1. NC State University Department of Materials Science and Engineering1 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,

2. NC State University Department of Materials Science and Engineering2 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?

3. NC State University Department of Materials Science and Engineering3 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?

4. NC State University Department of Materials Science and Engineering4 Homogeneous Nucleation Consider free energy change when small spherical nuclei of solid is formed in a liquid L S G = H – TS ΔG = ΔH – TΔS At T m, ΔG = 0, ΔH = L ΔS = L/T m ΔG v = L – T(L/T m ) = L(1-T/T m )

5. NC State University Department of Materials Science and Engineering5 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* =2  /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?

6. NC State University Department of Materials Science and Engineering6 Homogeneous Nucleation Note that r* and ΔGv* decrease with increasing undercooling Quiz : The effect of  T on solidification speed and microstructure.

7. NC State University Heterogeneous Nucleation Department of Materials Science and Engineering7

8. NC State University Heterogeneous Nucleation Rate Department of Materials Science and Engineering8 Innoculants (seeds): Nucleation of Melting:  SL +  LV <  SV Low undercooling is needed for heterogeneous nucleation

9. NC State University Department of Materials Science and Engineering9 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 of 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

10. NC State University Department of Materials Science and Engineering10 Commercial Practice Characteristics of a good inoculant - low interfacial energy between nucleant and growing solid - γ SP 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 Tm inoc > Tm melt - possess a high surface area (rough or pitted) -Smaller particles

11. NC State University Department of Materials Science and Engineering11 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

12. NC State University Reading Assignment Read Chapter 5 HW: Department of Materials Science and Engineering12