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Homework 12

# Homework 12 - HW 12 The Kinetics of Phase Transformations...

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HW 12. The Kinetics of Phase Transformations Will Note Be Collected, but please complete by December 12. 1. (a) Rewrite the expression for the total free energy change for nucleation (Equation 11.1) for the case of a cubic nucleus of edge length a (instead of a sphere of radius r). Now differentiate this expression with respect to a (per Equation 11.2) and solve for both the critical cube edge length, a*, and also ΔG*. (b) Is ΔG* greater for a cube or a sphere? Why? 2. (a) For the solidification of nickel, calculate the critical radius r* and the activation free energy ΔG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are –2.53 × 10 9 J/m 3 and 0.255 J/m 2 , respectively. Use the supercooling value found in Table 11.1. (b) Now calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.360 nm for solid nickel at its melting temperature. 3. (11.5) The kinetics of the austenite-to-pearlite transformation obey the Avrami relationship. Using the fraction

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