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Unformatted text preview: Solution to Problem Set #9 Problem 1. (a) Metal, M, undergoes an allotropic phase transformation between α and β at 1100 K. The low temperature phase is α . A sample of M containing 10 8 cm-3 small oxide inclusions which act as effective nucleation sites even for small supercooling is rapidly quenched from 1200 K to 900 K. Estimate the grain size at the end of the transformation from β to α . Assume growth to be normal. (b) Alternatively, suppose that the sample containing the same number of oxide inclusions had been very slowly cooled from 1200 K to 900 K. What would be the grain size at the end of the transformation? DATA: enthalpy of transformation, ∆ H = 0.6 RT e molar volume of α , V α = 15 cm 3 mol-1 lattice parameter in α , a o = 3.2 x 10-8 cm surface energy along α- β , γ αβ = 40 erg cm-2 lattice diffusivities at 900 K, D L = 10-10 cm 2 s-1 diffusivity across α- β interface at 900 K, D I = 10-9 cm 2 s-1 Solution: (a) First calculate the homogeneous nucleation rate at 900 K The free energy change for transformation is: α α V T R V T T H G e v ∆ = ∆ ∆ = ∆ 6 ....
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- Spring '02
- DI, α, nucleation rate, Vβ