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diff --git a/sample_notebooks/SPANDANAARROJU/Chapter4_J3M7PEz.ipynb b/sample_notebooks/SPANDANAARROJU/Chapter4_J3M7PEz.ipynb new file mode 100644 index 00000000..e9783bbb --- /dev/null +++ b/sample_notebooks/SPANDANAARROJU/Chapter4_J3M7PEz.ipynb @@ -0,0 +1,211 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 4: Defects in Crystals" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 1, Page number 4.14" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "equilibrium concentration of vacancy at 300K is 7.577 *10**5\n", + "equilibrium concentration of vacancy at 900K is 6.502 *10**19\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N=6.023*10**26; #avagadro number\n", + "T1=1/float('inf'); #temperature 0K(K)\n", + "T2=300;\n", + "T3=900; #temperature(K)\n", + "k=1.38*10**-23; #boltzmann constant \n", + "deltaHv=120*10**3*10**3/N; #enthalpy(J/vacancy)\n", + "\n", + "#Calculation\n", + "#n1=N*math.exp(-deltaHv/(k*T1)); #equilibrium concentration of vacancy at 0K\n", + "#value of n1 cant be calculated in python, as the denominator is 0 and it shows float division error\n", + "n2=N*math.exp(-deltaHv/(k*T2)); #equilibrium concentration of vacancy at 300K \n", + "n3=N*math.exp(-deltaHv/(k*T3)); #equilibrium concentration of vacancy at 900K \n", + "\n", + "#Result\n", + "#print \"equilibrium concentration of vacancy at 0K is\",n1\n", + "print \"equilibrium concentration of vacancy at 300K is\",round(n2/10**5,3),\"*10**5\"\n", + "print \"equilibrium concentration of vacancy at 900K is\",round(n3/10**19,3),\"*10**19\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 2, Page number 4.15" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fraction of vacancies at 1000 is 8.5 *10**-7\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "nbyN1=1*10**-10; #fraction of vacancies\n", + "T1=500+273;\n", + "T2=1000+273;\n", + "\n", + "#Calculation\n", + "lnx=T1*math.log(nbyN1)/T2;\n", + "x=math.exp(lnx); #fraction of vacancies at 1000\n", + "\n", + "#Result\n", + "print \"fraction of vacancies at 1000 is\",round(x*10**7,1),\"*10**-7\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 3, Page number 4.16" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "concentration of schottky defects is 6.42 *10**11 per m**3\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "d=2.82*10**-10; #interionic distance(m)\n", + "T=300; #temperature(K)\n", + "k=1.38*10**-23; #boltzmann constant \n", + "e=1.6*10**-19; #charge(coulomb)\n", + "n=4; #number of molecules\n", + "deltaHs=1.971*e; #enthalpy(J)\n", + "\n", + "#Calculation\n", + "V=(2*d)**3; #volume of unit cell(m**3)\n", + "N=n/V; #number of ion pairs\n", + "x=deltaHs/(2*k*T);\n", + "n=N*math.exp(-x); #concentration of schottky defects(per m**3)\n", + "\n", + "#Result\n", + "print \"concentration of schottky defects is\",round(n*10**-11,2),\"*10**11 per m**3\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example number 4, Page number 4.17" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "concentration of schottky defects is 9.23 *10**12 per cm**3\n", + "amount of climb down by the dislocations is 0.1846 step or 0.3692 *10**-8 cm\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N=6.026*10**23; #avagadro number \n", + "T=500; #temperature(K)\n", + "k=1.38*10**-23; #boltzmann constant \n", + "deltaHv=1.6*10**-19; #charge(coulomb)\n", + "V=5.55; #molar volume(cm**3)\n", + "nv=5*10**7*10**6; #number of vacancies\n", + "\n", + "#Calculation\n", + "n=N*math.exp(-deltaHv/(k*T))/V; #concentration of schottky defects(per m**3)\n", + "x=round(n/nv,4); #amount of climb down by the dislocations(step)\n", + "xcm=2*x*10**-8; #amount of climb down by the dislocations(cm)\n", + "\n", + "#Result\n", + "print \"concentration of schottky defects is\",round(n/10**12,2),\"*10**12 per cm**3\"\n", + "print \"amount of climb down by the dislocations is\",x,\"step or\",xcm*10**8,\"*10**-8 cm\" " + ] + } + ], + "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": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |