{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3: X-Ray Diffraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 1, Page number 3.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum order of diffraction is 1.53\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "d=1.181;       #lattice spacing(angstrom)\n",
    "theta=90*math.pi/180;     #glancing angle(radian)\n",
    "lamda=1.540;    #wavelength of X-rays(angstrom)\n",
    "\n",
    "#Calculation\n",
    "n=2*d*math.sin(theta)/lamda;       #maximum order of diffraction \n",
    "\n",
    "#Result\n",
    "print \"maximum order of diffraction is\",round(n,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 2, Page number 3.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cube edge of unit cell is 3.514 angstrom\n",
      "answer given in the book varies due to rounding off errors\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n=1;     #order\n",
    "theta=9.5*math.pi/180;     #glancing angle(radian)\n",
    "lamda=0.58;                 #wavelength(angstrom)\n",
    "h=2;\n",
    "k=0;\n",
    "l=0;\n",
    "\n",
    "#Calculation\n",
    "d=n*lamda/(2*math.sin(theta));       #lattice parameter(angstrom)\n",
    "a=d*math.sqrt(h**2+k**2+l**2);       #cube edge of unit cell(angstrom)\n",
    "\n",
    "#Result\n",
    "print \"cube edge of unit cell is\",round(a,3),\"angstrom\"\n",
    "print \"answer given in the book varies due to rounding off errors\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 3, Page number 3.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "glancing angle for 3rd order is 26 degrees 35 minutes\n",
      "answer for minutes given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "theta=(8+(35/60))*math.pi/180;     #glancing angle(radian)\n",
    "lamda=0.842;   #wavelength of X-rays(angstrom)\n",
    "n1=1;                  #order\n",
    "n3=3;                  #order \n",
    "\n",
    "#Calculation\n",
    "theta3=math.asin(n3*lamda*math.sin(theta)/(n1*lamda))*180/math.pi;    #glancing angle for 3rd order(degrees)\n",
    "theta3d=int(theta3);                             #glancing angle for 3rd order(degrees)  \n",
    "theta3m=(theta3-theta3d)*60;                     #glancing angle for 3rd order(minutes)\n",
    "\n",
    "#Result\n",
    "print \"glancing angle for 3rd order is\",theta3d,\"degrees\",int(theta3m),\"minutes\"\n",
    "print \"answer for minutes given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 4, Page number 3.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "interplanar spacing is 2.22 angstrom\n",
      "value of h**2+k**2+l**2 is 2\n",
      "miller indices are (110) or (011) or (101)\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "theta=20.3*math.pi/180;     #glancing angle(radian)\n",
    "lamda=1.54;   #wavelength of X-rays(angstrom)\n",
    "n=1;          #order\n",
    "a=3.16;       #lattice parameter(angstrom)\n",
    "\n",
    "#Calculation\n",
    "d=n*lamda/(2*math.sin(theta));       #interplanar spacing(angstrom)\n",
    "x=(a/d)**2;        #assume x=(h**2+k**2+l**2)\n",
    "\n",
    "#Result\n",
    "print \"interplanar spacing is\",round(d,2),\"angstrom\"\n",
    "print \"value of h**2+k**2+l**2 is\",int(x)\n",
    "print \"miller indices are (110) or (011) or (101)\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 5, Page number 3.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "wavelength is 1.553 angstrom\n",
      "energy of X-rays is 8 *10**3 eV\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "n=4;     #order\n",
    "A=107.87;     #atomic weight(kg)\n",
    "theta=(19+(12/60))*math.pi/180;     #glancing angle(radian)\n",
    "h=1;\n",
    "k=1;\n",
    "l=1;\n",
    "N=6.02*10**26;          #avagadro number\n",
    "rho=10500;              #density(kg/m**3)\n",
    "H=6.625*10**-34;        #plancks constant(Js)\n",
    "c=3*10**8;              #velocity of light(m/s)\n",
    "e=1.6*10**-19;          #charge(coulomb)\n",
    "\n",
    "#Calculation\n",
    "a=round(((n*A/(N*rho))**(1/3))*10**10,2);   #lattice parameter(angstrom)\n",
    "d=a/math.sqrt((h**2)+(k**2)+(l**2));     #lattice parameter(angstrom)\n",
    "lamda=2*d*math.sin(theta);         #wavelength(angstrom)\n",
    "E=H*c/(lamda*10**-10*e);                   #energy of X-rays(eV)\n",
    "\n",
    "#Result\n",
    "print \"wavelength is\",round(lamda,3),\"angstrom\"\n",
    "print \"energy of X-rays is\",int(round(E/10**3)),\"*10**3 eV\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example number 6, Page number 3.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "specimen distance is 7.559 cm\n",
      "answer given in the book varies due to rounding off errors\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "h=1;\n",
    "k=1;\n",
    "l=1;\n",
    "a=4.57;   #lattice parameter(angstrom)\n",
    "lamda=1.52;         #wavelength(angstrom)\n",
    "r=5;        #radius(cm)\n",
    "\n",
    "#Calculation\n",
    "d=a/math.sqrt(h**2+k**2+l**2);     #lattice parameter(angstrom)\n",
    "theta=math.asin(lamda/(2*d));      #glancing angle(degrees)\n",
    "X=r/math.tan(2*theta);             #specimen distance(cm)\n",
    "\n",
    "#Result\n",
    "print \"specimen distance is\",round(X,3),\"cm\"\n",
    "print \"answer given in the book varies due to rounding off errors\""
   ]
  }
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