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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#3: X-ray Diffraction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 3.1, Page number 3.9"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"wavelength of X-rays is 0.08496 nm\n",
"answer varies due to rounding off errors\n",
"when theta=90, maximum order of diffraction possible is 7\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=0.313; #lattice spacing(m)\n",
"theta=7+(48/60); #angle(degrees)\n",
"n=1;\n",
"\n",
"#Calculation\n",
"theta=theta*math.pi/180; #angle(radian)\n",
"lamda=2*d*math.sin(theta)/n; #wavelength of X-rays(nm)\n",
"#when theta=90\n",
"n=2*d/lamda; #maximum order of diffraction possible\n",
"\n",
"#Result\n",
"print \"wavelength of X-rays is\",round(lamda,5),\"nm\"\n",
"print \"answer varies due to rounding off errors\"\n",
"print \"when theta=90, maximum order of diffraction possible is\",int(n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 3.2, Page number 3.10"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"interatomic spacing is 2.67 angstrom\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"lamda=1.5418; #wavelength(angstrom)\n",
"theta=30; #angle(degrees)\n",
"n=1; #first order\n",
"h=1;\n",
"k=1;\n",
"l=1;\n",
"\n",
"#Calculation\n",
"theta=theta*math.pi/180; #angle(radian)\n",
"d=n*lamda/(2*math.sin(theta)); \n",
"a=d*math.sqrt(h**2+k**2+l**2); #interatomic spacing(angstrom)\n",
"\n",
"#Result\n",
"print \"interatomic spacing is\",round(a,2),\"angstrom\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 3.3, Page number 3.10"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"glancing angle is 21 degrees\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d100=0.28; #spacing(nm)\n",
"lamda=0.071; #wavelength of X rays(nm)\n",
"n=2; #second order\n",
"\n",
"#Calculation\n",
"d110=round(d100/math.sqrt(2),3); #spacing(nm)\n",
"x=n*lamda/(2*d110);\n",
"theta=math.asin(x); #glancing angle(radian)\n",
"theta=theta*180/math.pi; #glancing angle(degrees)\n",
"\n",
"#Result\n",
"print \"glancing angle is\",int(theta),\"degrees\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 3.4, Page number 3.11"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"distance between planes is 0.27 nm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.38; #lattice constant(nm)\n",
"h=1;\n",
"k=1;\n",
"l=0;\n",
"\n",
"#Calculation\n",
"d=a/math.sqrt(h**2+k**2+l**2); #distance between planes(nm)\n",
"\n",
"#Result\n",
"print \"distance between planes is\",round(d,2),\"nm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 3.5, Page number 3.11"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"glancing angle is 32.0 degrees\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.19; #lattice constant(nm)\n",
"h=1;\n",
"k=1;\n",
"l=1;\n",
"lamda=0.058; #wavelength of X rays(nm)\n",
"n=2; #second order\n",
"\n",
"#Calculation\n",
"d=a/math.sqrt(h**2+k**2+l**2); #distance between planes(nm)\n",
"x=n*lamda/(2*d);\n",
"theta=math.asin(x); #glancing angle(radian)\n",
"theta=theta*180/math.pi; #glancing angle(degrees)\n",
"\n",
"#Result\n",
"print \"glancing angle is\",round(theta),\"degrees\""
]
}
],
"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"
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},
"nbformat": 4,
"nbformat_minor": 0
}
|
