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Chapter 10.2

Chapter 10.2 - Homogeneous nucleation 1 2 supercooled...

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6 MSE 2090: Introduction to Materials Science Chapter 10, Phase Transformations Homogeneous nucleation solid liquid Is the transition from undercooled liquid to a solid spherical particle in the liquid a spontaneous one? That is, is the Gibbs free energy decreases? supercooled liquid The formation of a solid nucleus leads to a Gibbs free energy change of Δ G = G 2 -G 1 = -V S (G v L –G v S ) + A SL γ SL negative below T m always positive 12 V S is the volume of the solid sphere A SL is the solid/liquid interfacial area γ SL is the solid/liquid interfacial energy Δ G v = G v L v S is the volume free energy difference at T < T m , G v S < G v L – solid is the equilibrium phase
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7 MSE 2090: Introduction to Materials Science Chapter 10, Phase Transformations Homogeneous nucleation Δ G = G 2 -G 1 = -V S Δ G v + A SL γ SL For a spherical nucleus with radius r: 3 S r π 3 4 V = SL 2 v 3 γ r 4 π Δ G r π 3 4 - Δ G + = 2 SL r 4 π A = r Δ G * Δ G * r Δ G interfacial energy ~ r 2 volume energy ~ r 3
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Chapter 10.2 - Homogeneous nucleation 1 2 supercooled...

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