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diff --git a/Engineering_Physics_By_G_Vijayakumari/Chapter3.ipynb b/Engineering_Physics_By_G_Vijayakumari/Chapter3.ipynb new file mode 100755 index 00000000..b55e472d --- /dev/null +++ b/Engineering_Physics_By_G_Vijayakumari/Chapter3.ipynb @@ -0,0 +1,1072 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#3: Crystal Physics"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.3, Page number 60"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The interplanar distance is 6.3589 *10**-11 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=3; #miller indices with respect to x axis\n",
+ "k=1; #miller indices with respect to y axis\n",
+ "l=1; #miller indices with respect to z axis\n",
+ "a=2.109*10**-10; #lattice constant of plane in a simple cubic lattice(m)\n",
+ "\n",
+ "#Calculation\n",
+ "d=(a/(math.sqrt(h**2+k**2+l**2))); #The interplanar distance(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"The interplanar distance is\",round(d*10**11,4),\"*10**-11 m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.4, Page number 60"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The lattice constant is 4.0447 *10**-10 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=1; #miller indices with respect to x axis\n",
+ "k=1; #miller indices with respect to y axis\n",
+ "l=0; #miller indices with respect to z axis\n",
+ "d=2.86*10**-10; #the distance between miller indices(m)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(d*(math.sqrt(h**2+k**2+l**2))); #The lattice constant(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lattice constant is\",round(a*10**10,4),\"*10**-10 m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.6, Page number 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The ratio of intercepts on the three axis by ( 1 1 1 ) plane is 1.0 : 1.0 : 1.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h=1; #miller indices of x-axis\n",
+ "k=1; #miller indices of y-axis\n",
+ "l=1; #miller indices of z-axis\n",
+ "\n",
+ "#Calculation\n",
+ "p=1/h; #intercept on x-axis\n",
+ "q=1/k; #intercept on y-axis\n",
+ "r=1/l; #intercept on z-axis\n",
+ "\n",
+ "#Result\n",
+ "print \"The ratio of intercepts on the three axis by (\",h,k,l,\") plane is\",p,\":\",q,\":\",r"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.7, Page number 61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The inter planar spacing distance in 1st plane is 2.0347 *10**-10 m\n",
+ "The inter planar spacing distance in 2nd plane is 1.7621 *10**-10 m\n",
+ "The inter planar spacing distance in 3rd plane is 1.246e-10 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=1.246*10**-10; #atomic radius of Fcc crystal(m)\n",
+ "h1=1; #miller indices with respect to x axis in 1st plane\n",
+ "k1=1; #miller indices with respect to y axis in 1st plane\n",
+ "l1=1; #miller indices with respect to z axis in 1st plane\n",
+ "h2=2; #miller indices with respect to x axis in 2nd plane\n",
+ "k2=0; #miller indices with respect to y axis in 2nd plane\n",
+ "l2=0; #miller indices with respect to z axis in 2nd plane\n",
+ "h3=2; #miller indices with respect to x axis in 3rd plane\n",
+ "k3=2; #miller indices with respect to y axis in 3rd plane\n",
+ "l3=0; #miller indices with respect to z axis in 3rd plane\n",
+ "\n",
+ "#Calculation\n",
+ "a=(4*r)/math.sqrt(2); #The lattice constant in a FCC crystal(m)\n",
+ "d1=(a/(math.sqrt(h1**2+k1**2+l1**2))); #inter planar spacing distance in 1st plane(m)\n",
+ "d2=(a/(math.sqrt(h2**2+k2**2+l2**2))); #inter planar spacing distance in 2nd plane(m)\n",
+ "d3=(a/(math.sqrt(h3**2+k3**2+l3**2))); #inter planar spacing distance in 3rd plane(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"The inter planar spacing distance in 1st plane is\",round(d1*10**10,4),\"*10**-10 m\"\n",
+ "print \"The inter planar spacing distance in 2nd plane is\",round(d2*10**10,4),\"*10**-10 m\"\n",
+ "print \"The inter planar spacing distance in 3rd plane is\",d3,\"m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.8, Page number 62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The inter planar spacing distance in 1st plane is a* 1.0 m\n",
+ "The inter planar spacing distance in 2nd plane is a* 0.707 m\n",
