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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

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,

1

solidification
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

nucleation and growth
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

homogeneous nucleation
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 = L– T(L/Tm)

= L(1-T/Tm)

4

homogeneous nucleation1
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

homogeneous nucleation2
Homogeneous Nucleation

Note that r* and ΔGv* decrease with increasing undercooling

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

6

heterogeneous nucleation rate
Heterogeneous Nucleation Rate

Innoculants (seeds):

Nucleation of Melting:

Low undercooling is needed for heterogeneous nucleation

gSL + gLV < gSV

8

commercial practice
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

9

commercial practice1
Commercial Practice
  • 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

growth practical results
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

reading assignment
Reading Assignment
  • Read Chapter 5
  • HW:

12

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