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{
"metadata": {
"name": "",
"signature": "sha256:e5ea4ff1709764161940877bdcbbb6d4676a6eced70f445ea6f3a31c76d16a31"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"8: X-rays"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.1, Page number 197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=4.255; #atomic spacing(angstrom)\n",
"lamda=1.549; #wavelength of K-copper line(angstrom) \n",
"n=1; #theta is smallest when n=1\n",
"\n",
"\n",
"#Calculation\n",
"theta=math.asin(lamda/(2*d)); #glancing angle(radian)\n",
"theta=theta*(180/math.pi); #glancing angle(degrees)\n",
"#max value of sin(theta)=1 for highest order\n",
"nmax=((2*d)/lamda); #highest bragg's order\n",
"\n",
"\n",
"#Result\n",
"print \"smallest glancing angle is\",round(theta,4),\"degrees\"\n",
"print \"maximum order of reflection is\",round(nmax,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"smallest glancing angle is 10.4875 degrees\n",
"maximum order of reflection is 5.494\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.2, Page number 197"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"V=60*10**3; #potential difference(volts)\n",
"c=3*10**8; #velocity of light(m/sec)\n",
"e=1.6*10**-19; #electron charge(coulomb)\n",
"lamda=0.194*10**-10; #minimum wavelength of x-rays(m)\n",
"\n",
"#Calculation\n",
"h=(lamda*e*V)/c; #planck's constant(Jsec)\n",
"\n",
"#Result\n",
"print \"planck's constant is\",h,\"Jsec\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"planck's constant is 6.208e-34 Jsec\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.3, Page number 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"#for 110 plane\n",
"h=1;\n",
"k=1;\n",
"l=0;\n",
"a=3; #lattice parameter(angstrom)\n",
"n=1;\n",
"theta=12.5; #glancing angle(degrees)\n",
"\n",
"#Calculation\n",
"theta1=theta*(math.pi/180); #glancing angle(radian)\n",
"d110=(a/math.sqrt((h**2)+(k**2)+(l**2))); \n",
"lamda=2*d110*math.sin(theta1)/n; #wavelength of x-ray(angstrom)\n",
"nmax=((2*d110)/lamda); #highest order possible\n",
"\n",
"#Result\n",
"print \"wavelength of x-ray beam is\",round(lamda,3),\"angstrom\"\n",
"print \"highest bragg's order possible is\",int(nmax)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"wavelength of x-ray beam is 0.918 angstrom\n",
"highest bragg's order possible is 4\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.4, Page number 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"d=2.81*10**-10; #interplanar spacing(m)\n",
"theta=14; #glancing angle(degrees) \n",
"e=1.6*10**-19; #electron charge(c)\n",
"V=9100; #voltage(V)\n",
"n=1;\n",
"c=3*10**8; #velocity of light(m/sec)\n",
"\n",
"#Calculation\n",
"theta=theta*(math.pi/180); #glancing angle(radian)\n",
"lamda=2*d*math.sin(theta)/n; #minimum wavelength\n",
"h=(lamda*e*V)/c; #planck's constant(Jsec)\n",
"\n",
"#Result\n",
"print \"planck's constant is\",round(h*10**34,4),\"*10**-34 Jsec\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"planck's constant is 6.5986 *10**-34 Jsec\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.5, Page number 198"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"thetaA=30; #glancing angle for line A(degrees)\n",
"lamdaB=0.97; #wavelength of line B(angstrom)\n",
"thetaB=60; #glancing angle for line B(degrees)\n",
"\n",
"#Calculation\n",
"#for line A-> 2*d*sin(thetaA)=lamdaA(n=1)\n",
