1

1

2

2

3

v ∝ r -1(1-r*/r)thermal

transportkinetics

thermodynamics

4

Simulation of a dendrite growing from

a small seed crystal

http://www.mathematik.uni-freiburg.de/IAM/homepages/alfred/DS_DFG.html

3

5http://www.its.caltech.edu/~atomic/snowcrystals/

Snowflake growth is vapor→solid deposition, but similar to solidification

6

Xsolute

liquidussolidus

Tmelt

TE

Xmax XE

β

α

X0

XαeXβ

e=kXα

e

X0

4

7

Last Batch of Liquid Forms Eutectic Solid (γ+β)

Comparable volume fraction of γ, β:Lamellar microstructure

Low volume fraction of β or γ:Rod-like microstructure

8

5

9

10

XE

X0

Scheil-Gulliver equation

Xα

Xβ = kXα

6

11

Recipe for Purification – Zone Refinement

12

7

13

14

8

15

16

α/β Ti-Alloy:

Formation of Sideplates

Basketweave / Widmanstättenmicrostructure

CAMM from Yunzhi Wang, Hamish Fraser, Mike Mills, OSU

Mullins-Sekerka Instability

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