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diff --git a/Engineering_Physics_by_S._Mani_Naidu/Chapter3_1.ipynb b/Engineering_Physics_by_S._Mani_Naidu/Chapter3_1.ipynb new file mode 100644 index 00000000..e0db4e17 --- /dev/null +++ b/Engineering_Physics_by_S._Mani_Naidu/Chapter3_1.ipynb @@ -0,0 +1,658 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#3: Crystal planes, X-ray diffraction and defects in solids"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.1, Page number 3.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "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",
+ "lamda=0.071*10**-9; #wavelength(m)\n",
+ "a=0.28*10**-9; #lattice constant(m)\n",
+ "h=1;\n",
+ "k=1;\n",
+ "l=0;\n",
+ "n=2; #order of diffraction\n",
+ "\n",
+ "#Calculation\n",
+ "d=a/math.sqrt(h**2+k**2+l**2);\n",
+ "x=n*lamda/(2*d); \n",
+ "theta=math.asin(x); #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 3.2, Page number 3.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "wavelength is 0.0842 nm\n",
+ "maximum order of diffraction is 7.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=1; #order of diffraction\n",
+ "theta1=8+(35/60); #angle(degrees)\n",
+ "d=0.282; #spacing(nm)\n",
+ "theta2=90;\n",
+ "\n",
+ "#Calculation\n",
+ "theta1=theta1*math.pi/180; #angle(radian)\n",
+ "lamda=2*d*math.sin(theta1)/n; #wavelength(nm)\n",
+ "theta2=theta2*math.pi/180; #angle(radian)\n",
+ "nmax=2*d/lamda; #maximum order of diffraction\n",
+ "\n",
+ "#Result\n",
+ "print \"wavelength is\",round(lamda,4),\"nm\"\n",
+ "print \"maximum order of diffraction is\",round(nmax)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.3, Page number 3.20"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "fraction of vacancy sites is 8.466 *10**-7\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "T1=500+273; #temperature(K)\n",
+ "T2=1000+273; #temperature(K)\n",
+ "f=1*10**-10; #fraction\n",
+ "\n",
+ "#Calculation\n",
+ "x=round(T1/T2,5);\n",
+ "y=round(math.log(f),3);\n",
+ "w=round(x*y,3);\n",
+ "F=math.exp(w); #fraction of vacancy sites\n",
+ "\n",
+ "#Result\n",
+ "print \"fraction of vacancy sites is\",round(F*10**7,3),\"*10**-7\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.4, Page number 3.21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "ratio is math.sqrt( 6.0 ): math.sqrt( 3.0 ): math.sqrt( 2.0 )\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=1; #assume\n",
+ "h1=1;\n",
+ "k1=0;\n",
+ "l1=0;\n",
+ "h2=1;\n",
+ "k2=1;\n",
+ "l2=0;\n",
+ "h3=1;\n",
+ "k3=1;\n",
+ "l3=1;\n",
+ "\n",
+ "#Calculation\n",
+ "d100=a*6/(h1**2+k1**2+l1**2);\n",
+ "d110=a*6/(h2**2+k2**2+l2**2);\n",
+ "d111=a*(6)/(h3**2+k3**2+l3**2);\n",
+ "\n",
+ "#Result\n",
+ "print \"ratio is math.sqrt(\",d100,\"): math.sqrt(\",d110,\"): math.sqrt(\",d111,\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.5, Page number 3.21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "lattice parameter of nickel is 3.522 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=1; #order of diffraction\n",
+ "theta=38.2; #angle(degrees)\n",
+ "lamda=1.54; #wavelength(angstrom)\n",
+ "h=2;\n",
+ "k=2;\n",
+ "l=0;\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); #lattice parameter of nickel(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"lattice parameter of nickel is\",round(a,3),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.6, Page number 3.22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "order of diffraction is 2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "theta=90; #angle(degrees)\n",
+ "lamda=1.5; #wavelength(angstrom)\n",
+ "d=1.6; #spacing(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*math.pi/180; #angle(radian)\n",
+ "n=2*d*math.sin(theta)/lamda; #order of diffraction\n",
+ "\n",
+ "#Result\n",
+ "print \"order of diffraction is\",int(n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.7, Page number 3.22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "length of unit cell is 0.287 *10**-9 m\n",
+ "volume of unit cell is 0.02366 *10**-27 m**3\n",
+ "radius of the atom is 0.1243 *10**-9 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=1;\n",
+ "k=1;\n",
+ "l=0;\n",
+ "d=0.203*10**-9; #spacing(m)\n",
+ "\n",
+ "#Calculation\n",
+ "a=d*math.sqrt(h**2+k**2+l**2); #length of unit cell(m)\n",
+ "V=a**3; #volume of unit cell(m**3)\n",
+ "r=math.sqrt(3)*a/4; #radius of the atom(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"length of unit cell is\",round(a*10**9,3),\"*10**-9 m\"\n",
+ "print \"volume of unit cell is\",round(V*10**27,5),\"*10**-27 m**3\"\n",
