{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#3: Crystal Physics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Example number 3.1, Page number 57" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "miller indices of 1st plane is ( 0.0 2.0 0.0 )\n", "miller indices of 2nd plane is ( 1.0 2.0 0.0 )\n", "miller indices of 3rd plane is ( 2.0 2.0 0.0 )\n" ] } ], "source": [ "#importing modules\n", "import math\n", "from __future__ import division\n", "\n", "#Variable declaration\n", "x1=float('inf'); #numerical intercept on X axis\n", "y1=1/2; #numerical intercept on Y axis\n", "z1=float('inf'); #numerical intercept on Z axis\n", "x2=1; #numerical intercept on X axis\n", "y2=1/2; #numerical intercept on Y axis\n", "z2=float('inf'); #numerical intercept on Z axis\n", "x3=1/2; #numerical intercept on X axis\n", "y3=1/2; #numerical intercept on Y axis\n", "z3=float('inf'); #numerical intercept on Z axis\n", "\n", "#Calculation\n", "p1=1/x1; #The miller indices of x-axis\n", "q1=1/y1; #The miller indices of y-axis\n", "r1=1/z1; #The miller indices of z-axis\n", "p2=1/x2; #The miller indices of x-axis\n", "q2=1/y2; #The miller indices of y-axis\n", "r2=1/z2; #The miller indices of z-axis\n", "p3=1/x3; #The miller indices of x-axis\n", "q3=1/y3; #The miller indices of y-axis\n", "r3=1/z3; #The miller indices of z-axis\n", "\n", "#Result\n", "print \"miller indices of 1st plane is (\",p1,q1,r1,\")\"\n", "print \"miller indices of 2nd plane is (\",p2,q2,r2,\")\"\n", "print \"miller indices of 3rd plane is (\",p3,q3,r3,\")\"" ] }, { "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 }