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authorkinitrupti2017-05-12 18:53:46 +0530
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-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "#4: Defects in Crystals"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 4.1, Page number 4.5"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "ratio of vacancies is 1.082 *10**5\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "Ev=1;\n",
- "k=1.38*10**-23; #boltzmann constant(J/K)\n",
- "e=1.6*10**-19; #charge(eV)\n",
- "\n",
- "#Calculation\n",
- "r=Ev/(2.303*1000*k/e); \n",
- "n=10**r; #ratio of n1000/n500\n",
- "\n",
- "#Result\n",
- "print \"ratio of vacancies is\",round(n/10**5,3),\"*10**5\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 4.2, Page number 4.5"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "number of vacancies per atom at 350K is 0.5486 *10**-17\n",
- "number of vacancies per atom at 500K is 0.827 *10**-12\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "Ev=1.2;\n",
- "k=1.38*10**-23; #boltzmann constant(J/K)\n",
- "e=1.6*10**-19; #charge(eV)\n",
- "T1=350; #temperature(K)\n",
- "T2=500; #temperature(K)\n",
- "\n",
- "#Calculation\n",
- "x1=Ev/(2.303*k*T1/e);\n",
- "n1=1/(10**x1); #number of vacancies per atom at 350K\n",
- "x2=Ev/(2.303*k*T2/e);\n",
- "n2=1/(10**x2); #number of vacancies per atom at 500K\n",
- "\n",
- "#Result\n",
- "print \"number of vacancies per atom at 350K is\",round(n1*10**17,4),\"*10**-17\"\n",
- "print \"number of vacancies per atom at 500K is\",round(n2*10**12,3),\"*10**-12\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 4.3, Page number 4.7"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "average energy required is 1.971 eV\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "d=2.82*10**-10; #distance(m)\n",
- "k=1.38*10**-23; #boltzmann constant(J/K)\n",
- "e=1.6*10**-19; #charge(eV)\n",
- "T=273+25; #temperature(K)\n",
- "sd=5*10**11; #schotky defects(per m**3)\n",
- "\n",
- "#Calculation\n",
- "V=(2*d)**3; #volume of unit cell(m**3)\n",
- "N=4/V; #density of ion pairs\n",
- "x=round(math.log10(N/sd),2);\n",
- "Es=2*(k/e)*T*2.303*x; #average energy required(eV)\n",
- "\n",
- "#Result\n",
- "print \"average energy required is\",round(Es,3),\"eV\""
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "##Example number 4.4, Page number 4.8"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {
- "collapsed": false
- },
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "ratio of Frenkel defects is 1.125 *10**-6\n"
- ]
- }
- ],
- "source": [
- "#importing modules\n",
- "import math\n",
- "from __future__ import division\n",
- "\n",
- "#Variable declaration\n",
- "T1=273+25; #temperature(K)\n",
- "T2=273+350; #temperature(K)\n",
- "Ef=1.35; #energy(eV)\n",
- "k=8.625*10**-5;\n",
- "\n",
- "#Calculation\n",
- "x=(Ef/k)*((1/(2*T1))-(1/(2*T2)))/2.303;\n",
- "r=1/(10**round(x,3)); #ratio of Frenkel defects\n",
- "\n",
- "#Result\n",
- "print \"ratio of Frenkel defects is\",round(r*10**6,3),\"*10**-6\""
- ]
- }
- ],
- "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
-}