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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
|---|---|---|
| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | db0855dbeb41ecb8a51dde8587d43e5d7e83620f (patch) | |
| tree | b95975d958cba9af36cb1680e3f77205354f6512 /Engineering_Physics_by_P.K.Palanisamy/Chapter2_2.ipynb | |
| parent | 5a86a20b9de487553d4ef88719fb0fd76a5dd6a7 (diff) | |
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diff --git a/Engineering_Physics_by_P.K.Palanisamy/Chapter2_2.ipynb b/Engineering_Physics_by_P.K.Palanisamy/Chapter2_2.ipynb new file mode 100755 index 00000000..dc0f7988 --- /dev/null +++ b/Engineering_Physics_by_P.K.Palanisamy/Chapter2_2.ipynb @@ -0,0 +1,559 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#2: Crystallography and Crystal Structures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.3, Page number 2.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of atoms in (100) is a**(-2) atoms/mm**2\n",
+ "number of atoms in (110) is 0.707106781186547/a**2 atoms/mm**2\n",
+ "number of atoms in (111) is 0.577350269189626/a**2 atoms/mm**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "from sympy import Symbol\n",
+ "import numpy as np\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=Symbol('a'); #lattice constant(mm)\n",
+ "x1=4;\n",
+ "x2=math.sqrt(2);\n",
+ "b=a*math.sqrt(2);\n",
+ "theta=30; #angle(degrees)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*math.pi/180; #angle(radian)\n",
+ "na1=x1*1/(x1*a**2); #number of atoms in (100)(per mm**2)\n",
+ "na2=1/(x2*a**2); #number of atoms in (110)(per mm**2)\n",
+ "A3=(1/2)*b*b*math.cos(theta); \n",
+ "t=60/360*3;\n",
+ "na3=t/A3; #number of atoms in (111)(per mm**2)\n",
+ "\n",
+ "#Result\n",
+ "print \"number of atoms in (100) is\",na1,\"atoms/mm**2\"\n",
+ "print \"number of atoms in (110) is\",na2,\"atoms/mm**2\"\n",
+ "print \"number of atoms in (111) is\",na3,\"atoms/mm**2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.4, Page number 2.11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "interplanar spacing for (110) is 0.2556 nm\n",
+ "interplanar spacing for (212) is 0.1205 nm\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=0.1278; #atomic radius(m)\n",
+ "h1=1;\n",
+ "k1=1;\n",
+ "l1=0;\n",
+ "h2=2;\n",
+ "k2=1;\n",
+ "l2=2;\n",
+ "\n",
+ "#Calculation\n",
+ "a=round(4*r/math.sqrt(2),4);\n",
+ "d110=a/math.sqrt(h1**2+k1**2+l1**2); #interplanar spacing for (110)(nm)\n",
+ "d212=a/math.sqrt(h2**2+k2**2+l2**2); #interplanar spacing for (212)(nm)\n",
+ "\n",
+ "#Result\n",
+ "print \"interplanar spacing for (110) is\",round(d110,4),\"nm\"\n",
+ "print \"interplanar spacing for (212) is\",d212,\"nm\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.5, Page number 2.11"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "seperation between successive lattice planes is 1 : 0.71 : 0.58\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\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=1/math.sqrt(h1**2+k1**2+l1**2); #interplanar spacing for (110)\n",
+ "d110=1/math.sqrt(h2**2+k2**2+l2**2); #interplanar spacing for (110)\n",
+ "d111=1/math.sqrt(h3**2+k3**2+l3**2); #interplanar spacing for (111)\n",
+ "\n",
+ "#Result\n",
+ "print \"seperation between successive lattice planes is\",int(d100),\":\",round(d110,2),\":\",round(d111,2)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.6, Page number 2.12"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "miller indices of plane is ( 3.0 6.0 1.0 )\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=1;\n",
+ "b=1/2;\n",
+ "c=3;\n",
+ "\n",
+ "#Calculation\n",
+ "A=1/a;\n",
+ "B=1/b;\n",
+ "C=1/c;\n",
+ "h=A*c;\n",
+ "k=B*c;\n",
+ "l=C*c; #miller indices of plane\n",
+ "\n",
+ "#Result\n",
+ "print \"miller indices of plane is (\",h,k,l,\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.7, Page number 2.22"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "radius of interstitial sphere is 0.155 r\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=1; #assume\n",
+ "\n",
+ "#Calculation\n",
+ "a=4/math.sqrt(3);\n",
+ "R=(a-(2*r))/2; #radius of interstitial sphere(r)\n",
+ "\n",
+ "#Result\n",
+ "print \"radius of interstitial sphere is\",round(R,3),\"r\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.8, Page number 2.23"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "decrease of volume is 0.5 %\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r1=1.258; #atomic radius(angstrom)\n",
