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diff --git a/Engineering_Physics_by_A._Marikani/Chapter_6.ipynb b/Engineering_Physics_by_A._Marikani/Chapter_6.ipynb new file mode 100755 index 00000000..f66bf1b2 --- /dev/null +++ b/Engineering_Physics_by_A._Marikani/Chapter_6.ipynb @@ -0,0 +1,900 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:be1bff093c78fabbeb6fefe6e4abb0ea03e38b876fbc4829ed2c2e8b1df1e947" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Crystallography" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.1, Page number 185" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "r=0.071; #radius in nm\n", + "N=6.022*10**26; \n", + "\n", + "#Calculation\n", + "r=r*10**-9; #converting r from nm to m\n", + "#mass of carbon atom m = 12/N\n", + "m=12/N;\n", + "#mass of diamond M = 8*mass of one carbon atom\n", + "M=8*m;\n", + "#volume of diamond V = (8*r/sqrt(3))^3\n", + "V=(8*r/math.sqrt(3))**3;\n", + "d=M/V; #density in kg/m^3\n", + "d=math.ceil(d*100)/100; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"density of diamond in kg/m^3 is\",d);\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('density of diamond in kg/m^3 is', 4520.31)\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.2, Page number 185" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "aBCC=0.332; #lattice constant in nm\n", + "aHCP=0.296; #lattice constant in nm\n", + "c=0.468; #c in nm\n", + "\n", + "#Calculation\n", + "aBCC=aBCC*10**-9; #converting nm to m\n", + "Vbcc=aBCC**3;\n", + "aHCP=aHCP*10**-9; #converting nm to m\n", + "c=c*10**-9; #converting nm to m\n", + "Vhcp=6*(math.sqrt(3)/4)*aHCP**2*c;\n", + "V=Vhcp-Vbcc;\n", + "Vch=(V*100)/Vbcc;\n", + "Vch=math.ceil(Vch*100)/100; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"percentage change in volume is\",Vch);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('percentage change in volume is', 191.12)\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.3, Page number 186" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "r=1.278; #atomic radius of Cu in Angstrom\n", + "A=63.54; #atomic weight of Cu\n", + "n=4; #for FCC n=4\n", + "Na=6.022*10**26;\n", + "\n", + "#Calculation\n", + "r=r*10**-10; #converting atomic radius from Angstrom to m\n", + "a=2*math.sqrt(2)*r; \n", + "rho=(n*A)/(Na*a**3);\n", + "rho=math.ceil(rho*100)/100; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"density of Cu in kg/m^3 is\",rho);\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('density of Cu in kg/m^3 is', 8935.92)\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.4, Page number 186" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "import numpy as np\n", + "\n", + "#Variable declaration\n", + "rho=2180; #density of NaCl in kg/m^3\n", + "wNa=23; #atomic weight of Na\n", + "wCl=35.5; #atomic weight of Cl\n", + "n=4; #for FCC n=4\n", + "Na=6.022*10**26;\n", + "\n", + "#Calculation\n", + "A=wNa+wCl; #molecular weight of NaCl\n", + "x=np.reciprocal(3.);\n", + "a=((n*A)/(Na*rho))**x;\n", + "\n", + "#Result\n", + "print(\"interatomic distance in NaCl in m is\",a); \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('interatomic distance in NaCl in m is', 5.6278114346454509e-10)\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.5, Page number 187" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "a=0.42; #lattice constant in nm\n", + "h1=1;\n", + "k1=0;\n", + "l1=1; #indices of the plane (101)\n", + "h2=2;\n", + "k2=2;\n", + "l2=1; #indices of the plane (221)\n", + "\n", + "#Calculation\n", + "a=a*10**-9; #converting from nm to m\n", + "d1=a/math.sqrt((h1**2)+(k1**2)+(l1**2)); #interplanar spacing for plane (101)\n", + "d1=d1*10**9; #converting from m to nm\n", + "d1=math.ceil(d1*10**5)/10**5; #rounding off to 5 decimals\n", + "d2=a/math.sqrt((h2**2)+(k2**2)+(l2**2)); #interplanar spacing for plane (221)\n", + "d2=d2*10**9; #converting from m to nm\n", + "\n", + "#Result\n", + "print(\"interplanar spacing for (101) in nm is\",d1);\n", + "print(\"interplanar spacing for (221) in nm is\",d2);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('interplanar spacing for (101) in nm is', 0.29699)\n", + "('interplanar spacing for (221) in