{ "metadata": { "name": "", "signature": "sha256:6f3332c2cf8866e9257d8f3e11193b59b2e8f54645aa9a7c58a49b95bb6e6cc9" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter7:SUPERCONDUCTIVITY" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg1:pg-272" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Tc=3.7 #critical temperature in K\n", "Hc_0=0.0306 #critical magnetic field in Tesla at 0K\n", "T=2 #temperature in K\n", "Hc=Hc_0*(1-(T/Tc)**2)\n", "print\"Critical field at 2 K is \",round(Hc,4),\"Tesla\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Critical field at 2 K is 0.0217 Tesla\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg2:pg-272" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Tc=7.2 #transition temperature in K\n", "T=5 #temperature in K\n", "Hc_T=3.3e4 #critical magnetic field at 5K in A/m\n", "Hc_0=Hc_T/(1-(T/Tc)**2)\n", "print\"Maximum value of H at 0 K is \",\"{:.2e}\".format(Hc_0),\"A/m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum value of H at 0 K is 6.37e+04 A/m\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg3:pg-273" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Tc=7.2 #critical temperature in K\n", "Hc_0=1 #let,critical magnetic field at 0K\n", "Hc_T=0.1*Hc_0 #critical magnetic field at T Kelvin\n", "T=sqrt(1-Hc_T/Hc_0)*Tc\n", "print\"Temperature is \",round(T,2),\"K\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature is 6.83 K\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg4:pg-273" ] }, { "cell_type": "code", "collapsed": false, "input": [ "T=4.2 #temperature in K\n", "Hc_0=0.0803 #critical magnetic field at 0K in Wb/m**2\n", "Tc=7.2 #critical temperature for Pb in K\n", "Hc_T=Hc_0*(1-(T/Tc)**2)\n", "print\"Critical field at 4.2 K is \",round(Hc_T,5),\"Tesla\"#answer is wrong in book" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Critical field at 4.2 K is 0.05298 Tesla\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg5:pg-273" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Hc_T=105e3 #critical magnetic field at T Kelvin in A/m\n", "Hc_0=150e3 #critical magnetic field at 0K in A/m\n", "Tc=9.2 #critical temperature in K\n", "T=sqrt(1-Hc_T/Hc_0)*Tc\n", "print\"Temperature is \",round(T,2),\"K\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature is 5.04 K\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg6:pg-274" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Hc_T=1e5 #critical magnetic field at 8K in A/m\n", "T=8 #temperature in K\n", "Hc_0=2e5 #critical magnetic field at 0K in A/m\n", "Tc=T/sqrt(1-Hc_T/Hc_0)\n", "print\"Transition temperature is \",round(Tc,1),\"K\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Transition temperature is 11.3 K\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg7:pg-274" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Tc=7.26 #critical temperature in K\n", "Hc_0=8e5 #critical magnetic field at 0K in A/m\n", "Hc_T=4e4 #critical magnetic field at T kelvin in A/m\n", "T=sqrt(1-Hc_T/Hc_0)*Tc\n", "print\"T =\",round(T,2),\"K\",\"\\nThe temperature of the metal should be held below\",round(T,2),\"K\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "T = 7.08 K \n", "The temperature of the metal should be held below 7.08 K\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg8:pg-275" ] }, { "cell_type": "code", "collapsed": false, "input": [ "T1=14 #temperature in K\n", "T2=12 #temperature in K\n", "T=4.2 #temperature in K\n", "Hc_T1=0.176 #critical magnetic field at temperature T1\n", "Hc_T2=0.528 #critical magnetic field at temperature T2\n", "Tc=sqrt((Hc_T2*T1**2-Hc_T1*T2**2)/(Hc_T2-Hc_T1))\n", "Tc=int(Tc*10)/10. #rounding off\n", "Hc_0=Hc_T1/(1-(T1/Tc)**2)\n", "Hc_T=Hc_0*(1-(T/Tc)**2)\n", "print\"Transition temperature is \",Tc,\"K\"\n", "print\"Critical field at 0 K is \",round(Hc_0,3),\"Tesla\"\n", "print\"Critical field at 4.2 K is \",round(Hc_T,2),\"Tesla\"\n", "#answers in book are wrong because value of T2 is taken as 13K in calculation which is wrong." