{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\chi$ parameters\n",
    "\n",
    "$\\chi$ parameters introduced by [Ackland and Jones](http://pyscal.com/en/latest/methods/angularmethods/chiparams.html) measures the angles generated by pairs of neighbor atom around the host atom, and assigns it to a histogram to calculate a local structure. In this example, we will create different crystal structures and see how the $\\chi$ parameters change with respect to the local coordination."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyscal.core as pc\n",
    "import pyscal.crystal_structures as pcs\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The :mod:`~pyscal.crystal_structures` module is used to create different perfect crystal structures. The created atoms and simulation box is then assigned to a :class:`~pyscal.core.System` object. For this example, fcc, bcc, hcp and diamond structures are created."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "fcc_atoms, fcc_box = pcs.make_crystal('fcc', lattice_constant=4, repetitions=[4,4,4])\n",
    "fcc = pc.System()\n",
    "fcc.atoms = fcc_atoms\n",
    "fcc.box = fcc_box"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "bcc_atoms, bcc_box = pcs.make_crystal('bcc', lattice_constant=4, repetitions=[4,4,4])\n",
    "bcc = pc.System()\n",
    "bcc.atoms = bcc_atoms\n",
    "bcc.box = bcc_box"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "hcp_atoms, hcp_box = pcs.make_crystal('hcp', lattice_constant=4, repetitions=[4,4,4])\n",
    "hcp = pc.System()\n",
    "hcp.atoms = hcp_atoms\n",
    "hcp.box = hcp_box"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "dia_atoms, dia_box = pcs.make_crystal('diamond', lattice_constant=4, repetitions=[4,4,4])\n",
    "dia = pc.System()\n",
    "dia.atoms = dia_atoms\n",
    "dia.box = dia_box"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before calculating $\\chi$ parameters, the [neighbors for each atom](http://pyscal.com/en/latest/methods/nearestneighbormethods/nearestneighbormethods.html) need to be found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "fcc.find_neighbors(method='cutoff', cutoff='adaptive')\n",
    "bcc.find_neighbors(method='cutoff', cutoff='adaptive')\n",
    "hcp.find_neighbors(method='cutoff', cutoff='adaptive')\n",
    "dia.find_neighbors(method='cutoff', cutoff='adaptive')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, $\\chi$ parameters can be calculated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "fcc.calculate_chiparams()\n",
    "bcc.calculate_chiparams()\n",
    "hcp.calculate_chiparams()\n",
    "dia.calculate_chiparams()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The calculated parameters for each atom can be accessed using the :attr:`~pyscal.catom.Atom.chiparams` attribute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "fcc_atoms = fcc.atoms\n",
    "bcc_atoms = bcc.atoms\n",
    "hcp_atoms = hcp.atoms\n",
    "dia_atoms = dia.atoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 0, 0, 0, 24, 12, 0, 24, 0]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fcc_atoms[10].chiparams"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output is an array of length 9 which shows the number of neighbor angles found within specific bins as explained [here](http://pyscal.com/en/latest/methods/angularmethods/chiparams.html). The output for one atom from each structure is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f2f4f408650>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(np.array(range(9))-0.3, fcc_atoms[10].chiparams, width=0.2, label=\"fcc\")\n",
    "plt.bar(np.array(range(9))-0.1, bcc_atoms[10].chiparams, width=0.2, label=\"bcc\")\n",
    "plt.bar(np.array(range(9))+0.1, hcp_atoms[10].chiparams, width=0.2, label=\"hcp\")\n",
    "plt.bar(np.array(range(9))+0.3, dia_atoms[10].chiparams, width=0.2, label=\"diamond\")\n",
    "plt.xlabel(\"$\\chi$\")\n",
    "plt.ylabel(\"Number of angles\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The atoms exhibit a distinct fingerprint for each structure. Structural identification can be made up comparing the ratio of various $\\chi$ parameters as described in the [original publication](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.73.054104)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "base"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}