{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "0", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:14.682977Z", "iopub.status.busy": "2026-04-14T14:54:14.682778Z", "iopub.status.idle": "2026-04-14T14:54:14.688085Z", "shell.execute_reply": "2026-04-14T14:54:14.687049Z" }, "tags": [ "hide-in-docs" ] }, "outputs": [], "source": [ "# Check whether easydiffraction is installed; install it if needed.\n", "# Required for remote environments such as Google Colab.\n", "import importlib.util\n", "\n", "if importlib.util.find_spec('easydiffraction') is None:\n", " %pip install easydiffraction==0.13.1" ] }, { "cell_type": "markdown", "id": "1", "metadata": {}, "source": [ "# Pair Distribution Function: Si, NPD\n", "\n", "This example demonstrates a pair distribution function (PDF) analysis\n", "of Si, based on data collected from a time-of-flight neutron powder\n", "diffraction experiment at NOMAD at SNS." ] }, { "cell_type": "markdown", "id": "2", "metadata": {}, "source": [ "## Import Library" ] }, { "cell_type": "code", "execution_count": 2, "id": "3", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:14.689968Z", "iopub.status.busy": "2026-04-14T14:54:14.689731Z", "iopub.status.idle": "2026-04-14T14:54:17.271288Z", "shell.execute_reply": "2026-04-14T14:54:17.270302Z" } }, "outputs": [], "source": [ "import easydiffraction as ed" ] }, { "cell_type": "markdown", "id": "4", "metadata": {}, "source": [ "## Create Project" ] }, { "cell_type": "code", "execution_count": 3, "id": "5", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:17.273222Z", "iopub.status.busy": "2026-04-14T14:54:17.272863Z", "iopub.status.idle": "2026-04-14T14:54:18.210566Z", "shell.execute_reply": "2026-04-14T14:54:18.209656Z" } }, "outputs": [ { "data": { "application/javascript": [ "\n", " (function() {\n", " var isDark = false;\n", "\n", " // Check JupyterLab theme\n", " if (document.body.classList.contains('jp-mod-dark') || \n", " document.body.classList.contains('theme-dark') ||\n", " document.body.classList.contains('vscode-dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check theme attribute\n", " var themeAttr = document.body.getAttribute('data-jp-theme-name');\n", " if (themeAttr && themeAttr.includes('dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check computed background color\n", " var notebookEl = document.querySelector('.jp-Notebook') || \n", " document.querySelector('.notebook_app') ||\n", " document.body;\n", " if (notebookEl) {\n", " var bgColor = window.getComputedStyle(notebookEl).backgroundColor;\n", " var rgb = bgColor.match(/\\d+/g);\n", " if (rgb && rgb.length >= 3) {\n", " var brightness = (parseInt(rgb[0]) + parseInt(rgb[1]) + parseInt(rgb[2])) / 3;\n", " if (brightness < 128) {\n", " isDark = true;\n", " }\n", " }\n", " }\n", "\n", " // Store result\n", " if (typeof IPython !== 'undefined' && IPython.notebook && IPython.notebook.kernel) {\n", " IPython.notebook.kernel.execute('_jupyter_dark_detect_result = ' + isDark);\n", " }\n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " if (typeof IPython !== 'undefined' && IPython.notebook) {\n", " IPython.notebook.kernel.execute(\"_jupyter_dark_detect_result = \" + \n", " (document.body.classList.contains('theme-dark') || \n", " document.body.classList.contains('jp-mod-dark') ||\n", " (document.body.getAttribute('data-jp-theme-name') && \n", " document.body.getAttribute('data-jp-theme-name').includes('dark'))));\n", " }\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project = ed.Project()" ] }, { "cell_type": "markdown", "id": "6", "metadata": {}, "source": [ "## Set Plotting Engine" ] }, { "cell_type": "code", "execution_count": 4, "id": "7", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:18.213484Z", "iopub.status.busy": "2026-04-14T14:54:18.213237Z", "iopub.status.idle": "2026-04-14T14:54:18.515240Z", "shell.execute_reply": "2026-04-14T14:54:18.514433Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mSupported engines\u001b[0m\n" ] }, { "data": { "application/javascript": [ "\n", " (function() {\n", " var isDark = false;\n", "\n", " // Check JupyterLab theme\n", " if (document.body.classList.contains('jp-mod-dark') || \n", " document.body.classList.contains('theme-dark') ||\n", " document.body.classList.contains('vscode-dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check theme attribute\n", " var themeAttr = document.body.getAttribute('data-jp-theme-name');\n", " if (themeAttr && themeAttr.includes('dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check computed background color\n", " var notebookEl = document.querySelector('.jp-Notebook') || \n", " document.querySelector('.notebook_app') ||\n", " document.body;\n", " if (notebookEl) {\n", " var bgColor = window.getComputedStyle(notebookEl).backgroundColor;\n", " var rgb = bgColor.match(/\\d+/g);\n", " if (rgb && rgb.length >= 3) {\n", " var brightness = (parseInt(rgb[0]) + parseInt(rgb[1]) + parseInt(rgb[2])) / 3;\n", " if (brightness < 128) {\n", " isDark = true;\n", " }\n", " }\n", " }\n", "\n", " // Store result\n", " if (typeof IPython !