3. Transformations & TTT [30 points]: This question makes use of the following properties Entropy of fusion (J/mole. K) AS = 2R and free energy of fusion (J/mole) AG = AS (Tm - T) Ideal gas constant (J/mole. K)= R = 8.3 Avogadro's number Navg = 6 1023 and Boltzmann's constant k = 1.381 10-23J/K Melting point Tm = 1000K Molar Volume Vm = 100 cm/mole and let a Solid-liquid interfacial energy = YSL = 0.02 J/m = Viscosity (Pas) Let AGnom (r*) = 10-4 exp 16 (AGf/Vm) 5000 T(K)-650 = 5.5 and f = 1 a) Plot the growth rate u (cm/s) for a crystal with the properties given above over the temperature range from 850 to 1000 K b) Plot the homogeneous nucleation rate ly (cms-1) for a crystal with the properties given above over the temperature range from 700 to 900 K c) Suppose that you can observe any nucleation rate within the range from 0.1 to 10 events per cm per second. Over what range of temperature would this range be observed for the material considered in part (a)? d) Plot the TTT diagram for this system, assuming that the crystals are spherical, and the nucleation and growth rates are given by parts (a) and (b). Show curves for volume fractions transformed of 10-6, 10-3, and 0.999 over the temperature range around 780-880K. [Hint: Using the Avrami equation, solve for the time and plot it on the vertical axis and temperature on the abscissa).