{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Calculating bond orientational order parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example illustrates the calculation of bond orientational order parameters. Bond order parameters, $q_l$ and their averaged versions, $\\bar{q}_l$ are widely used to identify atoms belong to different crystal structures. In this example, we will consider bcc, fcc, and hcp, and calculate the $q_4$ and $q_6$ parameters and their averaged versions which are widely used in literature. More details can be found [here](https://pyscal.readthedocs.io/en/latest/steinhardtparameters.html). " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pyscal as pc\n", "import pyscal.crystal_structures as pcs\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we analyse MD configurations, first a set of perfect bcc, fcc and hcp structures and another set with thermal vibrations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Perfect structures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To create atoms and box for perfect structures, the :mod:~pyscal.crystal_structures module is used. The created atoms and boxes are then assigned to System objects." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "bcc_atoms, bcc_box = pcs.make_crystal('bcc', lattice_constant=3.147, repetitions=[4,4,4])\n", "bcc = pc.System()\n", "bcc.box = bcc_box\n", "bcc.atoms = bcc_atoms" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "fcc_atoms, fcc_box = pcs.make_crystal('fcc', lattice_constant=3.147, repetitions=[4,4,4])\n", "fcc = pc.System()\n", "fcc.box = fcc_box\n", "fcc.atoms = fcc_atoms" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "hcp_atoms, hcp_box = pcs.make_crystal('hcp', lattice_constant=3.147, repetitions=[4,4,4])\n", "hcp = pc.System()\n", "hcp.box = hcp_box\n", "hcp.atoms = hcp_atoms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next step is calculation of nearest neighbors. There are two ways to calculate neighbors, by using a cutoff distance or by using the voronoi cells. In this example, we will use the cutoff method and provide a cutoff distance for each structure." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Finding the cutoff distance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The cutoff distance is normally calculated in a such a way that the atoms within the first shell is incorporated in this distance. The :func:pyscal.core.System.calculate_rdf function can be used to find this cutoff distance." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "bccrdf = bcc.calculate_rdf()\n", "fccrdf = fcc.calculate_rdf()\n", "hcprdf = hcp.calculate_rdf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the calculated rdf is plotted" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "