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Diffstat (limited to 'Materials_Science_and_Engineering/Chapter8.ipynb')
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diff --git a/Materials_Science_and_Engineering/Chapter8.ipynb b/Materials_Science_and_Engineering/Chapter8.ipynb new file mode 100755 index 00000000..3048ed1f --- /dev/null +++ b/Materials_Science_and_Engineering/Chapter8.ipynb @@ -0,0 +1,245 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 08 : Diffusion in Solids"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.1, Page No 180"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "t = 5.0 # thickness in mm\n",
+ "c = 10.0 # concentration\n",
+ "D = 1e-9 # diffusion coefficient\n",
+ "\n",
+ "#Calculations\n",
+ "j = D*c/(t*1e-3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Outward flux is %.0e kg m^-2 s^-1\" %j)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Outward flux is 2e-06 kg m^-2 s^-1\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.2, Page No 186"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "D_0 = 0.24e-4 \t# diffusion coefficient\n",
+ "Q = 121e3\n",
+ "R = 8.314\t# Universal gas constant\n",
+ "T = 550 \t# temperature in Celsius\n",
+ "k = 0.2 \t# thickness of pure Al sheet in mm\n",
+ "d = 0.1 \t# penetration depth in mm\n",
+ "c_x = 0.4 \t# concentration in percentage\n",
+ "A = 2.0 \t# Constant in percentage\n",
+ "B = 2.0\t\t# Constant in percentage\n",
+ "\n",
+ "#Calculations\n",
+ "x = d-k\n",
+ "D_cu_al = D_0*math.exp(-Q/(R*(T+273))) \n",
+ "k = (A-c_x)/B\n",
+ "if k ==0.8 :\n",
+ " z = 0.9 # from table\n",
+ "\n",
+ "t = (x*1e-3)**2/(z**2*4*D_cu_al)\t# time in sec\n",
+ "\n",
+ "#Results\n",
+ "print(\"Material can be kept at %d degree Celsius for nearly %d minute\" %(T,(t/60)))\t# answer in book is 100 min\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Material can be kept at 550 degree Celsius for nearly 102 minute\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3, Page No 188"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "D_0 = 0.7e-4 \t # diffusion coefficient\n",
+ "Q = 157.0\t\t # Energy in kJ mol^-1, considered from table 8.2\n",
+ "R = 8.314\t\t # Universal gas constant\n",
+ "T = 950.0\t\t # temperature in Celsius\n",
+ "c2 = 0.8 \t\t # concentration in percentage\n",
+ "cs = 0 \t\t\t # concentration in percentage\n",
+ "c_x = 0.6 # concentration in percentage\n",
+ "t = 4.0 # time in hours\n",
+ "a = 1.0 #let\n",
+ "\n",
+ "#Calculations\n",
+ "A = cs\n",
+ "B = c2-cs \n",
+ "D = D_0*math.exp(-Q*1e3/(R*(T+273)))\n",
+ "k = math.erf(((A-c_x)/B))*-1\n",
+ "if k >0.7 :\n",
+ " if k<0.712 :\n",
+ " z = 0.81 # from table\n",
+ "\n",
+ "x = z*2*math.sqrt(D*t*3600.0)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Depth up to which machining is required is nearly %.2f mm\" %(x*1e3))\n",
+ "\n",
+ "# numerical value of answer in book is 0.75\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Depth up to which machining is required is nearly 0.72 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Page No 189"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "D = 4e-17 \t\t# diffusion coefficient\n",
+ "c1 = 0\n",
+ "cs = 3e26\n",
+ "c_x = 1e23 \t\t# number of atoms\n",
+ "x = 2e-6 \t\t# depth in m\n",
+ "\n",
+ "#Calculations\n",
+ "A = cs\n",
+ "B = cs - c1\n",
+ "k = (A-c_x)/B\n",
+ "if k >0.99966 :\n",
+ " if k< 0.9997 :\n",
+ " z = 2.55 # from table\n",
+ "\n",
+ "t = x**2/(z**2*4*D) # time in sec\n",
+ "\n",
+ "#Results\n",
+ "print(\"Time required to get required boron concentration is %d sec\" %t) # answer in book is 3845 sec\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time required to get required boron concentration is 3844 sec\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.5, Page No 194"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "r = 10.0 # radius in mm\n",
+ "t = 4.0 # thickness in angstrom\n",
+ "\n",
+ "#Calculations\n",
+ "r = 2*math.pi*r*1e-3*t*1e-10/(math.pi*(r*1e-3)**2)\n",
+ "\n",
+ "#Results\n",
+ "print(\"Ratio of cross sectional areas is %.0e \" %r)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Ratio of cross sectional areas is 8e-08 \n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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