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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4: Defects in Crystals"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Example number 4.1, Page number 97"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"fraction of vacancy sites at 1000 C is 8.4663 *10**-7\n",
"answer varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration \n",
"T1=773; #temperature(K)\n",
"T2=1273; #temperature(K)\n",
"n=1*10**-10; #fraction of vacancy sites\n",
"\n",
"#Calculations\n",
"X=round(T1*math.log(n)/T2,3);\n",
"x=math.exp(X); #fraction of vacancy sites at 1000 C\n",
"\n",
"#Result\n",
"print \"fraction of vacancy sites at 1000 C is\",round(x*10**7,4),\"*10**-7\"\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Example number 4.2, Page number 98"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"energy required is 1.971 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration \n",
"T=273+25; #temperature(K)\n",
"m=4; \n",
"n=5*10**11; #density(per m**3)\n",
"V=(2*2.82*10**-10)**3; #volume(m**3)\n",
"kB=8.625*10**-5;\n",
"\n",
"#Calculations\n",
"N=m/V;\n",
"Ep=2*kB*T*math.log(N/n);\n",
"\n",
"#Result\n",
"print \"energy required is\",round(Ep,3),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Example number 4.3, Page number 99"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ratio of frenkel defects is 2.802 *10**-3\n",
"answer in the book is wrong\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration \n",
"T1=273+20; #temperature(K)\n",
"T2=273+300; #temperature(K)\n",
"Ei=1.4; #energy(eV)\n",
"kB=8.625*10**-5;\n",
"\n",
"#Calculations\n",
"x=(1/(2*T1))-(1/(2*T2));\n",
"n=1/math.exp((Ei/(2.303*kB))*x); #ratio of frenkel defects\n",
"\n",
"#Result\n",
"print \"ratio of frenkel defects is\",round(n*10**3,3),\"*10**-3\"\n",
"print \"answer in the book is wrong\""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
