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{
"metadata": {
"name": "",
"signature": "sha256:fde95e6d9c736121aaabaa0d5609f06ddf07df078e4e974cfe128a5769da216f"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"17: Statistics and band theory of solids"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 17.1, Page number 23"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rhoCu=8.96*10**3; #density of Cu(kg/m**3)\n",
"awCu=63.55; #atomic weight of Cu\n",
"nfCu=1*10**3; #number of free electrons per Cu atom\n",
"rhoZn=7.14*10**3; #density of Zn(kg/m**3)\n",
"awZn=65.38; #atomic weight of Zn\n",
"nfZn=2*10**3; #number of free electrons per Zn atom\n",
"rhoAl=2.7*10**3; #density of Al(kg/m**3)\n",
"awAl=27; #atomic weight of Al\n",
"nfAl=3*10**3; #number of free electrons per Al atom\n",
"N=6.022*10**23; #avagadro constant\n",
"h=6.626*10**-34; #planck's constant\n",
"me=9.1*10**-31; #mass of electron(kg)\n",
"e=1.6*10**-19; #electron charge(c)\n",
"\n",
"#Calculation\n",
"nCu=rhoCu*N*nfCu/awCu; #concentration of electrons in Cu(per m**3)\n",
"EF0Cu=(h**2/(8*me))*(3*nCu/math.pi)**(2/3); #fermi energy of Cu at 0K(J)\n",
"EF0Cu=EF0Cu/e; #fermi energy of Cu at 0K(eV)\n",
"nZn=rhoZn*N*nfZn/awZn; #concentration of electrons in Zn(per m**3)\n",
"EF0Zn=(h**2/(8*me))*(3*nZn/math.pi)**(2/3); #fermi energy of Zn at 0K(J)\n",
"EF0Zn=EF0Zn/e; #fermi energy of Zn at 0K(eV)\n",
"nAl=rhoAl*N*nfAl/awAl; #concentration of electrons in Al(per m**3)\n",
"EF0Al=(h**2/(8*me))*(3*nAl/math.pi)**(2/3); #fermi energy of Al at 0K(J)\n",
"EF0Al=EF0Al/e; #fermi energy of Al at 0K(eV)\n",
"\n",
"#Result\n",
"print \"fermi energy of Cu at 0K is\",round(EF0Cu,4),\"eV\"\n",
"print \"fermi energy of Zn at 0K is\",round(EF0Zn,2),\"eV\"\n",
"print \"fermi energy of Al at 0K is\",round(EF0Al,2),\"eV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fermi energy of Cu at 0K is 7.0608 eV\n",
"fermi energy of Zn at 0K is 9.45 eV\n",
"fermi energy of Al at 0K is 11.68 eV\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 17.2, Page number 25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"nCu=8.4905*10**28; #concentration of electrons in Cu(per m**3)\n",
"h=6.626*10**-34; #planck's constant\n",
"me=9.1*10**-31; #mass of electron(kg)\n",
"gama=6.82*10**27;\n",
"\n",
"#Calculation\n",
"EF0=(h**2/(8*me))*(3*nCu/math.pi)**(2/3); #fermi energy of Cu at 0K(J)\n",
"EF=EF0/e; #fermi energy of Cu at 0K(eV)\n",
"DE=(gama/2)*math.sqrt(EF); #density of states for Cu at fermi level(per m**3)\n",
"\n",
"#Result\n",
"print \"density of states for Cu at fermi level is\",int(DE/10**27),\"*10**27 per m**3\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"density of states for Cu at fermi level is 9 *10**27 per m**3\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 17.3, Page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rhoNi=69*10**-9; #resistivity of Ni(ohm m)\n",
"rhoCr=129*10**-9; #resistivity of Cr(ohm m)\n",
"rho=1120*10**-9; #resistivity(ohm m) \n",
"X=0.8; \n",
"\n",
"#Calculation\n",
"C=rho/(X*(1-X)); #Nordheim's coefficient(ohm m)\n",
"\n",
"#Result\n",
"print \"Nordheim's coefficient is\",C,\"ohm m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Nordheim's coefficient is 7e-06 ohm m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 17.4, Page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rho=2.7*10**3; #density of Al(kg/m**3)\n",
"M=27; #atomic weight of Al \n",
"tow_r=10**-14; #relaxation time(s)\n",
"e=1.6*10**-19; #charge of electron(c) \n",
"NA=6.022*10**23; #avagadro constant\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"f=3*10**3; #number of free electrons per atom\n",
"\n",
"#Calculation\n",
"n=rho*NA*f/M; #number of electrons available per m**3\n",
"sigma=n*e**2*tow_r/m; #conductivity of Al(ohm m) \n",
"\n",
"#Result\n",
"print \"conductivity of Al is\",round(sigma/10**7,4),\"*10**7 ohm m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"conductivity of Al is 5.0823 *10**7 ohm m\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