nm is', 0.14)\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.6, Page number 187" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#Variable declaration\n", + "h1=1;\n", + "k1=0;\n", + "l1=2; #indices for plane (102)\n", + "h2=2;\n", + "k2=3;\n", + "l2=1; #indices for plane (231)\n", + "h3=3;\n", + "k3=-1;\n", + "l3=2; #indices for plane (31'2)\n", + "\n", + "#Calculation\n", + "#intercepts made by the plane is a/h, b/k, c/l\n", + "#for plane (102) intercepts are a/1=a, b/0=infinite, c/2\n", + "#for plane (231) intercepts are a/2, b/3, c/1=c\n", + "#for plane (31'2) intercepts are a/3=a, b/-1=-b, c/2\n", + "\n", + "#Result\n", + "print(\"for plane (102) intercepts are a/1=a, b/0=infinite, c/2\");\n", + "print(\"for plane (231) intercepts are a/2, b/3, c/1=c\");\n", + "print(\"for plane (312) intercepts are a/3=a, b/-1=-b, c/2\");\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "for plane (102) intercepts are a/1=a, b/0=infinite, c/2\n", + "for plane (231) intercepts are a/2, b/3, c/1=c\n", + "for plane (312) intercepts are a/3=a, b/-1=-b, c/2\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.7, Page number 188" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "u1=1;\n", + "v1=1;\n", + "w1=1; #indices for plane (111)\n", + "u2=2;\n", + "v2=1;\n", + "w2=2; #indices for plane (212)\n", + "\n", + "#Calculation\n", + "A=u1*u2+v1*v2+w1*w2; \n", + "B1=math.sqrt((u1**2)+(v1**2)+(w1**2));\n", + "B2=math.sqrt((u2**2)+(v2**2)+(w2**2));\n", + "B=A/(B1*B2);\n", + "B=math.ceil(B*10**4)/10**4; #rounding off to 4 decimals\n", + "theta=math.acos(B); #angle in radian\n", + "theta=theta*57.2957795; #converting radian to degrees\n", + "theeta=math.ceil(theta*10**3)/10**3; #rounding off to 3 decimals\n", + "deg=int(theta); #converting to degrees\n", + "t=60*(theta-deg);\n", + "mi=int(t); #converting to minutes\n", + "sec=60*(t-mi); #converting to seconds\n", + "sec=math.ceil(sec*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print(\"angle between the planes in degrees is\",theeta);\n", + "print(\"angle between the planes is\",deg,\"degrees\",mi,\"minutes\",sec,\"seconds\");\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('angle between the planes in degrees is', 15.783)\n", + "('angle between the planes is', 15, 'degrees', 46, 'minutes', 57.85, 'seconds')\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.8, Page number 188" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.9, Page number 189" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "d=0.2338; #interplanar distance in nm\n", + "h=-1;\n", + "k=1;\n", + "l=1; #indices of the plane (1'11)\n", + "\n", + "#Calculation\n", + "d=d*10**-9; #converting from nm to m\n", + "a=d*math.sqrt((h**2)+(k**2)+(l**2));\n", + "a=a*10**9; #converting lattice constant from m to nm\n", + "a=math.ceil(a*10**5)/10**5; #rounding off to 5 decimals\n", + "\n", + "#Result\n", + "print(\"lattice constant in nm is\",a);\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('lattice constant in nm is', 0.40496)\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.10, Page number 189" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#variable declaration\n", + "h1=1;\n", + "k1=0;\n", + "l1=0; #indices for plane (100)\n", + "h2=1;\n", + "k2=1;\n", + "l2=0; #indices for plane (110)\n", + "h3=1;\n", + "k3=1;\n", + "l3=1; #indices for plane (111)\n", + "\n", + "#Calculation\n", + "#d=a/math.sqrt((h**2)+(k**2)+(l**2))\n", + "#d100=a/math.sqrt((h1**2)+(k1**2)+(l1**2))\n", + "x1=math.sqrt((h1**2)+(k1**2)+(l1**2));\n", + "#d100=a/x1 = a/1 = a\n", + "#d110=a/math.sqrt((h2**2)+(k2**2)+(l2**2))\n", + "x2=math.sqrt((h2**2)+(k2**2)+(l2**2));\n", + "x2=math.ceil(x2*10**4)/10**4; #rounding off to 4 decimals\n", + "#d110=a/x2 = a/sqrt(2)\n", + "#d111=a/math.sqrt((h3**2)+(k3**2)+(l3**2))\n", + "x3=math.sqrt((h3**2)+(k3**2)+(l3**2));\n", + "x3=math.ceil(x3*10**4)/10**4; #rounding off to 4 decimals\n", + "#d111=a/x3 = a/sqrt(3)\n", + "#hence d100:d110:d111=a:a/sqrt(2):a/sqrt(3)\n", + "#multiplying RHS by sqrt(6) we get d100:d110:d111=sqrt(6):sqrt(3):sqrt(2)\n", + "\n", + "#Result\n", + "print(\"value of x1 is\",x1);\n", + "print(\"value of x2 is\",x2);\n", + "print(\"value of