From f270f72badd9c61d48f290c3396004802841b9df Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:53:46 +0530 Subject: Removed duplicates --- .../material_science_ch_7.ipynb | 573 +++++++++++++++++++++ 1 file changed, 573 insertions(+) create mode 100755 Material_Science_by_V._Rajendran/material_science_ch_7.ipynb (limited to 'Material_Science_by_V._Rajendran/material_science_ch_7.ipynb') diff --git a/Material_Science_by_V._Rajendran/material_science_ch_7.ipynb b/Material_Science_by_V._Rajendran/material_science_ch_7.ipynb new file mode 100755 index 00000000..9cb2cb86 --- /dev/null +++ b/Material_Science_by_V._Rajendran/material_science_ch_7.ipynb @@ -0,0 +1,573 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 7: Elecron theory of Solids" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.1, page no-160" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Mobility ofelectrons\n", + "\n", + "import math\n", + "#variable declaration\n", + "rho=1.73*10**-8 # Resistivity of copper\n", + "z=63.5 # atomic weight of copper\n", + "d=8.92*10**3 # density of copper\n", + "avg=6.023*10**26 # Avogadro's number\n", + "e=1.6*10**-19 # charge of an electron\n", + "m=9.11*10**-31 # mass of an electron\n", + "\n", + "#variable declaration\n", + "n=avg*d/z\n", + "sig=1/rho\n", + "tau=sig*m/(n*e**2)\n", + "mu=sig/(n*e)\n", + "\n", + "#Result\n", + "print(\"Mobility of electrons in copper is %.2f *10^-3 m^2/V-s\"%(mu*10**3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Mobility of electrons in copper is 4.27 *10^-3 m^2/V-s\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.2, page no-161" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Resistivity of copper\n", + "\n", + "import math\n", + "#variable declaration\n", + "r=1.85*10**-10 # radius of the sodium atom\n", + "t=3*10**-14 # mean free time of sodium atom\n", + "m=9.11*10**-31 # mass of electron\n", + "e=1.6*10**-19 # charge of an atom\n", + "n= 2.0 # No of atoms per unit cell\n", + "\n", + "#calculations\n", + "a=r*(4.0/math.sqrt(3.0)) \n", + "a= math.floor(a*10**12)/10**12 \n", + "ne=n/a**3\n", + "ne= math.ceil(ne*10**-26)/10**-26\n", + "rho=m/(ne*t*e**2)\n", + "\n", + "#Result\n", + "print(\"Resistivity of copper is %.3f*10^-8 Ohm-m\"%(rho*10**8))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Resistivity of copper is 4.616*10^-8 Ohm-m\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.3, page no-161" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Electrical resistivity of sodium\n", + "\n", + "import math\n", + "#variable declaration\n", + "t=3.1*10**14 # mean free time of electron\n", + "m=9.11*10**-31 # mass of an electron\n", + "e=1.6*10**-19 # charge of an electron \n", + "n=25.33*10**27 # no of electrons per unit volume\n", + "\n", + "#calculations\n", + "rho=m/(n*t*e**2)\n", + "\n", + "#Result\n", + "print(\"The electric resistivity of sodium at 0\u00b0C is %.3f*10^-36 Ohm-m\"%(rho*10**36))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electric resistivity of sodium at 0\u00b0C is 4.532*10^-36 Ohm-m\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.4, page no-162" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# mobility of the electron\n", + "\n", + "import math\n", + "#variable declaration\n", + "t=3.4*10**-14 # relaxation time of conduction electrons\n", + "m=9.11*10**-31 # mass of electron\n", + "e=1.6*10**-19 # charge of electron\n", + "n=5.8*10**28 # no of force electrons per unit volume\n", + "\n", + "#calculations\n", + "rho=m/(n*t*e**2)\n", + "print(\"\\nThe electric resistivity of material is %.3f*10^-8 Ohm-m\"%(rho*10**8))\n", + "mu=e*t/m\n", + "print(\"\\nThe mobility of the electron in a metal is %.2f*10^-3 m^2/v-s\"%(mu*10**3))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "The electric resistivity of material is 1.805*10^-8 Ohm-m\n", + "\n", + "The mobility of the electron in a metal is 5.97*10^-3 m^2/v-s\n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.5, page no-163" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# drift velocity\n", + "\n", + "import math\n", + "#variable declaration\n", + "rho=1.54*10**-8 # resistivity of silver\n", + "E=100 # electric field along the wire\n", + "n=5.8*10**28 # carrier concentration of electron\n", + "e=1.6*10**-19 # charge on electron\n", + "\n", + "#calculation\n", + "mu=1/(rho*n*e)\n", + "vd=mu*E\n", + "\n", + "#Result\n", + "print(\"\\nMobility of electron in silvetr is %.4f*10^-3 m^2/v-s\\n\\nThe drift velocity of the electron in silver is %.5f m/s \"%(mu*10**3,vd))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Mobility of electron in silvetr is 6.9973*10^-3 m^2/v-s\n", + "\n", + "The drift velocity of the electron in silver is 0.69973 m/s \n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.6, page no-163" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# mobility ofelectron\n", + "\n", + "import math\n", + "#variable declaration\n", + "d=10.5*10**3 # density of silver\n", + "sig=6.8*10**7 # conductivity of silver\n", + "wt=107.9 # atomic weight of silver\n", + "e=1.609*10**-19 # charge of electron\n", + "avg=6.023*10**26 # avogadro's number\n", + "\n", + "#calculations\n", + "n=avg*d/wt\n", + "mu=sig/(n*e)\n", + "\n", + "#Result\n", + "print(\"The mobility of electron is %.2f *10^-2 m^2.V/s\"%(mu*10**2))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mobility of electron is 0.72 *10^-2 m^2.V/s\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.7, page no-164" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Lorentz number\n", + "\n", + "import math\n", + "#variable declaration\n", + "sig=5.87*10**7 # electrical conductivity of copper\n", + "k=390.0 # thermal conductivity of copper\n", + "T=293.0 # temperature\n", + "\n", + "#calculation\n", + "L=k/(sig*T)\n", + "\n", + "#Result\n", + "print(\"The Lorentz number is %.3f *10^-8 W.Ohm/K^2\"%(L*10**8))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Lorentz number is 2.268 *10^-8 W.Ohm/K^2\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.8, page no-164" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Lorentz number\n", + "import math\n", + "\n", + "#variable declaration\n", + "t=1*10**-14 # relaxation time\n", + "T=300 # temperature\n", + "m=9.1*10**-31 # mass of electron\n", + "e=1.6*10**-19 # charge of electron\n", + "n=6*10**28 # electron concentration\n", + "\n", + "#calculations\n", + "sig=(n*t*e**2)/m\n", + "k=1.38*10**-23\n", + "k1=n*math.pi**2*k**2*T*t/(3*m)\n", + "L=k1/(sig*T)\n", + "\n", + "#Result\n", + "print(\"\\nThe electrical conductivity is %.4f * 10^7/ohm-m\"%(sig*10**-7))\n", + "print(\"\\n\\nThermal conductivity is %.2f W/m-k\"%k1)\n", + "print(\"\\n\\nThe Lorentz number is %.4f *10^-8 W.Ohm/k^2\"%(L*10**8))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "The electrical conductivity is 1.6879 * 10^7/ohm-m\n", + "\n", + "\n", + "Thermal conductivity is 123.93 W/m-k\n", + "\n", + "\n", + "The Lorentz number is 2.4474 *10^-8 W.Ohm/k^2\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.9, page no-165" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Electrical conductivity\n", + "\n", + "import math\n", + "\n", + "#variable declaration\n", + "d=8900 # Density of copper\n", + "cu=63.5 # Atomic weight of Cu\n", + "t=10**-14 # Relaxation time\n", + "avg=6.022*10**23 # Avogadro's number\n", + "m=9.1*10**-31 # mass of electron\n", + "e=1.6*10**-19 # charge of electron\n", + "\n", + "#Calculations\n", + "n=avg*d*1000/cu\n", + "sig=(n*t*e**2)/m\n", + "print(\"The electrical conductivity is %.3f *10^7 /Ohm-m\"%(sig*10**-7))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electrical conductivity is 2.374 *10^7 /Ohm-m\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.10, page no-166" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Drift velocity of electrons\n", + "import math\n", + "\n", + "#variable declaration\n", + "rho=1.6*10**-8 # resistivity of the silver piece\n", + "e=1.603*10**-19 # charge of an electron\n", + "fe=5.5*e # energy of the silver\n", + "avg=6.023*10**23 # avogadro's number\n", + "d=1.05*10**4 # density of silver\n", + "wt=107.9*10**-3 # atomic weight of silver\n", + "m=9.1*10**-31 # mass of electron\n", + "c=3*10**8 # speed of light\n", + "\n", + "#calculations\n", + "sig=1/rho\n", + "n=avg*d/wt\n", + "t=sig*m/(n*e**2)\n", + "lam=c*t\n", + "vd=sig*100/(n*e)\n", + "\n", + "#Result\n", + "print(\"\\nThe conductivity of silver piece is %.2f*10^7 per Ohm-m\\n\\nThe relaxation time is %.2f*10^-14 s\"%(sig*10**-7,t*10**14))\n", + "print(\"\\nThe drift velocity of electrons in the silver piece is %.2f m/s\"%(math.floor(vd*100)/100))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "The conductivity of silver piece is 6.25*10^7 per Ohm-m\n", + "\n", + "The relaxation time is 3.78*10^-14 s\n", + "\n", + "The drift velocity of electrons in the silver piece is 0.66 m/s\n" + ] + } + ], + "prompt_number": 51 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.11, page no-167" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# resistivityy of the copper\n", + "\n", + "import math\n", + "#variable declaration\n", + "r1=1.7*10**-8 # resistivity of copper at T1\n", + "t2=300.0 # temperature(T1)\n", + "t1=700.0+273 # temperature(T2)\n", + "\n", + "#calculation\n", + "r2=r1*math.sqrt((t1/t2))\n", + "print(\"The resistivityy of the copper wire is %.4f*10^-8 Ohm-m\"%(r2*10**8))\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The resistivityy of the copper wire is 3.0616*10^-8 Ohm-m\n" + ] + } + ], + "prompt_number": 52 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 7.12, page no-168" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Relaxation time, Drift velocity, Fermi velocity, mean free path\n", + "\n", + "import math\n", + "#variable declarations\n", + "rho=1.54*10**-8 # Resistivity \n", + "e=1.6*10**-19 # charge of electron\n", + "ef=5.5*e # Fermi energy\n", + "n=5.8*10**28 # concentration of electrons\n", + "m=9.1*10**-31 # mass of electron \n", + "\n", + "#(i)\n", + "t=m/(rho*n*e**2)\n", + "mu=e*t/m\n", + "print(\"\\n(i)\\nThe relaxation time is %.2f*10^-14 s\\nThe mobility of the electrons is %.4f *10^-3 m^2/V-s\"%(t*10**14,mu*10**3))\n", + "\n", + "#(ii)\n", + "vd=e*t*100/m\n", + "print(\"\\n\\n(ii)\\nthe drift velocity of elctron is %.5f m/s\"%vd)\n", + "\n", + "#(iii)\n", + "vf=math.sqrt(2*ef/m)\n", + "print(\"\\n\\n(iii)\\nFermi velocity is %.2f*10^6 m/s\"%(vf*10**-6))\n", + "\n", + "#(iv)\n", + "lam=vf*t\n", + "print(\"\\n\\n(iv)\\nThe mean free path is %.3f*10^-8 m\"%(lam*10**8))" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "(i)\n", + "The relaxation time is 3.98*10^-14 s\n", + "The mobility of the electrons is 6.9973 *10^-3 m^2/V-s\n", + "\n", + "\n", + "(ii)\n", + "the drift velocity of elctron is 0.69973 m/s\n", + "\n", + "\n", + "(iii)\n", + "Fermi velocity is 1.39*10^6 m/s\n", + "\n", + "\n", + "(iv)\n", + "The mean free path is 5.535*10^-8 m\n" + ] + } + ], + "prompt_number": 55 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit