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+{

+ "cells": [

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "#Crystal Structures"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example 1.1, Page number 1.36"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 6,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "a= 5.43 Angstorm\n",

+      "density = 6.88 kg/m**3\n",

+      "#Answer given in the textbook is wrong\n"

+     ]

+    }

+   ],

+   "source": [

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#variable declaration\n",

+    "d=2.351                 #bond lenght\n",

+    "N=6.02*10**26           #Avagadro number\n",

+    "n=8                     #number of atoms in unit cell\n",

+    "A=28.09                 #Atomin mass of silicon\n",

+    "m=6.02*10**26           #1mole\n",

+    "\n",

+    "#Calculations\n",

+    "a=(4*d)/math.sqrt(3)\n",

+    "p=(n*A)/((a*10**-10)*m)    #density\n",

+    "\n",

+    "#Result\n",

+    "print \"a=\",round(a,2),\"Angstorm\"\n",

+    "print \"density =\",round(p*10**16,2),\"kg/m**3\"\n",

+    "print\"#Answer given in the textbook is wrong\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example 1.2, Page number 1.36"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 1,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "radius of largest sphere is 0.154700538379252*r\n",

+      "maximum radius of sphere is 0.414213562373095*r\n"

+     ]

+    }

+   ],

+   "source": [

+    " import math\n",

+    "from __future__ import division\n",

+    "from sympy import Symbol\n",

+    "\n",

+    "#Variable declaration\n",

+    "r=Symbol('r')\n",

+    "\n",

+    "#Calculation\n",

+    "a1=4*r/math.sqrt(3);\n",

+    "R1=(a1/2)-r;           #radius of largest sphere\n",

+    "a2=4*r/math.sqrt(2);\n",

+    "R2=(a2/2)-r;       #maximum radius of sphere\n",

+    "\n",

+    "#Result\n",

+    "print \"radius of largest sphere is\",R1\n",

+    "print \"maximum radius of sphere is\",R2    \n",

+    "   "

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example 1.3, Page number 1.37"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 1,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "a1= 2.905 Angstrom\n",

+      "Unit cell volume =a1**3 = 24.521 *10**-30 m**3\n",

+      "Volume occupied by one atom = 12.26 *10**-30 m**3\n",

+      "a2= 3.654 Angstorm\n",

+      "Unit cell volume =a2**3 = 48.8 *10**-30 m**3\n",

+      "Volume occupied by one atom = 12.2 *10**-30 m**3\n",

+      "Volume Change in % = 0.493\n",

+      "Density Change in % = 0.5\n",

+      "Thus the increase of density or the decrease of volume is about 0.5%\n"

+     ]

+    }

+   ],

+   "source": [

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#variable declaration\n",

+    "r1=1.258            #Atomic radius of BCC\n",

+    "r2=1.292            #Atomic radius of FCC\n",

+    "\n",

+    "#calculations\n",

+    "a1=(4*r1)/math.sqrt(3)       #in BCC\n",

+    "b1=((a1)**3)*10**-30         #Unit cell volume\n",

+    "v1=(b1)/2                    #Volume occupied by one atom\n",

+    "a2=2*math.sqrt(2)*r2         #in FCC\n",

+    "b2=(a2)**3*10**-30                   #Unit cell volume\n",

+    "v2=(b2)/4                    #Volume occupied by one atom  \n",

+    "v_c=((v1)-(v2))*100/(v1)     #Volume Change in % \n",

+    "d_c=((v1)-(v2))*100/(v2)     #Density Change in %\n",

+    "\n",

+    "#Results\n",

+    "print \"a1=\",round(a1,3),\"Angstrom\" \n",

+    "print \"Unit cell volume =a1**3 =\",round((b1)/10**-30,3),\"*10**-30 m**3\"\n",

+    "print \"Volume occupied by one atom =\",round(v1/10**-30,2),\"*10**-30 m**3\"\n",

+    "print \"a2=\",round(a2,3),\"Angstorm\"\n",

+    "print \"Unit cell volume =a2**3 =\",round((b2)/10**-30,3),\"*10**-30 m**3\"\n",

+    "print \"Volume occupied by one atom =\",round(v2/10**-30,2),\"*10**-30 m**3\"\n",

+    "print \"Volume Change in % =\",round(v_c,3)\n",

+    "print \"Density Change in % =\",round(d_c,2)\n",

+    "print \"Thus the increase of density or the decrease of volume is about 0.5%\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {

+    "collapsed": true

+   },

+   "source": [

+    "##Example 1.4, Page number 1.38"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 13,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "a= 0.563 *10**-9 metre\n",

+      "spacing between the nearest neighbouring ions = 0.2814 nm\n"

+     ]

+    }

+   ],

+   "source": [

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#variable declaration\n",

+    "n=4     \n",

+    "M=58.5                  #Molecular wt. of NaCl\n",

+    "N=6.02*10**26           #Avagadro number\n",

+    "rho=2180                #density\n",

+    "\n",

+    "#Calculations\n",

+    "a=((n*M)/(N*rho))**(1/3)    \n",

+    "s=a/2\n",

+    "\n",

+    "#Result\n",

+    "print \"a=\",round(a/10**-9,3),\"*10**-9 metre\"\n",

+    "print \"spacing between the nearest neighbouring ions =\",round(s/10**-9,4),\"nm\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "##Example 1.5, Page number 1.38"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 14,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "lattice constant, a= 0.36 nm\n"

+     ]

+    }

+   ],

+   "source": [

+    "import math\n",

+    "from __future__ import division\n",

+    "\n",

+    "#variable declaration\n",

+    "n=4     \n",

+    "A=63.55                 #Atomic wt. of NaCl\n",

+    "N=6.02*10**26           #Avagadro number\n",

+    "rho=8930                #density\n",

+    "\n",

+    "#Calculations\n",

+    "a=((n*A)/(N*rho))**(1/3)      #Lattice Constant\n",

+    "\n",

+    "#Result\n",

+    "print \"lattice constant, a=\",round(a*10**9,2),\"nm\""

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {

+    "collapsed": true

+   },

+   "source": [

+    "##Example 1.6, Page number 1.39"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 16,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Density of iron = 8805.0 kg/m**-3\n"

+     ]

+    }

+   ],

+   "source": [

+    "import math\n",

+    "\n",

+    "#variable declaration\n",

+    "r=0.123                  #Atomic radius\n",

+    "n=4\n",

+    "A=55.8                   #Atomic wt\n",

+    "a=2*math.sqrt(2) \n",

+    "N=6.02*10**26           #Avagadro number\n",

+    "\n",

+    "#Calculations\n",

+    "rho=(n*A)/((a*r*10**-9)**3*N)\n",

+    "\n",

+    "#Result\n",

+    "print \"Density of iron =\",round(rho),\"kg/m**-3\""

+   ]

+  }

+ ],

+ "metadata": {

+  "kernelspec": {

+   "display_name": "Python 2",

+   "language": "python",

+   "name": "python2"

+  },

+  "language_info": {

+   "codemirror_mode": {

+    "name": "ipython",

+    "version": 2

+   },

+   "file_extension": ".py",

+   "mimetype": "text/x-python",

+   "name": "python",

+   "nbconvert_exporter": "python",

+   "pygments_lexer": "ipython2",

+   "version": "2.7.9"

+  }

+ },

+ "nbformat": 4,

+ "nbformat_minor": 0

+}