{
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  "name": ""
 },
 "nbformat": 3,
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 2: Crystal Structure"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.2, page no-30"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lattice spacing from Miller indices\n",
      "\n",
      "import math\n",
      "# Intercepts are in the ratio 3a:4b along X,Y and parallel to Z axis\n",
      "# x-intercept 3, y-intercept 4 and z-intercept infinity \n",
      "\n",
      "#variable declaration\n",
      "a=2.0*10**-10       # 2 Angstrom\n",
      "h=4.0               # Miller indices wrt X-axis\n",
      "k=3.0               # Miller indices wrt Y-axis\n",
      "l=0.0               # Miller indices wrt Z-axis\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#result\n",
      "print('The lattice spacing for the plane (%d%d%d) is %.1f*10^-10 m'%(h,k,l,d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lattice spacing for the plane (430) is 0.4*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.3, page no-31"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Lattice constant of Sodium\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "d=9.6*10**2          # Density of sodium in kg/m^3\n",
      "awt=23               # Atomic weight of sodium\n",
      "n=2                  # No of sodium atoms present in one unit cell\n",
      "avg=6.023*10**26     # Avogadro number\n",
      "\n",
      "\n",
      "#calculation\n",
      "m=n*awt/avg\n",
      "a=(m/d)**(1.0/3.0)\n",
      "\n",
      "#Result\n",
      "print('The lattice constant of sodium is %.1f A\u00b0'%(a*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lattice constant of sodium is 4.3 A\u00b0\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.4, page no-31"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Avogadro Constant \n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "d=4.0*10**3                 # Density of CsCl in kg/m^3\n",
      "awtcs=132.9                 # Atomic weigt of Cs \n",
      "awtcl=35.5                  # Atomic weigt of Cl\n",
      "a=4.12*10**-10              # Lattice constant\n",
      "\n",
      "#Calculations\n",
      "m=d*a**3\n",
      "N=(awtcs+awtcl)/m\n",
      "\n",
      "#Result\n",
      "print('The value of Avogadro Constant %.4f *10^26 per kg mole'%(N*10**-26))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of Avogadro Constant 6.0199 *10^26 per kg mole\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.5, page no-31"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Interatomic spacing\n",
      "\n",
      "import math \n",
      "#variable declaration\n",
      "lam=1.5418*10**-10         # Wavelength of X-rays\n",
      "theta=30.0                 # Angle of diffracted angle\n",
      "h=1.0                      # Miller indices wrt X-axis\n",
      "k=1.0                      # Miller indices wrt Y-axis\n",
      "l=1.0                      # Miller indices wrt Z-axis\n",
      "\n",
      "#Calculation\n",
      "a=lam*math.sqrt(h**2+k**2+l**2)/(2*math.sin(theta*math.pi/180))\n",
      "\n",
      "#Result\n",
      "print('The lattice constant is %.4f *10^-10 m'%(a*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lattice constant is 2.6705 *10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.6, page no-33"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Lattice spacing in a rock salt\n",
      "\n",
      "import math\n",
      "#variable cdeclaration\n",
      "h=1.0                      # Miller indices wrt X-axis\n",
      "k=0.0                      # Miller indices wrt Y-axis\n",
      "l=0.0                      # Miller indices wrt Z-axis\n",
      "a=2.814*10**-10            # interatomic spacing\n",
      "\n",
      "#calculations\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('The lattice spacing for the plane(%d%d%d) is %.3f*10^-10 m'%(h,k,l,d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lattice spacing for the plane(100) is 2.814*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.7, page no-33"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Lattice spacing from Miller indices\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "h=3.0                       # Miller indices wrt X-axis\n",
      "k=2.0                       # Miller indices wrt Y-axis\n",
      "l=1.0                       # Miller indices wrt Z-axis\n",
      "a=4.12*10**-10              # interatomic spacing\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#result\n",
