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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11: Crystal Structure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 1, Page number 299"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lattice constant is 4 angstrom\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "n=4;        #number of molecules per unit cell\n",
    "M=60.2;     #molecular weight\n",
    "N=6.02*10**26;     #avagadro number(kg mol-1)\n",
    "rho=6250;          #density(kg/m**3)\n",
    "\n",
    "#Calculations\n",
    "a=(n*M/(rho*N))**(1/3);     #lattice constant(m)\n",
    "\n",
    "#Result\n",
    "print \"lattice constant is\",int(a*10**10),\"angstrom\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 2, Page number 299"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lattice constant is 2.867 angstrom\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "n=2;        #number of molecules per unit cell\n",
    "M=55.8;     #molecular weight\n",
    "N=6.02*10**26;     #avagadro number(kg mol-1)\n",
    "rho=7870;          #density(kg/m**3)\n",
    "\n",
    "#Calculations\n",
    "a=(n*M/(rho*N))**(1/3);     #lattice constant(m)\n",
    "\n",
    "#Result\n",
    "print \"lattice constant is\",round(a*10**10,3),\"angstrom\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3, Page number 299"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "distance between two nearest copper atoms is 2.55 angstrom\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "n=4;        #number of molecules per unit cell\n",
    "M=63.5;     #molecular weight\n",
    "N=6.02*10**23;     #avagadro number(kg mol-1)\n",
    "rho=8.96;          #density(gm/cm**3)\n",
    "\n",
    "#Calculations\n",
    "a=(n*M/(rho*N))**(1/3);     #lattice constant(m)\n",
    "d=a/math.sqrt(2);           #distance between two nearest copper atoms(cm)\n",
    "\n",
    "#Result\n",
    "print \"distance between two nearest copper atoms is\",round(d*10**8,2),\"angstrom\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 4, Page number 303"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "miller indices of plane are ( 3 2 1 )\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration  \n",
    "a=1/2;\n",
    "b=1/3;\n",
    "c=1/6;     #intercepts along the three axes\n",
    "\n",
    "#Calculations\n",
    "def lcm(x, y):\n",
    "    if x > y:\n",
    "        greater = x\n",
    "    else:\n",
    "        greater = y\n",
    "    while(True):\n",
    "        if((greater % x == 0) and (greater % y == 0)):\n",
    "            lcm = greater\n",
    "            break\n",
    "        greater += 1\n",
    "        \n",
    "    return lcm\n",
    "\n",
    "z=lcm(1/a,1/b);\n",
    "lcm=lcm(z,1/c);\n",
    "h=a*lcm;\n",
    "k=b*lcm;\n",
    "l=c*lcm;      #miller indices of plane\n",
    "\n",
    "#Result\n",
    "print \"miller indices of plane are (\",int(h),int(k),int(l),\")\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 5, Page number 303"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "miller indices of plane are ( 3 4 0 )\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration  \n",
    "a=1/4;\n",
    "b=1/3;\n",
    "x=float(\"inf\");\n",
    "c=1/x;     #intercepts along the three axes\n",
    "\n",
    "#Calculations\n",
    "def lcm(x, y):\n",
    "    if x > y:\n",
    "        greater = x\n",
    "    else:\n",
    "        greater = y\n",
    "    while(True):\n",
    "        if((greater % x == 0) and (greater % y == 0)):\n",
    "            lcm = greater\n",
    "            break\n",
    "        greater += 1\n",
    "        \n",
    "    return lcm\n",
    "\n",
    "lcm=lcm(1/a,1/b);\n",
    "h=a*lcm;\n",
    "k=b*lcm;\n",
    "l=c*lcm;      #miller indices of plane\n",
    "\n",
    "#Result\n",
    "print \"miller indices of plane are (\",int(h),int(k),int(l),\")\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 6, Page number 303"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "miller indices of plane are ( 6 -2 3 )\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration  \n",
    "a=1/1;\n",
    "b=-1/3;\n",
    "c=1/2;     #intercepts along the three axes\n",
    "\n",
    "#Calculations\n",
    "def lcm(x, y):\n",
    "    if x > y:\n",
    "        greater = x\n",
    "    else:\n",
    "        greater = y\n",
    "    while(True):\n",
    "        if((greater % x == 0) and (greater % y == 0)):\n",
    "            lcm = greater\n",
    "            break\n",
    "        greater += 1\n",
    "        \n",
    "    return lcm\n",
    "\n",
    "z=lcm(1/a,1/b);\n",
    "lcm=lcm(z,1/c);\n",
    "h=a*lcm;\n",
    "k=b*lcm;\n",
    "l=c*lcm;      #miller indices of plane\n",
    "\n",
    "#Result\n",
    "print \"miller indices of plane are (\",int(h),int(k),int(l),\")\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 7, Page number 304"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept on y-axis is 1.2 angstrom\n",
      "intercept on z-axis is 4.0 angstrom\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration    \n",
    "p1=1.2;       #x-primitive(angstrom)\n",
    "p2=1.8;       #y-primitive(angstrom)\n",
    "p3=2.0;       #z-primitive(angstrom)\n",
    "x=2;          #x-intercept\n",
    "y=3;          #y-intercept\n",
    "z=1;          #z-intercept\n",
    "h=1.2;        #intercept on x-axis(angstrom)\n",
    "\n",
    "#Calculations\n",
    "h1=p1/x;      \n",
    "k1=p2/y;\n",
    "l1=p3/z;\n",
    "k=h*k1/h1;    #intercept on y-axis(angstrom)\n",
    "l=h*p3/h1;    #intercept on z-axis(angstrom)\n",
    "\n",
    "#Result\n",
    "print \"intercept on y-axis is\",k,\"angstrom\"\n",
    "print \"intercept on z-axis is\",l,\"angstrom\""
   ]
  }
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