+ "r2=1.292; #atomic radius(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "a1=4*r1/math.sqrt(3); #spacing(angstrom)\n",
+ "n1=((1/8)*8)+1; #number of atoms per unit cell\n",
+ "v1=a1**3/n1; #volume occupied by 1 atom(m**3)\n",
+ "n2=(1/2*6)+(1/8*8); #number of atoms per unit cell\n",
+ "a2=2*math.sqrt(2)*r2; #spacing(angstrom)\n",
+ "v2=a2**3/n2; #volume occupied by 1 atom(m**3)\n",
+ "dc=(v1-v2)*100/v1; #change in volume(%)\n",
+ "\n",
+ "#Result\n",
+ "print \"decrease of volume is\",round(dc,1),\"%\" "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.9, Page number 2.24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "volume of unit cell is 9.356 *10**-29 m**3\n",
+ "density of zinc is 6960 kg/m**3\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",
+ "a=0.27*10**-9; #spacing(m)\n",
+ "c=0.494*10**-9;\n",
+ "n=6; #number of atoms\n",
+ "M=65.37; #atomic weight\n",
+ "N=6.023*10**26; #avagadro number\n",
+ "\n",
+ "#Calculation\n",
+ "V=3*math.sqrt(3)*a**2*c/2; #volume of unit cell(m**3)\n",
+ "rho=n*M/(N*V); #density of zinc(kg/m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"volume of unit cell is\",round(V*10**29,3),\"*10**-29 m**3\"\n",
+ "print \"density of zinc is\",int(rho),\"kg/m**3\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.10, Page number 2.24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "radius of interstitial sphere is 0.414 r\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=1; #assume\n",
+ "\n",
+ "#Calculation\n",
+ "a=4*r/math.sqrt(2);\n",
+ "R=(a/2)-r; #radius of interstitial sphere(r)\n",
+ "\n",
+ "#Result\n",
+ "print \"radius of interstitial sphere is\",round(R,3),\"r\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.11, Page number 2.25"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "number of atoms per m**3 is 1.77 *10**29\n",
+ "density of diamond is 3535.7 kg/m**3\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",
+ "a=0.356*10**-9; #cube edge(m)\n",
+ "m=12.01; #atomic weight of carbon\n",
+ "N=6.023*10**26; #avagadro number\n",
+ "\n",
+ "#Calculation\n",
+ "n=8/a**3; #number of atoms per m**3\n",
+ "M=m/N;\n",
+ "d=M*n; #density of diamond(kg/m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"number of atoms per m**3 is\",round(n/10**29,2),\"*10**29\"\n",
+ "print \"density of diamond is\",round(d,1),\"kg/m**3\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.12, Page number 2.26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "distance between 2 adjacent atoms is 2.81 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "mw=23+35.5; #molecular weight of NaCl(gm/mol)\n",
+ "N=6.023*10**23; #avagadro number(per mol)\n",
+ "d=2.18; #mass of unit volume\n",
+ "\n",
+ "#Calculation\n",
+ "M=mw/N; #mass of NaCl molecule(gm)\n",
+ "n=2*d/M; #number of atoms per unit volume(atoms/cm**3)\n",
+ "a=(1/n)**(1/3); #distance between 2 adjacent atoms(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"distance between 2 adjacent atoms is\",round(a*10**8,2),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.13, Page number 2.26"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "density of copper crystal is 8.929 gm/cm**3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "M=63.5; #atomic weight\n",
+ "N=6.023*10**23; #avagadro number\n",
+ "r=1.278*10**-8; #radius(m)\n",
+ "n=4;\n",
+ "\n",
+ "#Calculation\n",
+ "m=M/N; #mass of copper atom(gm)\n",
+ "a=4*r/math.sqrt(2);\n",
+ "Mu=n*m; #mass of unit cell\n",
+ "d=Mu/a**3; #density of copper crystal(gm/cm**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"density of copper crystal is\",round(d,3),\"gm/cm**3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 2.14, Page number 2.27"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "free volume per unit cell is 7.6795 *10**-30 m**3\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",
+ "r=0.1249*10**-9; #radius(m)\n",
+ "pf=0.68; #packing factor\n",
+ "\n",
+ "#Calculation\n",
+ "a=4*r/math.sqrt(3); #lattice constant(m)\n",
+ "v=a**3; #volume of unit cell(m**3)\n",
+ "Fv=(1-pf)*v; #free volume per unit cell(m**3)\n",
+ "\n",
+ "#Result\n",
+ "print \"free volume per unit cell is\",round(Fv*10**30,4),\"*10**-30 m**3\"\n",
+ "print \"answer 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": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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