Phase Diagrams

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:


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


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.

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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


Again, here we go left and right and find aand b.

What is in the white region?

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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.

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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.

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2 wt% Sn < Co < 18.3 wt% Sn Result:

Initially liquid + a

then a alone

finally two phases

a fine b-phase inclusions


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.


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


Pb-Sn System: Hypereutectic

Primary b(grey)

Eutectic (white)

Eutectic (black)

Hyper = above

b

b


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.

Documents

Phase Diagrams