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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# 3: X-Ray Diffraction"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 1, Page number 3.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "maximum order of diffraction is 1.53\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "d=1.181; #lattice spacing(angstrom)\n",
+ "theta=90*math.pi/180; #glancing angle(radian)\n",
+ "lamda=1.540; #wavelength of X-rays(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "n=2*d*math.sin(theta)/lamda; #maximum order of diffraction \n",
+ "\n",
+ "#Result\n",
+ "print \"maximum order of diffraction is\",round(n,2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 2, Page number 3.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "cube edge of unit cell is 3.514 angstrom\n",
+ "answer given in the book varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=1; #order\n",
+ "theta=9.5*math.pi/180; #glancing angle(radian)\n",
+ "lamda=0.58; #wavelength(angstrom)\n",
+ "h=2;\n",
+ "k=0;\n",
+ "l=0;\n",
+ "\n",
+ "#Calculation\n",
+ "d=n*lamda/(2*math.sin(theta)); #lattice parameter(angstrom)\n",
+ "a=d*math.sqrt(h**2+k**2+l**2); #cube edge of unit cell(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"cube edge of unit cell is\",round(a,3),\"angstrom\"\n",
+ "print \"answer given in the book varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 3, Page number 3.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "glancing angle for 3rd order is 26 degrees 35 minutes\n",
+ "answer for minutes given in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "theta=(8+(35/60))*math.pi/180; #glancing angle(radian)\n",
+ "lamda=0.842; #wavelength of X-rays(angstrom)\n",
+ "n1=1; #order\n",
+ "n3=3; #order \n",
+ "\n",
+ "#Calculation\n",
+ "theta3=math.asin(n3*lamda*math.sin(theta)/(n1*lamda))*180/math.pi; #glancing angle for 3rd order(degrees)\n",
+ "theta3d=int(theta3); #glancing angle for 3rd order(degrees) \n",
+ "theta3m=(theta3-theta3d)*60; #glancing angle for 3rd order(minutes)\n",
+ "\n",
+ "#Result\n",
+ "print \"glancing angle for 3rd order is\",theta3d,\"degrees\",int(theta3m),\"minutes\"\n",
+ "print \"answer for minutes given in the book is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 4, Page number 3.10"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "interplanar spacing is 2.22 angstrom\n",
+ "value of h**2+k**2+l**2 is 2\n",
+ "miller indices are (110) or (011) or (101)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "theta=20.3*math.pi/180; #glancing angle(radian)\n",
+ "lamda=1.54; #wavelength of X-rays(angstrom)\n",
+ "n=1; #order\n",
+ "a=3.16; #lattice parameter(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "d=n*lamda/(2*math.sin(theta)); #interplanar spacing(angstrom)\n",
+ "x=(a/d)**2; #assume x=(h**2+k**2+l**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"interplanar spacing is\",round(d,2),\"angstrom\"\n",
+ "print \"value of h**2+k**2+l**2 is\",int(x)\n",
+ "print \"miller indices are (110) or (011) or (101)\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 5, Page number 3.11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "wavelength is 1.553 angstrom\n",
+ "energy of X-rays is 8 *10**3 eV\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=4; #order\n",
+ "A=107.87; #atomic weight(kg)\n",
+ "theta=(19+(12/60))*math.pi/180; #glancing angle(radian)\n",
+ "h=1;\n",
+ "k=1;\n",
+ "l=1;\n",
+ "N=6.02*10**26; #avagadro number\n",
+ "rho=10500; #density(kg/m**3)\n",
+ "H=6.625*10**-34; #plancks constant(Js)\n",
+ "c=3*10**8; #velocity of light(m/s)\n",
+ "e=1.6*10**-19; #charge(coulomb)\n",
+ "\n",
+ "#Calculation\n",
+ "a=round(((n*A/(N*rho))**(1/3))*10**10,2); #lattice parameter(angstrom)\n",
+ "d=a/math.sqrt((h**2)+(k**2)+(l**2)); #lattice parameter(angstrom)\n",
+ "lamda=2*d*math.sin(theta); #wavelength(angstrom)\n",
+ "E=H*c/(lamda*10**-10*e); #energy of X-rays(eV)\n",
+ "\n",
+ "#Result\n",
+ "print \"wavelength is\",round(lamda,3),\"angstrom\"\n",
+ "print \"energy of X-rays is\",int(round(E/10**3)),\"*10**3 eV\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example number 6, Page number 3.12"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "specimen distance is 7.559 cm\n",
+ "answer given in the book varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=1;\n",
+ "k=1;\n",
+ "l=1;\n",
+ "a=4.57; #lattice parameter(angstrom)\n",
+ "lamda=1.52; #wavelength(angstrom)\n",
+ "r=5; #radius(cm)\n",
+ "\n",
+ "#Calculation\n",
+ "d=a/math.sqrt(h**2+k**2+l**2); #lattice parameter(angstrom)\n",
+ "theta=math.asin(lamda/(2*d)); #glancing angle(degrees)\n",
+ "X=r/math.tan(2*theta); #specimen distance(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"specimen distance is\",round(X,3),\"cm\"\n",
+ "print \"answer given in the book varies due to rounding off errors\""
+ ]
+ }
+ ],
+ "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
+}
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