x3 is\",x3);\n", + "print(\"d100:d110:d111=sqrt(6):sqrt(3):sqrt(2)\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('value of x1 is', 1.0)\n", + "('value of x2 is', 1.4143)\n", + "('value of x3 is', 1.7321)\n", + "d100:d110:d111=sqrt(6):sqrt(3):sqrt(2)\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.11, Page number 190" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#variable declaration\n", + "h=2;\n", + "k=3;\n", + "l=1; #indices for plane (231)\n", + "\n", + "#Calculation\n", + "#intercepts made by the plane is a/h, b/k, c/l\n", + "#for a cubic unit cell, a=b=c\n", + "#for plane (231) intercepts are a/2, a/3, a/1 = a\n", + "#ratio of the intercepts is 1/2:1/3:1\n", + "#LCM is 6. multiplying by LCM, we get ratio l1:l2:l3 = 3:2:6\n", + "\n", + "#Result\n", + "print(\"l1:l2:l3 = 3:2:6\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "l1:l2:l3 = 3:2:6\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.12, Page number 190" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#variable declaration\n", + "h=1;\n", + "k=2;\n", + "l=3; #indices for plane (123)\n", + "l1=0.8; #l1 in armstrong\n", + "a=0.8; #a in armstrong\n", + "b=1.2; #b in armstrong\n", + "c=1.5; #c in armstrong\n", + "\n", + "#Calculation\n", + "#intercepts made by the plane is a/h, b/k, c/l\n", + "#for plane (123) intercepts are a/1 = a, b/2, c/3\n", + "#ratio of the intercepts l1:l2:l3 = a:b/2:c/3\n", + "#thus 0.8:l2:l3 = 0.8:1.2/2:1.5/3\n", + "l2=1.2/2; #l2 in armstrong\n", + "l3=1.5/3; #l3 in armstrong\n", + "\n", + "#Result\n", + "print(\"value of l2 in armstrong is\",l2);\n", + "print(\"value of l3 in armstrong is\",l3);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('value of l2 in armstrong is', 0.6)\n", + "('value of l3 in armstrong is', 0.5)\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.13, Page number 191" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#Result\n", + "print(\"in simple cubic unit cell nearest neighbour distance is a\");\n", + "print(\"in body centered cubic unit cell nearest neighbour distance is sqrt(3)*a/2\");\n", + "print(\"in face centered cubic unit cell nearest neighbour distance is a/sqrt(2)\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "in simple cubic unit cell nearest neighbour distance is a\n", + "in body centered cubic unit cell nearest neighbour distance is sqrt(3)*a/2\n", + "in face centered cubic unit cell nearest neighbour distance is a/sqrt(2)\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.14, Page number 191" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#variable declaration\n", + "a=2.04; #lattice parameter in armstrong\n", + "h=2;\n", + "k=1;\n", + "l=2; #indices for plane (212)\n", + "\n", + "#Calculation\n", + "a=a*10**-10; #converting from armstrong to m\n", + "d=a/math.sqrt((h**2)+(k**2)+(l**2));\n", + "d=d*10**10; #converting from m to armstrong\n", + "d=math.ceil(d*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print(\"interplanar distance in armstrong is\",d);\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('interplanar distance in armstrong is', 0.681)\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.15, Page number 191" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#variable declaration\n", + "r=1.278; #radius of Cu in armstrong\n", + "M=63.54; #atomic weight of Cu\n", + "rho=8980; #density in kg/m^3\n", + "Na=6.022*10**26;\n", + "\n", + "#Calculation\n", + "r=r*10**-10; #radius in m\n", + "a=math.sqrt(8)*r;\n", + "n=(rho*Na*a**3)/M;\n", + "\n", + "#Result\n", + "print(\"interatomic distance in m is\",a);\n", + "print(\"number of atoms per Cu unit cell is\",int(n));" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('interatomic distance in m is', 3.6147298654256317e-10)\n", + "('number of atoms per Cu unit cell is', 4)\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.16, Page number 192" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#variable declaration\n", + "a=0.429;\n", + "b=1;\n", + "c=0.379; #intercepts of an orthorhombic crystal\n", + "\n", + "#Calculation\n", + "#ratio of intercepts are 0.214:1:0.188 = (a/0.429)*0.214:1:(c/0.379)*0.188 = a/2:b:c/2\n", + "#thus the coefficients are 1/2:1:1/2. inverses are 2,1,2.