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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#4: Defects in Crystals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.1, Page number 4.5"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ratio of vacancies is 1.082 *10**5\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Ev=1;\n",
"k=1.38*10**-23; #boltzmann constant(J/K)\n",
"e=1.6*10**-19; #charge(eV)\n",
"\n",
"#Calculation\n",
"r=Ev/(2.303*1000*k/e); \n",
"n=10**r; #ratio of n1000/n500\n",
"\n",
"#Result\n",
"print \"ratio of vacancies is\",round(n/10**5,3),\"*10**5\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.2, Page number 4.5"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of vacancies per atom at 350K is 0.5486 *10**-17\n",
"number of vacancies per atom at 500K is 0.827 *10**-12\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Ev=1.2;\n",
"k=1.38*10**-23; #boltzmann constant(J/K)\n",
"e=1.6*10**-19; #charge(eV)\n",
"T1=350; #temperature(K)\n",
"T2=500; #temperature(K)\n",
"\n",
"#Calculation\n",
"x1=Ev/(2.303*k*T1/e);\n",
"n1=1/(10**x1); #number of vacancies per atom at 350K\n",
"x2=Ev/(2.303*k*T2/e);\n",
"n2=1/(10**x2); #number of vacancies per atom at 500K\n",
"\n",
"#Result\n",
"print \"number of vacancies per atom at 350K is\",round(n1*10**17,4),\"*10**-17\"\n",
"print \"number of vacancies per atom at 500K is\",round(n2*10**12,3),\"*10**-12\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.3, Page number 4.7"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"average energy required is 1.971 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=2.82*10**-10; #distance(m)\n",
"k=1.38*10**-23; #boltzmann constant(J/K)\n",
"e=1.6*10**-19; #charge(eV)\n",
"T=273+25; #temperature(K)\n",
"sd=5*10**11; #schotky defects(per m**3)\n",
"\n",
"#Calculation\n",
"V=(2*d)**3; #volume of unit cell(m**3)\n",
"N=4/V; #density of ion pairs\n",
"x=round(math.log10(N/sd),2);\n",
"Es=2*(k/e)*T*2.303*x; #average energy required(eV)\n",
"\n",
"#Result\n",
"print \"average energy required is\",round(Es,3),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.4, Page number 4.8"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ratio of Frenkel defects is 1.125 *10**-6\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"T1=273+25; #temperature(K)\n",
"T2=273+350; #temperature(K)\n",
"Ef=1.35; #energy(eV)\n",
"k=8.625*10**-5;\n",
"\n",
"#Calculation\n",
"x=(Ef/k)*((1/(2*T1))-(1/(2*T2)))/2.303;\n",
"r=1/(10**round(x,3)); #ratio of Frenkel defects\n",
"\n",
"#Result\n",
"print \"ratio of Frenkel defects is\",round(r*10**6,3),\"*10**-6\""
]
}
],
"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": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
