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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4: Defects in Crystals"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 1, Page number 4.14"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"equilibrium concentration of vacancy at 300K is 7.577 *10**5\n",
"equilibrium concentration of vacancy at 900K is 6.502 *10**19\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"N=6.023*10**26; #avagadro number\n",
"T1=1/float('inf'); #temperature 0K(K)\n",
"T2=300;\n",
"T3=900; #temperature(K)\n",
"k=1.38*10**-23; #boltzmann constant \n",
"deltaHv=120*10**3*10**3/N; #enthalpy(J/vacancy)\n",
"\n",
"#Calculation\n",
"#n1=N*math.exp(-deltaHv/(k*T1)); #equilibrium concentration of vacancy at 0K\n",
"#value of n1 cant be calculated in python, as the denominator is 0 and it shows float division error\n",
"n2=N*math.exp(-deltaHv/(k*T2)); #equilibrium concentration of vacancy at 300K \n",
"n3=N*math.exp(-deltaHv/(k*T3)); #equilibrium concentration of vacancy at 900K \n",
"\n",
"#Result\n",
"#print \"equilibrium concentration of vacancy at 0K is\",n1\n",
"print \"equilibrium concentration of vacancy at 300K is\",round(n2/10**5,3),\"*10**5\"\n",
"print \"equilibrium concentration of vacancy at 900K is\",round(n3/10**19,3),\"*10**19\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 2, Page number 4.15"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"fraction of vacancies at 1000 is 8.5 *10**-7\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"nbyN1=1*10**-10; #fraction of vacancies\n",
"T1=500+273;\n",
"T2=1000+273;\n",
"\n",
"#Calculation\n",
"lnx=T1*math.log(nbyN1)/T2;\n",
"x=math.exp(lnx); #fraction of vacancies at 1000\n",
"\n",
"#Result\n",
"print \"fraction of vacancies at 1000 is\",round(x*10**7,1),\"*10**-7\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 3, Page number 4.16"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"concentration of schottky defects is 6.42 *10**11 per m**3\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=2.82*10**-10; #interionic distance(m)\n",
"T=300; #temperature(K)\n",
"k=1.38*10**-23; #boltzmann constant \n",
"e=1.6*10**-19; #charge(coulomb)\n",
"n=4; #number of molecules\n",
"deltaHs=1.971*e; #enthalpy(J)\n",
"\n",
"#Calculation\n",
"V=(2*d)**3; #volume of unit cell(m**3)\n",
"N=n/V; #number of ion pairs\n",
"x=deltaHs/(2*k*T);\n",
"n=N*math.exp(-x); #concentration of schottky defects(per m**3)\n",
"\n",
"#Result\n",
"print \"concentration of schottky defects is\",round(n*10**-11,2),\"*10**11 per m**3\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example number 4, Page number 4.17"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"concentration of schottky defects is 9.23 *10**12 per cm**3\n",
"amount of climb down by the dislocations is 0.1846 step or 0.3692 *10**-8 cm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"N=6.026*10**23; #avagadro number \n",
"T=500; #temperature(K)\n",
"k=1.38*10**-23; #boltzmann constant \n",
"deltaHv=1.6*10**-19; #charge(coulomb)\n",
"V=5.55; #molar volume(cm**3)\n",
"nv=5*10**7*10**6; #number of vacancies\n",
"\n",
"#Calculation\n",
"n=N*math.exp(-deltaHv/(k*T))/V; #concentration of schottky defects(per m**3)\n",
"x=round(n/nv,4); #amount of climb down by the dislocations(step)\n",
"xcm=2*x*10**-8; #amount of climb down by the dislocations(cm)\n",
"\n",
"#Result\n",
"print \"concentration of schottky defects is\",round(n/10**12,2),\"*10**12 per cm**3\"\n",
"print \"amount of climb down by the dislocations is\",x,\"step or\",xcm*10**8,\"*10**-8 cm\" "
]
}
],
"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
}
|
