83
Microsegregation
Microsegregation
Partition coeff.
k=Cs/CL at constant temp. and press.
• if mL < 0 k < 1
• İf mL > 0 k >1
Models for Microsegregation
• 1 no mixing in liquid no diffusion in solid no coarsening
• 2. partial mixing in liquid no diffusion in solid no coarsening
• 3. complete mixing in liquid no diffusion in solid no coarsening
• 4. complete mixing in liquid diffusion in solid no coarsening
• 5. complete mixing in liquid diffusion in solid coarsening
• 6. complete mixing in liquid complete diffusion in solid
• 1 no mixing in liquid no diffusion in solid no coarsening
• 2. partial mixing in liquid no diffusion in solid no coarsening
• 3. complete mixing in liquid no diffusion in solid no coarsening
• 4. complete mixing in liquid diffusion in solid no coarsening
• 5. complete mixing in liquid diffusion in solid coarsening
• 6. complete mixing in liquid complete diffusion in solid
(6 Model). Eq solidification
(Level Rule)
p=1-k
• 1 no mixing in liquid no diffusion in solid no coarsening
• 2. partial mixing in liquid no diffusion in solid no coarsening
• 3. complete mixing in liquid no diffusion in solid no coarsening
• 4. complete mixing in liquid diffusion in solid no coarsening
• 5. complete mixing in liquid diffusion in solid coarsening
• 6. complete mixing in liquid complete diffusion in solid
1 model
• 1 no mixing in liquid no diffusion in solid no coarsening
• 2. partial mixing in liquid no diffusion in solid no coarsening
• 3. complete mixing in liquid no diffusion in solid no coarsening
• 4. complete mixing in liquid diffusion in solid no coarsening
• 5. complete mixing in liquid diffusion in solid coarsening
• 6. complete mixing in liquid complete diffusion in solid
2 model
• 1 no mixing in liquid no diffusion in solid no coarsening
• 2. partial mixing in liquid no diffusion in solid no coarsening
• 3. complete mixing in liquid no diffusion in solid no coarsening
• 4. complete mixing in liquid diffusion in solid no coarsening
• 5. complete mixing in liquid diffusion in solid coarsening
• 6. complete mixing in liquid complete diffusion in solid
CL=Co(1-fs)^(k-1)
CL=Cofl^(k-1)
Cs=kCofl^(k-1)
fs+fl=1 k=Cs/Cl
Co=4.5
Gulliver-Scheil Eq.
fs
0.0 0.2 0.4 0.6 0.8 1.0
Cs
0
5
10
15
20
k=0.1
k=0.2
k=0.4
k=0.6
k=0.8
k=09
Gulliver-Scheil Eq. Co=4.5Cu
fs
0.0 0.2 0.4 0.6 0.8 1.0
CL
0
10
20
30
40
50
k=0.1
k=0.2
k=0.4
k=0.6
k=0.8
k=09
• 1 no mixing in liquid no diffusion in solid no coarsening
• 2. partial mixing in liquid no diffusion in solid no coarsening
• 3. complete mixing in liquid no diffusion in solid no coarsening
• 4. complete mixing in liquid diffusion in solid no coarsening
• 5. complete mixing in liquid diffusion in solid coarsening
• 6. complete mixing in liquid complete diffusion in solid
Cs=kCo(1-(1-k*beta)*fs)^((k-1)/(1-k*beta))
Beta=2*alpha/(1+2*alpha) Ohnaka
Beta=2*alpha/(1+2*alpha+1/2k)
Ohnaka Eq. Co=4.5Cu k=0.166
fs
0.0 0.2 0.4 0.6 0.8 1.0
CL
0
10
20
30
40
50
Beta=0
beta=0.01
beta=0.1
beta=0.4
beta=0.8
beta=1
Ohnaka Eq. Co=4.5Cu k=0.166
fs
0.0 0.2 0.4 0.6 0.8 1.0
T
520
