{ "metadata": { "name": "", "signature": "sha256:ab6a8819ae55a050f752b7af592620b211f459f05ec8dc687c071a119643f8a0" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 3: Specific Heat of Solids and\n", "Lattice Vibrations" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.1,Page number 79" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "V0 = 9.1*10**-5; # Atomic volume of Pb, metre cube per kg\n", "K = 2.3*10**-11; # Compressibility of Pb, metre square per newton\n", "alpha = 86*10**-6; # Coefficient of thermal expansion, per K\n", "Cv = 1.4*10**2; # Specific heat at constant volume, J/kg\n", "gama = alpha*V0/(K*Cv); # Grunesien parameter for Pb\n", "print\"The Grunesien parameter for Pb = \",round(gama,3);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Grunesien parameter for Pb = 2.43\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.2,Page number 79" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "V0 = 11*10**-5; # Atomic volume of Cu, metre cube per kg\n", "K = 0.75*10**-11; # Compressibility of Cu, metre square per newton\n", "alpha = 49*10**-6; # Coefficient of thermal expansion, per K\n", "gama = 1.9; # The Grunesien parameter for Cu = 2.4 \n", "Cv = alpha*V0/(K*gama); # Specific heat of Cu at constant volume, J/kg\n", "print\"The specific heat capacity of Cu = \",round(Cv,3),\"J/kg\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The specific heat capacity of Cu = 378.246 J/kg\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.3,Page number 88" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "\n", "N = 6.02*10**26; # Avogadro's number, per kmole\n", "C_t = 6.32*10**3; # Velocity of transverse wave, m/s\n", "C_l = 3.1*10**3; # Velocity of longitudinal wave, m/s\n", "rho = 2.7*10**3; # Density of Al, kg per metre cube\n", "M = 26.97; # Atomic weight of Al, gram per mol\n", "V = M/rho; # Atomic volume of Al, metre cube\n", "f_c = (9*N/(4*pi*V*(1.0/C_t**3+2.0/C_l**3)))**(1.0/3);\n", "print\"The Debye cut-off frequency of Al = \",\"{0:.3e}\".format(f_c),\"per sec\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Debye cut-off frequency of Al = 8.468e+12 per sec\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.4,Page number 89" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "\n", "N = 6.02*10**23; # Avogadro's number, per mole\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "R = N*k; # Molar gas constant, J/mol/K\n", "theta_D = 2230; # Debye temperature for diamond, K\n", "T = 300.0; # Room temperature, K\n", "C_v = 12.0/5*(pi**4*R)*(T/theta_D)**3; # Specific heat capacity per unit volume of diamond, J/mol-K\n", "print\"The heat capacity per unit volume of diamond = \",round(C_v,3),\"J/mol-K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The heat capacity per unit volume of diamond = 4.729 J/mol-K\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.5,Page number 89" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "theta_D = 1440.0; # Debye temperature for Be, K\n", "h = 6.626*10**-34; # Planck's constant, Js\n", "f_D = k*theta_D/h; # Debye cut off frequency of Be, Hz\n", "print\"The Debye cut off frequency of Be = \",\"{0:.3e}\".format(f_D),\"sec\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Debye cut off frequency of Be = 2.999e+13 sec\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.6,Page number 89" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "N = 6.023*10**23; # Avogadro's number, per kmol\n", "e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "R = N*k; # Molar gas constant, J/kmol/K\n", "E_F = 7; # Fermi energy of Cu, eV\n", "theta_D = 348.0; # Debye temperature of