{ "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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" ], "text/plain": [ "<_NotebookFigure size 2280x1320 with 1 Axes>" ] }, "execution_count": 2, "metadata": { "image/png": { "width": 672 } }, "output_type": "execute_result" } ], "source": [ "TRUE_PROFILE = dict(u=0.004, v=-0.003, w=0.003, x=0.015, y=0.02) # deg² and deg, 2θ\n", "TRUE_ZERO = 0.02 # degrees 2θ\n", "TRUE_SIZE = 300.0 # Å, coherent domain size\n", "TRUE_STRAIN = 1.0e-3 # Δd/d\n", "\n", "instrument = rx.Instrument.bragg_brentano(radiation=\"CuKa\")\n", "for name, value in TRUE_PROFILE.items():\n", " getattr(instrument.profile, name).value = value\n", "instrument.zero_shift.value = TRUE_ZERO\n", "instrument.background = rx.BackgroundChebyshev.with_terms(1)\n", "instrument.background.coefficients[0].value = 150.0\n", "\n", "wavelength = instrument.source.lines[0].wavelength.value\n", "ceo2.phases[0].lor_size.value = size_coefficient_for_size(TRUE_SIZE, wavelength)\n", "ceo2.phases[0].lor_strain.value = strain_coefficient_for_microstrain(TRUE_STRAIN)\n", "\n", "two_theta = np.arange(15, 130, 0.015)\n", "rng = np.random.default_rng(0)\n", "\n", "\n", "def measure(structure, strongest_peak):\n", " \"\"\"Poisson counts from the true model, scaled so the strongest peak has the counts given.\"\"\"\n", " structure = structure.model_copy(deep=True)\n", " y = rx.Refinement(structure, instrument).predict(two_theta)\n", " structure.phases[0].scale.value *= strongest_peak / (y.max() - 150.0)\n", " y = rx.Refinement(structure, instrument).predict(two_theta)\n", " return rx.PatternData(two_theta=two_theta, intensity=rng.poisson(y).astype(float))\n", "\n", "\n", "standard_data = measure(lab6, 30000)\n", "sample_data = measure(ceo2, 20000)\n", "standard_data.plot(two_theta_range=(15, 70))" ] }, { "cell_type": "markdown", "id": "04-06", "metadata": {}, "source": [ "The sample's broadening is all Lorentzian, so the Gaussian specimen terms are truly zero.\n", "\n", "## Calibrate the instrument on the standard\n", "\n", "The `lab_calibrate` plan refines the instrument's widths and its position corrections.\n", "The standard's cell is certified, so we hold it.\n", "A held cell is what lets the fit separate the zero shift and displacement from the cell.\n", "We start from a default instrument, as you would with a real diffractometer." ] }, { "cell_type": "code", "execution_count": 3, "id": "04-07", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "converged\n", "instrument.profile.u 0.00396 +/- 0.00015 true 0.004\n", "instrument.profile.v -0.00299 +/- 0.00020 true -0.003\n", "instrument.profile.w 0.00301 +/- 0.00006 true 0.003\n", "instrument.profile.x 0.01480 +/- 0.00032 true 0.015\n", "instrument.profile.y 0.02045 +/- 0.00082 true 0.02\n", "instrument.zero_shift 0.01977 +/- 0.00081 true 0.02\n", "instrument.geometry.sample_displacement -0.00104 +/- 0.00197 true 0.0\n", "[warning] FLOOR_HIT: ['instrument.geometry.axial_hl']\n", "[warning] HIGH_CORRELATION: ['instrument.geometry.axial_sl', 'instrument.geometry.axial_hl']\n", "[warning] FLAT_DIRECTION: ['instrument.geometry.axial_sl', 'instrument.geometry.axial_hl']\n", "[warning] HIGH_CORRELATION: ['instrument.zero_shift', 'instrument.geometry.sample_displacement']\n" ] } ], "source": [ "start = rx.Instrument.bragg_brentano(radiation=\"CuKa\")\n", "start.background = rx.BackgroundChebyshev.with_terms(4)\n", "calibration = rx.Refinement(lab6.model_copy(deep=True), start)\n", "calibration.hold([\"phases.0.cell.*\"])\n", "calibrated = calibration.fit(standard_data, plan=\"lab_calibrate\")\n", "\n", "print(calibrated.status)\n", "truths = {f\"instrument.profile.{k}\": v for k, v in TRUE_PROFILE.items()}\n", "truths[\"instrument.zero_shift\"] = TRUE_ZERO\n", "truths[\"instrument.geometry.sample_displacement\"] = 0.0\n", "for path, true in truths.items():\n", " p = calibrated.parameter(path)\n", " print(f\"{path:40} {p.value:8.5f} +/- {p.stderr:.5f} true {true}\")\n", "for d in calibrated.diagnostics:\n", " print(f\"[{d.level}] {d.code}: {d.where}\")" ] }, { "cell_type": "markdown", "id": "04-08", "metadata": {}, "source": [ "Every term lands within about one esd of the truth.\n", "\n", "The diagnostics are about corrections the synthetic instrument does not have.\n", "Its axial divergence is zero, so the two axial terms sit at their bound and the data cannot separate them.\n", "The zero shift and the displacement still correlate strongly, even with the cell held.\n", "Both came back within an esd of the truth, and on real data you would read the displacement's esd before quoting it.\n", "\n", "Save the calibrated instrument.\n", "`load_instrument_profile` reads it back with every term held, ready for any sample measured on this instrument." ] }, { "cell_type": "code", "execution_count": 4, "id": "04-09", "metadata": {}, "outputs": [], "source": [ "profile_file = work / \"instrument.json\"\n", "rx.save_instrument_profile(calibration.instrument, profile_file)\n", "calibrated_instrument = rx.load_instrument_profile(profile_file)\n", "calibrated_instrument.background = rx.BackgroundChebyshev.with_terms(4)" ] }, { "cell_type": "markdown", "id": "04-10", "metadata": {}, "source": [ "## Measure the sample\n", "\n", "`lab_sample_refine` holds the instrument and refines the sample's own size and strain terms.