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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# PS4 Qn6\n",
      "This notebook provides the solution to Qn 6 of PS4."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Part a\n",
      "\n",
      "The reciprocal basis vectors are given by\n",
      "\n",
      "$\\mathbf{e_x'} = \\frac{\\mathbf{e_x}}{a}$\n",
      "\n",
      "$\\mathbf{e_y'} = \\frac{\\mathbf{e_y}}{a}$\n",
      "\n",
      "$\\mathbf{e_z'} = \\frac{\\mathbf{e_z}}{c}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Part b\n",
      "\n",
      "The Bragg condition is given by $2d_{hkl}\\sin\\theta = \\lambda$.\n",
      "Since we know that $d_{hkl} = \\frac{1}{|\\mathbf{g_{hkl}}|}$, we have\n",
      "\n",
      "$\\theta = \\sin^{-1}(\\frac{\\lambda |\\mathbf{g_{hkl}}|}{2})$\n",
      "\n",
      "Also, because the reciprocal basis vectors are mutually orthgonal, we have the lengths simply as\n",
      "\n",
      "$|\\mathbf{g_{hkl}}| = (h^2/a^2 + k^2/a^2 + l^2 / c^2)^{1/2}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "a = 3.9039\n",
      "c = 4.1348\n",
      "\n",
      "def calculate_two_theta(hkl):\n",
      "    two_theta = 2 * math.asin(1.541 * (hkl[0] / a ** 2 + hkl[1] / a ** 2 + hkl[2] / c ** 2) ** 0.5 / 2)\n",
      "    return math.degrees(two_theta)\n",
      "\n",
      "two_thetas = {}\n",
      "for hkl in [(0, 1, 1), (0, 1, 0), (0, 0, 1)]:\n",
      "    two_theta = calculate_two_theta(hkl)\n",
      "    print \"Peak position for %s is %.1f degrees\" % (hkl, two_theta)\n",
      "    #Store this as we will use these later.\n",
      "    two_thetas[hkl] = two_theta"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Peak position for (0, 1, 1) is 31.5 degrees\n",
        "Peak position for (0, 1, 0) is 22.8 degrees\n",
        "Peak position for (0, 0, 1) is 21.5 degrees\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Part c\n",
      "\n",
      "To calculate the structure factor, we need the positions of all atoms in the unit cell. Note that one of the oxygen has Wyckoff symbol 2c. From the International Tables, we find that the orbit for this site is given by (1/2, 0, z) and (0, 1/2, z). So there are 5 atoms in the cell with positions:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "elements = [\"Pb\", \"Ti\", \"O\", \"O\", \"O\"]\n",
      "\n",
      "coords = [\n",
      "    [0, 0, 0], \n",
      "    [0.5, 0.5, 0.5281],\n",
      "    [0.5, 0, 0.6130], \n",
      "    [0, 0.5, 0.6130], \n",
      "    [0.5, 0.5, 0.1339]\n",
      "]\n",
      "\n",
      "#We will also set up the parameters for the atomic scattering factors\n",
      "\n",
      "asf_params = {\n",
      "    \"Pb\": [82, 3.510, 52.914, 4.552, 11.884, 3.154, 2.571, 1.359, 0.321],\n",
      "    \"Ti\": [22, 3.565, 81.982, 2.818, 19.049, 1.893, 3.590, 0.483, 0.386],\n",
      "    \"O\": [8, 0.455, 23.780, 0.917, 7.622, 0.472, 2.144, 0.138, 0.296]\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The atomic scattering factor is given by:\n",
      "\n",
      "$f(s) = Z - 41.78214 s^2 \\sum(a_i e ^ {-b_i s^2})$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wavelength = 1.541 / 10 #Convert to nm\n",
      "\n",
      "#Let's write a function to calculate the atomic scattering factor for a given element and angle. \n",
      "def get_atomic_scattering_factor(el, two_theta):\n",
      "    params = asf_params[el]\n",
      "    theta = math.radians(two_theta / 2)\n",
      "    s = math.sin(theta) / wavelength\n",
      "    return params[0] - 41.78214 * s ** 2 * sum([params[2*i + 1] * math.exp(-params[2*i + 2] * s ** 2) for i in xrange(4)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The structure factor is given by the sum of the atomic scattering factor times the position factor.\n",
      "\n",
      "$F_{hkl} = \\sum f_j(s) \\exp(2\\pi i (hx_j + ky_j + lz_j))$\n",
      "\n",
      "and the intensity is simply given by the modulus squared of the structure factor."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import cmath # We need complex representation for this.\n",
      "\n",
      "I = {}\n",
      "\n",
      "for hkl in [(0, 1, 1), (0, 1, 0), (0, 0, 1)]:\n",
