Part 7 – Phase Diagrams
A.
Fundamentals of Phase Diagrams
a) Pure Element or Compound
Points of
arrest
Temp
Tmp
Latent heat given out on
freezing (solidification)
Time (slowly)
Start of
solidification
-
End of
solidification
called cooling curve T vs. t plot
points of arrest
latent heat
freezing ≡ solidification
start and end of solidification
Tmp constant - ∴ line is horizontal
Temperature stays constant at Tmp until all liquid has solidified.
fs = 0
liquid
fs = 1
T
fs = 0.5
time
solid
liquid
solid
(dendrites)
where dendrites meet we will have grain boundaries.
b) Solid Solution System (e.g., Cu and Ni)
- both are fcc
- substitutional solid solution system
- between A & B, Tcooling curve and Laten heat removed
- solid begins to form at A (Tsolidus ) and ends forming at B (Tliquidus )
- Tsolidus = f (composition)
- Tliquidus = f (composition)
- plot TS and Te as a function of composition
- mp's of pure Ni and pure Cu
- show mapping of TL and TS
- upper region is for liquid
- lowest region is for solid (use α to denote solid)
- intermediate region is (α + L ) . Both solid and liquid co-exist. Latent heat is being
removed.
c) Phase and Component
Defn Phase - a homogeneous portion of a system that has uniform chem. and phys.
characteristics.
in L region
α region
α + L region
1 Phase
1 Phase
2 Phases ( α and L )
Defn Component - an element or compound of an alloy, which may be used to
specify a composition (e.g., Components are Ni and Cu).
A
L
T
T1
C
α+L
B
α
Ni
-
wt % →
Cu
A weight pct of alloy
Draw a 'tie line' at T1
B and C are the points of intersection of solidus and liquidus
Composition of solid is B
Composition of liquid is C
How much liquid and solid co-exist at T1 ?
d) Lever Rule:
AC
× 100
BC
AB
%L =
× 100%
BC
%α =
e.g., 40% Cu/Ni alloy at 1300°C
L
T
1300°C
α+L
α
Ni
1 40
2
wt % Cu →
Cu
Comp of α ⇒ Point 1
37% Cu
63% Ni
Comp of L ⇒ Point 2
53% Cu
47% Ni
53 − 40
% Solid =
× 100 = 81.3%
53 − 37
40 − 37
× 100 = 18.7%
% Liquid =
53 − 37
e) Eutectic
Eutectic Reaction: L → S1 + S2 (reaction occurs isothermally)
S1
S2
1. Cooling curve of alloy of composition E;
Composition TE
T
horizontal line 'like' pure
element or compound
TE
t
Microstructure of solid at C E .
Eutectic Microstructure
Two phase microstructure.
Phases are lamelae alternating
of S1 and S2 .
Grain S1 S2
boundaries
f) Composition −.
T
L
L
horiz
T2
TE
2
change of slope
L + S1
L + S1
S1 + S2
L + S2
S1 + S2
t
S1
S2
2
TA
L
TB
TC
T
L + S1
TE
L + S2
S1 + S2
C
S1
C2
CC
CE
%S2 →
S2
@ TA we have all liquid.
@ TB we have liquid of C2 at its liquidus.
@ TC we have L + S1 .
Composition of liquid CC
Composition of solid C
wt% of liquid
=
C2 - C
× 100
CC - C
wt% of solid
=
CC - C2
× 100
CC - C
@ TE we have L + S1 (just above TE )
Composition of liquid C E
Composition of solid C
wt% of liquid
C -C
= 2 C × 100% ⇒ will solidify @ TE with eutectic composition
CE - C
wt% of solid
=
CC - C2
× 100 %
CC - C
Example: Eutectic system with limited solid solubility
α field - Lead atoms with Sn soluble
β field - Sn atoms with Pb soluble
(NOTE: Pb and Sn dissolved - varies with temperature)
1. Eutectic alloy - 63% Sn
at T > 183° C liquid solution of Sn and Pb
at T = 183° C L → α(solid ) + β(solid )
Composition of eutectic is:
97 − 62
× 100 = 44%
97 − 20
62 − 20
%β =
× 100 = 56%
97 − 20
%α =
Composition of β is 97% Sn
α is 20% Sn
2. Alloy with 50% Sn
A - Homogeneous solution of 50 Pb:50 Sn
L
B - α begins to form with 16% Sn. α is called the primary phase or primary α .
α
C - In C (e.g., 200°C), C L = 55% Sn and Cα = 18% Sn .
50 − 18
% liquid =
× 100 = 87%
55 − 18
%α
=
55 − 50
× 100 = 13%
55 − 18
α
D - Just above 183ºC
50 − 20
× 100 = 71%
62 − 20
% liquid
=
%α
= 29%
Composition of L is 62% Sn
Composition of α is 20% Sn
α
29% Sn is α
20% Sn in α
Just below 183ºC
L → α (20% Sn ) + β (97% Sn )
α
α
α
β
α
eutectic
% α in eutectic as before 100 - 44 = 56
% β (this is all eutectic β ) in µ structure = 0.56(71) = 40%
E - As Teutectic, the solubility of Sn in Pb (α ) decreases and the solubility of Pb in
Sn (β ) decreases.
g) Intermetallic compound
L
T
θ
α 5
Al 4
Al 2Cu − xtalstructure
10
20
30
% Cu
40
50
52% Cu
Al
- FCC
Cu
- FCC
Al 2Cu - Body centered tetragonal - ~33 atoms of Cu and ~66 atoms of Al.
θ has isothermal transformation. May have composition range (small).
@ 4% Cu and room temperature.
%CuAl 2 =
4−0
× 100 = 7.3%
52 − 0
Al 2Cu large precipitate
If we quenched, over a period of time, we would see [age hardening alloy].
Small Al 2Cu precipitates
- initially get supersaturated soln
- Al 2Cu precipitates out
Improves strength and ductility (hardens the alloy).
- Ferrous Materials
where α
= ferrite b.c.
C in solid sol'n max solubility 0.02%
γ
= autenite f.c.c. C in solid sol'n max solubility 2%
Fe3C = cementile orthorombic intermetallic compound.
eutectoid reaction
S1 → S2 + S3
γ → α + Fe3C
called pearlite
α
Fe3C
0.8%C
Steels with %C < 0.8
α is pro-eutectoid α (pre-eutectoid)
Steels with %C > 0.8
Fe3C is hypereutectoid ceucutite