+ "The inter planar spacing distance in 3rd plane is a* 0.577 fm\n",
+ "Ratio of interplanar distance of three planes d100:d110:d111= 1.0 : 0.707 : 0.577\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=1; #assume\n",
+ "h1=1; #miller indices with respect to x axis in 1st plane\n",
+ "k1=0; #miller indices with respect to y axis in 1st plane\n",
+ "l1=0; #miller indices with respect to z axis in 1st plane\n",
+ "h2=1; #miller indices with respect to x axis in 2nd plane\n",
+ "k2=1; #miller indices with respect to y axis in 2nd plane\n",
+ "l2=0; #miller indices with respect to z axis in 2nd plane\n",
+ "h3=1; #miller indices with respect to x axis in 3rd plane\n",
+ "k3=1; #miller indices with respect to y axis in 3rd plane\n",
+ "l3=1; #miller indices with respect to z axis in 3rd plane\n",
+ "\n",
+ "#Calculation\n",
+ "x1=math.sqrt(h1**2+k1**2+l1**2);\n",
+ "d100=a/x1; #inter planar spacing distance in 1st plane(m)\n",
+ "x2=math.sqrt(h2**2+k2**2+l2**2);\n",
+ "d110=a/x2; #inter planar spacing distance in 2nd plane(m)\n",
+ "x3=math.sqrt(h3**2+k3**2+l3**2);\n",
+ "d111=a/x3; #inter planar spacing distance in 3rd plane(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"The inter planar spacing distance in 1st plane is a*\",d100,\"m\"\n",
+ "print \"The inter planar spacing distance in 2nd plane is a*\",round(d110,3),\"m\"\n",
+ "print \"The inter planar spacing distance in 3rd plane is a*\",round(d111,3),\"fm\"\n",
+ "print \"Ratio of interplanar distance of three planes d100:d110:d111=\",(1/x1),\":\",round((1/x2),3),\":\",round((1/x3),3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.9, Page number 62"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The miller indices of the plane is (h k l)=( 3.0 6.0 1.0 )\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "p=1; #x-intercept of the plane\n",
+ "q=1/2; #y-intercept of the plane\n",
+ "r=3; #z-intercept of the plane\n",
+ "\n",
+ "#Calculation\n",
+ "h=(1/p)*3; #miller indices with respect to x axis\n",
+ "k=(1/q)*3; #miller indices with respect to y axis\n",
+ "l=(1/r)*3; #miller indices with respect to z axis\n",
+ "\n",
+ "#Result\n",
+ "print \"The miller indices of the plane is (h k l)=(\",h,k,l,\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.10, Page number 63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The inter planar d-spacing distance is 2.814 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=2.814; #the lattice constant of a simple cubic system(angstrom)\n",
+ "h1=1; #miller indices with respect to x axis\n",
+ "k1=0; #miller indices with respect to y axis\n",
+ "l1=0; #miller indices with respect to z axis\n",
+ "\n",
+ "#Calculation\n",
+ "d=a/math.sqrt(h1**2+k1**2+l1**2); #inter planar d spacing distance(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The inter planar d-spacing distance is\",d,\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.11, Page number 63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The miller indices of the set of parallel lines is ( 2.0 2.0 3.0 )\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "OA=0.025; #The unit cell makes intercepts on a(nm)\n",
+ "OB=0.02; #The unit cell makes intercepts on b(nm)\n",
+ "OC=0.01; #The unit cell makes intercepts on c(nm)\n",
+ "a=0.05; #The unit cell edge of an orthorhombic crystal(nm)\n",
+ "b=0.04; #The unit cell edge of an orthorhombic crystal(nm)\n",
+ "c=0.03; #The unit cell edge of an orthorhombic crystal(nm)\n",
+ "\n",
+ "#Calculation\n",
+ "p=a/OA; #miller indices with respect to x axis\n",
+ "q=b/OB; #miller indices with respect to y axis\n",
+ "r=c/OC; #miller indices with respect to z axis\n",
+ "\n",
+ "#Result\n",
+ "print \"The miller indices of the set of parallel lines is (\",p,q,r,\")\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.12, Page number 63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 36,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The miller indices are 2 1 2\n",
+ "The miller indices are 1 2 1\n",
+ "The miller indices are 1 0 3.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=0.424; #value of one axial unit\n",
+ "b=1; #value of second axial unit\n",
+ "c=0.367; #value of third axial unit\n",
+ "i1=0.212; #value at x-intercept\n",
+ "j1=1; #value at y-intercept\n",
