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Solidification Theory: Understanding the Process of Metal Solidification

Learn about solidification theory in metal processing, including the concepts of nucleation and growth, homogeneous and heterogeneous nucleation, and the practical implications of solidification. Homework problem and reading assignment included.

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Solidification Theory: Understanding the Process of Metal Solidification

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  1. MSE 440/540: Processing of Metallic Materials Instructors: Yuntian Zhu Office: 308 RBII Ph: 513-0559 ytzhu@ncsu.edu Lecture 2: Solidification Theory Homework: Problem from notes, 1

  2. Solidification Nearly every metal product started as a liquid at some point in time. • What is Solidification • What is the Melting Point? • What’s composition? 2

  3. Nucleation and Growth During solidification, solid nuclei form in the liquid and subsequently grow until the entire volume is a solid. • What is the driving force for nucleation and growth? 3

  4. Homogeneous Nucleation Consider free energy change when small spherical nuclei of solid is formed in a liquid G = H – TS L S ΔG = ΔH – TΔS At Tm, ΔG = 0, ΔH = L ΔS = L/Tm ΔGv(T) = L– T(L/Tm) = L(1-T/Tm) 4

  5. Homogeneous Nucleation There is a critical radius r*, at a given undercooling ΔT where embryos can grow and reduce the free energy. • r* occurs at • HOMEWORK: Show that: • r* =-2g/ΔGv • ΔG at r* , • If ΔGv = LΔT/Tm, then • = thermodynamic barrier to nucleation or work of nucleation Quiz: What is the physical origin of energy barrier for nucleation? 5

  6. Homogeneous Nucleation Note that r* and ΔGv* decrease with increasing undercooling Quiz: The effect of ΔT on solidification speed and microstructure. https://www.youtube.com/watch?v=-kIOXusTgoU Freeze beer/2:22 6

  7. Heterogeneous Nucleation 7

  8. Heterogeneous Nucleation Rate Innoculants (seeds): Nucleation of Melting: Low undercooling is needed for heterogeneous nucleation gSL + gLV < gSV 8

  9. Commercial Practice Dynamic Nucleation - Vibrate melt to collapse internal cavities - Fragmentation of existing solids; breaking of dendrite arms (crystal multiplication) - Electromagnetic mixing and stirring Nucleation during Melting - Why does melting usually occur at Tm, even at high heating rates? Most liquid metals wet their own solid, so the wetting angle Θ = 0  no energy barrier for nucleation 9

  10. Commercial Practice • Characteristics of a good inoculant • - low interfacial energy, γSP, between nucleant and growing solid • - γSP decreases with decreasing lattice mismatch between solids and nucleant with increasing chemical affinity (coherent interface) • Should be as stable as possible in the liquid melt Tminoc > Tmmelt • possess a high surface area (rough or pitted) • Smaller particles 10

  11. Growth: Practical Results • Crystals grow in two ways after nucleating • Planar growth – heat extraction through the solid phase and a smooth solid/liquid interface • Dendritic growth – formation of branched skeleton structures. http://www.youtube.com/watch?v=S07fPo45BvM 11

  12. Reading Assignment • Read Chapter 5 • HW: 1. Calculate the volume change from fcc γ-iron to bcc α-iron. Hint: the atom radius is R, which does not change during phase transformation. 12

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