MATE1412: Materials Engineering I
Lecture 13: Phase Diagrams
Prof. Tim SercombeRoom: 2.12Phone: 6488 3124email:: [email protected]
1
Callister: 8th Ed - Chapter 9, pages 281-290, 292-3097th Ed - Chapter 9 p252-260, 264-282.
Learning Objectives
At the end of this lecture you should be able to:
Understand the concept of a phase diagram
Be able to extract information such as phases present and their relative proportions
Determine the microstructure for a simple eutectic alloy based on its composition and phase diagram.
2
Phase Diagrams
A phase may be solid (ice), liquid (water) or gas (steam).
Usually consider only solid and liquid phases
In materials, a phase differs in structure or composition from another region.
Homogenous structure Same chemical and physical properties Have a definite interface
4 Components: The elements or compounds which are present in the mixture (e.g., Al and Cu) Phases: The physically and chemically distinct material regions that result (e.g., a and b).
Aluminum-CopperAlloy
Components and Phases
a (darker
phase)
b (lighter
phase)
Adapted from chapter-opening photograph, Chapter 9, Callister 3e.
Pressure-Temperature Diagramsfor Water
Solid, liquid & vapour co-exist
2 phases are indistinguishable
Phase boundary:2 phases in equilibrium
Solubility
Solubility of one element/substance in another varies greatly
Insoluble: Partial solubility:
Complete solubility:oil and water, Al & Si
salt or sugar in water,
Cu in Al, C in Fe
Alcohol & water, Cu & Ni, Ag & Au
Solubility Limit:Max concentration forwhich only a solutionoccurs.
Eg: Phase Diagram:Water-Sugar System
Question: What is thesolubility limit at 30oC?
Solubility limit increases with T:e.g., if T = 100C, solubility limit = 80wt% sugar.
THE SOLUBILITY LIMIT
Answer: 65wt% sugar.If Comp < 65wt% sugar: syrupIf Comp > 65wt% sugar: syrup + sugar coexist 65 wt% sugar
Adapted from Fig. 9.1, Callister & Rethwisch 8e
8Effect of T & Composition (Co)
Changing T can change # of phases:
Adapted from Fig. 9.1, Callister & Rethwisch 8e
D (100C,90)2 phases
B (100C,70)1 phase
path A to B.
Changing Co can change # of phases: path B to D.
A (20C,70)2 phases
70 80 1006040200
Tem
per
atu
re (
C)
Co =Composition (wt% sugar)
L
(liquid solution i.e., syrup)
20
100
40
60
80
0
L
(liquid)
+
S
(solid sugar)
water-sugar
system
9Phase Equilibria
CrystalStructure
electroneg r (nm)
Ni FCC 1.9 0.1246
Cu FCC 1.8 0.1278
Both haveThe same crystal structure (FCC) Similar electronegativitiesSimilar atomic radii suggesting high mutual solubility.
Simple solution system (e.g., Ni-Cu solution)
Ni and Cu are totally miscible.
10
Phase Diagrams
Maps of phases present as function of T, Co, and P. For this unit:
- binary systems: just 2 components.- independent variables: T and Co (P = 1 atm is almost always used).
PhaseDiagramfor Cu-Nisystem Adapted from Fig. 9.3(a), Callister &
Rethwisch 8e
2 phases:
L (liquid)a (FCC solid solution)
3 phase fields: LL + a
a
wt% Ni20 40 60 80 10001000
1100
1200
1300
1400
1500
1600T(C)
L (liquid)
a
(FCC solid solution)
11
wt% Ni20 40 60 80 10001000
1100
1200
1300
1400
1500
1600
T(C)
L (liquid)
a(FCC solid
solution)
Cu-Niphase
diagram
Phase Diagrams: # and types of phases Rule 1: If we know T and Co, then we know:
- the # and types of phases present.
Examples:
A(1100C, 60%): 1 phase: a
B(1250C, 35%): 2 phases: L + a
Adapted from Fig. 9.3(a , Callister & Rethwisch 8e
B(1
25
0
C,3
5)
A(1100C,60)
C (1350oC, 35%)??
