{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# freud.order.Steinhardt\n", "## Steinhardt Order Parameters\n", "The `freud.order` module provids the tools to calculate various [order parameters](https://en.wikipedia.org/wiki/Phase_transition#Order_parameters) that can be used to identify phase transitions.\n", "In the context of crystalline systems, some of the best known order parameters are the Steinhardt order parameters $q_l$ and $w_l$.\n", "These order parameters are mathematically defined according to certain rotationally invariant combinations of spherical harmonics calculated between particles and their nearest neighbors, so they provide information about local particle environments.\n", "As a result, considering distributions of these order parameters across a system can help characterize the overall system's ordering.\n", "The primary utility of these order parameters arises from the fact that they often exhibit certain characteristic values for specific crystal structures.\n", "\n", "In this notebook, we will use the order parameters to identify certain basic structures: BCC, FCC, and simple cubic.\n", "FCC, BCC, and simple cubic structures each exhibit characteristic values of $q_l$ for some $l$ value, meaning that in a perfect crystal all the particles in one of these structures will have the same value of $q_l$.\n", "As a result, we can use these characteristic $q_l$ values to determine whether a disordered fluid is beginning to crystallize into one structure or another.\n", "The $l$ values correspond to the $l$ quantum number used in defining the underlying spherical harmonics; for example, the $q_4$ order parameter would provide a measure of 4-fold ordering. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import freud\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "# Try to plot using KDE if available, otherwise revert to histogram\n", "try:\n", " from sklearn.neighbors.kde import KernelDensity\n", "\n", " kde = True\n", "except:\n", " kde = False\n", "\n", "np.random.seed(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first construct ideal crystals and then extract the characteristic value of $q_l$ for each of these structures.\n", "In this case, we know that simple cubic has a coordination number of 6, BCC has 8, and FCC has 12, so we are looking for the values of $q_6$, $q_8$, and $q_{12}$, respectively.\n", "Therefore, we can also enforce that we require 6, 8, and 12 nearest neighbors to be included in the calculation, respectively." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The Q6 values computed for simple cubic are 0.354 +/- 3.938e-08\n", "The Q8 values computed for bcc are 0.213 +/- 1.137e-12\n", "The Q12 values computed for fcc are 0.600 +/- 1.155e-12\n" ] } ], "source": [ "L = 6\n", "sc = freud.data.UnitCell.sc()\n", "sc_system = sc.generate_system(5)\n", "ql = freud.order.Steinhardt(L)\n", "ql_sc = ql.compute(sc_system, neighbors={\"num_neighbors\": L}).particle_order\n", "mean_sc = np.mean(ql_sc)\n", "print(\n", " \"The Q{} values computed for simple cubic are {:.3f} +/- {:.3e}\".format(\n", " L, mean_sc, np.std(ql_sc)\n", " )\n", ")\n", "\n", "L = 8\n", "bcc = freud.data.UnitCell.bcc()\n", "bcc_system = bcc.generate_system(5, sigma_noise=0)\n", "ql = freud.order.Steinhardt(L)\n", "ql.compute(bcc_system, neighbors={\"num_neighbors\": L})\n", "ql_bcc = ql.particle_order\n", "mean_bcc = np.mean(ql_bcc)\n", "print(\n", " \"The Q{} values computed for bcc are {:.3f} +/- {:.3e}\".format(\n", " L, mean_bcc, np.std(ql_bcc)\n", " )\n", ")\n", "\n", "L = 12\n", "fcc = freud.data.UnitCell.fcc()\n", "fcc_system = fcc.generate_system(5)\n", "ql = freud.order.Steinhardt(L)\n", "ql_fcc = ql.compute(fcc_system, neighbors={\"num_neighbors\": L}).particle_order\n", "mean_fcc = np.mean(ql_fcc)\n", "print(\n", " \"The Q{} values computed for fcc are {:.3f} +/- {:.3e}\".format(\n", " L, mean_fcc, np.std(ql_fcc)\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given that the per-particle order parameter values are essentially identical to within machine precision, we can be confident that we have found the characteristic value of $q_l$ for each of these systems.