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diff --git a/Material_Science_In_Engineering/ch5.ipynb b/Material_Science_In_Engineering/ch5.ipynb new file mode 100755 index 00000000..701408be --- /dev/null +++ b/Material_Science_In_Engineering/ch5.ipynb @@ -0,0 +1,384 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 5 : Miller Indices and X-Ray Crystallograph Techniques" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.1 pageno : 96" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "p = 1.;\n", + "q = 1./2;\n", + "r = 3.;\n", + "\n", + "# Calculations\n", + "h = 1./p;\n", + "k = 1./q;\n", + "l = 1./r;\n", + "h1 = 3.*h;\n", + "k1 = 3.*k;\n", + "l1 = 3.*l;\n", + "\n", + "# Results\n", + "print \"MILLER INDICES OF THE PLANE are h = \",h1\n", + "print \"k = \",k1\n", + "print \"l = \",l1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "MILLER INDICES OF THE PLANE are h = 3.0\n", + "k = 6.0\n", + "l = 1.0\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.3 pageno : 97" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "# Variables\n", + "p = 2./4;\t\t\t#intercepts\n", + "q = 3./3;\n", + "r = 4./2;\n", + "\n", + "# Calculations\n", + "h = 1./p;\n", + "k = 1./q;\n", + "l = 1./r;\n", + "h1 = 2.*h;\n", + "k1 = 2.*k;\n", + "l1 = 2.*l;\n", + "\n", + "# Results\n", + "print \"MILLER INDICES ARE \",l1,k1,h1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "MILLER INDICES ARE 1.0 2.0 4.0\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.5 pageno : 105" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "# Variables\n", + "r = 1.246;\t\t\t#radius in angstorm\n", + "h = 2.;\n", + "k = 0.;\n", + "l = 0.;\n", + "h1 = 2.;\n", + "k1 = 2.;\n", + "l1 = 0.;\n", + "h2 = 1.;\n", + "k2 = 1.;\n", + "l2 = 1.;\n", + "\n", + "# Calculations\n", + "x = math.sqrt(h**2+k**2+l**2);\n", + "a = 2*math.sqrt(2)*r;\t\t\t#in angstorm\n", + "d_200 = a/x;\t\t\t #interplanar spacing in angstorm\n", + "x1 = math.sqrt(h1**2+k1**2+l1**2);\n", + "d_220 = a/x1; \t\t\t#interplanar spacing in angstorm\n", + "x2 = math.sqrt(h2**2+k2**2+l2**2);\n", + "d_111 = a/x2;\t\t \t#interplanar spacing in angstorm\n", + "\n", + "\n", + "print \"Interplanar Spacing (200) (in Angstorm) = %.3f A\"%d_200\n", + "print \"Interplanar Spacing (220) (in Angstorm) = %.3f A\"%d_220\n", + "print \"Interplanar Spacing (111) (in Angstorm) = %.3f A\"%d_111\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Interplanar Spacing (200) (in Angstorm) = 1.762 A\n", + "Interplanar Spacing (220) (in Angstorm) = 1.246 A\n", + "Interplanar Spacing (111) (in Angstorm) = 2.035 A\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.6 pageno : 106" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "# Variables\n", + "a = 3.61*10**-10;\t\t\t#unit cell in m\n", + "\n", + "# Calculations\n", + "r_110 = 2/(math.sqrt(2)*a);\t\t\t#in atoms/m\n", + "r_a = r_110/10**3;\t \t\t#in atoms/mm\n", + "r_111 = 1/(math.sqrt(3)*a);\t\t\t#in atoms/m\n", + "r_b = r_111/10**3;\t\t\t #in atoms/mm\n", + "\n", + "# Results\n", + "print \"Linear Density per unit length along direction [110] (in atoms/mm) = %.2e atoms/mm\"%r_a\n", + "print \"Linear Density per unit length along direction [111] (in atoms/mm) = %.2e atoms/mm\"%r_b\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Linear Density per unit length along direction [110] (in atoms/mm) = 3.92e+06 atoms/mm\n", + "Linear Density per unit length along direction [111] (in atoms/mm) = 1.60e+06 atoms/mm\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.7 