Cu, K\n", "T = 300.0; # Room temperature, K\n", "T_F = E_F/k; # Fermi temperature of Cu, K\n", "C_e = pi**2/2*R*10**3*(T/(T_F*e)); # Electronic heat capacity of Cu, J/kmol/K\n", "C_l = 12.0/5*(pi**4*R)*(T/theta_D)**3; # Lattice heat capacity of Cu, J/kmol/K\n", "print\"The electronic heat capacity of Cu = \",round(C_e,3),\"J/kmol/K\";\n", "print\"The lattice heat capacity of Cu = \",round(C_l,3),\"J/mol/K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The electronic heat capacity of Cu = 151.616 J/kmol/K\n", "The lattice heat capacity of Cu = 1244.884 J/mol/K\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.7,Page number 90" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "N = 6.023*10**23; # Avogadro's number, per kmol\n", "e = 1.602*10**-19; # Energy equivalent of 1 eV, J/eV\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "R = N*k; # Molar gas constant, J/kmol/K\n", "E_F = 7.0; # Fermi energy of Cu, eV\n", "theta_D = 348.0; # Debye temperature of Cu, K\n", "T = 0.01; # Room temperature, K\n", "T_F = E_F/k; # Fermi temperature of Cu, K\n", "C_e = pi**2/2*R*(T/(T_F*e)); # Electronic heat capacity of Cu, J/mol/K\n", "C_l = 12.0/5*(pi**4*R)*(T/theta_D)**3; # Lattice heat capacity of Cu, J/kmol/K\n", "print\"The electronic heat capacity of Cu = \",\"{0:.3e}\".format(C_e),\"J/mol/K\";\n", "print\"The lattice heat capacity of Cu = \",\"{0:.3e}\".format(C_l),\"J/mol/K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The electronic heat capacity of Cu = 5.048e-06 J/mol/K\n", "The lattice heat capacity of Cu = 4.611e-11 J/mol/K\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.8,Page number 90" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "N = 6.023*10**23; # Avogadro's number, per kmol\n", "e = 1.602*10**-19; # Energy equivalent of 1 eV, J/eV\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "R = N*k; # Molar gas constant, J/kmol/K\n", "E_F = 3.2; # Fermi energy of Cu, eV\n", "theta_D = 150.0; # Debye temperature of Cu, K\n", "T = 20.0; # Given temperature, K\n", "T_F = E_F/k; # Fermi temperature of Cu, K\n", "C_e = pi**2/2*R*(T/(T_F*e)); # Electronic heat capacity of Cu, J/mol/K\n", "C_l = 12.0/5*(pi**4*R)*(T/theta_D)**3; # Lattice heat capacity of Cu, J/kmol/K\n", "print\"The electronic heat capacity of Na = \",\"{0:.3e}\".format(C_e),\"J/mol/K\";\n", "print\"The lattice heat capacity of Na = \",round(C_l,4),\"J/mol/K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The electronic heat capacity of Na = 2.208e-02 J/mol/K\n", "The lattice heat capacity of Na = 4.6059 J/mol/K\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.9,Page number 91" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "N = 6.023*10**23; # Avogadro's number, per kmol\n", "e = 1.602*10**-19; # Energy equivalent of 1 eV, J/eV\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "R = N*k; # Molar gas constant, J/kmol/K\n", "E_F = 3.2; # Fermi energy of Hf, eV\n", "theta_D = 242.0; # Debye temperature of Hf, K\n", "T_F = E_F/k; # Fermi temperature of Hf, K\n", "T = [300.0, 200.0, 100.0, 10.0, 5.0]; # Declare a vector of 5 temperature values, K\n", "print\"________________________\";\n", "print\"T(K) C_l (J/kmol/K)\";\n", "print\"________________________\";\n", "for i in xrange(len(T)):\n", " C_l = 12.0/5*(pi**4*R)*(T[i]/theta_D)**3; # Lattice heat capacity of Hf, J/kmol/K \n", " print\"\",T[i],\" \",round(C_l,3);\n", "print\"________________________\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "________________________\n", "T(K) C_l (J/kmol/K)\n", "________________________\n", " 300.0 3701.863\n", " 200.0 1096.848\n", " 100.0 137.106\n", " 10.0 