\n", "We can now compare these values to the values of $q_l$ in thermalized systems to determine the extent to which they are exhibiting the ordering expected of one of these perfect crystals." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def make_noisy_replicas(unitcell, sigmas):\n", " \"\"\"Given a unit cell, return a noisy system.\"\"\"\n", " systems = []\n", " for sigma in sigmas:\n", " systems.append(unitcell.generate_system(5, sigma_noise=sigma))\n", " return systems" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "sigmas = [0.01, 0.02, 0.03, 0.05]\n", "sc_systems = make_noisy_replicas(sc, sigmas)\n", "bcc_systems = make_noisy_replicas(bcc, sigmas)\n", "fcc_systems = make_noisy_replicas(fcc, sigmas)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(16, 5))\n", "\n", "# Zip up the data that will be needed for each structure type.\n", "zip_obj = zip(\n", " [sc_systems, bcc_systems, fcc_systems],\n", " [mean_sc, mean_bcc, mean_fcc],\n", " [6, 8, 12],\n", " [\"Simple Cubic\", \"BCC\", \"FCC\"],\n", ")\n", "\n", "for i, (systems, ref_val, L, title) in enumerate(zip_obj):\n", " ax = axes[i]\n", " for j, (system, sigma) in enumerate(zip(systems, sigmas)):\n", " ql = freud.order.Steinhardt(L)\n", " ql.compute(system, neighbors={\"num_neighbors\": L})\n", " if not kde:\n", " ax.hist(ql.particle_order, label=rf\"$\\sigma$ = {sigma}\", density=True)\n", " else:\n", " padding = 0.02\n", " N = 50\n", " bins = np.linspace(\n", " np.min(ql.particle_order) - padding,\n", " np.max(ql.particle_order) + padding,\n", " N,\n", " )\n", "\n", " kde = KernelDensity(bandwidth=0.004)\n", " kde.fit(ql.particle_order[:, np.newaxis])\n", " ql = np.exp(kde.score_samples(bins[:, np.newaxis]))\n", "\n", " ax.plot(bins, ql, label=rf\"$\\sigma$ = {sigma}\")\n", " ax.set_title(title, fontsize=20)\n", " ax.tick_params(axis=\"both\", which=\"both\", labelsize=14)\n", " if j == 0:\n", " # Can choose any element, all are identical in the reference case\n", " ax.vlines(ref_val, 0, np.max(ax.get_ylim()[1]), label=\"Reference\")\n", "fig.legend(*ax.get_legend_handles_labels(), fontsize=18) # Only have one legend\n", "fig.subplots_adjust(right=0.78)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From this figure, we can see that for each type of structure, increasing the amount of noise makes the distribution of the order parameter values less peaked at the expected reference value.\n", "As a result, we can use this method to identify specific structures.\n", "Choosing the appropriate parameterization for the order parameter (which quantum number $l$ to use, how to choose neighbors, etc.) can be very important." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to the $q_l$ parameters demonstrated here, this class can also compute the third-order invariant $w_l$.\n", "The $w_l$ may be better at identifying some structures, so some experimentation and reference to the appropriate literature can be useful (as a starting point, see [Steinhardt, Nelson, and Ronchetti (1983)](https://doi.org/10.1103/PhysRevB.28.784)).\n", "\n", "By setting `average=True` in the constructor, the `Steinhardt` class will perform an additional level of averaging over the second neighbor shells of particles, to accumulate more information on particle environments (see [Lechner and Dellago (2008)](https://doi.org/10.1063/1.2977970)).\n", "To get a sense for the best method for analyzing a specific system, the best course of action is try out different parameters or to consult the literature to see how these have been used in the past." ] } ], "metadata": { "anaconda-cloud": {}, "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", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }