{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "0", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:53.417706Z", "iopub.status.busy": "2026-04-14T15:03:53.417489Z", "iopub.status.idle": "2026-04-14T15:03:53.421951Z", "shell.execute_reply": "2026-04-14T15:03:53.421136Z" }, "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": [ "# Structure Refinement: LBCO, HRPT\n", "\n", "This minimalistic example is designed to show how Rietveld refinement\n", "can be performed when both the crystal structure and experiment are\n", "defined directly in code. Only the experimentally measured data is\n", "loaded from an external file.\n", "\n", "For this example, constant-wavelength neutron powder diffraction data\n", "for La0.5Ba0.5CoO3 from HRPT at PSI is used.\n", "\n", "It does not contain any advanced features or options, and includes no\n", "comments or explanations — these can be found in the other tutorials.\n", "Default values are used for all parameters if not specified. Only\n", "essential and self-explanatory code is provided.\n", "\n", "The example is intended for users who are already familiar with the\n", "EasyDiffraction library and want to quickly get started with a simple\n", "refinement. It is also useful for those who want to see what a\n", "refinement might look like in code. For a more detailed explanation of\n", "the code, please refer to the other tutorials." ] }, { "cell_type": "markdown", "id": "2", "metadata": {}, "source": [ "## Import Library" ] }, { "cell_type": "code", "execution_count": 2, "id": "3", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:53.423690Z", "iopub.status.busy": "2026-04-14T15:03:53.423520Z", "iopub.status.idle": "2026-04-14T15:03:56.024098Z", "shell.execute_reply": "2026-04-14T15:03:56.023142Z" } }, "outputs": [], "source": [ "import easydiffraction as ed" ] }, { "cell_type": "markdown", "id": "4", "metadata": {}, "source": [ "## Step 1: Define Project" ] }, { "cell_type": "code", "execution_count": 3, "id": "5", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.025901Z", "iopub.status.busy": "2026-04-14T15:03:56.025579Z", "iopub.status.idle": "2026-04-14T15:03:56.549227Z", "shell.execute_reply": "2026-04-14T15:03:56.548415Z" } }, "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": [ "## Step 2: Define Structure" ] }, { "cell_type": "code", "execution_count": 4, "id": "7", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.551388Z", "iopub.status.busy": "2026-04-14T15:03:56.551208Z", "iopub.status.idle": "2026-04-14T15:03:56.554915Z", "shell.execute_reply": "2026-04-14T15:03:56.554129Z" } }, "outputs": [], "source": [ "project.structures.create(name='lbco')" ] }, { "cell_type": "code", "execution_count": 5, "id": "8", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.556678Z", "iopub.status.busy": "2026-04-14T15:03:56.556524Z", "iopub.status.idle": "2026-04-14T15:03:56.559770Z", "shell.execute_reply": "2026-04-14T15:03:56.559081Z" } }, "outputs": [], "source": [ "structure = project.structures['lbco']" ] }, { "cell_type": "code", "execution_count": 6, "id": "9", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.561554Z", "iopub.status.busy": "2026-04-14T15:03:56.561373Z", "iopub.status.idle": "2026-04-14T15:03:56.565923Z", "shell.execute_reply": "2026-04-14T15:03:56.564647Z" } }, "outputs": [], "source": [ "structure.space_group.name_h_m = 'P m -3 m'\n", "structure.space_group.it_coordinate_system_code = '1'" ] }, { "cell_type": "code", "execution_count": 7, "id": "10", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.567575Z", "iopub.status.busy": "2026-04-14T15:03:56.567391Z", "iopub.status.idle": "2026-04-14T15:03:56.570954Z", "shell.execute_reply": "2026-04-14T15:03:56.569868Z" } }, "outputs": [], "source": [ "structure.cell.length_a = 3.88" ] }, { "cell_type": "code", "execution_count": 8, "id": "11", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.572559Z", "iopub.status.busy": "2026-04-14T15:03:56.572395Z", "iopub.status.idle": "2026-04-14T15:03:56.579628Z", "shell.execute_reply": "2026-04-14T15:03:56.578830Z" } }, "outputs": [], "source": [ "structure.atom_sites.create(\n", " label='La',\n", " type_symbol='La',\n", " fract_x=0,\n", " fract_y=0,\n", " fract_z=0,\n", " wyckoff_letter='a',\n", " adp_iso=0.5,\n", " occupancy=0.5,\n", ")\n", "structure.atom_sites.create(\n", " label='Ba',\n", " type_symbol='Ba',\n", " fract_x=0,\n", " fract_y=0,\n", " fract_z=0,\n", " wyckoff_letter='a',\n", " adp_iso=0.5,\n", " occupancy=0.5,\n", ")\n", "structure.atom_sites.create(\n", " label='Co',\n", " type_symbol='Co',\n", " fract_x=0.5,\n", " fract_y=0.5,\n", " fract_z=0.5,\n", " wyckoff_letter='b',\n", " adp_iso=0.5,\n", ")\n", "structure.atom_sites.create(\n", " label='O',\n", " type_symbol='O',\n", " fract_x=0,\n", " fract_y=0.5,\n", " fract_z=0.5,\n", " wyckoff_letter='c',\n", " adp_iso=0.5,\n", ")" ] }, { "cell_type": "markdown", "id": "12", "metadata": {}, "source": [ "## Step 3: Define Experiment" ] }, { "cell_type": "code", "execution_count": 9, "id": "13", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.581438Z", "iopub.status.busy": "2026-04-14T15:03:56.581276Z", "iopub.status.idle": "2026-04-14T15:03:56.592431Z", "shell.execute_reply": "2026-04-14T15:03:56.591505Z" } }, "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;36m3\u001b[0m: La0.5Ba0.5CoO3, HRPT \u001b[1m(\u001b[0mPSI\u001b[1m)\u001b[0m, \u001b[1;36m300\u001b[0m K\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "✅ Data #\u001b[1;36m3\u001b[0m already present at \u001b[32m'data/ed-3.xye'\u001b[0m. Keeping existing file.\n" ] } ], "source": [ "data_path = ed.download_data(id=3, destination='data')" ] }, { "cell_type": "code", "execution_count": 10, "id": "14", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.594022Z", "iopub.status.busy": "2026-04-14T15:03:56.593839Z", "iopub.status.idle": "2026-04-14T15:03:56.849134Z", "shell.execute_reply": "2026-04-14T15:03:56.848071Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mData loaded successfully\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Experiment 🔬 \u001b[32m'hrpt'\u001b[0m. Number of data points: \u001b[1;36m3098\u001b[0m.\n" ] } ], "source": [ "project.experiments.add_from_data_path(\n", " name='hrpt',\n", " data_path=data_path,\n", " sample_form='powder',\n", " beam_mode='constant wavelength',\n", " radiation_probe='neutron',\n", ")" ] }, { "cell_type": "code", "execution_count": 11, "id": "15", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.851448Z", "iopub.status.busy": "2026-04-14T15:03:56.851190Z", "iopub.status.idle": "2026-04-14T15:03:56.854276Z", "shell.execute_reply": "2026-04-14T15:03:56.853462Z" } }, "outputs": [], "source": [ "experiment = project.experiments['hrpt']" ] }, { "cell_type": "code", "execution_count": 12, "id": "16", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.856115Z", "iopub.status.busy": "2026-04-14T15:03:56.855942Z", "iopub.status.idle": "2026-04-14T15:03:56.858937Z", "shell.execute_reply": "2026-04-14T15:03:56.858233Z" } }, "outputs": [], "source": [ "experiment.instrument.setup_wavelength = 1.494\n", "experiment.instrument.calib_twotheta_offset = 0.6" ] }, { "cell_type": "code", "execution_count": 13, "id": "17", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.860912Z", "iopub.status.busy": "2026-04-14T15:03:56.860739Z", "iopub.status.idle": "2026-04-14T15:03:56.865188Z", "shell.execute_reply": "2026-04-14T15:03:56.864302Z" } }, "outputs": [], "source": [ "experiment.peak.broad_gauss_u = 0.1\n", "experiment.peak.broad_gauss_v = -0.1\n", "experiment.peak.broad_gauss_w = 0.1\n", "experiment.peak.broad_lorentz_y = 0.1" ] }, { "cell_type": "code", "execution_count": 14, "id": "18", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.866733Z", "iopub.status.busy": "2026-04-14T15:03:56.866563Z", "iopub.status.idle": "2026-04-14T15:03:56.871415Z", "shell.execute_reply": "2026-04-14T15:03:56.870455Z" } }, "outputs": [], "source": [ "experiment.background.create(id='1', x=10, y=170)\n", "experiment.background.create(id='2', x=30, y=170)\n", "experiment.background.create(id='3', x=50, y=170)\n", "experiment.background.create(id='4', x=110, y=170)\n", "experiment.background.create(id='5', x=165, y=170)" ] }, { "cell_type": "code", "execution_count": 15, "id": "19", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.873007Z", "iopub.status.busy": "2026-04-14T15:03:56.872851Z", "iopub.status.idle": "2026-04-14T15:03:56.876497Z", "shell.execute_reply": "2026-04-14T15:03:56.875476Z" } }, "outputs": [], "source": [ "experiment.excluded_regions.create(id='1', start=0, end=5)\n", "experiment.excluded_regions.create(id='2', start=165, end=180)" ] }, { "cell_type": "code", "execution_count": 16, "id": "20", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.878122Z", "iopub.status.busy": "2026-04-14T15:03:56.877906Z", "iopub.status.idle": "2026-04-14T15:03:56.881667Z", "shell.execute_reply": "2026-04-14T15:03:56.880716Z" } }, "outputs": [], "source": [ "experiment.linked_phases.create(id='lbco', scale=10.0)" ] }, { "cell_type": "markdown", "id": "21", "metadata": {}, "source": [ "## Step 4: Perform Analysis (no constraints)" ] }, { "cell_type": "code", "execution_count": 17, "id": "22", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.883290Z", "iopub.status.busy": "2026-04-14T15:03:56.883042Z", "iopub.status.idle": "2026-04-14T15:03:56.887560Z", "shell.execute_reply": "2026-04-14T15:03:56.886809Z" } }, "outputs": [], "source": [ "structure.cell.length_a.free = True\n", "\n", "structure.atom_sites['La'].adp_iso.free = True\n", "structure.atom_sites['Ba'].adp_iso.free = True\n", "structure.atom_sites['Co'].adp_iso.free = True\n", "structure.atom_sites['O'].adp_iso.free = True" ] }, { "cell_type": "code", "execution_count": 18, "id": "23", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.889525Z", "iopub.status.busy": "2026-04-14T15:03:56.889325Z", "iopub.status.idle": "2026-04-14T15:03:56.894926Z", "shell.execute_reply": "2026-04-14T15:03:56.893874Z" } }, "outputs": [], "source": [ "experiment.instrument.calib_twotheta_offset.free = True\n", "\n", "experiment.peak.broad_gauss_u.free = True\n", "experiment.peak.broad_gauss_v.free = True\n", "experiment.peak.broad_gauss_w.free = True\n", "experiment.peak.broad_lorentz_y.free = True\n", "\n", "experiment.background['1'].y.free = True\n", "experiment.background['2'].y.free = True\n", "experiment.background['3'].y.free = True\n", "experiment.background['4'].y.free = True\n", "experiment.background['5'].y.free = True\n", "\n", "experiment.linked_phases['lbco'].scale.free = True" ] }, { "cell_type": "code", "execution_count": 19, "id": "24", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:03:56.896486Z", "iopub.status.busy": "2026-04-14T15:03:56.896315Z", "iopub.status.idle": "2026-04-14T15:04:11.261171Z", "shell.execute_reply": "2026-04-14T15:04:11.260340Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mStandard fitting\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📋 Using experiment 🔬 \u001b[32m'hrpt'\u001b[0m for \u001b[32m'single'\u001b[0m fitting\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "🚀 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": [ "📈 Goodness-of-fit \u001b[1m(\u001b[0mreduced χ²\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", " \n", 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 iterationχ²improvement [%]
11165.02
22833.5879.7% ↓
34510.8267.8% ↓
4636.4940.0% ↓
5813.3548.4% ↓
6982.2433.1% ↓
71161.9114.7% ↓
81331.5021.3% ↓
91501.453.6% ↓
101671.347.8% ↓
111851.293.4% ↓
122761.29
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// 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", " (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", " (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", " (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", " (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", " (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", " (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", " (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", " (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", " (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", " (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", " (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": [ "🏆 Best goodness-of-fit \u001b[1m(\u001b[0mreduced χ²\u001b[1m)\u001b[0m is \u001b[1;36m1.29\u001b[0m at iteration \u001b[1;36m275\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "✅ Fitting complete.\n" ] } ], "source": [ "project.analysis.fit()" ] }, { "cell_type": "code", "execution_count": 20, "id": "25", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:04:11.262965Z", "iopub.status.busy": "2026-04-14T15:04:11.262776Z", "iopub.status.idle": "2026-04-14T15:04:11.798176Z", "shell.execute_reply": "2026-04-14T15:04:11.797402Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mFit results\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "✅ Success: \u001b[3;92mTrue\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "⏱️ Fitting time: \u001b[1;36m13.87\u001b[0m seconds\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 Goodness-of-fit \u001b[1m(\u001b[0mreduced