From 4a1f703f1c1808d390ebf80e80659fe161f69fab Mon Sep 17 00:00:00 2001 From: Thomas Stephen Lee Date: Fri, 28 Aug 2015 16:53:23 +0530 Subject: add books --- .../Chapter4.ipynb | 370 +++++++++++++++++++++ 1 file changed, 370 insertions(+) create mode 100755 Materials_Science_by_Dr._M._Arumugam/Chapter4.ipynb (limited to 'Materials_Science_by_Dr._M._Arumugam/Chapter4.ipynb') diff --git a/Materials_Science_by_Dr._M._Arumugam/Chapter4.ipynb b/Materials_Science_by_Dr._M._Arumugam/Chapter4.ipynb new file mode 100755 index 00000000..8da77cca --- /dev/null +++ b/Materials_Science_by_Dr._M._Arumugam/Chapter4.ipynb @@ -0,0 +1,370 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#4: Electron Theory of Solids" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.1, Page number 4.57" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "de broglie wavelength is 0.00286 angstrom\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "E=10**4*1.6*10**-19; #kinetic energy(J)\n", + "m=1.675*10**-27; #mass(kg)\n", + "h=6.625*10**-34; #planck's constant\n", + "\n", + "#Calculation\n", + "v=math.sqrt(2*E/m); #velocity(m/s)\n", + "lamda=h/(m*v); #de broglie wavelength(m)\n", + "\n", + "#Result\n", + "print \"de broglie wavelength is\",round(lamda*10**10,5),\"angstrom\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.2, Page number 4.58" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "energy difference is 1.81 *10**-37 J\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "m=9.1*10**-31; #mass(kg)\n", + "nx=ny=nz=1;\n", + "n=6;\n", + "a=1; #edge(m)\n", + "h=6.63*10**-34; #planck's constant\n", + "\n", + "#Calculation\n", + "E1=h**2*(nx**2+ny**2+nz**2)/(8*m*a**2);\n", + "E2=h**2*n/(8*m*a**2);\n", + "E=E2-E1; #energy difference(J)\n", + "\n", + "#Result\n", + "print \"energy difference is\",round(E*10**37,2),\"*10**-37 J\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.3, Page number 4.58" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "temperature is 1261 K\n", + "answer varies due to rounding off errors\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "y=1/100; #percentage of probability\n", + "x=0.5*1.6*10**-19; #energy(J)\n", + "k=1.38*10**-23; #boltzmann constant\n", + "\n", + "#Calculation\n", + "xbykT=math.log((1/y)-1);\n", + "T=x/(k*xbykT); #temperature(K)\n", + "\n", + "#Result\n", + "print \"temperature is\",int(T),\"K\"\n", + "print \"answer varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.4, Page number 4.58" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "fermi energy is 3.15 eV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "d=970; #density(kg/m**3)\n", + "Na=6.02*10**26; #avagadro number\n", + "w=23; #atomic weight\n", + "m=9.1*10**-31; #mass(kg)\n", + "h=6.62*10**-34; #planck's constant\n", + "\n", + "#Calculation\n", + "N=d*Na/w; #number of atoms/m**3\n", + "x=h**2/(8*m);\n", + "y=(3*N/math.pi)**(2/3);\n", + "EF=x*y; #fermi energy(J)\n", + "\n", + "#Result\n", + "print \"fermi energy is\",round(EF/(1.6*10**-19),2),\"eV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.5, Page number 4.59" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "work function is 4.14 eV\n", + "maximum kinetic energy is 0.758 eV\n", + "answer varies due to rounding off errors\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h=6.625*10**-34; #planck's constant\n", + "c=3*10**8; #velocity of light(m/s)\n", + "lamda0=3000*10**-10; #wavelength(m)\n", + "e=1.6*10**-19; #charge(coulomb)\n", + "lamda=2536*10**-10; #wavelength(m)\n", + "\n", + "#Calculation\n", + "hf0=c*h/(lamda0*e); #work function(eV)\n", + "E=c*h*((1/lamda)-(1/lamda0))/e; #maximum kinetic energy(eV)\n", + "\n", + "#Result\n", + "print \"work function is\",round(hf0,2),\"eV\"\n", + "print \"maximum kinetic energy is\",round(E,3),\"eV\"\n", + "print \"answer varies due to rounding off errors\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.6, Page number 4.59" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "lowest energy of neutron is 2.05 MeV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n=1;\n", + "hbar=1.054*10**-34; \n", + "m=1.67*10**-27; #mass of neutron(kg)\n", + "a=10**-14; #size(m)\n", + "\n", + "#Calculation\n", + "E=n**2*math.pi**2*hbar**2/(2*m*a**2); #lowest energy of neutron(J)\n", + "\n", + "#Result\n", + "print \"lowest energy of neutron is\",round(E/(1.6*10**-13),2),\"MeV\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.7, Page number 4.59" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "probability of particle is 0.0158\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "from scipy.integrate import quad\n", + "\n", + "#Variable declaration\n", + "k=1;\n", + "\n", + "#Calculation\n", + "def zintg(x):\n", + "\treturn math.exp(-2*k*x)\n", + "\n", + "a=quad(zintg,2/k,3/k)[0]; #probability of particle\n", + "\n", + "#Result\n", + "print \"probability of particle is\",round(2*a,4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Example number 4.8, Page number 4.60" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "voltage appeared is 1.83 mV\n" + ] + } + ], + "source": [ + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "i=10**-2; #current(ampere)\n", + "A=0.01*0.001; #area(m**2)\n", + "RH=3.66*10**-4; #hall coefficient(m**3/coulomb)\n", + "Bz=0.5; #magnetic induction(weber/m**2)\n", + "\n", + "#Calculation\n", + "Jx=i/A; \n", + "Ey=RH*Bz*Jx; \n", + "Vy=Ey*i; #voltage appeared(V)\n", + "\n", + "#Result\n", + "print \"voltage appeared is\",Vy*10**3,\"mV\"" + ] + } + ], + "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