      "print('The lattice spacing for the plane(%d%d%d) is %.4f*10^-10 m'%(h,k,l,d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lattice spacing for the plane(321) is 1.1011*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.8, page no-34"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Lattice spacing from Miller indices\n",
      "\n",
      "import math\n",
      "#(i)\n",
      "#variable declaration\n",
      "h=1.0                              # Miller indices wrt X-axis\n",
      "k=0.0                              # Miller indices wrt Y-axis\n",
      "l=1.0                              # Miller indices wrt Z-axis\n",
      "a=4.2*10**-10                    # lattice constant\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\nThe lattice spacing for the plane(%d%d%d) is %.4f*10^-10 m'%(h,k,l,d*10**10))\n",
      "\n",
      "#(ii)\n",
      "#variable declaration\n",
      "h=2                            # Miller indices wrt X-axis\n",
      "k=2                            # Miller indices wrt Y-axis\n",
      "l=1                            # Miller indices wrt Z-axis\n",
      "a=4.12*10**-10                 # Lattice constant \n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\nThe lattice spacing for the plane(%d%d%d) is %.1f*10^-10 m'%(h,k,l,d*10**10))\n",
      "\n",
      "#Answer in the book for plane(101) is wrong"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The lattice spacing for the plane(101) is 2.9698*10^-10 m\n",
        "\n",
        "The lattice spacing for the plane(221) is 1.4*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.13, page no-37"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Lattice spacing from Miller indices\n",
      "\n",
      "import math\n",
      "\n",
      "#(i)\n",
      "#variable declaration\n",
      "h=1.0                    # Miller indices wrt X-axis\n",
      "k=1.0                    # Miller indices wrt Y-axis\n",
      "l=1.0                    # Miller indices wrt Z-axis\n",
      "a=4.12*10**-10           # lattice Constant\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\nFor (%d%d%d) plane\\nThe lattice spacing is %.4f*10^-10 m'%(h,k,l,d*10**10))\n",
      "\n",
      "#(ii)\n",
      "\n",
      "#variable declaration\n",
      "h=1.0                  # Miller indices wrt X-axis\n",
      "k=1.0                  # Miller indices wrt Y-axis\n",
      "l=2.0                  # Miller indices wrt Z-axis\n",
      "a=4.12*10**-10         # Lattice Constant\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\n\\nFor (%d%d%d) plane\\nThe lattice spacing is %.4f*10^-10 m'%(h,k,l,d*10**10))\n",
      "\n",
      "\n",
      "#(iii)\n",
      "\n",
      "#variable declaration\n",
      "h=1.0                   # Miller indices wrt X-axis\n",
      "k=2.0                   # Miller indices wrt Y-axis  \n",
      "l=3.0                   # Miller indices wrt Z-axis\n",
      "a=4.12*10**-10          # Lattice Constant\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\n\\nFor (%d%d%d) plane\\nThe lattice spacing is %.4f*10^-10 m'%(h,k,l,d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "For (111) plane\n",
        "The lattice spacing is 2.3787*10^-10 m\n",
        "\n",
        "\n",
        "For (112) plane\n",
        "The lattice spacing is 1.6820*10^-10 m\n",
        "\n",
        "\n",
        "For (123) plane\n",
        "The lattice spacing is 1.1011*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.15, page no-38"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lattice spacing from Miller indice\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "h=2.0                     # Miller indices wrt X-axis\n",
      "k=2.0                     # Miller indices wrt Y-axis \n",
      "l=0.0                     # Miller indices wrt Z-axis\n",
      "a=4.938*10**-10           # Lattice Constant\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\nThe lattice spacing for (%d%d%d) plane is %.4f*10^-10 m'%(h,k,l,d*10**10))\n",
      "\n",
      "#Note: Final answer in the book is as follow:\n",
      "# The lattice spacing for the plane (110) is 2.968 x 10^-10 m "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The lattice spacing for (220) plane is 1.7458*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.16, page no-39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Number of atoms in Al foil\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "a=0.405*10**-10      # lattice constant\n",
      "t=0.005              # thickness of Al foil\n",
      "A=25*10**-2          # side length of Al foil\n",
      "\n",
      "#calculation\n",
      "n=t*A/a**3\n",
