{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# freud.diffraction.StaticStructureFactorDirect and freud.diffraction.StaticStructureFactorDebye\n", "\n", "The `freud.diffraction` module provides two methods for calculating a one-dimensional [static structure factor](https://en.wikipedia.org/wiki/Structure_factor) $S(k)$ which can be used to characterize structure of crystals, liquids or amorphous phases.\n", "\n", "The `freud.diffraction.StaticStructureFactorDirect` class implements a \"direct\" $S(k)$ method. First, the following expression is computed over a $k$-space (reciprocal space) grid:\n", "\n", "$$S(\\vec{k}) = {\\frac{1}{N}}\\sum_{i=1}^{N}\\sum_{j=1}^{N}\\mathrm{e}^{-i\\vec{k}\\cdot(\\vec{r}_{i} - \\vec{r}_{j})}$$\n", "\n", "Then, the angular dependence is integrated out, resulting in $S(|\\vec{k}|)$, otherwise denoted $S(k)$. For an excellent introduction to the theory of scattering and $S(k)$, please refer to the documentation of the [dynasor package](https://dynasor.materialsmodeling.org/), which performs a number of calculations related to scattering. The **freud** library implements the core method of static structure factor calculation based on the dynasor package, with some additional performance optimizations in parallelized C++ code, as well as an interface to compute $S(k)$ that aligns with the APIs and conventions of the **freud** library.\n", "\n", "The `freud.diffraction.StaticStructureFactorDebye` class computes static structure factor based on the Debye scattering equation:\n", "\n", "$$ S(k) = {\\frac{1}{N}} \\sum_{i=1}^{N}\\sum_{j=1}^{N}{\\frac{\\sin(kr_{ij})}{kr_{ij}}} $$\n", "\n", "which is obtained by integrating out the angular dependence from the original formula. This implementation provides a much faster algorithm, but gives worse results than the \"direct\" method at low $k$ values.\n", "\n", "Note that freud employs the usual physics convention, as opposed to the crystallographic convention, with the following expression linking the two: $k = 2\\pi q$. The static structure factor is related to the radial distribution function, $g(r)$, by a Fourier Transform:\n", "\n", "$$S(k) = 1 + \\rho \\int_{V}\\mathrm{d}\\vec{r}e^{-i\\vec{k}\\cdot\\vec{r}}g(r). $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lennard-Jones Liquid Example\n", "\n", "One of the use cases for $S(k)$ is to characterize structure of liquids. The example shown here uses data generated by a HOOMD-blue simulation of a 1000 particle system subject to the Lennard-Jones potential. See the HOOMD-blue [documentation](https://hoomd-blue.readthedocs.io/en/latest/) and [examples](https://github.com/glotzerlab/hoomd-examples) for more information." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import freud\n", "import gsd.hoomd\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "bins = 100\n", "k_max = 30\n", "k_min = 3\n", "sfDirect = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfDebye = freud.diffraction.StaticStructureFactorDebye(\n", " num_k_values=bins, k_max=k_max, k_min=k_min\n", ")\n", "\n", "with gsd.hoomd.open(\"data/LJsampletraj.gsd\", \"r\") as traj:\n", " for frame in traj:\n", " sfDebye.compute(frame, reset=False)\n", " sfDirect.compute(frame, reset=False)\n", "\n", "plt.plot(sfDebye.k_values, sfDebye.S_k, label=\"Debye\")\n", "plt.plot(sfDirect.bin_centers, sfDirect.S_k, label=\"Direct\")\n", "plt.title(\"Static Structure Factor\")\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$S(k)$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Crystal Comparison Example\n", "\n", "The static structure factor $S(k)$ can also be used to characterize and compare crystal structures. In the below example we compare the computed static structure factors $S(k)$ of a face-centered cubic (fcc) crystal and simple cubic (sc) crystal." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sf = freud.diffraction.StaticStructureFactorDirect(bins=200, k_max=25, k_min=1)\n", "fcc_system = freud.data.UnitCell.fcc().generate_system(10, sigma_noise=0.10)\n", "sf.compute(fcc_system)\n", "plt.plot(sf.bin_centers, sf.S_k, label=\"fcc\")\n", "\n", "sc_system = freud.data.UnitCell.sc().generate_system(10, sigma_noise=0.10)\n", "sf.compute(sc_system)\n", "plt.plot(sf.bin_centers, sf.S_k, label=\"sc\")\n", "\n", "plt.title(\"Static Structure Factor\")\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$S(k)$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "tags": [] }, "source": [ "## Calculation of Partial Structure Factors\n", "\n", "Both methods support calculation of partial structure factors according to [Faber-Ziman decomposition](https://freud.readthedocs.io/en/latest/modules/diffraction.html#freud.diffraction.StaticStructureFactorDirect). In the conventions adopted in **freud**, the summation of partials reproduces the total scattering. In this example we load a simulation trajectory of $\\text{GeS}_2$ and calculate the Ge-Ge partial, the S-S partial and the mixed Ge-S partial (which is the same as S-Ge partial). The calculation of the partials requires the usage of `query_points` and `N_total` parameters for the compute method." