{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 03 : Crystalgeometry and Structure Determination" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.2, Page No 25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "sc_n = 1.0/8 \t\t# sharing of one lattice point in a unit cell\n", "sc_N = 8.0\t\t \t# Number of lattice points in Simple cubic \n", "bcc_n_e = 1.0/4\t\t# sharing of one edge lattice point in a BCC \n", "bcc_N_e = 4.0\t\t# Number of edge lattice point in a BCC \n", "bcc_n_c = 1.0\t\t# sharing of one body center lattice point in a BCC \n", "bcc_N_c = 1.0\t\t# Number of body center lattice point in a BCC \n", "fcc_n_e = 1.0/8 \t# sharing of one corner lattice point in a FCC \n", "fcc_N_e = 8.0\t\t# Number of corner lattice point in a FCC \n", "fcc_n_f = 1.0/2 \t# sharing of one face center lattice point in a FCC \n", "fcc_N_f = 6.0\t\t# Number of face center lattice point in a FCC \n", "\n", "#Calculations\n", "sc_net = sc_n*sc_N\n", "bcc_net = bcc_n_e*bcc_N_e+bcc_n_c*bcc_N_c\n", "fcc_net = fcc_n_e*fcc_N_e+fcc_n_f*fcc_N_f\n", "\n", "#Results\n", "\n", "print(\"Effective number of lattice points are as:\")\n", "print(\"Space lattice \\t Abbreviation \\t Effective number of lattice point in unit cell \\n\")\n", "print(\"Simple cubic \\t\\tSC \\t\\t %.2f \" %sc_net)\n", "print(\"Body center cubic\\tBCC \\t\\t %.2f \" %bcc_net)\n", "print(\"Face centered cubic\\tFCC \\t\\t %.2f \" %fcc_net)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Effective number of lattice points are as:\n", "Space lattice \t Abbreviation \t Effective number of lattice point in unit cell \n", "\n", "Simple cubic \t\tSC \t\t 1.00 \n", "Body center cubic\tBCC \t\t 2.00 \n", "Face centered cubic\tFCC \t\t 4.00 \n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.7, Page No 40" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "a = 3.16 #lattice parameter in angstrom\n", "l1 = 1.0 # line number\n", "l2 = 2.0 # line number\n", "l3 = 3.0 # line number\n", "l4 = 4.0 # line number\n", "theta1 = 20.3 # angle for line 1\n", "theta2 = 29.2 # angle for line 2\n", "theta3 = 36.7 # angle for line 3\n", "theta4 = 43.6 # angle for line 4\n", "n = 1 # order \n", "lambda1 = 1.54 # wavelength in angstrom\n", "\n", "#Calculations\n", "d1 = lambda1/(2*math.sin(theta1*math.pi/180))\n", "d2 = lambda1/(2*math.sin(theta2*math.pi/180))\n", "d3 = lambda1/(2*math.sin(theta3*math.pi/180))\n", "d4 = lambda1/(2*math.sin(theta4*math.pi/180))\n", "x1 = a**2/d1**2 \n", "x2 = a**2/d2**2 \n", "x3 = a**2/d3**2 \n", "x4 = a**2/d4**2 \t\t# where x is function of h,k and l\n", "\n", "#Results\n", "print(\"Interplanar spacing is %.3f angstrom \" %x1) # answer in book is 2.220 angstrom\n", "if math.floor(x1) == 2 :\n", " print(\"For a^2/d^2 = %.2f \\t Reflection plane is 110\" %math.floor(x1))\n", "\n", "if math.floor(x2) == 4 :\n", "\tprint(\"For a^2/d^2 = %.2f \\t Reflection plane is 200\" %math.floor(x2))\n", "\n", "if math.floor(x3) == 6 :\n", " print(\"For a^2/d^2 = %.2f \\t Reflection plane is 211\" %math.floor(x3))\n", "\n", "if math.floor(x4) == 8 :\n", "\tprint(\"For a^2/d^2 = %.2f \\t Reflection plane is 220\" %math.floor(x4))\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Interplanar spacing is 2.027 angstrom \n", "For a^2/d^2 = 2.00 \t Reflection plane is 110\n", "For a^2/d^2 = 4.00 \t Reflection plane is 200\n", "For a^2/d^2 = 6.00 \t Reflection plane is 211\n", "For a^2/d^2 = 8.00 \t Reflection plane is 220\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.8, Page No 45" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#initialisation of variables\n", "d = 114.6 # diameter of power camera in angstrom\n", "lambda1 = 1.54 # wavelength in angstrom\n", "s1 = 86.0\n", "s2 = 100.0\n", "s3 = 148.0\n", "s4 = 180.0\n", "s5 = 188.0\n", "s6 = 232.0 \n", "s7 = 272.0\n", "\n", "#Calculations\n", "R = d/2 # Radius \n", "if R==57.3 :\n", " k = 1.0/4 \t\t\t# Bragg angle factor\n", "a1 = (math.sin(s1*k*math.pi/180))**2\n", "a2 = (math.sin(s2*k*math.pi/180))**2\n", "a3 = (math.sin(s3*k*math.pi/180))**2\n", "a4 = (math.sin(s4*k*math.pi/180))**2\n", "a5 = (math.sin(s5*k*math.pi/180))**2\n", "a6 = (math.sin(s6*k*math.pi/180))**2\n", "a7 = (math.sin(s7*k*math.pi/180))**2\n", "\n", "c = 22 # constant to convert into integral number\n", "\n", "#Results\n", "print(\"Within experimental error, values are as in integral ratio are as:\")\n", "print(\"%.2f \" %math.ceil(c*a1))\n", "print(\"%.2f \" %math.ceil(c*a2))\n", "print(\"%.2f \" %math.ceil(c*a3))\n", "print(\"%.2f \" %math.ceil(c*a4))\n", "print(\"%.2f \" %math.ceil(c*a5))\n", "print(\"%.2f \" %math.ceil(c*a6))\n", "print(\"%.2f \" %math.ceil(c*a7))\n", "\n", "print(\"\\n So, this structure is FCC and material is copper with 3.62 angstrom lattice parameter\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Within experimental error, values are as in integral ratio are as:\n", "3.00 \n", "4.00 \n", "8.00 \n", "11.00 \n", "12.00 \n", "16.00 \n", "19.00 \n", "\n", " So, this structure is FCC and material is copper with 3.62 angstrom lattice parameter\n" ] } ], "prompt_number": 3 } ], "metadata": {} } ] }