Part 7 – Phase Diagrams
A. Fundamentals of Phase Diagrams a) Pure Element or Compound
Temp Points of arrest T mp 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
f = 1 solid T s liquid f = 05. s solid (dendrites) time
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 1 Phase α region 1 Phase α+L region 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
C T 1 B α + L T 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 % α= ×100 BC AB %L =×100% BC e.g., 40% Cu/Ni alloy at 1300°C
T L
1300°C
α + L α
Ni 1 40 2 Cu wt % 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 % Liquid = × 100=18. 7% 53− 37 e) Eutectic
Eutectic Reaction: L→ S12 + S (reaction occurs isothermally)
S1
S2
1. Cooling curve of alloy of composition E;
T Composition TE
horizontal line 'like' pure TE element or compound
t Microstructure of solid at CE . Eutectic Microstructure
Two phase microstructure. Phases are lamelae alternating
of S12 and S .
S S Grain 1 2 boundaries
f) Composition −.
2 change of slope T L L horiz T2 L+S1 L+S L+S T 1 2 E S+S 12 S+S 12
t S1 S2
2 TA L TB T T C L+S L+S T 1 2 E S+S12
C C2 CC CE S1 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
C-C wt% of liquid =×2 100 C-CC
C-C wt% of solid =×C2100 C-CC
@ TE we have L+S1 (just above TE )
Composition of liquid CE Composition of solid C
wt% of liquid C-C2C =×⇒100%will solidify @ TE with eutectic composition C-CE
C-C wt% of solid =×C2100 % C-CC
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 % α= ×=100 44% 97− 20 62− 20 % β= ×=100 56% 97− 20
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), CL = 55% Sn and Cα = 18% Sn . 50− 18 % liquid = ×=100 87% 55− 18
55− 50 %α = ×=100 13% 55− 18
α
D - Just above 183ºC
50− 20 % liquid = ×=100 71% 62− 20
% α = 29%
Composition of L is 62% Sn Composition of α is 20% Sn
29% Sn isα α 20% Sn in α
Just below 183ºC
L → α ()()20%Sn + β 97%Sn
α α α α eutectic β
% 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
5 θ α Al Cu− xtalstructure 2
Al 4 10 20 30 40 50 52% Cu % Cu
Al - FCC Cu - FCC Al2 Cu - 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.
40− %.CuAl = ×=100 7 3% 2 52− 0
Al Cu large precipitate 2
If we quenched, over a period of time, we would see [age hardening alloy].
Small Al Cu precipitates 2
- initially get supersaturated soln
- Al2 Cu 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%
Fe3 C = cementile orthorombic intermetallic compound.
eutectoid reaction SSS123→ + γ → α + Fe3 C called pearlite
α
0.8%C Fe C 3
Steels with %C < 0.8 α is pro-eutectoid α (pre-eutectoid)
Steels with %C > 0.8 Fe3 C is hypereutectoid ceucutite