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diff --git a/Materials_Science_and_Engineering/Chapter9.ipynb b/Materials_Science_and_Engineering/Chapter9.ipynb new file mode 100755 index 00000000..3c213c69 --- /dev/null +++ b/Materials_Science_and_Engineering/Chapter9.ipynb @@ -0,0 +1,205 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 09 : Phase Transformations"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.1, Page No 206"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "del_t1 = 0\t\t# temperature difference in degree Celsius\n",
+ "del_t2 = -5 # temperature difference in degree Celsius\n",
+ "del_t3 = -40 # temperature difference in degree Celsius\n",
+ "del_h = 6.02 # enthalpy of fusion in kJ/mol\n",
+ "T_m = 273.0 # mean temperature\n",
+ "Gamma = 0.076 # energy of ice water interface in J /m^2\n",
+ "v = 19.0 # molar volume of ice\n",
+ "\n",
+ "#Calculations\n",
+ "print(\" Part A\")\n",
+ "print(\" At del_t = %d, there is no supercooling. So there is no critical radius\" %del_t1)\n",
+ "print(\" Part B\")\n",
+ "del_f = 16.0/3*math.pi*(Gamma)**3*T_m**2/((del_h*1e3*1e6/v)**2*del_t2**2)\n",
+ "r = 2*T_m*Gamma/(-del_h*1e3*1e6/v*del_t2)\n",
+ "print(\" Critical free energy of nucleation is %.1eJ\" %del_f)\n",
+ "print(\" Critical radius is %d angstrom\" %math.ceil(r*1e10))\n",
+ "print(\" Part C\")\n",
+ "temp_r = del_t3/del_t2\n",
+ "del_f_ = del_f/temp_r**2\n",
+ "r_ = r/temp_r\n",
+ "\n",
+ "#Results\n",
+ "print(\" Critical free energy of nucleation is %.1eJ\" %del_f_)\n",
+ "print(\" Critical radius is %d angstrom.\" %math.ceil(r_*1e10))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " Part A\n",
+ " At del_t = 0, there is no supercooling. So there is no critical radius\n",
+ " Part B\n",
+ " Critical free energy of nucleation is 2.2e-16J\n",
+ " Critical radius is 262 angstrom\n",
+ " Part C\n",
+ " Critical free energy of nucleation is 3.4e-18J\n",
+ " Critical radius is 33 angstrom.\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.2, Page No 208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "T= 300.0 # temperature in kelvin\n",
+ "R = 8.314 # universal gas constant\n",
+ "k = 2.303 # conversion factor\n",
+ "a1 = 1e42\n",
+ "a2 = 1e6 \t # nucleation rate\n",
+ "a3 = 1e10 # nucleation rate\n",
+ "\n",
+ "#Calculations\n",
+ "I1 = (math.log(a1,10)-math.log(a2,10))*k*R*T #exponent factor\n",
+ "I2 = (math.log(a1)-math.log(a3))*k*R*T # exponent factor\n",
+ "del_f = I1-I2 # difference \n",
+ "a = 10**(math.log(a3,10)-math.log(a2,10))\n",
+ "\n",
+ "#Results\n",
+ "print(\"A change of %d KJ mol^-1 energy is required to increase nucleation factor from \\n %.0e m^-3 s^-1 to %.0e m^-3 s^-1 \" %(math.ceil(del_f/1e3),a,a3))\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "A change of -216 KJ mol^-1 energy is required to increase nucleation factor from \n",
+ " 1e+04 m^-3 s^-1 to 1e+10 m^-3 s^-1 \n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4, Page No 211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "Gamma_alpha_del = 0.5 # in J m^-2\n",
+ "Gamma_alpha_beta = 0.5 # in J m^-2\n",
+ "Gamma_beta_del = 0.01 # in J m^-2\n",
+ "\n",
+ "#Calculations\n",
+ "theta = math.acos((Gamma_alpha_del -Gamma_beta_del)/Gamma_alpha_beta)\n",
+ "del_f_ratio = 1.0/4*(2-3*math.cos(theta)+(math.cos(theta))**3)\n",
+ "\n",
+ "#Results\n",
+ "print(\"del_f_het is %0.4f th fraction of del_f_homo.\" %del_f_ratio)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "del_f_het is 0.0003 th fraction of del_f_homo.\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page No 229"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#initialisation of variables\n",
+ "mu = 45.5e9\n",
+ "b = 2.55e-10\n",
+ "n1 = 1e9 \t\t# initial dislocation density\n",
+ "n2 = 1e13 # final dislocation density\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "E = 1.0/2*mu*b**2*n2\n",
+ "del_g = E # as difference between initial and final dislocation energy is four order magnitude\n",
+ "\n",
+ "#Results\n",
+ "print(\"Free energy change during recrystallization is %d J m^-3\" %-del_g)\n",
+ "\n",
+ "#Numerical value of answer in book is 14800\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Free energy change during recrystallization is -14793 J m^-3\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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