0.137\n", " 5.0 0.017\n", "________________________\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.10,Page number 91" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "N = 6.023*10**23; # Avogadro's number, per kmol\n", "e = 1.602*10**-19; # Energy equivalent of 1 eV, J/eV\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "R = N*k; # Molar gas constant, J/kmol/K\n", "E_F = 7.0; # Fermi energy of Hf, eV\n", "theta_D = 343.0; # Debye temperature of Hf, K\n", "T_F = E_F/k; # Fermi temperature of Hf, K\n", "# As C_l = 12/5*(pi**4*R)*(T/theta_D)**3 and C_e = pi**2/2*R*(T/(T_F*e)) so that\n", "# For C_l = C_e, we have\n", "T = sqrt((pi**2/2*R*1/(T_F*e))/(12.0/5*pi**4*R)*theta_D**3); # Required temperature when C_l = C_e, K\n", "print\"The temperature at which lattice specific heat equals electronic specific heat for Cu =\",round(T,3),\"K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The temperature at which lattice specific heat equals electronic specific heat for Cu = 3.238 K\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.11,Page number 92" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "C11 = 1.08*10**12; C12 = 0.62*10**12; C44 = 0.28*10**12; # Elastic constants of Al, dynes/cm square\n", "a = 4.05*10**-8; # Lattice constant for Al cubic structure, cm\n", "rho = 2.70; # g/cm cube \n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "h = 6.626*10**-34; # Planck's constant, Js\n", "s = 4.0; # Number of atoms in Al unit cell\n", "Va = a**3; # Volume of unit cell, cm cube\n", "theta_D =(3.15/(8*pi)*(h/k)**3*s/(rho**(3.0/2)*Va)*(C11-C12)**(1.0/2)*(C11+C12+2*C44)**(1.0/2)*C44**(1.0/2))**(1.0/3);\n", "print\"The Debye temperature of Al =\",round(theta_D,3),\"K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Debye temperature of Al = 466.605 K\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.12,Page number 93" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "h = 6.626*10**-34; # Planck's constant, Js\n", "A =[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14,15,16]]; # Declare a matrix of 2X8\n", "A[0][0] = 'Cu';\n", "A[0][1] = 1.684*10**12;\n", "A[0][2] = 1.214*10**12;\n", "A[0][3] = 0.754*10**12;\n", "A[0][4] = 4;\n", "A[0][5] = 3.61*10**-8;\n", "A[0][6] = 8.96;\n", "A[1][0] = 'Na';\n", "A[1][1] = 0.055*10**12;\n", "A[1][2] = 0.047*10**12;\n", "A[1][3] = 0.049*10**12;\n", "A[1][4] = 2;\n", "A[1][5] = 4.225*10**-8;\n", "A[1][6] = 0.971;\n", "\n", "# For Cu\n", "Va = A[0][5]**3; # Volume of unit cell, cm cube\n", "A[0][7] = (3.15/(8*pi)*(h/k)**3*A[0][4]/(A[0][6]**(3.0/2)*Va)*(A[0][1]-A[0][2])**(1.0/2)*(A[0][1]+A[0][2]+2*A[0][3])**(1.0/2)*A[0][3]**(1.0/2))**(1.0/3);\n", "\n", "# For Na\n", "Va =A[1][5]**3; # Volume of unit cell, cm cube\n", "A[1][7] = (3.15/(8*pi)*(h/k)**3*A[1][4]/(A[1][6]**(3.0/2)*Va)*(A[1][1]-A[1][2])**(1.0/2)*(A[1][1]+A[1][2]+2*A[1][3])**(1.0/2)*A[1][3]**(1.0/2))**(1.0/3);\n", "\n", "print\"________________________________________\";\n", "print\"Metal C11 C12 C44 thetaD\";\n", "print\"________________________________________\";\n", "for i in range (0,2) :\n", " print\"\",A[i][0],\" \",A[i][1]/10**12,\" \",A[i][2]/10**12,\" \",A[i][3]/10**12,\" \",round(A[i][7],2);\n", "print\"________________________________________\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "________________________________________\n", "Metal C11 C12 C44 thetaD\n", "________________________________________\n", " Cu 1.684 1.214 0.754 380.2\n", " Na 0.055 0.047 0.049 150.44\n", "________________________________________\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.13,Page number 93" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "k = 1.38*10**-23; # Boltzmann constant, J/K\n", "h = 6.626*10**-34; # Planck's constant, Js\n", "A =[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20]]; # Declare a matrix of 4X5\n", "A[0][0] = 300;\n", "A[0][1] = 0.878*10**10;\n", "A[0][2] = 0.483*10**10;\n", "A[0][3] = 0.448*10**10;\n", "A[1][0] = 200;\n", "A[1][1] = 0.968*10**10;\n", "A[1][2] = 0.508*10**10;\n", "A[1][3] = 0.512*10**10;\n", "A[2][0] = 100;\n", "A[2][1] = 1.050*10**10;\n", "A[2][2] = 0.540*10**10;\n", "A[2][3] = 0.579*10**10;\n", "A[3][0] = 20;\n", "A[3][1] = 1.101*10**10;\n", "A[3][2] = 0.551*10**10;\n", "A[3][3] = 0.624*10**10;\n", "s = 2; # Number of atoms in a unit cell\n", "a = 4.225*10**-10; # Lattice parameter of Na, m\n", "rho = 0.971*10**3; # Density of Na, kg/metre-cube\n", "Va = a**3; # Volume of unit cell, metre cube\n", "print\"________________________________________\";\n", "print\"T C11 C12 C44 thetaD\"\n", "print\"________________________________________\";\n", "for i in range (0,4) :\n", " A[i][4] = (3.15/(8*pi)*(h/k)**3*s/(rho**(3.0/2)*Va)*(A[i][1]-A[i][2])**(1.0/2)*(A[i][1]+A[i][2]+2*A[i][3])**(1.0/2)*A[i][3]**(1.0/2))**(1.0/3);\n", " print\"\",A[i][0],\" \",A[i][1]/10**10,\" \",A[i][2]/10**10,\" \",A[i][3]/10**10,\" \",round(A[i][4],2);\n", "\n", "print\"________________________________________\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "________________________________________\n", "T C11 C12 C44 thetaD\n", "________________________________________\n", " 300 0.878 0.483 0.448 197.33\n", " 200 0.968 0.508 0.512 210.52\n", " 100 1.05 0.54 0.579 222.08\n", " 20 1.101 0.551 0.624 229.77\n", "________________________________________\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.14,Page number 93" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import scipy\n", "from scipy.integrate import quad\n", "\n", "#Given Data\n", "Lu =[[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15],[16,17,18,19,20],[21,22,23,24,25],[26,27,28,29,30]]; # Declare a matrix of 6X5\n", "Lu[0][0] = 0;\n", "Lu[0][1] = 5.58;\n", "Lu[0][2] = 3.517;\n", "Lu[0][4] = 0.750;\n", "Lu[1][0] = 36;\n", "Lu[1][1] = 5.409;\n", "Lu[1][2] = 3.440;\n", "Lu[1][4] = 0.560;\n", "Lu[2][0] = 103;\n", "Lu[2][1] = 5.213;\n", "Lu[2][2] = 3.341;\n", "Lu[2][4] = 0.492;\n", "Lu[3][0] = 157;\n", "Lu[3][1] = 5.067;\n", "Lu[3][2] = 3.259;\n", "Lu[3][4] = 0.388;\n", "Lu[4][0] = 191;\n", "Lu[4][1] = 4.987;\n", "Lu[4][2] = 3.217;\n", "Lu[4][4] = 0.357;\n", "Lu[5][0] = 236;\n", "Lu[5][1] = 4.921;\n", "Lu[5][2] = 3.179;\n", "Lu[5][4] = 0.331;\n", "V0 = 3*sqrt(3)/2*Lu[0][2]**2*Lu[0][1];\n", "V = [0,0,0,0,0,0]; # Declare volume array\n", "print\"______________________________________________________________\";\n", "print\"P(kbar) c(angstrom) a(angstrom) gamma_G nu_G \";\n", "print\"______________________________________________________________\";\n", "for i in range (0,6) :\n", " V[i] = 3*sqrt(3)/2*Lu[i][2]**2*Lu[i][1];\n", " Lu[i][3] = Lu[i][4]*V[i]/V0+2.0/3*(1-V[i]/V0)**(1.0/2);\n", " print\"\",Lu[i][0],\" \",Lu[i][1],\" \",Lu[i][2],\" \",round(Lu[i][3],3),\" \",Lu[i][4];\n", "\n", "print\"______________________________________________________________\";\n", "\n", "cnt = 0;\n", "print\"________________________\";\n", "print\"P(kbar) Theta_D(K)\";\n", "print\"________________________\";\n", "for i in range (0,6) :\n", " def integrand(x, a, b):\n", " return (-1*Lu[i][4]*(exp(x)/V0)-(2.0/3)*(1-exp(x)/V0)**(1.0/2))\n", " a=1;\n", " b=1;\n", " I = quad(integrand,-0.8+cnt,log(V[i]/1000000), args=(a,b));\n", " theta_D = exp(I);\n", " cnt = cnt + 