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{
"metadata": {
"name": "",
"signature": "sha256:0a8e4e4ffe1102aa0e8d709fa097c42aa3e09b9945c321059b30f1ddc8f4e107"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"16: Electron theory of solids"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 16.1, Page number 10"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"sigma=5.87*10**7; #electrical conductivity of Cu(per ohm m)\n",
"K=390; #thermal conductivity(W/mK)\n",
"T=20+273; #temperature(K)\n",
"\n",
"#Calculation\n",
"L=K/(sigma*T); #Lorentz number(W ohm/K**2)\n",
"\n",
"#Result\n",
"print \"Lorentz number is\",round(L*10**8,4),\"*10**-8 W ohm/K**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Lorentz number is 2.2676 *10**-8 W ohm/K**2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 16.2, Page number 11"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"tow_r=10**-14; #relaxation time(s)\n",
"T=300; #temperature(K)\n",
"kB=1.38*10**-23; #boltzmann constant\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"n=6*10**28; #electron concentration(per m**3)\n",
"\n",
"#Calculation\t\n",
"sigma=n*e**2*tow_r/m; #electrical conductivity(per ohm m)\n",
"K=n*math.pi**2*kB**2*T*tow_r/(3*m); #thermal conductivity(W/mK)\n",
"L=K/(sigma*T); #Lorentz number(W ohm/K**2)\n",
"\n",
"#Result\n",
"print \"electrical conductivity is\",round(sigma/10**7,4),\"*10**7 per ohm m\"\n",
"print \"thermal conductivity is\",round(K,4),\"W/mK\"\n",
"print \"Lorentz number is\",round(L*10**8,4),\"*10**-8 W ohm/K**2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"electrical conductivity is 1.6879 *10**7 per ohm m\n",
"thermal conductivity is 123.9275 W/mK\n",
"Lorentz number is 2.4474 *10**-8 W ohm/K**2\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 16.3, Page number 11"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"tow_r=10**-14; #relaxation time(s)\n",
"rho=8900; #density of Cu(kg/m**3)\n",
"aw=63.5; #atomic weight of Cu\n",
"N=6.022*10**23; #avagadro constant\n",
"f=1*10**3; #number of free electrons per atom\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"\n",
"#Calculation\t\n",
"n=N*rho*f/aw; #electron concentration(per m**3)\n",
"sigma=n*e**2*tow_r/m; #electrical conductivity(per ohm m)\n",
"\n",
"#Result\n",
"print \"electrical conductivity is\",round(sigma/10**7,3),\"*10**7 per ohm m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"electrical conductivity is 2.374 *10**7 per ohm m\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 16.4, Page number 12"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rho=1.54*10**-8; #resistivity(ohm m)\n",
"EF=5.5; #fermi energy(eV)\n",
"e=1.6*10**-19; #charge of electron(c)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"E=100;\n",
"n=5.8*10**28; #electron concentration(per m**3)\n",
"\n",
"#Calculation\t\n",
"tow_r=m/(rho*n*e**2); #relaxation time(s)\n",
"mew=e*tow_r/m; #mobility of electrons(m**2/Vs)\n",
"v=e*tow_r*E/m; #drift velocity(m/s)\n",
"EF=EF*e; #fermi energy(J)\n",
"vF=math.sqrt(2*EF/m); #fermi velocity(m/s)\n",
"lamda=vF*tow_r; #mean free path(m)\n",
"\n",
"#Result\n",
"print \"relaxation time is\",round(tow_r*10**14,2),\"*10**-14 s\"\n",
"print \"mobility of electrons is\",round(mew*10**3,3),\"*10**-3 m**2/Vs\"\n",
"print \"drift velocity is\",round(v,4),\"m/s\"\n",
"print \"fermi velocity is\",round(vF/10**6,2),\"*10**6 m/s\"\n",
"print \"mean free path is\",round(lamda*10**8,2),\"*10**-8 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"relaxation time is 3.98 *10**-14 s\n",
"mobility of electrons is 6.997 *10**-3 m**2/Vs\n",
"drift velocity is 0.6997 m/s\n",
"fermi velocity is 1.39 *10**6 m/s\n",
"mean free path is 5.53 *10**-8 m\n"
]
}
],
"prompt_number": 15
}
],
"metadata": {}
}
]
}
|
