1. Fully Miscible Solution
Simple solution system (e.g., Ni-Cu solution)
Crystal
Structure
electroneg
r (nm) Ni
FCC
1.9
0.1246 Cu
1.8
0.1278
Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility.
Ni and Cu are totally miscible at all mixture compositions – isomorphous

2. Copper-Nickel Binary Equilibrium Phase Diagram
Solid solutions are typically designated by lower case Greek letters: a, B, g, etc.
Liquidus line separates liquid from two phase field
Solidus line separates two phase field from a solid solution
Pure metals have melting points
Alloys have melting ranges
What do we have? What’s the composition?

3. The Lever Rule
Draw Tie line – connects the phases in equilibrium with each other - essentially an isotherm
wt% Ni 20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 3 4 5 B T
tie line C o S R
Derived from Conservation of Mass:
(1) Wa + WL = 1
(2) WaCa + WLCL = Co
Let W = mass fraction (amount of phase)
Adapted from Fig. 9.3(b), Callister 7e.

4. Example Calculation WL = S R + Wa wt% Ni T(°C) L (liquid) a (solid) L20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 3 4 5
Cu-Ni system C o
= 35 wt% Ni
At T B :
Both a
and L
= 27 wt% WL = S R + Wa
tie line 35 C o B T 32 C L R S 4 C a 3

5. Equilibrium Cooling in a Cu-Ni Binary
• Phase diagram:
Cu-Ni system.
• System is:
--binary
i.e., 2 components:
Cu and Ni.
--isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100 wt% Ni.
• Consider
Co = 35 wt%Ni.

6. Cored vs Equilibrium Phases
• Ca changes as we solidify.
• Cu-Ni case:
First a to solidify has Ca = 46 wt% Ni.
Last a to solidify has Ca = 35 wt% Ni.
• Fast rate of cooling:
Cored structure
• Slow rate of cooling:
Equilibrium structure
First a
to solidify:
46 wt% Ni
Uniform C :
35 wt% Ni
Last
< 35 wt% Ni

7. Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
--Tensile strength (TS)
--Ductility (%EL,%AR)
Tensile Strength (MPa)
Composition, wt% Ni Cu Ni 20 40 60 80
100
200
300
400
TS for
pure Ni
TS for pure Cu
Elongation (%EL)
Composition, wt% Ni Cu Ni 20 40 60 80
100 30 50
%EL
for
pure Ni
for pure Cu
--Peak as a function of Co
--Min. as a function of Co

8. Consider Pb-Sn System Simple solution system (e.g., Pb-Sn solution)
Crystal
Structure
electroneg
r (nm) Pb
FCC
1.8
0.175 Sn
Tetragonal
0.151
13.7%
W. Hume – Rothery Rules:
Atomic size is within 15%
Same electronegativity
Do not have same crystal structure
Will have some miscibility, but will not have complete miscibility

9. Binary-Eutectic System
From Greek eut ktos, easily melted
Liquidus
Solidus
Eutectic Point
Solvus
Eutectic Reaction:
L(CE) (CE) + (CE)

10. Microstructural Evolution in EutecticL + a
200
T(°C) Co ,
wt% Sn 10 2 20
300
100 30 b
400
(room T solubility limit) TE
(Pb-Sn
System)
L: Co wt% Sn
a: Co wt% Sn
Consider (1): Co < 2 wt% Sn
Result:
--at extreme ends
--polycrystal of a grains
i.e., only one solid phase.

11. Microstructural Evolution in Eutectic
L: Co wt% Sn
Consider (2):
2 wt% Sn < Co < 18.3 wt% Sn
Result:
Initially liquid + 
then  alone
finally two phases
a polycrystal
fine -phase inclusions
Pb-Sn
system L + a
200
T(°C) Co ,
wt% Sn 10
18.3 20
300
100 30 b
400
(sol. limit at TE) TE 2
(sol. limit at T
room ) L a
a: Co wt% Sn a b

12. Microstructural Evolution in Eutectic
Consider (3): Co = CE
• Result: Eutectic microstructure (lamellar structure)
--alternating layers (lamellae) of a and b crystals.
Pb-Sn
system
L
a
200
T(°C)
C, wt% Sn 20 60 80
100
300 L a b +
183°C 40 TE
160 m
Micrograph of Pb-Sn
eutectic
microstructure
L: Co wt% Sn CE
61.9
18.3
: 18.3 wt%Sn
97.8
: 97.8 wt% Sn

13. Lamellar Eutectic Structure

14. Microstructural Evolution in Eutectic
Consider (4): wt% Sn < Co < 61.9 wt% Sn
T(°C) L a
L: Co
wt% Sn
Result:
a crystals and a eutectic microstructure L a
300 L
Pb-Sn
system L + a a b
200
18.3
61.9 S R L + b TE
97.8 S R
primary a
eutectic b
100 a + b 20 40 60 80
100
Co, wt% Sn

15. Hypoeutectic vs HypereutecticL + a b
200
Co, wt% Sn 20 60 80
100
300 TE 40
(Pb-Sn
System)
160 mm
eutectic micro-constituent
hypereutectic: (illustration only)
T(°C)
61.9
eutectic
eutectic: Co = 61.9 wt% Sn
175 mm a
hypoeutectic: Co = 50 wt% Sn