== 'undefined' && IPython.notebook && IPython.notebook.kernel) {\n", " IPython.notebook.kernel.execute('_jupyter_dark_detect_result = ' + isDark);\n", " }\n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " if (typeof IPython !== 'undefined' && IPython.notebook) {\n", " IPython.notebook.kernel.execute(\"_jupyter_dark_detect_result = \" + \n", " (document.body.classList.contains('theme-dark') || \n", " document.body.classList.contains('jp-mod-dark') ||\n", " (document.body.getAttribute('data-jp-theme-name') && \n", " document.body.getAttribute('data-jp-theme-name').includes('dark'))));\n", " }\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
 EngineDescription
1asciichartpyConsole ASCII line charts
2plotlyInteractive browser-based graphing library
\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mCurrent engine\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[32m'plotly'\u001b[0m\n" ] } ], "source": [ "project.plotter.show_supported_engines()\n", "project.plotter.show_current_engine()" ] }, { "cell_type": "code", "execution_count": 5, "id": "8", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:18.516850Z", "iopub.status.busy": "2026-04-14T14:54:18.516666Z", "iopub.status.idle": "2026-04-14T14:54:18.519333Z", "shell.execute_reply": "2026-04-14T14:54:18.518637Z" } }, "outputs": [], "source": [ "# Set global plot range for plots\n", "project.plotter.x_max = 40" ] }, { "cell_type": "markdown", "id": "9", "metadata": {}, "source": [ "## Add Structure" ] }, { "cell_type": "code", "execution_count": 6, "id": "10", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:18.520986Z", "iopub.status.busy": "2026-04-14T14:54:18.520826Z", "iopub.status.idle": "2026-04-14T14:54:18.524750Z", "shell.execute_reply": "2026-04-14T14:54:18.524056Z" } }, "outputs": [], "source": [ "project.structures.create(name='si')" ] }, { "cell_type": "code", "execution_count": 7, "id": "11", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:18.526532Z", "iopub.status.busy": "2026-04-14T14:54:18.526349Z", "iopub.status.idle": "2026-04-14T14:54:18.531285Z", "shell.execute_reply": "2026-04-14T14:54:18.530423Z" } }, "outputs": [], "source": [ "structure = project.structures['si']\n", "structure.space_group.name_h_m.value = 'F d -3 m'\n", "structure.space_group.it_coordinate_system_code = '1'\n", "structure.cell.length_a = 5.43146\n", "structure.atom_sites.create(\n", " label='Si',\n", " type_symbol='Si',\n", " fract_x=0,\n", " fract_y=0,\n", " fract_z=0,\n", " wyckoff_letter='a',\n", " adp_iso=0.5,\n", ")" ] }, { "cell_type": "markdown", "id": "12", "metadata": {}, "source": [ "## Add Experiment" ] }, { "cell_type": "code", "execution_count": 8, "id": "13", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:18.532709Z", "iopub.status.busy": "2026-04-14T14:54:18.532545Z", "iopub.status.idle": "2026-04-14T14:54:18.802207Z", "shell.execute_reply": "2026-04-14T14:54:18.801012Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mGetting data\u001b[0m\u001b[1;34m...\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Data #\u001b[1;36m5\u001b[0m: NOM_9999_Si_640g_PAC_50_ff_ftfrgr_up-to-\u001b[1;36m50.\u001b[0mgr\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "โœ… Data #\u001b[1;36m5\u001b[0m downloaded to \u001b[32m'data/ed-5.gr'\u001b[0m\n" ] } ], "source": [ "data_path = ed.download_data(id=5, destination='data')" ] }, { "cell_type": "code", "execution_count": 9, "id": "14", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:18.804092Z", "iopub.status.busy": "2026-04-14T14:54:18.803865Z", "iopub.status.idle": "2026-04-14T14:54:19.110028Z", "shell.execute_reply": "2026-04-14T14:54:19.109117Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "โš ๏ธ No uncertainty (sy) column provided. Defaulting to 0.03. \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mData loaded successfully\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Experiment ๐Ÿ”ฌ \u001b[32m'nomad'\u001b[0m. Number of data points: \u001b[1;36m5033\u001b[0m.