"thetaA=thetaA*(math.pi/180); #glancing angle for line A(radian)\n",
"#for line B-> 2*d*sin(thetaB)=3*lamdaB(n=3)\n",
"thetaB=thetaB*(math.pi/180); #glancing angle for line B(radian) \n",
"d=(3*lamdaB)/(2*math.sin(thetaB)); #interplanar spacing(angstrom)\n",
"lamdaA=2*d*math.sin(thetaA); #wavelength of line A(angstrom)\n",
"\n",
"#Result\n",
"print \"wavelength of line A is\",round(lamdaA,2),\"angstrom\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"wavelength of line A is 1.68 angstrom\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.6, Page number 199"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3.615; #lattice constant(angstrom)\n",
"h=1;\n",
"k=1;\n",
"l=1;\n",
"theta=21.7; #glancing angle(degrees)\n",
"\n",
"#Calculation\n",
"d111=a/math.sqrt(h**2+k**2+l**2); #interplanar spacing(angstrom)\n",
"theta=theta*(math.pi/180); #glancing angle(radian)\n",
"lamda=2*d111*math.sin(theta); #wavelength of X-rays(angstrom)\n",
"\n",
"#Result\n",
"print \"wavelength of X-rays is\",round(lamda,3),\"angstrom\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"wavelength of X-rays is 1.543 angstrom\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.7, Page number 199"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"V=50*10**3; #voltage(V)\n",
"n=4; #FCC crystal\n",
"m=74.6; #molecular mass(kg)\n",
"N=6.02*10**26; #avagadro number(per kg mol)\n",
"rho=1.99*10**3; #density(kg/m**3) \n",
"\n",
"#Calculation\n",
"lamda=(12400/V); #short wavelength(angstrom)\n",
"a=(((n*m)/(N*rho))**(1/3)); #lattice constant(m)\n",
"#for kcl ionic crystal\n",
"d=a/2;\n",
"sintheta=lamda*10**-10/(2*d); #value of sintheta\n",
"theta=math.asin(sintheta); #glancing angle(radian)\n",
"theta=theta*(180/math.pi); #glancing angle(degrees)\n",
"\n",
"#Result\n",
"print \"short wavelength of spectrum from tube is\",lamda,\"angstrom\"\n",
"print \"glancing angle for that wavelength is\",round(theta,4),\"degrees\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"short wavelength of spectrum from tube is 0.248 angstrom\n",
"glancing angle for that wavelength is 2.2589 degrees\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 8.8, Page number 199"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"theta1=5.4; #glancing angle(degrees)\n",
"theta2=7.6; #glancing angle(degrees)\n",
"theta3=9.4; #glancing angle(degrees) \n",
"\n",
"#Calculation\n",
"#from bragg's law 2*d*sin(theta)=n*lamda, n=1\n",
"theta1=theta1*(math.pi/180); #glancing angle(radian)\n",
"theta2=theta2*(math.pi/180); #glancing angle(radian)\n",
"theta3=theta3*(math.pi/180); #glancing angle(radian)\n",
"d100=lamda/2*math.sin(theta1); #interplanar spacing\n",
"d110=lamda/2*math.sin(theta2); #interplanar spacing\n",
"d111=lamda/2*math.sin(theta3); #interplanar spacing\n",
"\n",
"#Result\n",
"print \"ratio of interplanar spacing (1/d100):(1/d110):(1/d111)=\",round(math.sin(theta1),4),\":\",round(math.sin(theta2),4),\":\",round(math.sin(theta3),4)\n",
"print \"as ratio (1/d100):(1/d110):(1/d111)=1:sqrt(2):sqrt(3). this relation is valid for simple cubic systems. therefore, this is a simple cubic crystal\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"ratio of interplanar spacing (1/d100):(1/d110):(1/d111)= 0.0941 : 0.1323 : 0.1633\n",
"as ratio (1/d100):(1/d110):(1/d111)=1:sqrt(2):sqrt(3). this relation is valid for simple cubic systems. therefore, this is a simple cubic crystal\n"
]
}
],
"prompt_number": 34
}
],
"metadata": {}
}
]
}
|
