{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cowley short range order parameter\n",
    "\n",
    "The [Cowley short range order parameter](https://doi.org/10.1103/PhysRev.77.669) can be used to find if an alloy is ordered or not. The order parameter is given by,\n",
    "\n",
    "$$\n",
    "\\alpha_i = 1 - \\frac{n_i}{m_A c_i}\n",
    "$$\n",
    "\n",
    "where $n_i$ is the number of atoms of the non reference type among the $c_i$ atoms\n",
    "in the $i$th shell. $m_A$ is the concentration of the non reference atom."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can start by importing the necessary modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyscal.core as pc\n",
    "import pyscal.crystal_structures as pcs\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need a binary alloy structure to calculate the order parameter. We will use the crystal structures modules to do this. Here, we will create a L12 structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "atoms, box = pcs.make_crystal('l12', lattice_constant=4.00, repetitions=[2,2,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to use the order parameter, we need to have two shells of neighbors around the atom. In order to get two shells of neighbors, we will first estimate a cutoff using the radial distribution function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "val, dist = sys.calculate_rdf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the rdf,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$g(r)$')"
      ]
     },
     "execution_count": 15,
     "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.plot(dist, val)\n",
    "plt.xlabel(r\"distance $\\AA$\")\n",
    "plt.ylabel(r\"$g(r)$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, a cutoff of about 4.5 will make sure that two shells are included. Now the neighbors are calculated using this cutoff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "sys.find_neighbors(method='cutoff', cutoff=4.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we can calculate the short range order. We will use the reference type as 1 and also specify the average keyword as True. This will allow us to get an average value for the whole simulation box."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.33333333,  1.        ])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.calculate_sro(reference_type=1, average=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Value for individual atoms can be accessed by,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "atoms = sys.atoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.33333333333333326, 1.0]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "atoms[4].sro"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Only atoms of the non reference type will have this value!"
   ]
  }
 ],
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