      "\n",
      "#Result\n",
      "print('The number of atoms in the Al foil is %.2f * 10^28'%(n*10**-28))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The number of atoms in the Al foil is 1.88 * 10^28\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.17, page no-39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#no of unit cells in 1 kg metal\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "a=2.88*10**-10          # lattice constant\n",
      "d=7200.0                # Density of metal in k/m^3\n",
      "\n",
      "#calculation\n",
      "n=1/(d*a**3)\n",
      "\n",
      "#Result\n",
      "print('The number of unit cells present in 1 kg metal is %.4f *10^24'%(n*10**-24))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The number of unit cells present in 1 kg metal is 5.8142 *10^24\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.18, page no-39"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#percentage volume change during structural changes\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "rbcc=0.1258*10**-9              # Atomic radius at bcc state\n",
      "rfcc=0.1292*10**-9              # Atomic radius at fcc state\n",
      "\n",
      "#calculation\n",
      "a=4*rbcc/math.sqrt(3)\n",
      "vbcc=(a**3)/2\n",
      "a1=4*rfcc/math.sqrt(2)\n",
      "vfcc=(a1**3)/4\n",
      "vp=(vbcc-vfcc)\n",
      "vp=math.floor(vp*10**32)\n",
      "vp=vp*10**-32/vbcc\n",
      "\n",
      "#Result\n",
      "print('The volume change in %% duringg the structural change is %.4f'%(vp*100))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The volume change in % duringg the structural change is 0.4894\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.19, page no-40"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Copper Density\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "awt=63.5*10**-3              # Atomic weight of copper\n",
      "avg=6.023*10**26             # Avagadro No. \n",
      "r=1.273*10**-10              # Atomic radius for fcc system\n",
      "n=4.0                        # No of atoms per unit cell for fcc\n",
      "\n",
      "#calculation\n",
      "a=4*r/math.sqrt(2)\n",
      "a= math.floor(a*10**11)/10**11\n",
      "d=n*awt/(avg*a**3)\n",
      "\n",
      "#Result\n",
      "print('The density of copper is %.5f gm/m^3'%d)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The density of copper is 9.03885 gm/m^3\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.20, page no-41"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Atomic Radius\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "d=7860.0                   # Density of alfa-iron\n",
      "m=55.85                    # atomic weight of alfa-iron\n",
      "n=2.0                      # No of atoms per unit cell for Bcc\n",
      "avg=6.023*10**26           # Avoigadro's Number\n",
      "\n",
      "#calculation\n",
      "a=(n*m*10**-3/(avg*d))**(1.0/3.0)\n",
      "r=a*math.sqrt(3)/4.0\n",
      "\n",
      "#Result\n",
      "print('\\nThe lattice constant of alfa-iron is %.4f A\u00b0'%(a*10**10))\n",
      "print('\\nThe atomic radius  of alfa-iron is %.5f *10^-10 m'%(r*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The lattice constant of alfa-iron is 0.2868 A\u00b0\n",
        "\n",
        "The atomic radius  of alfa-iron is 0.12420 *10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.21, page no-42"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Lattice constant\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "d=8960.0                     # Density of copper\n",
      "m=63.54                      # Atomic weight of copper\n",
      "n=4.0                        # No of atoms per unit cell for Fcc\n",
      "avg=6.023*10**26             # Avogadro's number\n",
      "\n",
      "#calculation\n",
      "a=(n*m*10**-3/(avg*d))**(1.0/3.0)\n",
      "\n",
      "#Result\n",
      "print('\\nThe lattice constant of copper is %.4f A\u00b0'%(a*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The lattice constant of copper is 0.3611 A\u00b0\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.22, page no-42"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Glancing angle \n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "a=3.81*10**-10               # lattice spacing\n",
      "h=1.0                        # Miller indices wrt X-axis\n",
      "k=3.0                        # Miller indices wrt Y-axis\n",
      "l=2.0                        # Miller indices wrt Z-axis\n",
      "lam=0.58*10**-10             # Wavelength of X-rays\n",
