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# MSE 440/540: Processing of Metallic Materials - PowerPoint PPT Presentation

MSE 440/540: Processing of Metallic Materials. Instructors: Yuntian Zhu Office: 308 RBII Ph: 513-0559 [email protected] Lecture 2: Solidification Theory Homework: Problem from notes,. Solidification. Nearly every metal product started as a liquid at some point in time.

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### MSE 440/540: Processing of Metallic Materials

Instructors: Yuntian Zhu

Office: 308 RBII

Ph: 513-0559

Lecture 2: Solidification Theory

Homework: Problem from notes,

1

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

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

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 = L– T(L/Tm)

= L(1-T/Tm)

4

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

Note that r* and ΔGv* decrease with increasing undercooling

Quiz: The effect of DT on solidification speed and microstructure.

6

Innoculants (seeds):

Nucleation of Melting:

Low undercooling is needed for heterogeneous nucleation

gSL + gLV < gSV

8

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

9

• Characteristics of a good inoculant

• - low interfacial energy 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

• 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.