# 10.14 - E45 Lecture Chapter 11 Homogeneous Nucleation...

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Chapter 11 - E45 Lecture 10/14/09

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Chapter 11 - 2 r * = critical nucleus : for r < r * nuclei shrink; for r > r * nuclei grow (to reduce energy) Adapted from Fig.11.2(b), Callister & Rethwisch 3e. Homogeneous Nucleation & Energy Effects GT = Total Free Energy = GS + GV Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) γ π = 2 4 r G S γ = surface tension Volume (Bulk) Free Energy stabilizes the nuclei (releases energy) υ π = G r G V 3 3 4 volume unit energy free volume = υ G
Chapter 11 - 3 Rate of Phase Transformations Kinetics - study of reaction rates of phase transformations To determine reaction rate – measure degree of transformation as function of time (while holding temp constant)

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Chapter 11 - Reaction rate , R, is a combination of nucleation rate, N, and growth Rate, G: R = NG TO N, G G ~ D N ~ (TO -T)
Chapter 11 - Reaction rate, R, is a combination of nucleation rate, N, and growth Rate, G: R = NG N, G TO G ~ D N ~ (TO -T) TO R = NG

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Chapter 11 - 6 Rate of Phase Transformation Avrami equation => y = 1- exp (- k t n ) k & n are transformation specific parameters transformation complete log t Fraction transformed, y Fixed T fraction transformed time 0.5 By convention rate = 1 / t 0.5 Adapted from Fig. 11.10, Callister & Rethwisch 3e. maximum rate reached – now amount unconverted decreases so rate slows t 0.5 rate increases as surface area increases & nuclei grow
Chapter 11 - % Transformation as f(time) %Transf Log time Fast nucleation At low T Fast growth at high T Slow growth at low T Slow nucleation at high T Time to grow at T %Transf = 1% TO Time to nucleate at Temp T time %Transf = 99%

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10.14 - E45 Lecture Chapter 11 Homogeneous Nucleation...

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