      "n=2.0                        # order of diffraction\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "theta=math.asin(n*lam/(2*d))\n",
      "\n",
      "#Result\n",
      "print('The angle of glancing at which 2nd order diffraction pattern of NaCl occurs is %.2f\u00b0'%(theta*180/math.pi))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The angle of glancing at which 2nd order diffraction pattern of NaCl occurs is 34.72\u00b0\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.23, page no-43"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lattice constant\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "h=3.0                          # Miller indices wrt X-axis                     \n",
      "k=0.0                          # Miller indices wrt Y-axis \n",
      "l=2.0                          # Miller indices wrt Z-axis \n",
      "theta=35                       # glancing angle\n",
      "lam=0.7*10**-10                # wavelength of X-rays \n",
      "n=1.0                          # order of diffraction\n",
      "\n",
      "#calculations\n",
      "d=n*lam/(2*math.sin(theta*math.pi/180))\n",
      "a=d*math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\nThe interplanar distance for(302) plane is %.3f*10^-11 m'%(d*10**11))\n",
      "print('\\nThe lattice constance is %.2f*10^-10 m'%(a*10**10))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The interplanar distance for(302) plane is 6.102*10^-11 m\n",
        "\n",
        "The lattice constance is 2.20*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.24, page no-44"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "For plane (0 0 1)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plane drawing 1\n",
      "\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "point = np.array([0, 0, 1])\n",
      "normal = np.array([0, 0, 1])\n",
      "\n",
      "# calculations\n",
      "d = -point.dot(normal)\n",
      "x, y = np.meshgrid(range(10), range(10))                           # create x,y\n",
      "z = (-normal[0] * x - normal[1] * y - d) * 1. / normal[2]          # calculate corresponding z\n",
      "\n",
      "# Result\n",
      "plt3d = plt.figure().gca(projection='3d')\n",
      "plt3d.plot_surface(x, y, z, rstride=1, cstride=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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kMpDztu5j27YOtm3bQTC4hnR6H2AxdepMlixZwimnHJ9t8JgwYcKgqLiWsePD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FAAAE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\n3AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa2a3780>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "For plane(1 0 1)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plane drawing 2\n",
      "\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "point = np.array([1, 0, 1])\n",
      "normal = np.array([1, 0, 1])\n",
      "\n",
      "# calculations\n",
      "d = -point.dot(normal)\n",
      "x, y = np.meshgrid(range(10), range(10))                           # create x,y\n",
      "z = (-normal[0] * x - normal[1] * y - d) * 1. / normal[2]          # calculate corresponding z\n",
      "\n",
      "# Result\n",
      "plt3d = plt.figure().gca(projection='3d')\n",
      "plt3d.plot_surface(x, y, z, rstride=1, cstride=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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J9evX0717d6699louvPDCivZVDh2OdI3IOxaL5T5AQ7aWtXmMeSq1U5Ex5vlQ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       "text": [
        "<matplotlib.figure.Figure at 0xaf62438>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "For plane(1 1 1)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plane drawing 3\n",
      "\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "point = np.array([1, 1, 1])\n",
      "normal = np.array([1, 1, 1])\n",
      "\n",
      "# calculations\n",
      "d = -point.dot(normal)\n",
      "x, y = np.meshgrid(range(10), range(10))                           # create x,y\n",
      "z = (-normal[0] * x - normal[1] * y - d) * 1. / normal[2]          # calculate corresponding z\n",
      "\n",
      "# Result\n",
      "plt3d = plt.figure().gca(projection='3d')\n",
      "plt3d.plot_surface(x, y, z, rstride=1, cstride=1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Drm9nka+XftdA01bQ3r6E971vd+bPn8vRRx/ts8/RQbpR6FrDrOGWsjmjYpDz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xad8ab00>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.25, page no-45"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# InterPlanar Spacing\n",
      "\n",
