Midterm 1 Solutions 11

Forming a surface always raises the energy gvgv sigmaa

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Unformatted text preview: ys positive). Forming a surface always raises the energy. G=V*Gv+ sigma*A = r^3 + r^2 When r is small (r<1), free energy is positive. When r is big(r>1), free energy is negative. When the temperature difference from the transformation temperature is small, the driving force of nucleation is also small. Thus, the activation energy/barrier is bigger and the rate is nucleation limited. If the temperature difference is large, nucleation is easier due to a bigger driving force. Thus, the barrier is smaller and nucleation is easier, so the rate is growth limited (diffusivity-driven). If the upper arrow cools material, the final microstructure contains nuclei of Beta almost exclusively in the grain boundaries of alpha. It is easier to nucleate on grain boundaries. The barrier to nucleation is the formation of surface energy but at grain boundaries, it wipes out some of the interfacial energy of the already existing grains. If the system is cooled slowly from the alpha phase, it allows enough time for the diffusion of beta particles. Thus, the beta diffuses to the boundaries...
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