\n" ] } ], "source": [ "project.experiments.add_from_data_path(\n", " name='nomad',\n", " data_path=data_path,\n", " sample_form='powder',\n", " beam_mode='time-of-flight',\n", " radiation_probe='neutron',\n", " scattering_type='total',\n", ")" ] }, { "cell_type": "code", "execution_count": 10, "id": "15", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:19.111872Z", "iopub.status.busy": "2026-04-14T14:54:19.111629Z", "iopub.status.idle": "2026-04-14T14:54:19.117148Z", "shell.execute_reply": "2026-04-14T14:54:19.116318Z" } }, "outputs": [], "source": [ "experiment = project.experiments['nomad']\n", "experiment.linked_phases.create(id='si', scale=1.0)\n", "experiment.peak.damp_q = 0.02\n", "experiment.peak.broad_q = 0.03\n", "experiment.peak.cutoff_q = 35.0\n", "experiment.peak.sharp_delta_1 = 0.0\n", "experiment.peak.sharp_delta_2 = 4.0\n", "experiment.peak.damp_particle_diameter = 0" ] }, { "cell_type": "markdown", "id": "16", "metadata": {}, "source": [ "## Select Fitting Parameters" ] }, { "cell_type": "code", "execution_count": 11, "id": "17", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:19.118730Z", "iopub.status.busy": "2026-04-14T14:54:19.118564Z", "iopub.status.idle": "2026-04-14T14:54:19.122071Z", "shell.execute_reply": "2026-04-14T14:54:19.121120Z" } }, "outputs": [], "source": [ "project.structures['si'].cell.length_a.free = True\n", "project.structures['si'].atom_sites['Si'].adp_iso.free = True\n", "experiment.linked_phases['si'].scale.free = True" ] }, { "cell_type": "code", "execution_count": 12, "id": "18", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:19.123697Z", "iopub.status.busy": "2026-04-14T14:54:19.123528Z", "iopub.status.idle": "2026-04-14T14:54:19.126907Z", "shell.execute_reply": "2026-04-14T14:54:19.126109Z" } }, "outputs": [], "source": [ "experiment.peak.damp_q.free = True\n", "experiment.peak.broad_q.free = True\n", "experiment.peak.sharp_delta_1.free = True\n", "experiment.peak.sharp_delta_2.free = True" ] }, { "cell_type": "markdown", "id": "19", "metadata": {}, "source": [ "## Run Fitting" ] }, { "cell_type": "code", "execution_count": 13, "id": "20", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T14:54:19.128472Z", "iopub.status.busy": "2026-04-14T14:54:19.128308Z", "iopub.status.idle": "2026-04-14T14:54:37.014881Z", "shell.execute_reply": "2026-04-14T14:54:37.013959Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mStandard fitting\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ“‹ Using experiment ๐Ÿ”ฌ \u001b[32m'nomad'\u001b[0m for \u001b[32m'single'\u001b[0m fitting\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿš€ Starting fit process with \u001b[32m'lmfit \u001b[0m\u001b[32m(\u001b[0m\u001b[32mleastsq\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m\u001b[33m...\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ“ˆ Goodness-of-fit \u001b[1m(\u001b[0mreduced ฯ‡ยฒ\u001b[1m)\u001b[0m change:\n" ] }, { "data": { "text/html": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
 iterationฯ‡ยฒimprovement [%]
113102.63
2112177.5529.8% โ†“
319345.2884.1% โ†“
427180.2347.8% โ†“
535170.605.3% โ†“
668170.54
\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " (function() {\n", " var isDark = false;\n", "\n", " // Check JupyterLab theme\n", " if (document.body.classList.contains('jp-mod-dark') || \n", " document.body.classList.contains('theme-dark') ||\n", " document.body.classList.contains('vscode-dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check theme attribute\n", " var themeAttr = document.body.getAttribute('data-jp-theme-name');\n", " if (themeAttr && themeAttr.includes('dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check computed background color\n", " var notebookEl = document.querySelector('.jp-Notebook') || \n", " document.querySelector('.notebook_app') ||\n", " document.body;\n", " if (notebookEl) {\n", " var bgColor = window.getComputedStyle(notebookEl).backgroundColor;\n", " var rgb = bgColor.match(/\\d+/g);\n", " if (rgb && rgb.length >= 3) {\n", " var brightness = (parseInt(rgb[0]) + parseInt(rgb[1]) + parseInt(rgb[2])) / 3;\n", " if (brightness < 128) {\n", " isDark = true;\n", " }\n", " }\n", " }\n", "\n", " // Store result\n", " if (typeof IPython !== 'undefined' && IPython.notebook && IPython.notebook.kernel) {\n", " IPython.notebook.kernel.execute('_jupyter_dark_detect_result = ' + isDark);\n", " }\n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " if (typeof IPython !