+ "k1=0.183; #value at z-intercept\n",
+ "i2=0.848; #value at x-intercept\n",
+ "j2=1; #value at y-intercept\n",
+ "k2=0.732; #value at z-intercept\n",
+ "i3=0.424; #value at x-intercept\n",
+ "k3=0.123; #value at z-intercept\n",
+ "\n",
+ "#Calculation\n",
+ "p1=1/(i1/a); #miller indices at x-intercept\n",
+ "q1=1/(j1/b); #miller indices at y-intercept\n",
+ "r1=1/(k1/c); #miller indices at z-intercept\n",
+ "p2=1/(i2/a)*2; #miller indices at x-intercept\n",
+ "q2=1/(j2/b)*2; #miller indices at y-intercept\n",
+ "r2=1/(k2/c)*2; #miller indices at z-intercept\n",
+ "p3=1/(i3/a); #miller indices at x-intercept\n",
+ "q3=0; #miller indices at y-intercept\n",
+ "r3=1/(k3/c); #miller indices at z-intercept\n",
+ "\n",
+ "#Result\n",
+ "print \"The miller indices are\",int(p1),int(q1),int(r1)\n",
+ "print \"The miller indices are\",int(p2),int(q2),int(r2)\n",
+ "print \"The miller indices are\",int(p3),int(q3),round(r3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.13, Page number 65"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Miller indices are (1/infinite 1/ 2 1/ 7 )= 0 7 2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "OB=2; #The intercept made by the parrell line ,OB=2b\n",
+ "OC=7; #The intercept made by the parrell line ,OC=2c\n",
+ "#OA=infinite The intercept made by the parrell line ,OB=2b\n",
+ "\n",
+ "#Calculation\n",
+ "A=0; #miller indice along x-axis\n",
+ "B=1/OB; #miller indice along y-axis\n",
+ "C=1/OC; #miller indice along z-axis\n",
+ "X=(B*(OC*OB)); #taking L.C.M\n",
+ "Y=(C*(OC*OB)); #taking L.C.M\n",
+ "\n",
+ "#Result\n",
+ "print \"Miller indices are (1/infinite 1/\",OB,\"1/\",OC,\")=\",A,int(X),int(Y)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.14, Page number 75"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The atomic radius of copper is 1.273 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=3.6; #lattice parameter of copper(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "r=(a*math.sqrt(2))/4; #The atomic radius of copper(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The atomic radius of copper is\",round(r,3),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.15, Page number 76"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The inter planar d-spacing distance is 1.1011 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=4.12; #the lattice constant of a simple cubic system(angstrom)\n",
+ "h1=3; #miller indices with respect to x axis\n",
+ "k1=2; #miller indices with respect to y axis\n",
+ "l1=1; #miller indices with respect to z axis\n",
+ "\n",
+ "#Calculation\n",
+ "d=a/math.sqrt(h1**2+k1**2+l1**2); #inter planar d spacing distance(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The inter planar d-spacing distance is\",round(d,4),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.16, Page number 76"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 40,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The density of copper is 8934 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",
+ "n=4; #no.of atoms in FCC structure\n",
+ "A=63.54; #Atomic weight of copper\n",
+ "r=1.278*10**-10; #atomic radius(m)\n",
+ "N=6.023*10**26; #Avogadro's Number(per Kg mol)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(4*r/math.sqrt(2)); #The lattice constant(m)\n",
+ "d=A*n/(N*a**3); #The density of copper(Kg/m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The density of copper is\",int(d),\"Kg/m^3\"\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.17, Page number 76"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 41,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The ratio of interplanar distance between successive lattice planes in a simple cubic lattice is d100:d110:d111= 1 : 0.707 : 0.577\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "h1=1; #miller indices with respect to x axis in 1st plane\n",
+ "k1=0; #miller indices with respect to y axis in 1st plane\n",
+ "l1=0; #miller indices with respect to z axis in 1st plane\n",
+ "h2=1; #miller indices with respect to x axis in 2nd plane\n",
+ "k2=1; #miller indices with respect to y axis in 2nd plane\n",
+ "l2=0; #miller indices with respect to z axis in 2nd plane\n",
+ "h3=1; #miller indices with respect to x axis in 3rd plane\n",