      "    F_hkl = 0\n",
      "    two_theta = two_thetas[hkl]\n",
      "    h, k, l = hkl\n",
      "    for el, coord in zip(elements, coords):\n",
      "        x, y, z = coord\n",
      "        F_hkl += get_atomic_scattering_factor(el, two_theta) * cmath.exp(2j * math.pi * (h * x + k * y + l * z))\n",
      "    print \"Structure factor for %s = %s\" % (hkl, str(F_hkl))\n",
      "    I_hkl = (F_hkl * F_hkl.conjugate()).real\n",
      "    I[hkl] = I_hkl\n",
      "    print \"Intensity for %s = %.0f\" % (hkl, I_hkl)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Structure factor for (0, 1, 1) = (19.3103357104-0.0383753645865j)\n",
        "Intensity for (0, 1, 1) = 373\n",
        "Structure factor for (0, 1, 0) = (18.5158066944+7.96497645578e-16j)\n",
        "Intensity for (0, 1, 0) = 343\n",
        "Structure factor for (0, 0, 1) = (19.9607043933-1.52195300723j)\n",
        "Intensity for (0, 0, 1) = 401\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Part d\n",
      "\n",
      "The Lorentz polarization factor has the form \n",
      "\n",
      "$L_p(\\theta) = \\frac{1 + \\cos^22\\theta}{\\sin^2\\theta cos \\theta}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lp = {}\n",
      "for hkl in [(0, 1, 1), (0, 0, 1)]:\n",
      "    theta = math.radians(two_thetas[hkl] / 2)\n",
      "    lp[hkl] = (1 + math.cos(2 * theta) ** 2) / (math.sin(theta) ** 2 * math.cos(theta))\n",
      "    print \"Lorentz factor for %s = %.3f\" % (hkl, lp[hkl])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Lorentz factor for (0, 1, 1) = 24.354\n",
        "Lorentz factor for (0, 0, 1) = 54.693\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Before correction, we have I_011/I_001 = %.4f\" % (I[(0, 1, 1)]/I[(0, 0, 1)])\n",
      "print \"After correction, we have I_011/I_001 = %.4f\" % (I[(0, 1, 1)] * lp[(0, 1, 1)] / (I[(0, 0, 1)]* lp[(0, 0, 1)]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Before correction, we have I_011/I_001 = 0.9305\n",
        "After correction, we have I_011/I_001 = 0.4143\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly, the Lorentz polarization factor has a significant impact on relative peak intensities! In this case, the relative peak intensity has decreased significantly. If you look at the experiment XRD pattern below, clearly the relative intensity is a lot closer to 0.4143 than 0.9305. The relative intensities are still wrong because there are other factors which have not been taken into account."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image, display\n",
      "display(Image(filename=('./PbTiO3.png')))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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M2ASALYg8AILYKvKcPBOAnW0VeRIPgJ3p2AQgCJEHQBAiD4AgRB4AQYg8AIIQeQAEIfIA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\n",
       "text": [
        "<IPython.core.display.Image at 0x1038381d0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is not part of the question, but just to show the actual computed pattern after taking all factors into account, which shows much better agreement with the experimental pattern."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymatgen import read_structure\n",
      "from pymatgen.analysis.diffraction.xrd import XRDCalculator\n",
      "%matplotlib inline\n",
      "\n",
      "c = XRDCalculator()\n",
      "c.get_xrd_plot(read_structure(\"PbTiO3.cif\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<module 'matplotlib.pyplot' from '/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/matplotlib/pyplot.pyc'>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OAAAg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6hZ\nsyauXLkCW1vbN9FlQgghpNwyLusOEEIIIYQQog9xcXGIi4vTKm/z5s2xb98+GjgihBBCtEAbZhNC\nCCGEkHKnUaNGKpepFcfV1RU//fQTTp06BScnp1LoGSGEEGJ4aNkaIYQQQggplxhjOH/+PEJDQ3H5\n8mVERUUhNjYWaWlpyM7OhrW1NSpVqgRXV1c0b94cbdq0QefOnWkDckIIIUQmGjwihBBCCCGEEEII\nIWrRsjVCCCGEEEIIIYQQohYNHhFCCCGEEEIIIYQQtWjwiBBCCCGEEEIIIYSoRYNHhBBCCCGEEEII\nIUQtGjwihBBCCCGEEEIIIWr9P8RyQ5g6ptvEAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1082a7f50>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}