12
wt% Ni
20
120 0
130 0
3 0 4 0 5 0
110 0
L (liquid)
a
(solid)
T(C)
A
35
C o
100% L
Cu-Nisystem
Adapted from Fig. 9.4, , Callister & Rethwisch 8e.
Co = 35 wt%Ni.
Cooling in a Cu-Ni Binary
75% a:
25% L
5%L
95% a:
B5% a
95% L
C
D
E
100% a
13
Labeling Phase Fields
Fig. 9.7 , Callister & Rethwisch 8e
Labeling Phase Fields
At top, Liquid
At the left, for low Ag content, a = solid solution of Cu with some Ag atoms substituting for the Cu.
On right, b = Ag with some Cu atoms substituting for the Ag.
14
Labeling Phase Fields
Between the single phase fields, we have areas with 2 phases.
To find what they are, go to the left and right.
Hit a and Liquid
So, contains a and Liq15
Labeling Phase Fields
Again, here we go left and right and find aand b.
What is in the white region?
16
Amount of Each Phase
The close you are to the single phase field, the more of that phase.
Point 1: mostly a, with a small amount of b
Point 2: about 50:50 a:b
Point 3: mostly b
So not only do you know what is there, but also how much.
17
1 2 3
18
: Min. melting TE
2 componentshas a special compositionwith a min. melting T.
Binary-Eutectic Systems
Eutectic: special composition where liquidsolidifies at a single temp into 2 solid phases
L(CE) a(CaE) + b(CbE)
3 single phase regions
(L, a, b )
Limited solubility:
a: mostly Pb
b: mostly Sn
TE : No liquid below TE
CE
composition
Eg. Pb-Sn system
L+ aL+b
a + b
200
T(C)
18.3
C, wt% Sn
20 60 80 1000
300
100
L (liquid)
a183C
61.9 97.8
b
Pb-Snsystem
TE
CE
19
For alloys for which C0 < 2 wt% Sn
Result: at room temperature-- polycrystalline with grains of
a phase having composition C0
Microstructural Developments in Eutectic Systems I
0
L+ a200
T(C)
C , wt% Sn10
2
20C0
300
100
L
a
30
a+b
400
(room T solubility limit)
TE(Pb-SnSystem)
aL
L: C0 wt% Sn
a: C0 wt% Sn
Adapted from Fig. 9.11, Callister & Rethwisch 8e.
20
2 wt% Sn < Co < 18.3 wt% Sn Result:
Initially liquid + a
then a alone
finally two phases
a fine b-phase inclusions
Adapted from Fig. 9.12, Callister & Rethwisch 8e
Microstructures in Eutectic Systems II
Pb-Snsystem
L + a
200
T(C)
Co , wt% Sn10
18.3
200Co
300
100
L
a
30
a+ b
400
(sol. limit at TE)
TE
2(sol. limit at Troom)
L
a
L: Co wt% Sn
ab
a: Co wt% Sn
Microstructures in Eutectic Systems: III
Co = CE
Result: Eutectic microstructure (lamellar structure)
alternating layers (lamellae) of a and b crystals.
21Adapted from Fig. 9.13, Callister & Rethwisch 8e.
Adapted from Fig. 9.14, Callister & Rethwisch 8e.
160m
Micrograph of Pb-Sn eutectic microstructure
Pb-Snsystem
L b
a b
200
T(C)
C, wt% Sn
20 60 80 1000
300
100
L
ab
L+a
183C
40
TE
ab
CE61.9
L: 61.9 wt% Sn
22
Lamellar Eutectic Structure
Adapted from Fig. 9.14 & 9.15, Callister & Rethwisch 8e.
Pb-Sn System: Hypoeutectic
Primary (black)
Eutectic (white)
Eutectic (black)
Hypo = below
Adapted from Fig. 9.16, Callister & Rethwisch 8e.
Pb-Sn System: Hypereutectic
Primary b(grey)
Eutectic (white)
Eutectic (black)
Hyper = above
b
b
Adapted from Fig. 9.16, Callister & Rethwisch 8e.
Summary
Phase diagrams are a map of the phases present at a given composition, temperature.
May be one or two phases, and either solid or liquid.
Each phase has
Homogenous structure Same chemical and physical properties Have a definite interface
Microstructure can be inferred from the phase diagram.