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v ∝ r -1(1-r*/r)thermal
transportkinetics
thermodynamics
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Simulation of a dendrite growing from
a small seed crystal
http://www.mathematik.uni-freiburg.de/IAM/homepages/alfred/DS_DFG.html
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Snowflake growth is vapor→solid deposition, but similar to solidification
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Xsolute
liquidussolidus
Tmelt
TE
Xmax XE
β
α
X0
XαeXβ
e=kXα
e
X0
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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
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XE
X0
Scheil-Gulliver equation
Xα
Xβ = kXα
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Recipe for Purification – Zone Refinement
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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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