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Unformatted text preview: VK250 Lecture 08 1 Kinetics of phase transformation Nucleation rate of phase changes Consider phase change at a temperature T 1 < T e (super-cooling) Decrease in Gibbs free energy G = G - G b J / unit volume transformed material Increase in G caused by the energy of the interface between the two phases J / unit area of interface between the two phases Total change in G by transforming a volume V of to forming an interfacial area A : ! G total = " V # ! G $% + A & $% Consider spherical particles of of radius r forming in V = 4 3 ! r 3 A = 4 ! r 2 " G total = # 4 3 $ r 3 " G %& + 4 $ r 2 %& Critical nucleus size is r o If r < r o : growing nucleus increases energy If r > r o : growing nucleus decreases energy r o given by finding r where d G total / d r = 0 dG total dr = ! 4 " r 2 # G $% + 8 " r & $% dG total dr = when r o = ! "# / $ G "# VK250 Lecture 08 2 But ! G "# = ! S "# T e $ T 1 ( ) = ! H "# T e T e $ T 1 ( ) (see appendix ) r o = 2 " #$ T e % H #$ T e & T 1 ( ) Larger degrees of undercooling smaller critical radii Smaller clusters are more likely to form randomly than larger clusters More likely to find critical sized nucleii with more undercooling Number of nucleation sites increases with increased undercooling Increased undercooling results in larger numbers of small precipitates Low undercooling results in fewer nucleation sites...
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This note was uploaded on 09/15/2010 for the course MATSCIE 250 taught by Professor Yalisove during the Fall '08 term at University of Michigan.
- Fall '08