+ "k3=1; #miller indices with respect to y axis in 3rd plane\n",
+ "l3=1; #miller indices with respect to z axis in 3rd plane\n",
+ "a=1; #The lattice constant in a in a simple cubic lattice(m)\n",
+ "\n",
+ "#Calculation\n",
+ "d100=a/math.sqrt(h1**2+k1**2+l1**2); #inter planar spacing distance in 1st plane(m)\n",
+ "d110=a/math.sqrt(h2**2+k2**2+l2**2); #inter planar spacing distance in 2nd plane(m)\n",
+ "d111=a/math.sqrt(h3**2+k3**2+l3**2); #inter planar spacing distance in 3rd plane(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"The ratio of interplanar distance between successive lattice planes in a simple cubic lattice is d100:d110:d111=\",int(d100),\":\",round(d110,3),\":\",round(d111,3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.18, Page number 76"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 42,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The distance between two adjacent atoms is 2.81 *10**-10 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "x=23; #atomic weight of sodium\n",
+ "y=35.45; #atomic weight of chloride\n",
+ "AW=58.45; #atomic weight of sodium chloride(NaCl)\n",
+ "n=4; #no.of atoms in FCC structure\n",
+ "d=2.18*10**6; #density of NaCl crystal of FCC structure(kg/m^3)\n",
+ "N=6.023*10**23; #Avogadro's Number(per Kg mol)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(n*AW/(d*N))**(1/3); #The lattice constant(m)\n",
+ "r=a/2; #The distance between two adjacent atoms(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"The distance between two adjacent atoms is\",round(r*10**10,2),\"*10**-10 m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.19, Page number 77"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 43,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The atomic radius of Fe which has BCC structure is 1.242 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=2; #no.of atoms in BCC structure\n",
+ "d=7.86*10**6; #density of iron of FCC structure(kg/m^3)\n",
+ "AW=55.85; #atomic weight of Fe\n",
+ "N=6.023*10**23; #Avogadro's Number(per Kg mol)\n",
+ "\n",
+ "#Calculation\n",
+ "a=(n*AW/(d*N))**(1/3); #The lattice constant(m)\n",
+ "r=a*math.sqrt(3)*10**10/4; #The atomic radius of Fe which has BCC structure(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The atomic radius of Fe which has BCC structure is\",round(r,3),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.20, Page number 77"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 44,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The lattice constant is 6.6 angstrom\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=4; #no.of atoms in FCC structure\n",
+ "d=2.7*10**3; #density of potassium bromide(Kg/m^3)\n",
+ "AW=119; #molecular weight of KBr\n",
+ "N=6.023*10**26; #Avagadro's number(Kg mol)\n",
+ "\n",
+ "#Calculation\n",
+ "a=((n*AW/(d*N))**(1/3))*10**10; #The lattice constant(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lattice constant is\",round(a,1),\"angstrom\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.21, Page number 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 45,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Number of atoms per unit cell of a crystal is 2.0\n",
+ "If n=2,the crystal system is body centered cubic\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "d=9.6*10**2; #density of crystal(Kg/m^3)\n",
+ "AW=23; #molecular weight of the crystal\n",
+ "N=6.023*10**26; #Avagadro's number(per Kg mol)\n",
+ "a=4.3*10**-10; #lattice constant(m)\n",
+ "\n",
+ "#Calculation\n",
+ "n=d*N*a**3/AW; #Number of atoms per unit cell of a crystal\n",
+ "\n",
+ "#Result\n",
+ "print \"Number of atoms per unit cell of a crystal is\",round(n)\n",
+ "print \"If n=2,the crystal system is body centered cubic\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.22, Page number 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 46,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The volume of cell is 2.128 *10**-29 m^3\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "r=1.2*10**-10; #atomic radius of crystal of BCC structure(m)\n",
+ "\n",
+ "#Calculation\n",
+ "a=4*r/math.sqrt(3); #lattice constant of BCC structure(m)\n",