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import freud\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# read in xyz file\n", "# read number of particles\n", "N_particles = int(np.genfromtxt(\"data/ges2.xyz\", max_rows=1, dtype=int))\n", "cleaned_data = []\n", "# remove lines that don't contain particle data\n", "with open(\"data/ges2.xyz\") as f:\n", " for line in f:\n", " if line[0] != \"\\n\" and line[0] != \" \":\n", " cleaned_data.append(line)\n", "\n", "positions = np.genfromtxt(cleaned_data)[:, 1:4].reshape(-1, N_particles, 3)\n", "particle_types = np.genfromtxt(cleaned_data, dtype=str)[:, 0].reshape(-1, N_particles)\n", "\n", "box = freud.Box.cube(19.21)\n", "\n", "# max_k_points is the number of k-points used in the calculation,\n", "# higher values give better S(k) but takes longer\n", "k_max = 15\n", "k_min = 1\n", "bins = 50\n", "sfGe_Ge = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfGe_S = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfS_S = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "sfTotal = freud.diffraction.StaticStructureFactorDirect(\n", " bins=bins, k_max=k_max, k_min=k_min\n", ")\n", "\n", "for frame_positions, frame_types in zip(positions, particle_types):\n", " Ge_positions = frame_positions[frame_types == \"Ge\"]\n", " S_positions = frame_positions[frame_types == \"S\"]\n", " sfGe_Ge.compute(\n", " (box, Ge_positions),\n", " query_points=Ge_positions,\n", " N_total=N_particles,\n", " reset=False,\n", " )\n", " sfGe_S.compute(\n", " (box, S_positions),\n", " query_points=Ge_positions,\n", " N_total=N_particles,\n", " reset=False,\n", " )\n", " sfS_S.compute(\n", " (box, S_positions),\n", " query_points=S_positions,\n", " N_total=N_particles,\n", " reset=False,\n", " )\n", " sfTotal.compute(\n", " (box, frame_positions),\n", " reset=False,\n", " )\n", "\n", "plt.plot(sfS_S.bin_centers, sfS_S.S_k, label=\"S-S partial\")\n", "plt.plot(sfGe_S.bin_centers, sfGe_S.S_k, label=\"Ge-S partial\")\n", "plt.plot(sfGe_Ge.bin_centers, sfGe_Ge.S_k, label=\"Ge-Ge partial\")\n", "\n", "# Note that the Ge-S partial must be included twice\n", "S_tot = sfS_S.S_k + 2 * sfGe_S.S_k + sfGe_Ge.S_k\n", "assert np.allclose(S_tot, sfTotal.S_k, atol=1e-5, rtol=1e-5)\n", "\n", "plt.plot(sfGe_Ge.bin_centers, S_tot, label=\"Total\")\n", "plt.title(\"Static Structure Factor\")\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$S(k)$\")\n", "plt.legend(loc=\"upper right\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To ensure that our computed partial structure factors are consistent with the overall normalization of the total structure factor, we can adopt an alternative normalization scheme. In this approach, each partial structure factor is reweighted so that, in the large‑𝑞 (high wavevector) limit, they all converge to unity—just like the total structure factor. This normalization is particularly useful when comparing simulation data with experimental results, as it guarantees that the asymptotic behavior of the partials is in line with the expected long‑𝑞 behavior." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now compute the mole fractions from the first frame\n", "x_Ge = np.sum(particle_types[0] == \"Ge\") / N_particles\n", "x_S = np.sum(particle_types[0] == \"S\") / N_particles\n", "\n", "# Normalize the partial S(k) so that it approaches 1.\n", "S_Ge_Ge_norm = sfGe_Ge.S_k / (x_Ge**2) + 1 - 1 / x_Ge\n", "S_S_S_norm = sfS_S.S_k / (x_S**2) + 1 - 1 / x_S\n", "S_Ge_S_norm = sfGe_S.S_k / (x_Ge * x_S) + 1\n", "\n", "# Plot the normalized S(k) partials\n", "plt.figure(figsize=(8, 6))\n", "plt.plot(sfS_S.bin_centers, S_S_S_norm, label=\"S-S partial (norm)\")\n", "plt.plot(sfGe_S.bin_centers, S_Ge_S_norm, label=\"Ge-S partial (norm)\")\n", "plt.plot(sfGe_Ge.bin_centers, S_Ge_Ge_norm, label=\"Ge-Ge partial (norm)\")\n", "plt.title(\"Normalized Static Structure Factor\")\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"Normalized $S(k)$\")\n", "plt.legend(loc=\"upper right\")\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "glotztools", "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", "version": "3.11.11" } }, "nbformat": 4, "nbformat_minor": 4 }