{
 "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 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.box = fcc_box\n",
    "fcc.atoms = fcc_atoms"
   ]
  },
  {
   "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.box = bcc_box\n",
    "bcc.atoms = bcc_atoms"
   ]
  },
  {
   "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.box = hcp_box\n",
    "hcp.atoms = hcp_atoms"
   ]
  },
  {
   "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.box = dia_box\n",
    "dia.atoms = dia_atoms"
   ]
  },
  {
   "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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f0f5a783b20>"
      ]
     },
     "execution_count": 10,
     "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": "pyscal-test",
   "language": "python",
   "name": "pyscal-test"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}