0.01;\n", " print\"\",Lu[i][0],\" \",round(theta_D[0],0);\n", "\n", "print\"________________________\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "______________________________________________________________\n", "P(kbar) c(angstrom) a(angstrom) gamma_G nu_G \n", "______________________________________________________________\n", " 0 5.58 3.517 0.75 0.75\n", " 36 5.409 3.44 0.699 0.56\n", " 103 5.213 3.341 0.679 0.492\n", " 157 5.067 3.259 0.615 0.388\n", " 191 4.987 3.217 0.602 0.357\n", " 236 4.921 3.179 0.591 0.331\n", "______________________________________________________________\n", "________________________\n", "P(kbar) Theta_D(K)\n", "________________________\n", " 0 185.0\n", " 36 195.0\n", " 103 210.0\n", " 157 222.0\n", " 191 230.0\n", " 236 237.0\n", "________________________\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.15,Page number 94" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#GIven Data\n", "T_M = 1356.0; # Melting temperature of Cu, K\n", "V = 7.114; # Atomic volume of Cu, cm cube per g-atom\n", "M = 63.5; # atomic weight of Cu, g/mole\n", "K = 138.5; # Lindemann constant\n", "theta_M = K*(T_M/M)**(1.0/2)*(1/V)**(1.0/3); # Debye temperature by Lindemann method, K\n", "\n", "print\"The Debye temperature by Lindemann method =\",round(theta_M,3),\"K\";\n", "print\"The values obtained from other methods are:\";\n", "print\"theta_s = 342 K; theta_R = 336 K; theta_E = 345 K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Debye temperature by Lindemann method = 332.778 K\n", "The values obtained from other methods are:\n", "theta_s = 342 K; theta_R = 336 K; theta_E = 345 K\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.16,Page number 100" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "N_A = 6.023*10**23; # Avogadro's number\n", "c = 3.0*10**8; # Speed of light, m/s\n", "epsilon_0 = 15.0; # Dielectric constant of the medium\n", "m = 2.0*10**-22; # Mass of ion, g\n", "e = 4.8*10**-10; # Charge on the ion, C\n", "rho = 7.0; # Average density of solid, g/cc\n", "A = 120.0; # Average atomic weight of solid, g\n", "N = rho/A*N_A; # Number of ions per cc, per cm cube\n", "f_P = 1/(2*pi)*sqrt(4*pi*N*e**2/(m*epsilon_0)); # Plasma frequency of vibrating ions in the crystal, Hz\n", "lamda_P = c/f_P; # Plasma wavelength of vibrating ions in the crystal, cm\n", "print\"The plasma frequency of vibrating ions in InSb crystal = \",\"{0:.3e}\".format(f_P),\"Hz\";\n", "print\"The plasma wavelength of vibrating ions in InSb crystal =\",round(lamda_P/10**-6,3),\"micron\";\n", "print\"The calculated frequency lies in the infrared region.\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The plasma frequency of vibrating ions in InSb crystal = 9.268e+11 Hz\n", "The plasma wavelength of vibrating ions in InSb crystal = 323.706 micron\n", "The calculated frequency lies in the infrared region.\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.17,Page number 103" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Given Data\n", "\n", "h = 6.624*10**-34; # Planck's constant, Js\n", "k = 1.38*10**-23; # Boltzmann constant, J/mol/K\n", "q = 1.486*10**11; # Young's modulus of diamond, N/metre-square\n", "rho = 3500; # Density of diamond, kg/metre-cube\n", "c = sqrt(q/rho); # Speed of transverse wave through diamond, m/s\n", "m = 12*1.66*10**-27; # Atomic weight of carbon, kg\n", "theta_D = (h/k)*c*(3*rho/(4*pi*m))**(1.0/3); # Debye temperature for diamond, K\n", "print\"The Debye temperature for diamond =\",round(theta_D,3),\"K\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The Debye temperature for diamond = 1086.709 K\n" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }