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{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from ase.io import read\n",
    "from ase.visualize import view\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma   = 3.405\n",
    "epsilon = 119.8*8.616733e-5 # eV\n",
    "unit_cell_side = 5.269\n",
    "cell_side = 6*unit_cell_side\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g_step(box, n_bin, d):\n",
    "    box    += 1\n",
    "    box    *= np.sqrt(2)/sigma\n",
    "    del_bin = box/n_bin  #width of a bin\n",
    "    \n",
    "    g    = np.zeros([n_bin,n_bin])\n",
    "    g[0] = np.linspace(0,box,n_bin)\n",
    "    g[0]+= del_bin*0.5\n",
    "    \n",
    "    for i in range(len(d)):\n",
    "        for j in range(i+1,len(d)):\n",
    "            g_index = d[i][j]/(del_bin)\n",
    "            #g_index = (d[i][j]-box*round(d[i][j]/box))/(del_bin)\n",
    "            g[1,g_index.astype(int)] += 2\n",
    "            # we count both for i and j.\n",
    "            \n",
    "    \n",
    "    #nomalized by number of particles\n",
    "    g[1] /= len(d[0])\n",
    "    #and by bin volume\n",
    "    \n",
    "    for k in range(len(g[1])):\n",
    "        g[1][k] /= ((k+1)**3 -k**3)*del_bin**3\n",
    "        \n",
    "    #side of the optimized cell: 5,269\n",
    "    vol = (unit_cell_side/sigma)**3\n",
    "    rho = 4./vol\n",
    "    g[1] /= np.pi*(4/3)*rho\n",
    "    return g;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 20 K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "trajectory = read('production_bulk_20-pos-1.xyz', index='::2')\n",
    "N = len(trajectory[0])    #number of atoms\n",
    "n_step = len(trajectory)  #number of step\n",
    "\n",
    "#create a distance array\n",
    "dist = np.empty([0,N,N])\n",
    "for frame in trajectory:\n",
    "    frame.set_cell([cell_side,cell_side,cell_side])\n",
    "    frame.set_pbc((True,True,True))\n",
    "    dist = np.append(dist, [frame.get_all_distances(mic=True)],axis=0)\n",
    "    \n",
    "\n",
    "#Lennard Jones units\n",
    "\n",
    "dist  /= sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'radial distribution function')"
      ]
     },
     "execution_count": 8,
     "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": [
    "n_bin = 300  #number of bin in the graph\n",
    "box   = cell_side   #side of the bon in the simulation \n",
    "g_20  = np.zeros([n_bin,n_bin])\n",
    "\n",
    "#average during the thermalized part of the simulation\n",
    "for i in range(n_step):\n",
    "    g_20 += g_step(box,n_bin,dist[i])\n",
    "g_20 /= n_step\n",
    "\n",
    "plt.plot(g_20[0],g_20[1])\n",
    "plt.xlim(0,box/(2*sigma))\n",
    "plt.xlabel('distance [ units of $\\sigma$]')\n",
    "plt.ylabel('radial distribution function')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 400 K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "trajectory = read('production_bulk_400-pos-1.xyz', index='::2')\n",
    "N = len(trajectory[0])    #number of atoms\n",
    "\n",
    "n_step = len(trajectory)  #number of step\n",
    "n_step\n",
    "#create a distance array\n",
    "dist = np.empty([0,N,N])\n",
    "for frame in trajectory:\n",
    "    frame.set_cell([cell_side,cell_side,cell_side])\n",
    "    frame.set_pbc((True,True,True))\n",
    "    dist = np.append(dist, [frame.get_all_distances(mic=True)],axis=0)\n",
    "\n",
    "#Lennard Jones units\n",
    "\n",
    "dist  /= sigma\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'radial distribution function')"
      ]
     },
     "execution_count": 5,
     "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": [
    "\n",
    "\n",
    "n_bin  = 300  #number of bin in the graph\n",
    "box    = cell_side #side of the simulation box\n",
    "g_400  = np.zeros([n_bin,n_bin])\n",
    "\n",
    "#average during the thermalized part of the simulation\n",
    "for i in range(n_step):\n",
    "    g_400 += g_step(box,n_bin,dist[i])\n",
    "g_400 /= n_step\n",
    "\n",
    "plt.plot(g_400[0],g_400[1])\n",
    "plt.xlim(0,box/(2*sigma))\n",
    "plt.xlabel('distance [ units of $\\sigma$]')\n",
    "plt.ylabel('radial distribution function')\n",