+ "print \"radius of the atom is\",round(r*10**9,4),\"*10**-9 m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.8, Page number 3.22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "order of diffraction is 2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "theta=90; #angle(degrees)\n",
+ "lamda=1.5; #wavelength(angstrom)\n",
+ "d=1.6; #spacing(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*math.pi/180; #angle(radian)\n",
+ "n=2*d*math.sin(theta)/lamda; #order of diffraction\n",
+ "\n",
+ "#Result\n",
+ "print \"order of diffraction is\",int(n)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.9, Page number 3.23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "glancing angle is 20 degrees 42 minutes 17 seconds\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=0.065; #wavelength(nm)\n",
+ "a=0.26; #edge length(nm)\n",
+ "h=1;\n",
+ "k=1;\n",
+ "l=0;\n",
+ "n=2;\n",
+ "\n",
+ "#Calculation\n",
+ "d=a/math.sqrt(h**2+k**2+l**2); \n",
+ "x=n*lamda/(2*d); \n",
+ "theta=math.asin(x); #glancing angle(radian)\n",
+ "theta=theta*180/math.pi; #glancing angle(degrees)\n",
+ "theta_d=int(theta); \n",
+ "theta_m=(theta-theta_d)*60;\n",
+ "theta_s=(theta_m-int(theta_m))*60;\n",
+ "\n",
+ "#Result\n",
+ "print \"glancing angle is\",theta_d,\"degrees\",int(theta_m),\"minutes\",int(theta_s),\"seconds\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.10, Page number 3.23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "cube edge of unit cell is 4.055 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=1.54; #wavelength(angstrom)\n",
+ "h=1;\n",
+ "k=1;\n",
+ "l=1;\n",
+ "n=1;\n",
+ "theta=19.2; #angle(degrees)\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); #cube edge of unit cell(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"cube edge of unit cell is\",round(a,3),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.11, Page number 3.24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "lattice parameter of nickel is 3.522 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=1.54; #wavelength(angstrom)\n",
+ "h=2;\n",
+ "k=2;\n",
+ "l=0;\n",
+ "n=1;\n",
+ "theta=38.2; #angle(degrees)\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); #lattice parameter of nickel(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"lattice parameter of nickel is\",round(a,3),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.12, Page number 3.24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "interplanar spacing for (111) is 0.208 nm\n",
+ "interplanar spacing for (321) is 0.096 nm\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=0.36; #edge length(nm)\n",
+ "h1=1;\n",
+ "k1=1;\n",
+ "l1=1;\n",
+ "h2=3;\n",
+ "k2=2;\n",
+ "l2=1;\n",
+ "\n",
+ "#Calculation\n",
+ "d1=a/math.sqrt(h1**2+k1**2+l1**2); #interplanar spacing for (111)(nm)\n",
+ "d2=a/math.sqrt(h2**2+k2**2+l2**2); #interplanar spacing for (321)(nm)\n",
+ "\n",
+ "#Result\n",
+ "print \"interplanar spacing for (111) is\",round(d1,3),\"nm\"\n",
+ "print \"interplanar spacing for (321) is\",round(d2,3),\"nm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.13, Page number 3.25"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "glancing angle is 16 degrees 27 minutes\n",
+ "answer varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=0.675; #wavelength(angstrom)\n",
+ "n=3; #order of diffraction\n",
+ "theta=5+(25/60); #angle(degrees)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*math.pi/180; #angle(radian)\n",
+ "d=lamda/(2*math.sin(theta)); \n",
+ "theta3=math.asin(3*lamda/(2*d)); #glancing angle(radian)\n",
+ "theta3=theta3*180/math.pi; #glancing angle(degrees)\n",
+ "theta_d=int(theta3); \n",
+ "theta_m=(theta3-theta_d)*60;\n",
+ "\n",
+ "#Result\n",
+ "print \"glancing angle is\",theta_d,\"degrees\",int(theta_m),\"minutes\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.14, Page number 3.25"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "glancing angle is 22 degrees 56 minutes 31 seconds\n",
+ "answer given in the book is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=0.79; #wavelength(angstrom)\n",
+ "n=3; #order of diffraction\n",
+ "d=3.04; #spacing(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "x=round(n*lamda/(2*d),4);\n",
+ "theta=math.asin(x); #glancing angle(radian)\n",
+ "theta=theta*180/math.pi; #glancing angle(degrees)\n",
+ "theta_d=int(theta); \n",
+ "theta_m=(theta-theta_d)*60;\n",
+ "theta_s=(theta_m-int(theta_m))*60;\n",
+ "\n",
+ "#Result\n",
+ "print \"glancing angle is\",theta_d,\"degrees\",int(theta_m),\"minutes\",int(theta_s),\"seconds\"\n",
+ "print \"answer given in the book is wrong\""
+ ]
+ }
+ ],
+ "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
+}
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