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{
"metadata": {
"name": "",
"signature": "sha256:c896524cb6d8dfdd75df5649979d411984ee380fa5c3cbff49f27851e63b1fb4"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 4:Defects in Solids"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.1, Page number 4.6"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"k = 1.38*10**-23 #Boltzmann constant(eV/K)\n",
"e = 1.6*10**-19 #Electronic charge(C)\n",
"T1 = 500 #First temperature for metal(K)\n",
"T2 = 1000 #Second temperature for metal(K)\n",
"Ev = 1 #Average energy required to create a vacancy in metal(eV)\n",
"\n",
"#Calculations\n",
"x = k/e\n",
"#n_500 = N*exp(-Ev/T1*k) ---(1)\n",
"#n_1000 = N*exp(-Ev/T2*k) ---(2)\n",
"#Dividing (1) by (2), we get the following expression\n",
"n = math.exp(Ev/(T2*x))\n",
"\n",
"#Result\n",
"print \"Ratio of vacancies=\",round((n/1E+5),3),\"*10^5\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Ratio of vacancies= 1.085 *10^5\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.2, Page number 4.7"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"n1_by_N = 1.*10**-10 #frequency of vacancy sites at 500 C\n",
"T1 = 500.+273. #K\n",
"T2 = 1000.+273. #K\n",
"\n",
"#Calculations\n",
"x = math.exp((T1/T2)*math.log(n1_by_N))\n",
"\n",
"#Result\n",
"print \"Frequency of vacancy sites at 1000 C =\",round((x/1E-7),4),\"*10^-7\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Frequency of vacancy sites at 1000 C = 8.467 *10^-7\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.3, Page number 4.9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"r = 2.82*10**-10 #interionic distance(m)\n",
"n = 5*10**11 #density of Schottky defect(per m^3)\n",
"T = 25+273 #temperature(K)\n",
"k = 8.625*10**-5 #Boltzmann constant(/K)\n",
"\n",
"#Calculations\n",
"v = (2*r)**3 #volume of one unit cell(m^3)\n",
"N = 4/v #density of ion pairs\n",
"Es = 2*k*T*2.303*math.log10(N/n)\n",
"\n",
"#Result\n",
"print \"The average energy required for creation of one Schottky defect is\",round(Es,3),\"eV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average energy required for creation of one Schottky defect is 1.971 eV\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.4, Page number 4.11"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"T1 = 20+273 #K\n",
"T2 = 300+273 #K\n",
"Ef = 1.4 #average energy for creating a Freknel defect(eV)\n",
"k = 8.625*10**-5 #Boltzmann constant(J/K)\n",
"N = 1 #For simplicity assume total number of metal ions to be unity\n",
"Ni = 1 #For simplicity assume total number of metal ions to be unity\n",
"\n",
"#Calculations\n",
"n1 = (N*Ni)**0.5*math.exp(-Ef/(2*k*T1)) \n",
"n2 = (N*Ni)**0.5*math.exp(-Ef/(2*k*T2)) \n",
"x = n1/n2\n",
"\n",
"#Result\n",
"print \"The ratio of the number of Frenkel defects is\",round((x/1E-6),2),\"*10^-6 or\",round(((1/x)/1E+5),2),\"*10^5\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The ratio of the number of Frenkel defects is 1.32 *10^-6 or 7.56 *10^5\n"
]
}
],
"prompt_number": 27
}
],
"metadata": {}
}
]
}
|
