{ "cells": [ { "cell_type": "markdown", "id": "04-00", "metadata": {}, "source": [ "# Peak shape and microstructure\n", "\n", "*Written by Claude Code, Anthropic's coding agent, for the rietx project.*\n", "\n", "A peak's width has two sources: the instrument, and the specimen's own small crystallites and strain.\n", "To measure the specimen you have to know the instrument first.\n", "We calibrate a synthetic instrument on a standard, save it, and use it to measure crystallite size and microstrain in a synthetic sample.\n", "Because both patterns are synthetic, we know the answers and can grade the fit.\n", "\n", "**You need** rietx 1.7 or later, which the next cell installs.\n", "Notebook 02 introduces plans and the parameter table.\n", "\n", "**Runtime** is under a minute on a laptop." ] }, { "cell_type": "code", "execution_count": null, "id": "04-01", "metadata": {}, "outputs": [], "source": [ "%pip install rietx" ] }, { "cell_type": "markdown", "id": "04-02", "metadata": {}, "source": [ "## How widths combine\n", "\n", "Each peak is a pseudo-Voigt: a Gaussian and a Lorentzian convolved.\n", "The two parts combine differently.\n", "Gaussian *variances* add, so the Gaussian width squared is\n", "\n", "$$\\Gamma_G^2 = (U + U_s)\\tan^2\\theta + V\\tan\\theta + W + P/\\cos^2\\theta$$\n", "\n", "Lorentzian *widths* add, so the Lorentzian width is\n", "\n", "$$\\Gamma_L = (X + X_s)/\\cos\\theta + (Y + Y_s)\\tan\\theta$$\n", "\n", "U, V, W, X and Y belong to the instrument.\n", "The specimen adds P and X_s, which go as 1/cos θ and carry crystallite size, and U_s and Y_s, which go as tan θ and carry microstrain.\n", "In rietx the specimen terms are each phase's `gauss_size`, `lor_size`, `gauss_strain` and `lor_strain`.\n", "\n", "The instrument and specimen terms have the same angular shapes.\n", "A fit on one pattern cannot tell them apart, so the instrument is measured separately, on a standard with no size or strain broadening of its own.\n", "\n", "## Two synthetic patterns\n", "\n", "The standard is LaB₆ and the sample is CeO₂.\n", "We write each structure as a short CIF." ] }, { "cell_type": "code", "execution_count": 1, "id": "04-03", "metadata": {}, "outputs": [], "source": [ "import tempfile\n", "from pathlib import Path\n", "\n", "import numpy as np\n", "\n", "import rietx as rx\n", "from rietx.model.profiles.caglioti import (\n", " size_coefficient_for_size,\n", " strain_coefficient_for_microstrain,\n", ")\n", "\n", "work = Path(tempfile.mkdtemp())\n", "\n", "\n", "def structure_from_rows(name, space_group, a, rows):\n", " \"\"\"A cubic structure from a few atom rows, by way of a CIF.\"\"\"\n", " cell = \"\".join(f\"_cell_length_{k} {a}\\n\" for k in \"abc\")\n", " cell += \"\".join(f\"_cell_angle_{k} 90\\n\" for k in (\"alpha\", \"beta\", \"gamma\"))\n", " atoms = \"\".join(\" \".join(map(str, row)) + \"\\n\" for row in rows)\n", " path = work / f\"{name}.cif\"\n", " path.write_text(\n", " f\"data_{name}\\n_space_group_name_H-M_alt '{space_group}'\\n{cell}\"\n", " \"loop_\\n_atom_site_label\\n_atom_site_type_symbol\\n_atom_site_fract_x\\n\"\n", " \"_atom_site_fract_y\\n_atom_site_fract_z\\n_atom_site_B_iso_or_equiv\\n\" + atoms,\n", " encoding=\"utf-8\")\n", " return rx.Structure.from_cif(path)\n", "\n", "\n", "lab6 = structure_from_rows(\"LaB6\", \"P m -3 m\", 4.15689,\n", " [(\"La1\", \"La\", 0, 0, 0, 0.25), (\"B1\", \"B\", 0.1996, 0.5, 0.5, 0.35)])\n", "ceo2 = structure_from_rows(\"CeO2\", \"F m -3 m\", 5.411,\n", " [(\"Ce1\", \"Ce\", 0, 0, 0, 0.3), (\"O1\", \"O\", 0.25, 0.25, 0.25, 0.6)])" ] }, { "cell_type": "markdown", "id": "04-04", "metadata": {}, "source": [ "Next, the true instrument and the true sample broadening.\n", "These numbers are the answers the fits should recover." ] }, { "cell_type": "code", "execution_count": 2, "id": "04-05", "metadata": {}, "outputs": [ { "data": { "image/png": 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