From d36fc3b8f88cc3108ffff6151e376b619b9abb01 Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:40:35 +0530 Subject: Revised list of TBCs --- .../8.DEFECTS IN SOLIDS.ipynb | 215 +++++++++++++++++++++ 1 file changed, 215 insertions(+) create mode 100755 backup/ENGINEERING_PHYSICS_by_M.ARUMUGAM_version_backup/8.DEFECTS IN SOLIDS.ipynb (limited to 'backup/ENGINEERING_PHYSICS_by_M.ARUMUGAM_version_backup/8.DEFECTS IN SOLIDS.ipynb') diff --git a/backup/ENGINEERING_PHYSICS_by_M.ARUMUGAM_version_backup/8.DEFECTS IN SOLIDS.ipynb b/backup/ENGINEERING_PHYSICS_by_M.ARUMUGAM_version_backup/8.DEFECTS IN SOLIDS.ipynb new file mode 100755 index 00000000..09325a4b --- /dev/null +++ b/backup/ENGINEERING_PHYSICS_by_M.ARUMUGAM_version_backup/8.DEFECTS IN SOLIDS.ipynb @@ -0,0 +1,215 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#8:Defects In Solids " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 8.1, Page number 8.16" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "at 0K, The number of vacancies per kilomole of copper is 0\n", + "at 300K, The number of vacancies per kilomole of copper is 7.577 *10**5\n", + "at 900K, The numb ber of vacancies per kilomole of copper 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\n", + "deltaHv=120\n", + "B=1.38*10**-23\n", + "k=6.023*10**23\n", + "\n", + "#Calculations\n", + "n0=0 # 0 in denominator\n", + "n300=N*math.exp(-deltaHv*10**3/(k*B*300)) #The number of vacancies per kilomole of copper\n", + "n900=N*math.exp(-(deltaHv*10**3)/(k*B*900))\n", + "\n", + "#Results\n", + "print\"at 0K, The number of vacancies per kilomole of copper is\",n0\n", + "print\"at 300K, The number of vacancies per kilomole of copper is\",round(n300/10**5,3),\"*10**5\"\n", + "print\"at 900K, The numb ber of vacancies per kilomole of copper is\",round(n900/10**19,3),\"*10**19\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 8.2, Page number 8.17" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fraction of vacancies at 1000 degrees C = 8.5 *10**-7\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "from sympy import Symbol\n", + "\n", + "#Variable declaration\n", + "F_500=1*10**-10\n", + "delta_Hv=Symbol('delta_Hv')\n", + "k=Symbol('k')\n", + "T1=500+273\n", + "T2=1000+273\n", + "\n", + "\n", + "#Calculations\n", + "lnx=math.log(F_500)*T1/T2;\n", + "x=math.exp(round(lnx,2))\n", + "\n", + "print\"Fraction of vacancies at 1000 degrees C =\",round(x*10**7,1),\"*10**-7\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 8.3, Page number 8.17" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Volume of unit cell of NaCl = 1.794 *10**-28 m**3\n", + "Total number of ion pairs 'N' =' 2.23 *10**28\n", + "The concentration of Schottky defects per m**3 at 300K = 6.42 *10**11\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "a=(2*2.82*10**-10)\n", + "delta_Hs=1.971*1.6*10**-19\n", + "k=1.38*10**-23\n", + "T=300\n", + "\n", + "#Calculations\n", + "V=a**3 #Volume of unit cell of NaCl\n", + "N=4/V #Total number of ion pairs\n", + "n=N*math.e**-(delta_Hs/(2*k*T)) \n", + "\n", + "#Result\n", + "print\"Volume of unit cell of NaCl =\",round(V*10**28,3),\"*10**-28 m**3\"\n", + "print\"Total number of ion pairs 'N' ='\",round(N/10**28,2),\"*10**28\"\n", + "print\"The concentration of Schottky defects per m**3 at 300K =\",round(n/10**11,2),\"*10**11\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 8.4, Page number 8.18" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The number that must be created on heating from 0 to 500K is n= 9.22 *10**12 per cm**3\n", + "As one step is 2 Angstorms, 5*10**7 vacancies are required for 1cm\n", + "The amount of climb down by the dislocation is 0.369 cm\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N=6.023*10**23\n", + "delta_Hv=1.6*10**-19\n", + "k=1.38*10**-23\n", + "T=500\n", + "mv=5.55; #molar volume\n", + "x=2*10**-8; #numbber of cm in 1 angstrom\n", + "\n", + "#Calculations\n", + "n=N*math.exp(-delta_Hv/(k*T))/mv\n", + "a=round(n/(5*10**7*10**6),4)*x;\n", + "\n", + "#Result\n", + "print\"The number that must be created on heating from 0 to 500K is n=\",round(n/10**12,2),\"*10**12 per cm**3\" #into cm**3\n", + "print\"As one step is 2 Angstorms, 5*10**7 vacancies are required for 1cm\"\n", + "print\"The amount of climb down by the dislocation is\",a*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": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} -- cgit