+ "V=a**3; #The volume of cell(m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The volume of cell is\",round(V*10**29,3),\"*10**-29 m^3\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.23, Page number 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 47,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The planar atomic density is 6.25e+12 atoms/mm^2\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=4*10**-7; #lattice constant of the crystal(mm)\n",
+ "h1=1; #miller indices with respect to x axis in 1st plane\n",
+ "k1=0; #miller indices with respect to y axis in 1st plane\n",
+ "l1=0; #miller indices with respect to z axis in 1st plane\n",
+ "\n",
+ "#Calculation\n",
+ "n=4*(1/4); #Number of atoms contained in a plane per unit cell\n",
+ "A=a**2; #Area of the plane(mm^2)\n",
+ "d=n/A; #The planar atomic density(atoms/mm^2)\n",
+ "\n",
+ "#Result\n",
+ "print \"The planar atomic density is\",d,\"atoms/mm^2\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.24, Page number 79"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 48,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The lattice constant is 4.0 *10**-10 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=4; #no.of atoms in Face centered cubic lattice\n",
+ "d=6250; #density of potassium bromide(Kg/m^3)\n",
+ "AW=60.2; #molecular weight of crysal with face centered cubic lattice\n",
+ "N=6.023*10**26; #Avagadro's number(per Kg mol)\n",
+ "\n",
+ "#Calculation\n",
+ "a=((n*AW/(d*N))**(1/3)); #The lattice constant(m)\n",
+ "\n",
+ "#Result\n",
+ "print \"The lattice constant is\",round(a*10**10),\"*10**-10 m\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.25, Page number 79"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 50,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The change in volume percentage is 0.49326\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",
+ "r1=0.1258*10**-9; #atomic radii of the iron atom in BCC structure(m)\n",
+ "r2=0.1292*10**-9; #atomic radii of the iron atom in FCC structure(m)\n",
+ "T=910; #metallic iron changes from BCC to FCC(C)\n",
+ "\n",
+ "#Calculation\n",
+ "a1=(4*r1/math.sqrt(3)); #lattice constant of BCC structure(m)\n",
+ "v1=a1**3/2; #The volume occupied by one BCC atom(m^3)\n",
+ "a2=4*r2/math.sqrt(2); #lattice constant of FCC structure(m)\n",
+ "v2=a2**3/4; #The volume occupied by one FCC atom(m^3)\n",
+ "V=((v1-v2)/v1)*100; #The change in volume percentage\n",
+ "\n",
+ "#Result\n",
+ "print \"The change in volume percentage is\",round(V,5)\n",
+ "print \"answer varies due to rounding off errors\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.26, Page number 80"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 52,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The Number of unit cells is 4.70419 *10**22\n"
+ ]
+ }
+ ],
+ "source": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "a=0.405*10**-9; #lattice constant of unit cell of aluminium which is face centered cubic(m)\n",
+ "s=25*10**-2; #Side of aluminium foil(m)\n",
+ "t=0.005*10**-2; #Thickness of aluminium foil(m)\n",
+ "\n",
+ "#Calculation\n",
+ "ar=s**2; #area of aluminium foil(m^2)\n",
+ "V=ar*t; #volume of the aluminium foil(m^3)\n",
+ "v=a**3; #volume of the unit cell(m^3)\n",
+ "n=(V/v); #Number of unit cells\n",
+ "\n",
+ "#Result\n",
+ "print \"The Number of unit cells is\",round(n/10**22,5),\"*10**22\""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example number 3.27, Page number 81"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 59,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The Volume of the unit cell of Magnesium which has HCP structure is 1.0 *10**-28 m^3\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",
+ "r=0.1605*10**-9; #radius of magnesium atom which has HCP structure(m)\n",
+ "\n",
+ "#Calculation\n",
+ "a=2*r; #lattice constant of magnesium which has HCP structure(m)\n",
+ "c=a*math.sqrt(8/3); #height of the HCP structure(m)\n",
+ "V=3*math.sqrt(3)*(a**2)*c/3; #Volume of the unit cell of Magnesium which has HCP structure(m^3)\n",
+ "\n",
+ "#Result\n",
+ "print \"The Volume of the unit cell of Magnesium which has HCP structure is\",round(V*10**28),\"*10**-28 m^3\"\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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