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 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 5 : Miller Indices and X-Ray Crystallograph Techniques"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.1 pageno : 96"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "p = 1.;\n",
      "q = 1./2;\n",
      "r = 3.;\n",
      "\n",
      "# Calculations\n",
      "h = 1./p;\n",
      "k = 1./q;\n",
      "l = 1./r;\n",
      "h1 = 3.*h;\n",
      "k1 = 3.*k;\n",
      "l1 = 3.*l;\n",
      "\n",
      "# Results\n",
      "print \"MILLER INDICES OF THE PLANE are h  = \",h1\n",
      "print \"k  =  \",k1\n",
      "print \"l  =  \",l1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "MILLER INDICES OF THE PLANE are h  =  3.0\n",
        "k  =   6.0\n",
        "l  =   1.0\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.3 pageno : 97"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "# Variables\n",
      "p = 2./4;\t\t\t#intercepts\n",
      "q = 3./3;\n",
      "r = 4./2;\n",
      "\n",
      "# Calculations\n",
      "h = 1./p;\n",
      "k = 1./q;\n",
      "l = 1./r;\n",
      "h1 = 2.*h;\n",
      "k1 = 2.*k;\n",
      "l1 = 2.*l;\n",
      "\n",
      "# Results\n",
      "print \"MILLER INDICES ARE \",l1,k1,h1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "MILLER INDICES ARE  1.0 2.0 4.0\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.5 pageno : 105"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math \n",
      "\n",
      "# Variables\n",
      "r = 1.246;\t\t\t#radius in angstorm\n",
      "h = 2.;\n",
      "k = 0.;\n",
      "l = 0.;\n",
      "h1 = 2.;\n",
      "k1 = 2.;\n",
      "l1 = 0.;\n",
      "h2 = 1.;\n",
      "k2 = 1.;\n",
      "l2 = 1.;\n",
      "\n",
      "# Calculations\n",
      "x = math.sqrt(h**2+k**2+l**2);\n",
      "a = 2*math.sqrt(2)*r;\t\t\t#in angstorm\n",
      "d_200 = a/x;\t\t\t        #interplanar spacing in angstorm\n",
      "x1 = math.sqrt(h1**2+k1**2+l1**2);\n",
      "d_220 = a/x1;       \t\t\t#interplanar spacing in angstorm\n",
      "x2 = math.sqrt(h2**2+k2**2+l2**2);\n",
      "d_111 = a/x2;\t\t        \t#interplanar spacing in angstorm\n",
      "\n",
      "\n",
      "print \"Interplanar Spacing (200) (in Angstorm)  =  %.3f A\"%d_200\n",
      "print \"Interplanar Spacing (220) (in Angstorm)  =  %.3f A\"%d_220\n",
      "print \"Interplanar Spacing (111) (in Angstorm)  =  %.3f A\"%d_111\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Interplanar Spacing (200) (in Angstorm)  =  1.762 A\n",
        "Interplanar Spacing (220) (in Angstorm)  =  1.246 A\n",
        "Interplanar Spacing (111) (in Angstorm)  =  2.035 A\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.6 pageno : 106"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math \n",
      "\n",
      "# Variables\n",
      "a = 3.61*10**-10;\t\t\t#unit cell in m\n",
      "\n",
      "# Calculations\n",
      "r_110 = 2/(math.sqrt(2)*a);\t\t\t#in atoms/m\n",
      "r_a = r_110/10**3;\t        \t\t#in atoms/mm\n",
      "r_111 = 1/(math.sqrt(3)*a);\t\t\t#in atoms/m\n",
      "r_b = r_111/10**3;\t\t\t        #in atoms/mm\n",
      "\n",
      "# Results\n",
      "print \"Linear Density per unit length along direction [110] (in atoms/mm)  = %.2e atoms/mm\"%r_a\n",
      "print \"Linear Density per unit length along direction [111] (in atoms/mm)  = %.2e atoms/mm\"%r_b\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Linear Density per unit length along direction [110] (in atoms/mm)  = 3.92e+06 atoms/mm\n",
        "Linear Density per unit length along direction [111] (in atoms/mm)  = 1.60e+06 atoms/mm\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.7 pageno : 110"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math \n",
