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{
"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": {}
}
]
}
|