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Transition temperature is 14.8 K\n", "Critical field at 0 K is 1.673 Tesla\n", "Critical field at 4.2 K is 1.54 Tesla\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9:pg-275" ] }, { "cell_type": "code", "collapsed": false, "input": [ "D=1.0 #diameter of Pb wire in mm\n", "Bc=0.0548 #in Tesla\n", "mu_0=4*math.pi*1e-7 #absolute permeability of air in N/A**2\n", "Ic=math.pi*D*1e-3*Bc/mu_0\n", "print\"Current is \",int(Ic),\"amp\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Current is 137 amp\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg10:pg-276" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Hc_0=6.5e3 #critical magnetic field at 0K in A/m\n", "Tc=7.18 #critical temperature in K\n", "Hc_T=4.5e3 #critical magnetic field at T Kelvin in A/m\n", "T=sqrt(1-Hc_T/Hc_0)*Tc\n", "print\"Temperature is \",round(T,2),\"K\"\n", "D=2 #diameter of the lead wire in mm\n", "r=D/2 \n", "Ic=2*math.pi*r*1e-3*Hc_T\n", "Jc=Ic/(math.pi*(r*1e-3)**2)\n", "print\"Critical current density is \",\"{:.1e}\".format(Jc),\"A/m**2\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Temperature is 3.98 K\n", "Critical current density is 9.0e+06 A/m**2\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg11:pg-281" ] }, { "cell_type": "code", "collapsed": false, "input": [ "T=3.5 #temperature in K\n", "lamda_T=750 #penetration depth of Hg at 3.5K in Angstrom\n", "Tc=4.153 #critical temperature in K\n", "lamda_0=lamda_T*sqrt(round(1-(T/Tc)**4,3))\n", "print\"Penetration depth at 0 K is\",round(lamda_0,1),\"Angstrom\"#answer is wrong in book because of calculation mistake " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Penetration depth at 0 K is 528.2 Angstrom\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg12:pg-281" ] }, { "cell_type": "code", "collapsed": false, "input": [ "m=9.1e-31 #mass of electron kg\n", "mu_0=12.56e-7 #absolute permeability of air in N/A**2\n", "e=1.6e-19 #charge of electron in coulomb\n", "ns=1e28 #number of super electrons per meter cube\n", "lamda_0=sqrt(m/(mu_0*ns*e**2))\n", "lamda_0=round(lamda_0,9)*1e10\n", "print\"Penetration depth at 0 K is \",int(lamda_0),\"Angstrom\"\n", "Tc=3 #critical temperature in K\n", "T=1. #temperature in K\n", "lamda_T=lamda_0/sqrt(1-(T/Tc)**4)\n", "print\"Penetration depth at 1 K is \",int(lamda_T),\"Angstrom\"\n", "#in book lamda(at 3K) is printed,which is wrong. Correct notation is lamda(at 1K)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Penetration depth at 0 K is 530 Angstrom\n", "Penetration depth at 1 K is 533 Angstrom\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg13:pg-286" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Tc=9.25 #critical temperature in K\n", "T=0 #temperature in K\n", "Kb=1.38e-23 #Boltzmann's constant in J/K\n", "Eg=3.53*Kb*Tc/(1.6e-19)\n", "h=6.63e-34 #planck constant joule-sec\n", "c=3e8 #speed of light in m/sec\n", "print\"Energy gap Eg is \",round(Eg*1e3,2),\"meV\"\n", "lamda_min=h*c/round(Eg*1.6e-19,23)\n", "print\"Minimum photon wavelength is \",\"{:.2e}\".format(lamda_min),\"m\"\n", "print\" This wavelength lie in the far-infrared region of electromagnetic radiations.\"\n", "v=round(Eg*1.6e-19,23)/h\n", "print\"Frequency needed is \",\"{:.2e}\".format(v),\"s**-1\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Energy gap Eg is 2.82 meV\n", "Minimum photon wavelength is 4.42e-04 m\n", " This wavelength lie in the far-infrared region of electromagnetic radiations.\n", "Frequency needed is 6.79e+11 s**-1\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg14:pg-286" ] }, { "cell_type": "code", "collapsed": false, "input": [ "M=200.59 #average atomic mass of Hg in amu\n", "m=204 #mass of isotope in amu\n", "T=4.153 #temperature in K\n", "t=4.118 #temperature in K\n", "dM=m-M\n", "dTc=t-T\n", "alpha=-(M*dTc/(dM*T))\n", "print\"Isotope effect coefficient is \",round(alpha,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Isotope effect coefficient is 0.496\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }