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diff --git a/ENGINEERING_PHYSICS_by_M.ARUMUGAM/6.MAGNETIC_PROPERTIES_AND_CRYSTAL_STRUCTURES..ipynb b/ENGINEERING_PHYSICS_by_M.ARUMUGAM/6.MAGNETIC_PROPERTIES_AND_CRYSTAL_STRUCTURES..ipynb new file mode 100644 index 00000000..392de89d --- /dev/null +++ b/ENGINEERING_PHYSICS_by_M.ARUMUGAM/6.MAGNETIC_PROPERTIES_AND_CRYSTAL_STRUCTURES..ipynb @@ -0,0 +1,555 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#Chapter 6:Magnetic Properties and Crystal Structures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.1, Page number 6.46"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "temperature rise is 8.43 K\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "El=10**-2*50; #energy loss(J)\n",
+ "H=El*60; #heat produced(J)\n",
+ "d=7.7*10**3; #iron rod(kg/m**3)\n",
+ "s=0.462*10**-3; #specific heat(J/kg K)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=H/(d*s); #temperature rise(K)\n",
+ "\n",
+ "#Result\n",
+ "print \"temperature rise is\",round(theta,2),\"K\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.2, Page number 6.46"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "magnetic field at the centre is 14.0 weber/m**2\n",
+ "dipole moment is 9.0 *10**-24 ampere/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "e=1.6*10**-19; #charge(coulomb)\n",
+ "new=6.8*10**15; #frequency(revolutions per second)\n",
+ "mew0=4*math.pi*10**-7;\n",
+ "R=5.1*10**-11; #radius(m)\n",
+ "\n",
+ "#Calculation\n",
+ "i=round(e*new,4); #current(ampere)\n",
+ "B=mew0*i/(2*R); #magnetic field at the centre(weber/m**2)\n",
+ "A=math.pi*R**2;\n",
+ "d=i*A; #dipole moment(ampere/m**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"magnetic field at the centre is\",round(B),\"weber/m**2\"\n",
+ "print \"dipole moment is\",round(d*10**24),\"*10**-24 ampere/m**2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.3, Page number 6.46"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "intensity of magnetisation is 5.0 ampere/m\n",
+ "flux density in material is 1.257 weber/m**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "chi=0.5*10**-5; #magnetic susceptibility\n",
+ "H=10**6; #field strength(ampere/m)\n",
+ "mew0=4*math.pi*10**-7;\n",
+ "\n",
+ "#Calculation\n",
+ "I=chi*H; #intensity of magnetisation(ampere/m)\n",
+ "B=mew0*(I+H); #flux density in material(weber/m**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"intensity of magnetisation is\",I,\"ampere/m\"\n",
+ "print \"flux density in material is\",round(B,3),\"weber/m**2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.4, Page number 6.47"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of Bohr magnetons is 2.22 bohr magneon/atom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "B=9.27*10**-24; #bohr magneton(ampere m**2)\n",
+ "a=2.86*10**-10; #edge(m)\n",
+ "Is=1.76*10**6; #saturation value of magnetisation(ampere/m)\n",
+ "\n",
+ "#Calculation\n",
+ "N=2/a**3;\n",
+ "mew_bar=Is/N; #number of Bohr magnetons(ampere m**2)\n",
+ "mew_bar=mew_bar/B; #number of Bohr magnetons(bohr magneon/atom)\n",
+ "\n",
+ "#Result\n",
+ "print \"number of Bohr magnetons is\",round(mew_bar,2),\"bohr magneon/atom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.5, Page number 6.47"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "average magnetic moment is 2.79 *10**-3 bohr magneton/spin\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "mew0=4*math.pi*10**-7;\n",
+ "H=9.27*10**-24; #bohr magneton(ampere m**2)\n",
+ "beta=10**6; #field(ampere/m)\n",
+ "k=1.38*10**-23; #boltzmann constant\n",
+ "T=303; #temperature(K)\n",
+ "\n",
+ "#Calculation\n",
+ "mm=mew0*H*beta/(k*T); #average magnetic moment(bohr magneton/spin)\n",
+ "\n",
+ "#Result\n",
+ "print \"average magnetic moment is\",round(mm*10**3,2),\"*10**-3 bohr magneton/spin\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.6, Page number 6.48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "hysteresis loss per cycle is 188.0 J/m**3\n",
+ "hysteresis loss per second is 9400.0 watt/m**3\n",
+ "power loss is 1.23 watt/kg\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "A=94; #area(m**2)\n",
+ "vy=0.1; #value of length(weber/m**2)\n",
+ "vx=20; #value of unit length\n",
+ "n=50; #number of magnetization cycles\n",
+ "d=7650; #density(kg/m**3)\n",
+ "\n",
+ "#Calculation\n",
+ "h=A*vy*vx; #hysteresis loss per cycle(J/m**3)\n",
+ "hs=h*n; #hysteresis loss per second(watt/m**3)\n",
+ "pl=hs/d; #power loss(watt/kg)\n",
+ "\n",
+ "#Result\n",
+ "print \"hysteresis loss per cycle is\",h,\"J/m**3\"\n",
+ "print \"hysteresis loss per second is\",hs,\"watt/m**3\"\n",
+ "print \"power loss is\",round(pl,2),\"watt/kg\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.7, Page number 6.48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a= 5.43 Angstorm\n",
+ "density = 6.88 kg/m**3\n",
+ "#Answer given in the textbook is wrong\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#variable declaration\n",
+ "d=2.351 #bond lenght\n",
+ "N=6.02*10**26 #Avagadro number\n",
+ "n=8 #number of atoms in unit cell\n",
+ "A=28.09 #Atomin mass of silicon\n",
+ "m=6.02*10**26 #1mole\n",
+ "\n",
+ "#Calculations\n",
+ "a=(4*d)/math.sqrt(3)\n",
+ "p=(n*A)/((a*10**-10)*m) #density\n",
+ "\n",
+ "#Result\n",
+ "print \"a=\",round(a,2),\"Angstorm\"\n",
+ "print \"density =\",round(p*10**16,2),\"kg/m**3\"\n",
+ "print\"#Answer given in the textbook is wrong\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.8, Page number 6.48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " radius of largest sphere is 0.154700538379252*r\n",
+ "maximum radius of sphere is 0.414213562373095*r\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math\n",
+ "from __future__ import division\n",
+ "from sympy import Symbol\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=Symbol('r')\n",
+ "\n",
+ "#Calculation\n",
+ "a1=4*r/math.sqrt(3);\n",
+ "R1=(a1/2)-r; #radius of largest sphere\n",
+ "a2=4*r/math.sqrt(2);\n",
+ "R2=(a2/2)-r; #maximum radius of sphere\n",
+ "\n",
+ "#Result\n",
+ "print \"radius of largest sphere is\",R1\n",
+ "print \"maximum radius of sphere is\",R2 "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.9, Page number 6.49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a1= 2.905 Angstrom\n",
+ "Unit cell volume =a1**3 = 24.521 *10**-30 m**3\n",
+ "Volume occupied by one atom = 12.26 *10**-30 m**3\n",
+ "a2= 3.654 Angstorm\n",
+ "Unit cell volume =a2**3 = 48.8 *10**-30 m**3\n",
+ "Volume occupied by one atom = 12.2 *10**-30 m**3\n",
+ "Volume Change in % = 0.493\n",
+ "Density Change in % = 0.5\n",
+ "Thus the increase of density or the decrease of volume is about 0.5%\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#variable declaration\n",
+ "r1=1.258 #Atomic radius of BCC\n",
+ "r2=1.292 #Atomic radius of FCC\n",
+ "\n",
+ "#calculations\n",
+ "a1=(4*r1)/math.sqrt(3) #in BCC\n",
+ "b1=((a1)**3)*10**-30 #Unit cell volume\n",
+ "v1=(b1)/2 #Volume occupied by one atom\n",
+ "a2=2*math.sqrt(2)*r2 #in FCC\n",
+ "b2=(a2)**3*10**-30 #Unit cell volume\n",
+ "v2=(b2)/4 #Volume occupied by one atom \n",
+ "v_c=((v1)-(v2))*100/(v1) #Volume Change in % \n",
+ "d_c=((v1)-(v2))*100/(v2) #Density Change in %\n",
+ "\n",
+ "#Results\n",
+ "print \"a1=\",round(a1,3),\"Angstrom\" \n",
+ "print \"Unit cell volume =a1**3 =\",round((b1)/10**-30,3),\"*10**-30 m**3\"\n",
+ "print \"Volume occupied by one atom =\",round(v1/10**-30,2),\"*10**-30 m**3\"\n",
+ "print \"a2=\",round(a2,3),\"Angstorm\"\n",
+ "print \"Unit cell volume =a2**3 =\",round((b2)/10**-30,3),\"*10**-30 m**3\"\n",
+ "print \"Volume occupied by one atom =\",round(v2/10**-30,2),\"*10**-30 m**3\"\n",
+ "print \"Volume Change in % =\",round(v_c,3)\n",
+ "print \"Density Change in % =\",round(d_c,2)\n",
+ "print \"Thus the increase of density or the decrease of volume is about 0.5%\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.10, Page number 6.50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a= 0.563 *10**-9 metre\n",
+ "spacing between the nearest neighbouring ions = 0.2814 nm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#variable declaration\n",
+ "n=4 \n",
+ "M=58.5 #Molecular wt. of NaCl\n",
+ "N=6.02*10**26 #Avagadro number\n",
+ "rho=2180 #density\n",
+ "\n",
+ "#Calculations\n",
+ "a=((n*M)/(N*rho))**(1/3) \n",
+ "s=a/2\n",
+ "\n",
+ "#Result\n",
+ "print \"a=\",round(a/10**-9,3),\"*10**-9 metre\"\n",
+ "print \"spacing between the nearest neighbouring ions =\",round(s/10**-9,4),\"nm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.11, Page number 6.51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "lattice constant, a= 0.36 nm\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#variable declaration\n",
+ "n=4 \n",
+ "A=63.55 #Atomic wt. of NaCl\n",
+ "N=6.02*10**26 #Avagadro number\n",
+ "rho=8930 #density\n",
+ "\n",
+ "#Calculations\n",
+ "a=((n*A)/(N*rho))**(1/3) #Lattice Constant\n",
+ "\n",
+ "#Result\n",
+ "print \"lattice constant, a=\",round(a*10**9,2),\"nm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 6.12, Page number 6.51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Density of iron = 8805.0 kg/m**-3\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "r=0.123 #Atomic radius\n",
+ "n=4\n",
+ "A=55.8 #Atomic wt\n",
+ "a=2*math.sqrt(2) \n",
+ "N=6.02*10**26 #Avagadro number\n",
+ "\n",
+ "#Calculations\n",
+ "rho=(n*A)/((a*r*10**-9)**3*N)\n",
+ "\n",
+ "#Result\n",
+ "print \"Density of iron =\",round(rho),\"kg/m**-3\""
+ ]
+ }
+ ],
+ "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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