== 'undefined' && IPython.notebook) {\n", " IPython.notebook.kernel.execute(\"_jupyter_dark_detect_result = \" + \n", " (document.body.classList.contains('theme-dark') || \n", " document.body.classList.contains('jp-mod-dark') ||\n", " (document.body.getAttribute('data-jp-theme-name') && \n", " document.body.getAttribute('data-jp-theme-name').includes('dark'))));\n", " }\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " 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IPython.notebook.kernel.execute(\"_jupyter_dark_detect_result = \" + \n", " (document.body.classList.contains('theme-dark') || \n", " document.body.classList.contains('jp-mod-dark') ||\n", " (document.body.getAttribute('data-jp-theme-name') && \n", " document.body.getAttribute('data-jp-theme-name').includes('dark'))));\n", " }\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " (function() {\n", " var isDark = false;\n", "\n", " // Check JupyterLab theme\n", " if (document.body.classList.contains('jp-mod-dark') || \n", " document.body.classList.contains('theme-dark') ||\n", " document.body.classList.contains('vscode-dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check theme attribute\n", " var themeAttr = document.body.getAttribute('data-jp-theme-name');\n", " if (themeAttr && themeAttr.includes('dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check computed background color\n", " var notebookEl = document.querySelector('.jp-Notebook') || \n", " document.querySelector('.notebook_app') ||\n", " document.body;\n", " if (notebookEl) {\n", " var bgColor = window.getComputedStyle(notebookEl).backgroundColor;\n", " var rgb = bgColor.match(/\\d+/g);\n", " if (rgb && rgb.length >= 3) {\n", " var brightness = (parseInt(rgb[0]) + parseInt(rgb[1]) + parseInt(rgb[2])) / 3;\n", " if (brightness < 128) {\n", " isDark = true;\n", " }\n", " }\n", " }\n", "\n", " // Store result\n", " if (typeof IPython !== 'undefined' && IPython.notebook && IPython.notebook.kernel) {\n", " IPython.notebook.kernel.execute('_jupyter_dark_detect_result = ' + isDark);\n", " }\n", " })();\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", " if (typeof IPython !== 'undefined' && IPython.notebook) {\n", " IPython.notebook.kernel.execute(\"_jupyter_dark_detect_result = \" + \n", " (document.body.classList.contains('theme-dark') || \n", " document.body.classList.contains('jp-mod-dark') ||\n", " (document.body.getAttribute('data-jp-theme-name') && \n", " document.body.getAttribute('data-jp-theme-name').includes('dark'))));\n", " }\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ† Best goodness-of-fit \u001b[1m(\u001b[0mreduced ฯ‡ยฒ\u001b[1m)\u001b[0m is \u001b[1;36m170.54\u001b[0m at iteration \u001b[1;36m67\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "โœ… Fitting complete.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mFit results\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "โœ… Success: \u001b[3;92mTrue\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "โฑ๏ธ Fitting time: \u001b[1;36m16.48\u001b[0m seconds\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ“ Goodness-of-fit \u001b[1m(\u001b[0mreduced ฯ‡ยฒ\u001b[1m)\u001b[0m: \u001b[1;36m170.54\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ“ R-factor \u001b[1m(\u001b[0mRf\u001b[1m)\u001b[0m: \u001b[1;36m8.40\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ“ R-factor squared \u001b[1m(\u001b[0mRfยฒ\u001b[1m)\u001b[0m: \u001b[1;36m8.30\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ“ Weighted R-factor \u001b[1m(\u001b[0mwR\u001b[1m)\u001b[0m: \u001b[1;36m8.30\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "๐Ÿ“ˆ Fitted parameters:\n" ] }, { "data": { "application/javascript": [ "\n", " (function() {\n", " var isDark = false;\n", "\n", " // Check JupyterLab theme\n", " if (document.body.classList.contains('jp-mod-dark') || \n", " document.body.classList.contains('theme-dark') ||\n", " document.body.classList.contains('vscode-dark')) {\n", " isDark = true;\n", " }\n", "\n", " // Check theme 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 datablockcategoryentryparameterstartfitteduncertaintyunitschange
1sicelllength_a5.43155.43060.0000ร…0.02 % โ†“
2siatom_siteSiadp_iso0.50000.71700.0055ร…ยฒ43.40 % โ†‘
3nomadlinked_phasessiscale1.00001.27280.001427.28 % โ†‘
4nomadpeakdamp_q0.02000.02510.0001ร…โปยน25.66 % โ†‘
5nomadpeakbroad_q0.03000.01830.0003ร…โปยฒ39.10 % โ†“
6nomadpeaksharp_delta_10.00002.54000.0529ร…N/A
7nomadpeaksharp_delta_24.0000-1.75250.1244ร…ยฒ143.81 % โ†“
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