21",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.027481Z",
"iopub.execute_input": "2026-11-12T16:10:28.027620Z",
"iopub.status.idle": "2026-11-12T16:10:28.081231Z",
"shell.execute_reply": "2026-11-12T16:10:28.080777Z"
}
},
"execution_count": 14,
"source": "project.display.pattern('expt_n2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<547,832 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "22",
"cell_type": "markdown",
"source": "### Peak widths\n\nEach bank's widths.",
"metadata": {}
},
{
"id": "23",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.085844Z",
"iopub.execute_input": "2026-11-12T16:10:28.085988Z",
"iopub.status.idle": "2026-11-12T16:10:28.109525Z",
"shell.execute_reply": "2026-11-12T16:10:28.109118Z"
}
},
"execution_count": 15,
"source": "bank_s2.peak.broad_gauss_sigma_0.free = True\nbank_s2.peak.broad_gauss_sigma_1.free = True\nbank_s2.peak.broad_gauss_sigma_2.free = True\nbank_s2.peak.broad_lorentz_gamma_0.free = True\nbank_n2.peak.broad_gauss_sigma_0.free = True\nbank_n2.peak.broad_gauss_sigma_1.free = True\nbank_n2.peak.broad_gauss_sigma_2.free = True\nbank_n2.peak.broad_lorentz_gamma_0.free = True",
"outputs": []
},
{
"id": "24",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.110697Z",
"iopub.execute_input": "2026-11-12T16:10:28.110842Z",
"iopub.status.idle": "2026-11-12T16:10:28.326034Z",
"shell.execute_reply": "2026-11-12T16:10:28.325589Z"
}
},
"execution_count": 16,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 72 free\n iter time (s) Rwp (%) reduced χ² change\n 18.05 44.16\n 1 0.120 16.38 36.35 17.7% ↓\n done · converged · 1 iters · reduced χ² 36.35 · Rwp 16.38 % · 0.13 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<185,924 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "25",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.328074Z",
"iopub.execute_input": "2026-11-12T16:10:28.328198Z",
"iopub.status.idle": "2026-11-12T16:10:28.380640Z",
"shell.execute_reply": "2026-11-12T16:10:28.380208Z"
}
},
"execution_count": 17,
"source": "project.display.pattern('expt_s2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<548,203 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "26",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.385686Z",
"iopub.execute_input": "2026-11-12T16:10:28.385846Z",
"iopub.status.idle": "2026-11-12T16:10:28.439839Z",
"shell.execute_reply": "2026-11-12T16:10:28.439422Z"
}
},
"execution_count": 18,
"source": "project.display.pattern('expt_n2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<548,113 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "27",
"cell_type": "markdown",
"source": "### Displacement\n\nLast, ferrite's displacement; austenite's follows it.",
"metadata": {}
},
{
"id": "28",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.445199Z",
"iopub.execute_input": "2026-11-12T16:10:28.445341Z",
"shell.execute_reply": "2026-11-12T16:10:28.450350Z",
"iopub.status.idle": "2026-11-12T16:10:28.450707Z"
}
},
"execution_count": 19,
"source": "ferrite.atom_sites['Fe'].adp_iso.free = True",
"outputs": []
},
{
"id": "29",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.451676Z",
"iopub.execute_input": "2026-11-12T16:10:28.451790Z",
"iopub.status.idle": "2026-11-12T16:10:28.681630Z",
"shell.execute_reply": "2026-11-12T16:10:28.681249Z"
}
},
"execution_count": 20,
"source": "project.analysis.fit()\nproject.display.fit.results()",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "edi fit: joint project pd-neut-tof_ferrite-austenite-beer, 2 banks (expt_n2, expt_s2), 5642 pts fitted / 5998 loaded, 73 free\n iter time (s) Rwp (%) reduced χ² change\n 16.38 36.36\n 1 0.088 7.13 6.89 81.0% ↓\n 2 0.134 7.13 6.89 \n done · converged · 2 iters · reduced χ² 6.89 · Rwp 7.13 % · 0.15 s\n"
},
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<187,241 characters>, height=376)",
"text/html": ""
}
}
]
},
{
"id": "30",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.683929Z",
"iopub.execute_input": "2026-11-12T16:10:28.684060Z",
"iopub.status.idle": "2026-11-12T16:10:28.737827Z",
"shell.execute_reply": "2026-11-12T16:10:28.737377Z"
}
},
"execution_count": 21,
"source": "project.display.pattern('expt_s2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<548,533 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "31",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.742841Z",
"iopub.execute_input": "2026-11-12T16:10:28.742972Z",
"iopub.status.idle": "2026-11-12T16:10:28.796636Z",
"shell.execute_reply": "2026-11-12T16:10:28.796255Z"
}
},
"execution_count": 22,
"source": "project.display.pattern('expt_n2')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<548,330 characters>, height=480)",
"text/html": ""
}
}
]
},
{
"id": "32",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.802246Z",
"iopub.execute_input": "2026-11-12T16:10:28.802387Z",
"iopub.status.idle": "2026-11-12T16:10:28.839914Z",
"shell.execute_reply": "2026-11-12T16:10:28.839523Z"
}
},
"execution_count": 23,
"source": "project.display.fit.correlations()",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<85,959 characters>, height=560)",
"text/html": ""
}
}
]
},
{
"id": "33",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.841351Z",
"iopub.execute_input": "2026-11-12T16:10:28.841478Z",
"iopub.status.idle": "2026-11-12T16:10:28.881436Z",
"shell.execute_reply": "2026-11-12T16:10:28.881054Z"
}
},
"execution_count": 24,
"source": "project.display.structure('ferrite')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<153,756 characters>, height=660)",
"text/html": ""
}
}
]
},
{
"id": "34",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.882547Z",
"iopub.execute_input": "2026-11-12T16:10:28.882667Z",
"iopub.status.idle": "2026-11-12T16:10:28.922599Z",
"shell.execute_reply": "2026-11-12T16:10:28.922176Z"
}
},
"execution_count": 25,
"source": "project.display.structure('austenite')",
"outputs": [
{
"output_type": "display_data",
"metadata": {},
"data": {
"text/plain": "View(html=<208,387 characters>, height=660)",
"text/html": ""
}
}
]
},
{
"id": "35",
"cell_type": "markdown",
"source": "## Save the project",
"metadata": {}
},
{
"id": "36",
"cell_type": "code",
"metadata": {
"execution": {
"iopub.status.busy": "2026-11-12T16:10:28.924778Z",
"iopub.execute_input": "2026-11-12T16:10:28.924923Z",
"shell.execute_reply": "2026-11-12T16:10:29.399411Z",
"iopub.status.idle": "2026-11-12T16:10:29.399824Z"
}
},
"execution_count": 26,
"source": "project.save_as('pd-neut-tof_ferrite-austenite-beer')\nproject.report.save_html('pd-neut-tof_ferrite-austenite-beer.html')",
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "Saving project to 'pd-neut-tof_ferrite-austenite-beer'\nSaving report to 'pd-neut-tof_ferrite-austenite-beer.html'\n"
}
]
}
]
}