      "import math\n",
      "#Variable Declaration\n",
      "theta=12                   # glancing angle\n",
      "lam=2.82*10**-10           # interplanar spacing\n",
      "n=1.0                      # order of diffraction\n",
      "\n",
      "#Calculation\n",
      "d=n*lam/(2*math.sin(theta*math.pi/180))\n",
      "\n",
      "#Result\n",
      "print('The interplanar spacing is %.3f *10^-10 m'%(d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The interplanar spacing is 6.782 *10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.26, page no-46"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lattice spacing and deBroglie wavelength\n",
      "\n",
      "import math\n",
      "#variable Declaration\n",
      "theta=27.5/2                 # glancing angle \n",
      "a=0.563*10**-9               # lattice constant\n",
      "n=1.0                        # order of diffraction\n",
      "h=1.0                        # Miller indices wrt X-axis\n",
      "k=1.0                        # Miller indices wrt Y-axis\n",
      "l=1.0                        # Miller indices wrt Z-axis\n",
      "\n",
      "#calaculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "lam=2*d*math.sin(theta*math.pi/180)/n\n",
      "\n",
      "#Result\n",
      "print('\\nThe lattice spacing for the plane (111) is %.2f * 10^-10 m'%(d*10**10))\n",
      "print('\\nThe deBroglie wavelength of the neutrons is %.3f *10^-10 m'%(lam*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The lattice spacing for the plane (111) is 3.25 * 10^-10 m\n",
        "\n",
        "The deBroglie wavelength of the neutrons is 1.545 *10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.27, page no-46"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lattice constant and atomic radius\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "h=1.0                       # Miller indices wrt X-axis\n",
      "k=1.0                       # Miller indices wrt Y-axis\n",
      "l=0.0                       # Miller indices wrt Z-axis\n",
      "d=2*10**-10                 #interplanar spacing\n",
      "\n",
      "#Calculation\n",
      "a=d*math.sqrt(h**2+k**2+l**2)\n",
      "R=a/(2*math.sqrt(2))\n",
      "\n",
      "#Result\n",
      "print('The lattice constant is %.3f*10^-10 m\\nThe atomic radius of the crystal is %.1f *10^-10 m'%(a*10**10,R*10**10))\n",
      "\n",
      "#Answer in the book for lattice constant is wrong"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lattice constant is 2.828*10^-10 m\n",
        "The atomic radius of the crystal is 1.0 *10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.28, page no-47"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#energy of the neutron\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "theta=22                     # glancing angle\n",
      "d=1.8*10**-10                # interplanar spacing\n",
      "n=1.0                        # order of diffraction\n",
      "h=6.626*10**-34              # planck's constant\n",
      "m=9.11*10**-31               # mass of an atom kg\n",
      "e=1.609*10**-19              # Charge of an electron\n",
      "\n",
      "#calculations\n",
      "lam=2*d*math.sin(theta*math.pi/180)/n\n",
      "lam= math.ceil(lam*10**13)/10**13\n",
      "E=(1/(2*m))*(h/lam)**(2)\n",
      "\n",
      "#result\n",
      "print('\\nThe deBroglie wavelength of the neutron is %.3f *10^-10\\nthe energy of the neutron is %.3f eV'%(lam*10**10,E/e))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The deBroglie wavelength of the neutron is 1.349 *10^-10\n",
        "the energy of the neutron is 82.295 eV\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.29, page no-48"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# InterPlanar Spacing\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "h=1.0                      # Miller indices wrt X-axis\n",
      "k=1.0                      # Miller indices wrt Y-axis\n",
      "l=1.0                      # Miller indices wrt Z-axis\n",
      "a=3*10**-10                # lattice spacing\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\nThe interplanar spacing for the plane(%d%d%d) is %.3f*10^-10 m'%(h,k,l,d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The interplanar spacing for the plane(111) is 1.732*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.30, page no-48"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lattice spacing from Miller indices \n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "h=3.0                      # Miller indices wrt X-axis\n",