χ²\u001b[1m)\u001b[0m: \u001b[1;36m1.29\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 R-factor \u001b[1m(\u001b[0mRf\u001b[1m)\u001b[0m: \u001b[1;36m5.63\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 R-factor squared \u001b[1m(\u001b[0mRf²\u001b[1m)\u001b[0m: \u001b[1;36m5.27\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 Weighted R-factor \u001b[1m(\u001b[0mwR\u001b[1m)\u001b[0m: \u001b[1;36m4.41\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📈 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 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) 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 datablockcategoryentryparameterstartfitteduncertaintyunitschange
1lbcocelllength_a3.88003.89090.0000Å0.28 % ↑
2lbcoatom_siteLaadp_iso0.50000.50523231.7297Ų1.04 % ↑
3lbcoatom_siteBaadp_iso0.50000.50495252.5594Ų0.97 % ↑
4lbcoatom_siteCoadp_iso0.50000.23700.0611Ų52.60 % ↓
5lbcoatom_siteOadp_iso0.50001.39350.0167Ų178.71 % ↑
6hrptlinked_phaseslbcoscale10.00009.13510.06428.65 % ↓
7hrptpeakbroad_gauss_u0.10000.08160.0031deg²18.43 % ↓
8hrptpeakbroad_gauss_v-0.1000-0.11590.0067deg²15.93 % ↑
9hrptpeakbroad_gauss_w0.10000.12040.0033deg²20.45 % ↑
10hrptpeakbroad_lorentz_y0.10000.08440.0021deg15.55 % ↓
11hrptinstrumenttwotheta_offset0.60000.62260.0010deg3.76 % ↑
12hrptbackground1y170.0000168.55851.36710.85 % ↓
13hrptbackground2y170.0000164.33570.99923.33 % ↓
14hrptbackground3y170.0000166.88810.73881.83 % ↓
15hrptbackground4y170.0000175.40060.65783.18 % ↑
16hrptbackground5y170.0000174.28130.91052.52 % ↑
\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "⚠️ \u001b[31mRed uncertainty:\u001b[0m exceeds the fitted value (consider adding constraints) \n" ] } ], "source": [ "project.analysis.display.fit_results()" ] }, { "cell_type": "code", "execution_count": 21, "id": "26", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:04:11.800057Z", "iopub.status.busy": "2026-04-14T15:04:11.799870Z", "iopub.status.idle": "2026-04-14T15:04:12.263137Z", "shell.execute_reply": "2026-04-14T15:04:12.262471Z" } }, "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" }, { "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": [ "
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.plotter.plot_param_correlations()" ] }, { "cell_type": "code", "execution_count": 22, "id": "27", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:04:12.265100Z", "iopub.status.busy": "2026-04-14T15:04:12.264917Z", "iopub.status.idle": "2026-04-14T15:04:12.296588Z", "shell.execute_reply": "2026-04-14T15:04:12.295793Z" } }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.plotter.plot_meas_vs_calc(expt_name='hrpt', show_residual=True)" ] }, { "cell_type": "markdown", "id": "28", "metadata": {}, "source": [ "## Step 5: Perform Analysis (with constraints)" ] }, { "cell_type": "code", "execution_count": 23, "id": "29", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:04:12.299491Z", "iopub.status.busy": "2026-04-14T15:04:12.299306Z", "iopub.status.idle": "2026-04-14T15:04:12.304206Z", "shell.execute_reply": "2026-04-14T15:04:12.303099Z" } }, "outputs": [], "source": [ "# As can be seen from the parameter-correlation plot, the isotropic\n", "# displacement parameters of La and Ba are highly correlated. Because\n", "# La and Ba share the same mixed-occupancy site, their contributions to\n", "# the neutron diffraction pattern are difficult to separate, especially\n", "# since their coherent scattering lengths are not very different.\n", "# Therefore, it is necessary to constrain them to be equal. First we\n", "# define aliases and then use them to create a constraint.\n", "project.analysis.aliases.create(\n", " label='biso_La',\n", " param=project.structures['lbco'].atom_sites['La'].adp_iso,\n", ")\n", "project.analysis.aliases.create(\n", " label='biso_Ba',\n", " param=project.structures['lbco'].atom_sites['Ba'].adp_iso,\n", ")\n", "project.analysis.constraints.create(expression='biso_Ba = biso_La')" ] }, { "cell_type": "code", "execution_count": 24, "id": "30", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:04:12.306159Z", "iopub.status.busy": "2026-04-14T15:04:12.305836Z", "iopub.status.idle": "2026-04-14T15:04:12.528015Z", "shell.execute_reply": "2026-04-14T15:04:12.526918Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mSupported types\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", " \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", "
 TypeDescription
1bumpsBumps library using the default Levenberg-Marquardt method
2bumps (amoeba)Bumps library with Nelder-Mead simplex method
3bumps (de)Bumps library with differential evolution method
4bumps (lm)Bumps library with Levenberg-Marquardt method
5dfolsDFO-LS library for derivative-free least-squares optimization
6lmfitLMFIT library using the default Levenberg-Marquardt least squares method
7lmfit (least_squares)LMFIT library with SciPy's trust region reflective algorithm
8lmfit (leastsq)LMFIT library with Levenberg-Marquardt least squares method
\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mCurrent minimizer\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "lmfit \u001b[1m(\u001b[0mleastsq\u001b[1m)\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mCurrent minimizer changed to\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "lmfit\n" ] } ], "source": [ "project.analysis.show_available_minimizers()\n", "project.analysis.show_current_minimizer()\n", "project.analysis.current_minimizer = 'lmfit'" ] }, { "cell_type": "code", "execution_count": 25, "id": "31", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:04:12.529756Z", "iopub.status.busy": "2026-04-14T15:04:12.529531Z", "iopub.status.idle": "2026-04-14T15:04:14.640136Z", "shell.execute_reply": "2026-04-14T15:04:14.639316Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mStandard fitting\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📋 Using experiment 🔬 \u001b[32m'hrpt'\u001b[0m for \u001b[32m'single'\u001b[0m fitting\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "🚀 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": [ "📈 Goodness-of-fit \u001b[1m(\u001b[0mreduced χ²\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", "
 iterationχ²improvement [%]
111.29
2361.29
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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": [ "🏆 Best goodness-of-fit \u001b[1m(\u001b[0mreduced χ²\u001b[1m)\u001b[0m is \u001b[1;36m1.29\u001b[0m at iteration \u001b[1;36m35\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "✅ Fitting complete.\n" ] } ], "source": [ "project.analysis.fit()" ] }, { "cell_type": "code", "execution_count": 26, "id": "32", "metadata": { "execution": { "iopub.execute_input": "2026-04-14T15:04:14.641748Z", "iopub.status.busy": "2026-04-14T15:04:14.641569Z", "iopub.status.idle": "2026-04-14T15:04:15.166284Z", "shell.execute_reply": "2026-04-14T15:04:15.165394Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;34mFit results\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "✅ Success: \u001b[3;92mTrue\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "⏱️ Fitting time: \u001b[1;36m1.66\u001b[0m seconds\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 Goodness-of-fit \u001b[1m(\u001b[0mreduced χ²\u001b[1m)\u001b[0m: \u001b[1;36m1.29\u001b[0m\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 R-factor \u001b[1m(\u001b[0mRf\u001b[1m)\u001b[0m: \u001b[1;36m5.63\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 R-factor squared \u001b[1m(\u001b[0mRf²\u001b[1m)\u001b[0m: \u001b[1;36m5.27\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📏 Weighted R-factor \u001b[1m(\u001b[0mwR\u001b[1m)\u001b[0m: \u001b[1;36m4.41\u001b[0m%\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "📈 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 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 = 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 datablockcategoryentryparameterstartfitteduncertaintyunitschange
1lbcocelllength_a3.89093.89090.0000Å0.00 % ↑
2lbcoatom_siteLaadp_iso0.50520.50510.0278Ų0.03 % ↓
3lbcoatom_siteCoadp_iso0.23700.23700.0564Ų0.00 % ↑
4lbcoatom_siteOadp_iso1.39351.39350.0160Ų0.00 % ↓
5hrptlinked_phaseslbcoscale9.13519.13510.05380.00 % ↓
6hrptpeakbroad_gauss_u0.08160.08160.0031deg²0.00 % ↑
7hrptpeakbroad_gauss_v-0.1159-0.11590.0066deg²0.00 % ↑
8hrptpeakbroad_gauss_w0.12040.12040.0032deg²0.00 % ↑
9hrptpeakbroad_lorentz_y0.08440.08440.0021deg0.00 % ↓
10hrptinstrumenttwotheta_offset0.62260.62260.0010deg0.00 % ↑
11hrptbackground1y168.5585168.55851.36690.00 % ↓
12hrptbackground2y164.3357164.33570.99900.00 % ↑
13hrptbackground3y166.8881166.88810.73860.00 % ↑
14hrptbackground4y175.4006175.40060.64880.00 % ↑
15hrptbackground5y174.2813174.28130.89440.00 % ↓
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