91Ó°ÊÓ

Name the two stages involved in the formation of particles of a new phase. Briefly describe each.

(a) Rewrite the expression for the total free energy change for nucleation (Equation 10.1) 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 10.2 ) and solve for both the critical cube edge length, \(a^{*},\) and also \(\Delta G^{*}\) (b) Is \(\Delta G^{*}\) greater for a cube or a sphere? Why?

If ice homogeneously nucleates at \(-40^{\circ} \mathrm{C}\) calculate the critical radius given values of \(-3.1 \times 10^{8} \mathrm{J} / \mathrm{m}^{3}\) and \(25 \times 10^{-3} \mathrm{J} / \mathrm{m}^{2},\) respec tively, for the latent heat of fusion and the surface free energy.

Compute the rate of some reaction that obeys Avrami kinetics, assuming that the constants \(n\) and \(k\) have values of 2.0 and \(5 \times 10^{-4}\), respectively, for time expressed in seconds

The kinetics of the austenite-to-pearlite transformation obey the Avrami relationship. Using the fraction transformed-time data given here, determine the total time required for \(95 \%\) of the austenite to transform to pearlite: $$\begin{array}{cc} \hline \text {Fraction Transformed} & \text {Time (s)} \\ \hline 0.2 & 280 \\ 0.6 & 425 \\ \hline \end{array}$$

The fraction recrystallized-time data for the recrystallization at \(350^{\circ} \mathrm{C}\) of a previously deformed aluminum are tabulated here. Assuming that the kinetics of this process obey the Avrami relationship, determine the fraction recrystallized after a total time of \(116.8 \mathrm{min}\) $$\begin{array}{cc} \hline \text { Fraction Recrystallized } & \text { Time (min) } \\ \hline 0.30 & 95.2 \\ 0.80 & 126.6 \\ \hline \end{array}$$

In terms of heat treatment and the development of microstructure, what are two major limitations of the iron-iron carbide phase diagram?

(a) Briefly describe the phenomena of superheating and supercooling. (b) Why do these phenomena occur?

Briefly cite the differences between pearlite, bainite, and spheroidite relative to microstructure and mechanical properties

What is the driving force for the formation of spheroidite?