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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Introduction\n",
      "\n",
      "This notebook shows how to plot an XRD plot for the two polymorphs of CsCl ($Pm\\overline{3}m$ and $Fm\\overline{3}m$) by computing the structure factors."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Set up some imports that we will need\n",
      "import math, cmath\n",
      "from pymatgen import Lattice, Structure\n",
      "from pymatgen.util.plotting_utils import get_publication_quality_plot\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib as mpl\n",
      "from IPython.display import Image, display\n",
      "import collections\n",
      "\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will now set up some data and variables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Atomic scattering factors for Cs and Cl obtained from Structure of Materials.\n",
      "data = {\n",
      "    \"Cs\": [55, 6.062, 155.837, 5.986, 19.695, 3.303, 3.335, 1.096, 0.379],\n",
      "    \"Cl\": [17, 1.452, 30.935, 2.292, 9.980, 0.787, 2.234, 0.322, 0.323]\n",
      "}\n",
      "\n",
      "CuKa = 0.1542 * 10 # Angstrom"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let us now write the actual method to plot the XRD. This method is a simpler replica of the version that Prof Ong has implemented in the Python Materials Genomics (www.pymatgen.org) materals analysis code. It is less efficient, but the steps are more clearly laid out."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_xrd(structure):\n",
      "    \"\"\"\n",
      "    Let's define the XRD plot generation in a function that works for any given structure.\n",
      "    This takes into account the Lorentz polarization factor and the multiplicity factors, \n",
      "    but not the Debye-Waller factor. \n",
      "    \"\"\"\n",
      "    latt = structure.lattice\n",
      "    \n",
      "    # Obtain crystallographic reciprocal lattice and points within\n",
      "    # limiting sphere (within 2/wavelength)\n",
      "    recip_latt = latt.reciprocal_lattice_crystallographic\n",
      "    recip_pts = recip_latt.get_points_in_sphere([[0, 0, 0]], [0, 0, 0], 2 / CuKa)\n",
      "    \n",
      "    intensities = {} \n",
      "    two_thetas = []\n",
      "    \n",
      "    for hkl, g_hkl, ind in sorted(recip_pts, key=lambda i: (i[1], -i[0][2], -i[0][1], -i[0][0])):\n",
      "        if g_hkl != 0:\n",
      "            theta = math.asin(CuKa / (2 / g_hkl))\n",
      "            s = g_hkl / 2\n",
      "            s_2 = s ** 2\n",
      "            \n",
      "            # Calculate the structure factor, given by the sum of the atomic scattering factors.\n",
      "            f_hkl = 0\n",
      "            for site in structure:\n",
      "                el = site.specie.symbol\n",
      "                d = data[el]\n",
      "                #Atomic scattering factor equation using parameters for Cs and Cl\n",
      "                fs = d[0] - 41.78214 * s_2 * sum([d[2 * i + 1] * math.exp(-d[2 * i + 2] * s_2) for i in xrange(4)])\n",
      "                f_hkl += fs * cmath.exp(2j * math.pi * np.dot(hkl, site.frac_coords))\n",
      "            \n",
      "            # Intensity is given by modulus squared of structure factor\n",
      "            i_hkl = (f_hkl * f_hkl.conjugate()).real\n",
      "\n",
      "            #This corrects for the Lorentz factor.\n",
      "            lorentz_factor = (1 + math.cos(2 * theta) ** 2) / (math.sin(theta) ** 2 * math.cos(theta))\n",
      "\n",
      "            two_theta = 2 * theta / math.pi * 180\n",
      "\n",
      "            #Deal with floating point precision issues.\n",
      "            ind = np.where(np.abs(np.subtract(two_thetas, two_theta)) <\n",
      "                           1e-5)\n",
      "            if len(ind[0]) > 0:\n",
      "                intensities[two_thetas[ind[0]]][0] += i_hkl * lorentz_factor\n",
      "            else:\n",
      "                intensities[two_theta] = [i_hkl * lorentz_factor, tuple(hkl)]\n",
      "                two_thetas.append(two_theta)\n",
      "\n",
      "    max_intensity = max([v[0] for v in intensities.values()])\n",
      "    plt = get_publication_quality_plot(16, 10)\n",
      "    for k in sorted(intensities.keys()):\n",
      "        if k < 90: # Let's limit the plot to < 90 degrees\n",
      "            v = intensities[k]\n",
      "            i = v[0] / max_intensity * 100\n",
      "            plt.plot([k, k], [0, i], color='k', linewidth=3, label=str(v[1]))\n",
      "            plt.annotate(str(v[1]), xy=[k, i], xytext=[k, i], fontsize=16)\n",
      "    plt.xlabel(\"2 \\\\theta (degrees)\")\n",
      "    plt.ylabel(\"Intensities (scaled)\")\n",
      "    plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# $\\alpha$-CsCl ($Pm\\overline{3}m$)\n",
      "\n",
      "Let's start with the typical $\\alpha$ form of CsCl."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create CsCl structure\n",
      "a = 4.209 #Angstrom\n",
      "latt = Lattice.cubic(a)\n",
      "structure = Structure(latt, [\"Cs\", \"Cl\"], [[0, 0, 0], [0.5, 0.5, 0.5]])\n",
      "plot_xrd(structure)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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69nk5LCyszD72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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ac0eb50>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compare it with the experimental XRD pattern below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "display(Image(filename=('./PDF - alpha CsCl.png')))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eAEFIHgBBSB4AQUgeAEFIHgBBSB4AQUgeAEFIHgBBSB4AQUgeAEFIHgBBSB4A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\nlJomAAAAAElFTkSuQmCC\n",
       "text": [
        "<IPython.core.display.Image at 0x10ad33390>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# $\\beta$-CsCl ($Fm\\overline{3}m$)\n",
      "\n",
      "Let's now look at the $\\beta$ (high-temperature) form of CsCl."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Create CsCl structure\n",
      "a = 6.923 #Angstrom\n",
      "latt = Lattice.cubic(a)\n",
      "structure = Structure(latt, [\"Cs\", \"Cs\", \"Cs\", \"Cs\", \"Cl\", \"Cl\", \"Cl\", \"Cl\"], \n",
      "                      [[0, 0, 0], [0.5, 0.5, 0], [0, 0.5, 0.5], [0.5, 0, 0.5], \n",
      "                       [0.5, 0.5, 0.5], [0, 0, 0.5], [0, 0.5, 0], [0.5, 0, 0]])\n",
      "\n",
      "plot_xrd(structure)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GrVCtHR0SatPxER1X4yQaLn7ZWWliI8PBzffPMNAMDDwwMxMTHo2rWrFOHJjOryYxipctSkx6HW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\nkgyfOlcDDRkyBPPnz1e+37lzJ+bNm1fh9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WmJwsJCpKam4vTp09i2bRvzDeXJkycxZswY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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1041618d0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compare it with the experimental XRD pattern below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "display(Image(filename=('./PDF - beta CsCl.png')))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h8gAIQuQBEITIAyAIkQdAECIPgCBEHgBBiDwAghB5AAQh8gAIQuQBEITIAyAIkQdAECIP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\nClZmcAAAAABJRU5ErkJggg==\n",
       "text": [
        "<IPython.core.display.Image at 0x1079197d0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}