pageno : 110" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "# Variables\n", + "r_po = 1.7*10**-10;\t\t\t #radius of polonium in m\n", + "r_rh = 1.34*10**-10;\t\t\t#radius of rhodium in m\n", + "r_cr = 1.25*10**-10;\t\t\t#radius of chromium in m\n", + "\n", + "# Calculations\n", + "a_po = 2*r_po;\t\t \t#in m\n", + "a_rh = 2*math.sqrt(2)*r_rh;\t\t#in m\n", + "a_cr = 4*r_cr/math.sqrt(3);\n", + "p_po = 1/a_po**2;\t\t\t # /sqm\n", + "p_rh = 1.414/a_rh**2;\t\t\t# /sqm\n", + "p_cr = 1.732/a_cr**2;\t\t\t# /sqm\n", + "\n", + "# Results\n", + "print \"Planar Density on [100] in Polonium (per sqm) = %.2e /m**2\"%p_po\n", + "print \"Planar Density on [110] in Rhodium (per sqm) = %.2e /m**2\"%p_rh\n", + "print \"Planar Density on [111] in Chromium (per sqm) = %.2e /m**2\"%p_cr\n", + "\n", + "# Note : To check answer , please calculate manually for p_rh" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Planar Density on [100] in Polonium (per sqm) = 8.65e+18 /m**2\n", + "Planar Density on [110] in Rhodium (per sqm) = 9.84e+18 /m**2\n", + "Planar Density on [111] in Chromium (per sqm) = 2.08e+19 /m**2\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.8 pageno : 113" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math \n", + "\n", + "# Variables\n", + "w = 0.824;\t\t\t#wavelength in angstorm\n", + "theta1 = 8.35;\t\t\t#angle at n = 1 in degrees\n", + "n1 = 1.;\n", + "n3 = 3.;\n", + "\n", + "# Calculations\n", + "d = w/(2*math.sin(math.radians(theta1)));\t\t\t#in angstorm\n", + "theta3 = math.degrees(math.asin(3*math.sin(math.radians(theta1))))\n", + "\n", + "# Results\n", + "print \"Glancing angle for third order diffraction = %f degrees\"%theta3\n", + "print \"Interplanar spacing of the crystal (in Angstorm) = %.3f A\"%d\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Glancing angle for third order diffraction = 25.827235 degrees\n", + "Interplanar spacing of the crystal (in Angstorm) = 2.837 A\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.9 pageno : 115" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "import math \n", + "\n", + "# Variables\n", + "a = 17.03;\t\t\t#in degrees\n", + "w = 0.71;\t\t\t#in angstorm\n", + "n = 1.;\n", + "\n", + "# Calculations\n", + "d = n*w/(2*math.sin(math.radians(a)));\t\t\t#interplanar spacing in angstorm\n", + "# given that h**2+k**2+l**2 = 8\n", + "a = math.sqrt(8)*d; \t\t\t#in angstorm\n", + "\n", + "# Results\n", + "print \"Interplanar Spacing (in angstorm) = %.3f A\"%d\n", + "print \"Lattice parameter of the crystal (in Angstorm) = %.2f A\"%a\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Interplanar Spacing (in angstorm) = 1.212 A\n", + "Lattice parameter of the crystal (in Angstorm) = 3.43 A\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 5.10 pageno : 117" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "# Variables\n", + "w = 0.0708;\t\t\t #wavelength in nm\n", + "h = 1.;\n", + "k = 0.;\n", + "l = 0.;\n", + "s = 0.0132; \t\t\t#a common divisor i.e.math.sin**2(theta) = 0.0132\n", + "\n", + "# Calculations\n", + "a = math.sqrt((w**2*(h**2+k**2+l**2))/(4*s));\t\t\t#in nm\n", + "a1 = 10.**3*a;\t\t\t #in pm\n", + "\n", + "# Results\n", + "print \"Dimension of unit cell (in Picometer) = %.1f pm\"%a1\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Dimension of unit cell (in Picometer) = 308.1 pm\n" + ] + } + ], + "prompt_number": 16 + } + ], + "metadata": {} + } + ] +}
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