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-{
- "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
-}
generated by cgit (git 2.34.1) at 2025-01-09 20:17:31 +0000