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+{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 19: Superconductivity"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.1, Page 19.13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Given \n",
+ "T_c = 7.2 # critical temperature in K\n",
+ "T = 5.1 # temperature in K\n",
+ "lambda_ = 380 # penetration depth at 0 K in A\n",
+ "\n",
+ "#Calculations\n",
+ "lamda = lambda_ * (1 - (T / T_c)**4)**(-1./2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Penetration depth is %.2f A\"%lamda"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Penetration depth is 439.30 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.2, Page 19.13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import *\n",
+ "\n",
+ "# Given \n",
+ "Hc1 = 1.41e5 # first critical field at 14.1K\n",
+ "Hc2 = 4.205e5 # second critical field at 12.9K \n",
+ "T1 = 14.11 # temperature in K\n",
+ "T2 = 12.9 # temperature in K \n",
+ "T = 4.2 # temperature in K\n",
+ "lambda_ = 380 # penetration depth at 0 K in A\n",
+ "\n",
+ "#Calculations\n",
+ "Tc = sqrt((Hc2*T1**2 - Hc1*T2**2) / (Hc2 - Hc1))\n",
+ "H_ = Hc1 / (1 - (T1 / Tc)**2)\n",
+ "Hc = H_ * (1 - (T/Tc)**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Transition temperature is %.2f K\\nCritical field at temperate at 4.2 k is %.2e A/m\"%(Tc,Hc)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Transition temperature is 14.68 K\n",
+ "Critical field at temperate at 4.2 k is 1.69e+06 A/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.3, Page 19.14"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from math import *\n",
+ "\n",
+ "# Given \n",
+ "d = 1e-3 # diameter of wire in m\n",
+ "T1 = 4.2 # temperature in K\n",
+ "T2 = 7.18 # temperature in K\n",
+ "H_ = 6.51e4 # critical magnetic field at 0 K\n",
+ "\n",
+ "#Calculations\n",
+ "r = d / 2\n",
+ "Hc = H_ * (1 - (T1 / T2)**2)\n",
+ "Jc = (2 * pi * r * Hc) / (pi * r**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Critical current density is %.3e A/m^2\"%Jc"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Critical current density is 1.713e+08 A/m^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.4, Page 19.15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " \n",
+ "# Given \n",
+ "w = 199.5 # isotopic mass of Hg\n",
+ "Tc = 4.186 # critical temperature in K \n",
+ "w_ = 203.4 # increased isotope mass of Hg\n",
+ "\n",
+ "#Calculations\n",
+ "Tc_ = Tc * (w / w_)**(1./2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Critical temperature is %.4f K\"%Tc_"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Critical temperature is 4.1457 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.5, Page 19.15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " \n",
+ "# Given \n",
+ "T_c = 4.2 # critical temperature in K\n",
+ "T = 2.9 # temperature in K\n",
+ "lamda = 57 # penetration depth at 2.9 K in nm\n",
+ "\n",
+ "#Calculations\n",
+ "lambda_ = lamda * (1 - (T / T_c)**4)**(1./2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Penetration depth at 0 K is %.2f nm\"%lambda_"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Penetration depth at 0 K is 50.10 nm\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.6, Page 19.15"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " \n",
+ "# Given\n",
+ "T1 = 2.18 # temperature in first case in K\n",
+ "lambda1 = 16 # penetration depth at 2.18 K in nm\n",
+ "T2 = 8.1 # temperature in second case in K\n",
+ "lambda2 = 96 # penetration depth at 8.1 K in nm\n",
+ "\n",
+ "#Calculations\n",
+ "Tc = (((lambda2**2 * T2**4) - (T1**4 * lambda1**2)) / (lambda2**2 - lambda1**2))**(1./4)\n",
+ "\n",
+ "#Result\n",
+ "print \"Critical temperature is %.2f K\"%Tc"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Critical temperature is 8.16 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.7, Page 19.16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " \n",
+ "# Given \n",
+ "w = 26.91 # isotopic mass of superconducting sample\n",
+ "Tc = 1.19 # first critical temperature in K \n",
+ "w_ = 32.13 # increased isotope mass of superconducting sample\n",
+ "\n",
+ "#Calculations\n",
+ "Tc_ = Tc * (w / w_)**(1./2)\n",
+ "\n",
+ "#Result\n",
+ "print \"Critical temperature is %.3f K\"%Tc_"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Critical temperature is 1.089 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 19.8, Page 19.16"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ " \n",
+ "# Given \n",
+ "k = 1.38e-23 # Boltzmann's constant in J/K\n",
+ "h = 6.62e-34 # Planck constant in J sec\n",
+ "Tc = 4.2 # critical temperature of Hg in K\n",
+ "c = 3e8 # speed of light in m/sec \n",
+ "\n",
+ "#Calculations\n",
+ "E = 3 * k * Tc\n",
+ "lamda = h * c / E\n",
+ "\n",
+ "#Result\n",
+ "print \"Energy gap is %.2e eV\\nWavelength of photon is %.2e m\"%(E/1.6e-19,lamda)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Energy gap is 1.09e-03 eV\n",
+ "Wavelength of photon is 1.14e-03 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+} \ No newline at end of file
generated by cgit (git 2.34.1) at 2024-12-22 11:57:30 +0000