\n", "We start the sample with no broadening, so the fit has to find it." ] }, { "cell_type": "code", "execution_count": 5, "id": "04-11", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "converged Rwp 0.0464\n", "phases.0.lor_size 298.9 +/- 2.2 Å\n", "phases.0.gauss_size unavailable (at_zero)\n", "phases.0.lor_strain 0.000966 +/- 4.2e-05\n", "phases.0.gauss_strain unavailable (at_zero)\n", "true: size 300 Å, strain 0.001\n" ] } ], "source": [ "def fresh_ceria():\n", " structure = ceo2.model_copy(deep=True)\n", " structure.phases[0].lor_size.value = 0.0\n", " structure.phases[0].lor_strain.value = 0.0\n", " return structure\n", "\n", "\n", "sample = rx.Refinement(fresh_ceria(), calibrated_instrument)\n", "result = sample.fit(sample_data, plan=\"lab_sample_refine\")\n", "\n", "\n", "def show_microstructure(result):\n", " block = result.microstructure[0]\n", " for term in block.terms:\n", " if term.unavailable:\n", " reading = f\"unavailable ({term.unavailable})\"\n", " elif term.kind == \"size\":\n", " reading = f\"{term.value:.4g} +/- {term.esd:.2g} Å\"\n", " else:\n", " reading = f\"{term.value:.3g} +/- {term.esd:.2g}\"\n", " print(f\"{term.path:22} {reading}\")\n", "\n", "\n", "print(result.status, f\"Rwp {result.statistics.rwp:.4f}\")\n", "show_microstructure(result)\n", "print(f\"true: size {TRUE_SIZE:.0f} Å, strain {TRUE_STRAIN}\")" ] }, { "cell_type": "markdown", "id": "04-12", "metadata": {}, "source": [ "The Lorentzian size and strain match the truth to within two esds.\n", "\n", "Read the Gaussian rows next.\n", "The fit drove both Gaussian terms onto their zero floor, and each row says so (`at_zero`).\n", "The synthetic specimen has no Gaussian broadening, so there is no Gaussian size or strain to quote.\n", "A Gaussian reading that does come back is quoted with its esd, and one whose esd dwarfs its value is not a measurement.\n", "\n", "Quote a size as an order of magnitude, with the Scherrer constant it was read with (0.9 here).\n", "The constant depends on crystallite shape, so the size is a coherent domain size and not a particle size.\n", "\n", "## The same sample without calibration\n", "\n", "Fit the sample again with the default instrument, as if we had skipped the standard." ] }, { "cell_type": "code", "execution_count": 6, "id": "04-13", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "converged Rwp 0.0464\n", "phases.0.lor_size 284.2 +/- 1.9 Å\n", "phases.0.gauss_size 2248 +/- 6.3e+02 Å\n", "phases.0.lor_strain 0.00115 +/- 4.2e-05\n", "phases.0.gauss_strain 6.87e-05 +/- 0.0019\n" ] } ], "source": [ "uncalibrated_instrument = rx.Instrument.bragg_brentano(radiation=\"CuKa\")\n", "uncalibrated_instrument.background = rx.BackgroundChebyshev.with_terms(4)\n", "uncalibrated = rx.Refinement(fresh_ceria(), uncalibrated_instrument).fit(\n", " sample_data, plan=\"lab_sample_refine\")\n", "\n", "print(uncalibrated.status, f\"Rwp {uncalibrated.statistics.rwp:.4f}\")\n", "show_microstructure(uncalibrated)" ] }, { "cell_type": "markdown", "id": "04-14", "metadata": {}, "source": [ "The fit converged to the same Rwp, so nothing in the agreement indices says anything is wrong.\n", "But the instrument's own width has gone into the sample terms.\n", "The Lorentzian size is too small, the strain is too large, and a Gaussian size appears that the sample does not have.\n", "Only the calibration separates the two.\n", "\n", "## The fit" ] }, { "cell_type": "code", "execution_count": 7, "id": "04-15", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ], "text/plain": [ "<_NotebookFigure size 2280x1320 with 1 Axes>" ] }, "execution_count": 7, "metadata": { "image/png": { "width": 693 } }, "output_type": "execute_result" } ], "source": [ "result.plot()" ] }, { "cell_type": "markdown", "id": "04-16", "metadata": {}, "source": [ "## Checking an agent's work\n", "\n", "When an agent reports a crystallite size or a strain, check these.\n", "The rules are in the rietx agent skill (`SKILL.md` §4b, the microstructure row).\n", "\n", "- **Was the instrument calibrated on a standard?** Without it, the size and strain absorb the instrument's broadening, and Rwp cannot show it. Ask which standard, and whether its cell was held.\n", "- **Every reading with its esd.** A reading whose esd is larger than its value was not measured.\n", "- **Do the Gaussian and Lorentzian readings agree?** When both are measured, `result.microstructure[0].size_agreement` compares them, and 1 means they agree.\n", "- **Is the size quoted as an order of magnitude, with its Scherrer constant?**\n", "- **Size and strain need a wide 2θ range** to be told apart, because 1/cos θ and tan θ look alike over a narrow one." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3" }, "rietx": { "version": "1.10.0.dev0" } }, "nbformat": 4, "nbformat_minor": 5 }