    "#plt.savefig(\"gr.png\",  dpi=300,transparent=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'radial distribution function')"
      ]
     },
     "execution_count": 11,
     "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(g_400[0],g_400[1])\n",
    "plt.plot(g_20[0],g_20[1])\n",
    "plt.xlim(0,box/(2*sigma))\n",
    "plt.xlabel('distance [ units of $\\sigma$]')\n",
    "plt.ylabel('radial distribution function')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data38  = np.loadtxt('production_38-1.ener' )\n",
    "data150 = np.loadtxt('production_150-1.ener')\n",
    "data450 = np.loadtxt('production_450-1.ener')\n",
    "data817 = np.loadtxt('production_817-1.ener')\n",
    "dataBulk = np.loadtxt('production_bulk_20-1.ener')\n",
    "\n",
    "data38   = np.transpose(data38)\n",
    "data150  = np.transpose(data150)\n",
    "data450  = np.transpose(data450)\n",
    "data817  = np.transpose(data817)\n",
    "dataBulk = np.transpose(dataBulk)\n",
    "\n",
    "\n",
    "#energy in simulation time in LJ units\n",
    "E38   = 27.1442*data38[4]/epsilon #eV / epsilon(eV)\n",
    "E150  = 27.1442*data150[4]/epsilon \n",
    "E450  = 27.1442*data450[4]/epsilon \n",
    "E817  = 27.1442*data817[4]/epsilon \n",
    "EBulk = 27.1442*dataBulk[4]/epsilon \n",
    "\n",
    "#compute average energy \n",
    "e_average    = np.zeros([2,4])\n",
    "e_average[0] = [38,150,450,817]\n",
    "e_average[1] = [np.mean(E38),np.mean(E150),np.mean(E450),np.mean(E817)]\n",
    "bulk_average = np.mean(EBulk)/864.\n",
    "\n",
    "#compute average energy per particle\n",
    "e_part    = np.zeros([2,4])\n",
    "e_part[0] = [38,150,450,817]\n",
    "e_part[1] = [np.mean(E38)/38.,np.mean(E150)/150.,np.mean(E450)/450.,np.mean(E817)/817.]\n",
    "\n",
    "#create an array of crystal energy per particle\n",
    "ecr_part  = np.ones(4)*bulk_average\n",
    "\n",
    "#first plot\n",
    "fig, ax = plt.subplots(1,2, figsize=(12,4), sharex='col')\n",
    "ax[0].plot(e_part[0],e_part[1], linestyle='-', marker='o', color='brown',markersize=12, label='Cluster')\n",
    "ax[0].plot(e_part[0],ecr_part*np.ones(4), color='green', label='Crystal')\n",
    "ax[0].set_xlabel('cluster size')\n",
    "ax[0].set_ylabel('<Energy> per particle [ units of ε]')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#compute surface energy\n",
    "e_surface    = np.zeros([2,4])\n",
    "e_surface[0] = e_part[0]\n",
    "#surface energy = (cluster energy) - N x (energy per particle in a crystal ) \n",
    "e_surface[1][0] = e_average[1][0]-bulk_average*38\n",
    "e_surface[1][1] = e_average[1][1]-bulk_average*150\n",
    "e_surface[1][2] = e_average[1][2]-bulk_average*450\n",
    "e_surface[1][3] = e_average[1][3]-bulk_average*817\n",
    "\n",
    "\n",
    "#from bulk knowledge:\n",
    "vol_part = (unit_cell_side)**3/4.\n",
    "\n",
    "#compute the ray approximating the cluster to a spere\n",
    "r38  = np.cbrt(vol_part*38*3/(4*np.pi))\n",
    "r150 = np.cbrt(vol_part*150*3/(4*np.pi))\n",
    "r450 = np.cbrt(vol_part*450*3/(4*np.pi))\n",
    "r817 = np.cbrt(vol_part*817*3/(4*np.pi))\n",
    "#and the surface\n",
    "S38  = 4*np.pi*r38**2\n",
    "S150 = 4*np.pi*r150**2\n",
    "S450 = 4*np.pi*r450**2\n",
    "S817 = 4*np.pi*r817**2\n",
    "S    = np.array([S38, S150, S450, S817])\n",
    "\n",
    "#plot <Surface Energy> per surface unity\n",
    "ax[1].plot(e_surface[0] ,1000*epsilon*e_surface[1]/S, linestyle='-', marker='o', color='brown',markersize=12)\n",
    "ax[1].set_xlabel('cluster size')\n",
    "ax[1].set_ylabel('<Surface Energy>/S [ meV$/\\AA^2$]')\n",
    "\n",
    "plt.subplots_adjust(wspace=0.3)\n",
    "\n",
    "ax[0].legend(loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
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  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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  },
  {
   "cell_type": "code",
   "execution_count": null,
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  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
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  },
  {
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 ],
 "metadata": {
  "kernelspec": {
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