Lecture15-Notes - ME 382 Lecture 15 INTRODUCTION TO...

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ME 382 Lecture 15 1 I NTRODUCTION TO K INETICS (2) Effects of phase boundaries Nucleation rate of phase changes Consider phase change α β at a temperature T 1 < T e (super-cooling) Decrease in Gibb’s free energy Δ G αβ = G α - G b J / unit volume transformed material Increase in G caused by the energy of the interface between the two phases γ αβ J / unit area of interface between the two phases Total change in G by transforming a volume V of α to β forming an interfacial area A : Δ G total = V × Δ G αβ + A γ Consider spherical particles of β of radius r forming in α V = 4 3 π r 3 A = 4 r 2 Δ G total = 4 3 r 3 Δ 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 Δ G total / d r = 0 d Δ G total dr = 4 r 2 Δ G + 8 r d Δ G total dr = 0 when r o = 2 / Δ G
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ME 382 Lecture 15 2 But Δ G αβ = Δ S T e T 1 ( ) = Δ H T e T e T 1 ( ) (see previous lecture) r o = 2 γ T e Δ 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 Fewer, but larger precipitates Examples: Small snow flakes on very cold days; large snowflakes when temperatures is near freezing Regions of castings that have slow cooling rates (thicker) have larger
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Lecture15-Notes - ME 382 Lecture 15 INTRODUCTION TO...

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