Transcript The lecture`s title goes here

Solidification, Lecture 3
NTNU
Interface stability
Constitutional undercooling
Planar / cellular / dendritic growth front
Cells and dendrites
Growth of dendrites
Primary & secondary arm spacing
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Growth
NTNU
Controlling phenomenon
Importance
Driving force
Diffusion of heat
Pure metals
ΔTt
Diffusion of solute
Alloys
ΔTc
Curvature
Nucleation
Dendrites
Eutectics
ΔTr
Interface kinteics
Facetted
crystals
ΔTk
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Morphologies of the s/l front
planar
cellular
NTNU
dendritic
Increasing growth rate
Causes instability of s/l front - more branching
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Solute redistribution
NTNU
• Lower solubility
of alloying elements
in s than in l
T
l
C0
C0k
T0
• k=Cs/Cl<1
C0/k
• m= dTl/dC<0
C0
s
• Enrichment of solute in
liquid during solidification
C
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Solute boundary layer
NTNU
Thickness,  depends
on diffusion, Dl and
growth velocity, V
  2Dl /V
V2>V1

Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
Vz
Cl  C0  C0 exp(  )
Dl
Ref. 1
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Steady state growth
NTNU
• Fully developed solute bondary
layer
• Rejected solute from solid
balanced by diffusion in liquid
Cl
Concentration gradient in liquid
at interface, Gc
dC l
V
Gc  (
) z 0   C0
dz
Dl
Gc

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Constitutional undercooling
NTNU
Local variations in
liquid concentration, Cl
causes local variations
in liquidus temperature, Tl
mGc
G
Temperature gradient: G
Liquidus temperature
gradient: mGc
Undercooling: φ=mGc-G
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
Ref. 1
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Constitutional undercooling
•
Undercooling if G<mGc
G T0

V
Dl
NTNU
Constitutional undercooling in all ”normal” casting
operations
•
Example:

Al-0.1%Si
ΔT0=4 K
D=3x10-9 m2/s
G=2x104 K/m
V>1.5x10-5 m/s
V needs to be less than 15 μm/s or G needs to
increase to avoid constitutional undercooling
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Stability of planar front
NTNU
Breakdown of planar front
with constitutional
undercooling
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Morphological development of the s/l front
NTNU
planar
cellular
dendritic
Increasing const. undercooling
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Cellular growth
NTNU
• Cells grow at low constitutional
undercooling
• No side branching
• Direction antiparallell to heat flow
• Accumulation of solute between cells
• Adjustment of cell spacing by
stopping or division of cells
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Transformation from cells to
dendrites
NTNU
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
form at higher const. undercooling
•Dendrites
•Side branches
•Growth in preferred crystallographic directions
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Growth temperatures of cells and
dendrites
NTNU
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Dendrites
NTNU
arms, λ
•Primary
1
•Secondary arms, λ2
angles
•Distinct
between arms
(90o for cubic)
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Columnar dendrite growth
NTNU
Al-30%Cu
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Equiaxed dendritic growth
NTNU
Al-30%Cu
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Solute boundary layer in dendritic
growth
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Al-30%Cu
Yellow-red: low C
Green-blue: high C
Faster growth and sharper
dendrite tips when thin
boundary layer
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Solute rejection from dendrite
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•Growth at low undercooling
•Radial solute diffusion
Growth determined by
•diffusion
and curvature
Supersaturation, , (undercooling)
•determines
growth rate & tip radius
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Secondary dendrite arm
coarsening
NTNU
Al-20%Cu
Secondary arm
spacing, λ ,increases during growth
2
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Secondary dendrite arm spacing
NTNU
2  At f
1
3
tf 
K
dT
dt
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Dendrite growth, summary
NTNU
Reproduced from:W. Kurz & D. J. Fisher:
Fundamentals of Solidification
Trans Tech Publications, 1998
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Summary/ Conclusions
NTNU
• Solute in an alloy will redistribute during solidification. In eutectic
systems (k<1), alloying elements will enrich in the liquid.
• With limited diffusion, solute will pile up at the s/l interface and form a
boundary layer. Width of the boundary layer is inversely proportional to
growth rate
• At steady state the boundary layer is fully developed. Growth of a solid
with constant composition = C0
• The liquid boundary layer causes local variations of liquidus
temperature ahead of the s/l interface. If the liquidus temperature
gradient, mGc is larger than the actual temperature gradient, G, the
liquid will be constitutionally undercooled.
• Constitutional undercooling occurs in most casting operations of alloys
• Constitutional undercooling leads to breakdown of a planar growth
front
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Summary/ Conclusions
NTNU
• Cells form at low constitutional undercooling, just after breakdown of
planar front. Cells have no side branches and grow independent of
crystallographic orientation, antiparallell to heat flow. Cells grow at
temperatures far below liquidus.
• Dendrites grow at high constitutional undercooling. They grow just
below liquidus in preferred crystallographic directions.
• Solute diffuses radially at the dendrite tip. Growth undercooling and
growth morphology is determined by curvature and diffusion.
• Dendrites are characterized by a primary arms (trunk) with a spacing,
λ1, and secondary arms (branches) with spacing λ2.
• Dendrites coarsen as they grow increasing λ2 with local solidification
time.
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