\n", + "#thus miller indices for the first plane are (212)\n", + "#ratio of intercepts are 0.858:1:0.754 = (a/0.429)*0.0.858:1:(c/0.379)*0.754 = 2a:b:2c\n", + "#thus the coefficients are 2:1:2. inverses are 1/2,1,1/2. LCM is 2. multiplying with LCM we get 1,2,1\n", + "#thus miller indices for the second plane are (121)\n", + "#ratio of intercepts are 0.429:infinite:0.126 = (a/0.429)*0.429:infinite:(c/0.379)*0.126 = a:infiniteb:c/3\n", + "#thus the coefficients are 1:infinte:1/3. inverses are 1,0,3.\n", + "#thus miller indices for the third plane are (103)\n", + "\n", + "#Result\n", + "print(\"miller indices for the first plane are (212)\");\n", + "print(\"miller indices for the second plane are (121)\");\n", + "print(\"miller indices for the third plane are (103)\");\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "miller indices for the first plane are (212)\n", + "miller indices for the second plane are (121)\n", + "miller indices for the third plane are (103)\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.17, Page number 193" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "import numpy as np\n", + "\n", + "#variable declaration\n", + "h1=1;\n", + "k1=0;\n", + "l1=0; #indices of the first plane (100)\n", + "h2=1;\n", + "k2=1;\n", + "l2=0; #indices of the second plane (110)\n", + "h3=1;\n", + "k3=1;\n", + "l3=1; #indices of the third plane (111)\n", + "\n", + "#Calculation\n", + "n_1=np.reciprocal(4.);\n", + "n_2=np.reciprocal(2.);\n", + "n_3=np.reciprocal(6.);\n", + "n1=(n_1*4)+1; #number of atoms per unit cell in (100)\n", + "#number of atoms per m^2 is 2/a**2. but a=sqrt(8)*r.\n", + "#hence number of atoms per m^2 is 1/(4*r**2)\n", + "n2=(n_1*4)+(2*n_2); #number of atoms per unit cell in (110)\n", + "#number of atoms per m^2 is 1/a*sqrt(2)*a. but a=sqrt(8)*r.\n", + "#hence number of atoms per m^2 is 1/(8*sqrt(2)*r**2)\n", + "n3=(n_3*3)+(3*n_2); #number of atoms per unit cell in (111)\n", + "#number of atoms per m^2 is 2/(sqrt(3)/4)*a**2. but a=4*r.\n", + "#hence number of atoms per m^2 is 1/(2*sqrt(3)*r**2)\n", + "\n", + "#Result\n", + "print(\"number of atoms per unit cell in (100)\",n1);\n", + "print(\"number of atoms per m^2 is 1/(4*r**2)\");\n", + "print(\"number of atoms per unit cell in (110)\",n2);\n", + "print(\"number of atoms per m^2 is 1/(8*sqrt(2)*r**2)\");\n", + "print(\"number of atoms per unit cell in (111)\",n3);\n", + "print(\"number of atoms per m^2 is 1/(2*sqrt(3)*r**2)\");\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "('number of atoms per unit cell in (100)', 2.0)\n", + "number of atoms per m^2 is 1/(4*r**2)\n", + "('number of atoms per unit cell in (110)', 2.0)\n", + "number of atoms per m^2 is 1/(8*sqrt(2)*r**2)\n", + "('number of atoms per unit cell in (111)', 2.0)\n", + "number of atoms per m^2 is 1/(2*sqrt(3)*r**2)\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.18, Page number 194" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#variable declaration\n", + "r=0.97; #radius of Na+ ion in armstrong\n", + "R=1.81; #radius of Cl- ion in armstrong\n", + "\n", + "#Calculation\n", + "#atomic packing factor=packing density PD\n", + "#PD=Volume of atoms/Volume of unit cell\n", + "#volume of unit cell=a**3\n", + "#volume of atoms=number of atoms*volume of 1 atom = 4*(4/3)*math.pi*r**3\n", + "#but r=a/sqrt(8). hence PD = 4*(4/3)*math.pi*(a/(2*sqrt(2)))**3*(1/a**3) = 0.74\n", + "#atomic packing factor = 0.74\n", + "r=r*10**-10; #radius of Na+ ion in m\n", + "R=R*10**-10; #radius of Cl- ion in m\n", + "Vna = (4*4*math.pi*r**3)/3; #volume of Na atoms\n", + "Vcl = (4*4*math.pi*R**3)/3; #volume of Cl atoms \n", + "V=(2*(r+R))**3; #volume of unit cell\n", + "IPF=(Vna+Vcl)/V; #ionic packing factor\n", + "IPF=math.ceil(IPF*10**4)/10**4; #rounding off to 4 decimals\n", + "\n", + "#Result\n", + "print(\"atomic packing factor = 0.74\");\n", + "print(\"ionic packing factor of NaCl crystal is\",IPF);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "atomic packing factor = 0.74\n", + "('ionic packing factor of NaCl crystal is', 0.6671)\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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