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+{

+ "metadata": {

+  "name": ""

+ },

+ "nbformat": 3,

+ "nbformat_minor": 0,

+ "worksheets": [

+  {

+   "cells": [

+    {

+     "cell_type": "heading",

+     "level": 1,

+     "metadata": {},

+     "source": [

+      "Chapter 03 : Crystalgeometry and Structure Determination"

+     ]

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 3.2, Page No 25"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "import math\n",

+      "#initialisation of variables\n",

+      "sc_n = 1.0/8 \t\t# sharing of one lattice point in a unit cell\n",

+      "sc_N = 8.0\t\t \t# Number of lattice points in Simple cubic \n",

+      "bcc_n_e = 1.0/4\t\t# sharing of one edge lattice point in a BCC \n",

+      "bcc_N_e = 4.0\t\t# Number of edge lattice point in a BCC \n",

+      "bcc_n_c  = 1.0\t\t# sharing of one body center lattice point in a BCC \n",

+      "bcc_N_c = 1.0\t\t# Number of body center lattice point in a BCC \n",

+      "fcc_n_e = 1.0/8 \t# sharing of one corner lattice point in a FCC \n",

+      "fcc_N_e = 8.0\t\t# Number of corner lattice point in a FCC \n",

+      "fcc_n_f = 1.0/2 \t# sharing of one face center lattice point in a FCC \n",

+      "fcc_N_f = 6.0\t\t# Number of face center lattice point in a FCC \n",

+      "\n",

+      "#Calculations\n",

+      "sc_net = sc_n*sc_N\n",

+      "bcc_net = bcc_n_e*bcc_N_e+bcc_n_c*bcc_N_c\n",

+      "fcc_net = fcc_n_e*fcc_N_e+fcc_n_f*fcc_N_f\n",

+      "\n",

+      "#Results\n",

+      "\n",

+      "print(\"Effective number of lattice points are as:\")\n",

+      "print(\"Space lattice \\t Abbreviation \\t Effective number of lattice point in unit cell \\n\")\n",

+      "print(\"Simple cubic \\t\\tSC \\t\\t %.2f \" %sc_net)\n",

+      "print(\"Body center cubic\\tBCC \\t\\t %.2f \" %bcc_net)\n",

+      "print(\"Face centered cubic\\tFCC \\t\\t %.2f \" %fcc_net)\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Effective number of lattice points are as:\n",

+        "Space lattice \t Abbreviation \t Effective number of lattice point in unit cell \n",

+        "\n",

+        "Simple cubic \t\tSC \t\t 1.00 \n",

+        "Body center cubic\tBCC \t\t 2.00 \n",

+        "Face centered cubic\tFCC \t\t 4.00 \n"

+       ]

+      }

+     ],

+     "prompt_number": 1

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 3.7, Page No 40"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "import math\n",

+      "#initialisation of variables\n",

+      "a = 3.16    #lattice parameter in angstrom\n",

+      "l1 = 1.0    # line number\n",

+      "l2 = 2.0    # line number\n",

+      "l3 = 3.0    # line number\n",

+      "l4 = 4.0    # line number\n",

+      "theta1 = 20.3   # angle for line 1\n",

+      "theta2 = 29.2   # angle for line 2\n",

+      "theta3 = 36.7   # angle for line 3\n",

+      "theta4 = 43.6   # angle for line 4\n",

+      "n = 1           # order \n",

+      "lambda1 = 1.54   # wavelength in angstrom\n",

+      "\n",

+      "#Calculations\n",

+      "d1 = lambda1/(2*math.sin(theta1*math.pi/180))\n",

+      "d2 = lambda1/(2*math.sin(theta2*math.pi/180))\n",

+      "d3 = lambda1/(2*math.sin(theta3*math.pi/180))\n",

+      "d4 = lambda1/(2*math.sin(theta4*math.pi/180))\n",

+      "x1 = a**2/d1**2  \n",

+      "x2 = a**2/d2**2  \n",

+      "x3 = a**2/d3**2  \n",

+      "x4 = a**2/d4**2 \t\t# where x is function of h,k and l\n",

+      "\n",

+      "#Results\n",

+      "print(\"Interplanar spacing is  %.3f angstrom \" %x1) # answer in book is 2.220 angstrom\n",

+      "if  math.floor(x1) == 2 :\n",

+      "    print(\"For a^2/d^2 = %.2f \\t Reflection plane is 110\" %math.floor(x1))\n",

+      "\n",

+      "if math.floor(x2) == 4 :\n",

+      "\tprint(\"For a^2/d^2 = %.2f \\t Reflection plane is 200\" %math.floor(x2))\n",

+      "\n",

+      "if math.floor(x3) == 6 :\n",

+      "    print(\"For a^2/d^2 = %.2f \\t Reflection plane is 211\" %math.floor(x3))\n",

+      "\n",

+      "if math.floor(x4) == 8 :\n",

+      "\tprint(\"For a^2/d^2 = %.2f \\t Reflection plane is 220\" %math.floor(x4))\n",

+      "\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Interplanar spacing is  2.027 angstrom \n",

+        "For a^2/d^2 = 2.00 \t Reflection plane is 110\n",

+        "For a^2/d^2 = 4.00 \t Reflection plane is 200\n",

+        "For a^2/d^2 = 6.00 \t Reflection plane is 211\n",

+        "For a^2/d^2 = 8.00 \t Reflection plane is 220\n"

+       ]

+      }

+     ],

+     "prompt_number": 2

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 3.8, Page No 45"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "import math\n",

+      "#initialisation of variables\n",

+      "d = 114.6 # diameter of power camera in angstrom\n",

+      "lambda1 = 1.54 # wavelength in angstrom\n",

+      "s1 = 86.0\n",

+      "s2 = 100.0\n",

+      "s3 = 148.0\n",

+      "s4 = 180.0\n",

+      "s5 = 188.0\n",

+      "s6 = 232.0 \n",

+      "s7 = 272.0\n",

+      "\n",

+      "#Calculations\n",

+      "R = d/2      # Radius \n",

+      "if R==57.3 :\n",

+      "    k = 1.0/4 \t\t\t# Bragg angle factor\n",

+      "a1 = (math.sin(s1*k*math.pi/180))**2\n",

+      "a2 = (math.sin(s2*k*math.pi/180))**2\n",

+      "a3 = (math.sin(s3*k*math.pi/180))**2\n",

+      "a4 = (math.sin(s4*k*math.pi/180))**2\n",

+      "a5 = (math.sin(s5*k*math.pi/180))**2\n",

+      "a6 = (math.sin(s6*k*math.pi/180))**2\n",

+      "a7 = (math.sin(s7*k*math.pi/180))**2\n",

+      "\n",

+      "c = 22 # constant to convert into integral number\n",

+      "\n",

+      "#Results\n",

+      "print(\"Within experimental error, values are as in integral ratio are as:\")\n",

+      "print(\"%.2f  \" %math.ceil(c*a1))\n",

+      "print(\"%.2f  \" %math.ceil(c*a2))\n",

+      "print(\"%.2f  \" %math.ceil(c*a3))\n",

+      "print(\"%.2f  \" %math.ceil(c*a4))\n",

+      "print(\"%.2f  \" %math.ceil(c*a5))\n",

+      "print(\"%.2f  \" %math.ceil(c*a6))\n",

+      "print(\"%.2f  \" %math.ceil(c*a7))\n",

+      "\n",

+      "print(\"\\n So, this structure is FCC and material is copper with 3.62 angstrom lattice parameter\")\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Within experimental error, values are as in integral ratio are as:\n",

+        "3.00  \n",

+        "4.00  \n",

+        "8.00  \n",

+        "11.00  \n",

+        "12.00  \n",

+        "16.00  \n",

+        "19.00  \n",

+        "\n",

+        " So, this structure is FCC and material is copper with 3.62 angstrom lattice parameter\n"

+       ]

+      }

+     ],

+     "prompt_number": 3

+    }

+   ],

+   "metadata": {}

+  }

+ ]

+}
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