EMA5001 Lecture 14
Growth of Alloys from Liquid
© 2016 by Zhe Cheng
Solidification of Single Phase Alloys (1)
Most commercial metals contain
alloy elements
Systems to be examined



T
T1
T2
T3
TE
Single phase
Eutectic alloy
Peritectic alloy
Case #1 Equilibrium solidification
of single phase alloys
Assuming straight solidus and liquidus lines
 Infinitely slow cooling
 Liquid and solid phase uniform
 Average liquid composition follow
liquidus line
 Average solid composition follows
solidus line
EMA 5001 Physical Properties of Materials
XS
XL
k
Zhe Cheng (2016)
XL
XS
kX0
Solid
X0
X0/k
XB
XL
X0
XB
Liquid
XS
Interface movement
14 Alloy Solidification
x
2
Solidification of Single Phase Alloys (2)
Case #2 No diffusion in solid,
perfect mixing in liquid
T
Example
Fast cooling with efficient stirring in liquid T1
 Uniform liquid composition at any time T2
T3
 Local equilibrium at the solid-liquid
TE
interface
 Liquid composition follow liquidus line
 Solid composition changes with
position as a result of solidification at
decreasing temperature with no
diffusion in solid
 Average solid composition lower (in
solute concentration) than solidus line
 Always reaches eutectic point
EMA 5001 Physical Properties of Materials
Zhe Cheng (2016)
k
XS
XS
XL
XL
XS
kX0
X0
14 Alloy Solidification
X0/k XE XB
3
Solidification of Single Phase Alloys (3)
T
Continue from p.3
Evolution of composition profile
k
Initial T  T1
XB
T1
T2
T3
TE
Liquid
X0
kX0
XS
XS
kX0
T1 < T = T2 < TE
XB
Liquid
Solid
X0
kX0
XL
x
Solid
XB
XS
XL
XL
XS
x
EMA 5001 Physical Properties of Materials
X0 Xmax X0/k XE XB
Final T  TE
Solid
Xmax
X0
kX0
Zhe Cheng (2016)
XE
x
14 Alloy Solidification
4
Solidification of Single Phase Alloys (4)
Continue from p.4
At any given extent of solidification
XL Liquid composition (uniform)
XL+dXL
XL
XB
Solid
Liquid
XS Solid composition at the interface
X0
XS
fS Total weight fraction of solid
kX0
fL=1-fS Total weight fraction of liquid
fS fS+dfS
dfS Small increase in solid weight fraction due to continued solidification
dXL Small increase in liquid composition due to solute diffusion from solid to liquid
df S
dX L
We have:

 X L  X S df S  1  f S dX L
1 fS X L  X S
Consider k  X S , we have df
1 dX S
L



XL
fL 1 k X S
kX 0
X0
Integral and consider when fS = 0, XS = kX0 , we have X S 
X

1 k
L
1 k


1

f
f
S
L
Implication: the system will always contain some eutectics
EMA 5001 Physical Properties of Materials
Zhe Cheng (2016)
14 Alloy Solidification
5
Solidification of Single Phase Alloys (5)
Case #3 No diffusion in solid,
diffusional mixing in liquid
T
Assumption:
T1
After initial stage, system can reach
XS
T2
steady state with stable solidification
T3
rate
TE
 Liquid composition decreases from
liquidus line to bulk concentration
 Local equilibrium at the solid-liquid
interface
kX0 X0
 System can reaches steady state:
balance of diffusion and cooling/solidification process
 Always reaches eutectic point
EMA 5001 Physical Properties of Materials
Zhe Cheng (2016)
14 Alloy Solidification
k
XS
XL
XL
X0/k XE XB
6
Solidification of Single Phase Alloys (6)
T
Continue from p.6
Evolution of composition profile
XB
k
T1 < T=T2 < T3
T1
T2
T3
TE
Liquid
X0
kX0
XS
kX0
X0
kX0
X0
Solid
k
XL
x
Solid
XB
XS
XL
T = T3
XB
Liquid
XL
XS
x
EMA 5001 Physical Properties of Materials
X0 Xmax X0/k XE XB
Final T  TE
Solid
XE
X0
kX0
Zhe Cheng (2016)
x
14 Alloy Solidification
7
Constitutional Supercooling
Solidification of an alloy with solid grows into superheated liquid


Example: Solidification of liquid alloy in a mold w/ wall colder is than liquid
“Equilibrium” temperature TEq changes as liquid composition changes near the
interface
If actual dT/dx is steep as in this region, will form
T
TC
Ti=Tm
Solid
XB
X0
kX0
planar solid/liquid interface as T
> TEq
T
TEq
k
If actual dT/dx is gradual as in this
region, will form cellular or
dendrite structure as T < TEq T1
- or constitutional supercooling
T3
TE
Liquid
X0
k
XL
kX0
XS
X0 Xmax X0/k XE XB
x
EMA 5001 Physical Properties of Materials
XS
XL
8
Zhe Cheng (2016)
14 Alloy Solidification