      "k=2.0                      # Miller indices wrt Y-axis\n",
      "l=1.0                      # Miller indices wrt Z-axis \n",
      "rfcc=0.1278*10**-9         # Atomic radius at Fcc State\n",
      "\n",
      "#calculation\n",
      "a=4*rfcc/math.sqrt(2)\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#Result\n",
      "print('\\nThe lattice constant = %.3f *10^-10\\nThe interplanar spacing for the plane(%d%d%d) is %.2f*10^-11 m'%(a*10**10,h,k,l,d*10**11))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The lattice constant = 3.615 *10^-10\n",
        "The interplanar spacing for the plane(321) is 9.66*10^-11 m\n"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.31, page no-49"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Number of atoms in Al foil\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "a=0.4049*10**-10             # lattice constant\n",
      "t=0.005                      # thickness of the coil\n",
      "A=25*10**-2                  # Area of the foil\n",
      "\n",
      "#calculation\n",
      "n=t*A/a**3\n",
      "\n",
      "#Result\n",
      "print('The number of atoms in the Al foil is %.2f * 10^28'%(n*10**-28))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The number of atoms in the Al foil is 1.88 * 10^28\n"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.32, page no-49"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# energy of the neutron\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "theta=20                   # glancing angle\n",
      "d=2*10**-10                # interplanar spacing\n",
      "n=1.0                      # order of diffraction\n",
      "h=6.626*10**-34            # planck's constant\n",
      "m=1.67*10**-27             # mass of an atom\n",
      "e=1.609*10**-19            # charge of an electron\n",
      "\n",
      "#Calculation\n",
      "lam=2*d*math.sin(theta*math.pi/180)/n\n",
      "E=(1/(2*m))*(h/lam)**(2)\n",
      "\n",
      "#Result\n",
      "print('\\nThe deBroglie wavelength of the neutron is %.3f *10^-10\\nthe energy of the neutron is %.5f eV'%(lam*10**10,E/e))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The deBroglie wavelength of the neutron is 1.368 *10^-10\n",
        "the energy of the neutron is 0.04365 eV\n"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.35, page no-51"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# deBroglie wavelength of electrons\n",
      "\n",
      "import math\n",
      "#variable declaration\n",
      "e=1.602*10**-19                 # charge of an electron\n",
      "h=6.626*10**-34                 # planck's constant\n",
      "m=9.11*10**-31                  # mass of an electron\n",
      "ek=235.2*e                      # kinetic energy\n",
      "n=1.0                           # order of diffraction\n",
      "theta=9.21                      # glancing angle\n",
      "\n",
      "#Calculation\n",
      "lam=h/math.sqrt(2*m*ek)\n",
      "d=n*lam/(2*math.sin(theta*math.pi/180))\n",
      "\n",
      "#Result\n",
      "print('\\nThe deBroglie wavelength of electron is %.3f *10^-11 m\\nThe interplanar spacing is %.3f *10^-10 m'%(lam*10**11,d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The deBroglie wavelength of electron is 7.997 *10^-11 m\n",
        "The interplanar spacing is 2.498 *10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.36, page no-52"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Lattice spacing from Miller indices\n",
      "\n",
      "import math\n",
      "# Intercepts are in the ratio 3a:4b along X,Y and parallel to Z axis\n",
      "# x-intercept 3, y-intercept 4 and z-intercept infinity \n",
      "\n",
      "#variable declaration\n",
      "a=2.0*10**-10       # 2 Angstrom\n",
      "h=4.0               # Miller indices wrt X-axis\n",
      "k=3.0               # Miller indices wrt Y-axis\n",
      "l=0.0               # Miller indices wrt Z-axis\n",
      "\n",
      "#calculation\n",
      "d=a/math.sqrt(h**2+k**2+l**2)\n",
      "\n",
      "#result\n",
      "print('The lattice spacing for the plane (%d%d%d) is %.1f*10^-10 m'%(h,k,l,d*10**10))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The lattice spacing for the plane (430) is 0.4*10^-10 m\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 2.38, page no-53"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plane Drawing\n",
      "print('Same as example 2.24 of the same chapter')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Same as example 2.24 of the same chapter\n"
       ]
      }
     ],
     "prompt_number": 35
    }
   ],
   "metadata": {}
  }
 ]
}