540
560
580
600
620
640
660
beta=0
beta=0.01
beta=0.1
beta=0.4
beta=0.8
beta=1
• 1 no mixing in liquid no diffusion in solid no coarsening
• 2. partial mixing in liquid no diffusion in solid no coarsening
• 3. complete mixing in liquid no diffusion in solid no coarsening
• 4. complete mixing in liquid diffusion in solid no coarsening
• 5. complete mixing in liquid diffusion in solid coarsening
• 6. complete mixing in liquid complete diffusion in solid
Beta=2*alpha/(1+2*alpha) Ohnaka
Solidification in Ternary System
Solidification in Al-Cu-Mg Alloys
7050 Plate
Components machined from 7050
alloy thick plate are widely used in
load bearing applications e.g. wing
spars
7050 composition specification
Focus on one alloy (7050) and product (thick
hot rolled plate)
Processing Sequence - 7050
PlateCastDirect chill
Homogenize~475oC, 24h
Hot roll~350-450oC
20+ passes
reduction~70%
Solution treat475oC, 1h
spray quenched
Age
Cast SolutionizedHomogenized Rolled
RD
Microstructural ChangesTe
mp
era
ture
Aged
Time
50nm
Simple Phase Diagrams
300
350
400
450
500
550
600
650
700
0 10 20 30 40 50 60
wt.% Mg
Te
mp
era
ture
(C
)
Liquid
Liquid + -Al
-Al
-Al + -AlMg
-A
lMg
-AlMg
-A
lMg
Al-Mg System (Al-Rich)
300
400
500
600
700
800
900
1000
1100
1200
0 20 40 60 80 100
wt.% Mg
Te
mp
era
ture
(C
)
Liquid
Liquid + Mg
CuMg2 + Mg
CuM
g2
L + CuMg2
L + -Cu
Laves - C15
-Cu
+
Laves - C15
Liquid +
Laves - C15
Cu-Mg System
Ternary Phases S - Al2CuMg, T - Mg32(Al,Cu)49, V - Al5Cu6Mg2, Q - Al7Cu3Mg6
Even for simple 2xxx alloy (Al-Cu-Mg), need data for 3 binaries
and information about ternary phases
400
450
500
550
600
650
700
0 10 20 30 40 50 60
wt.% Cu
Tem
pera
ture
(C
)
Liquid
Liquid + -Al
-Al
Liquid + -Al2Cu
-Al + -Al2Cu -Al2Cu
Al-Cu System (Al-Rich)
MTDATA predicted phase diagrams
Real, commercial Al-alloys may contain > 10 alloying
elements!
Success of thermodynamic models relies on availability of
sufficient, high quality, thermodynamic data
Predictions for Binary Al-Cu
Alloy
Freezing Range
520 540 560 580 600 620 640 660 680 700
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Ma
ss P
ha
se F
ract
ion
Liquidfcc -Al
- Al2Cu
Eutectic
Reaction
Temperature (C) fcc -Al
dendrites
- Al2Cu
eutectic fcc -Al
eutectic
Predictions for Ternary Al-Cu-
Mg alloy
470 490 510 530 550 570 590 610 630 650
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0M
ass
Ph
ase
Fra
ctio
n
Temperature (C)
Liquid
fcc -Al
TLTSDT
S - Al2CuMg
- Al2Cu
Ternary Eutectic Predicted at ~ 500ºC
Predictions for 2xxx (Al-4.5Cu-1.5wt%) Mg alloy
Prediction of Freezing RangeTo reduce tendency for solidification cracking, need to
minimize absolute freezing range
Use thermodynamic model to predict freezing range
for different alloy compositions
Effect of Mg
content on freezing
range of eutectic in
Al-4.5Cu-x Mg alloy
0
5
10
15
20
25
30
35
40
45
50
0 0.5 1 1.5 2 2.5 3
wt.% Mg
DT
(F
ree
zin
g R
an
ge
of
Eu
tec
tic
)
Binary Eutectic
[ + ]
Ternary Eutectic
[ + S]Saddle Point
[ + S]
Optimum
composition
range
• Fe-C-Mn Aloys
Fe-C-Mn Phase Diagram
Color Etching
Color Etching