      "\n",
      "# Variables\n",
      "r_po = 1.7*10**-10;\t\t\t    #radius of polonium in m\n",
      "r_rh = 1.34*10**-10;\t\t\t#radius of rhodium in m\n",
      "r_cr = 1.25*10**-10;\t\t\t#radius of chromium in m\n",
      "\n",
      "# Calculations\n",
      "a_po = 2*r_po;\t\t        \t#in m\n",
      "a_rh = 2*math.sqrt(2)*r_rh;\t\t#in m\n",
      "a_cr = 4*r_cr/math.sqrt(3);\n",
      "p_po = 1/a_po**2;\t\t\t    # /sqm\n",
      "p_rh = 1.414/a_rh**2;\t\t\t# /sqm\n",
      "p_cr = 1.732/a_cr**2;\t\t\t# /sqm\n",
      "\n",
      "# Results\n",
      "print \"Planar Density on [100] in Polonium (per sqm)  =  %.2e /m**2\"%p_po\n",
      "print \"Planar Density on [110] in Rhodium (per sqm)  =  %.2e /m**2\"%p_rh\n",
      "print \"Planar Density on [111] in Chromium (per sqm)  =  %.2e /m**2\"%p_cr\n",
      "\n",
      "# Note : To check answer , please calculate manually for p_rh"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Planar Density on [100] in Polonium (per sqm)  =  8.65e+18 /m**2\n",
        "Planar Density on [110] in Rhodium (per sqm)  =  9.84e+18 /m**2\n",
        "Planar Density on [111] in Chromium (per sqm)  =  2.08e+19 /m**2\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.8 pageno : 113"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math \n",
      "\n",
      "# Variables\n",
      "w = 0.824;\t\t\t#wavelength in angstorm\n",
      "theta1 = 8.35;\t\t\t#angle at n = 1 in degrees\n",
      "n1 = 1.;\n",
      "n3 = 3.;\n",
      "\n",
      "# Calculations\n",
      "d = w/(2*math.sin(math.radians(theta1)));\t\t\t#in angstorm\n",
      "theta3 = math.degrees(math.asin(3*math.sin(math.radians(theta1))))\n",
      "\n",
      "# Results\n",
      "print \"Glancing angle for third order diffraction  =  %f degrees\"%theta3\n",
      "print \"Interplanar spacing of the crystal (in Angstorm)  =  %.3f A\"%d\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Glancing angle for third order diffraction  =  25.827235 degrees\n",
        "Interplanar spacing of the crystal (in Angstorm)  =  2.837 A\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.9 pageno : 115"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "import math \n",
      "\n",
      "# Variables\n",
      "a = 17.03;\t\t\t#in degrees\n",
      "w = 0.71;\t\t\t#in angstorm\n",
      "n = 1.;\n",
      "\n",
      "# Calculations\n",
      "d = n*w/(2*math.sin(math.radians(a)));\t\t\t#interplanar spacing in angstorm\n",
      "# given that h**2+k**2+l**2 = 8\n",
      "a = math.sqrt(8)*d;                     \t\t\t#in angstorm\n",
      "\n",
      "# Results\n",
      "print \"Interplanar Spacing (in angstorm)  =  %.3f A\"%d\n",
      "print \"Lattice parameter of the crystal (in Angstorm)  =  %.2f A\"%a\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Interplanar Spacing (in angstorm)  =  1.212 A\n",
        "Lattice parameter of the crystal (in Angstorm)  =  3.43 A\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example 5.10 pageno : 117"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "\n",
      "# Variables\n",
      "w = 0.0708;\t\t\t        #wavelength in nm\n",
      "h = 1.;\n",
      "k = 0.;\n",
      "l = 0.;\n",
      "s = 0.0132;     \t\t\t#a common divisor i.e.math.sin**2(theta) = 0.0132\n",
      "\n",
      "# Calculations\n",
      "a = math.sqrt((w**2*(h**2+k**2+l**2))/(4*s));\t\t\t#in nm\n",
      "a1 = 10.**3*a;\t\t\t    #in pm\n",
      "\n",
      "# Results\n",
      "print \"Dimension of unit cell (in Picometer)  =  %.1f pm\"%a1\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Dimension of unit cell (in Picometer)  =  308.1 pm\n"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}