MSE 3300-Lecture Note 14-Chapter 09 Phase Diagrams

8/18/2019 MSE 3300-Lecture Note 14-Chapter 09 Phase Diagrams

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MSE 3300 / 5300 UTA Spring 2015 Lecture 14 -

Lecture 14. Phase Diagrams (1)

Learning Objectives After this lecture, you should be able to do the following:

1. Understand terminology associated with phase diagrams and

interpretate phase diagrams.

2. Sketch isomorphous phase diagrams and label the various regions

and liquidus, solidus, and solvus lines.3. Given a binary phase diagram, the composition of an alloy, and its

temperature, determine what phases are present, the compositions of

the phases, and the mass fractions of the phases.

Reading• Chapter 9: Phase Diagrams (9.1–9.10)

Multimedia

• Virtual Materials Science & Engineering (VMSE):

http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/

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1. Definitions and Basic Concepts

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• Components: pure metals and/or compounds of which an alloy is composed

(e.g., in a copper–zinc brass, Cu and Zn).

• Solute and solvent

• System: (1) a specific body of material under consideration and (2) the series

of possible alloys consisting of the same components, but without regard to

alloy composition (e.g., the iron–carbon system).

• Solubility limit: maximum

concentration of solute

atoms that may dissolve in

the solvent to form a solid

solution.

Figure 9.1: The solubility of

sugar in a sugar–water syrup.


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Phases

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• Phase: a homogeneous portion of a system that has uniform physical and

chemical characteristics (e.g., phase 1: sugar–water syrup solution; phase 2:solid sugar).

• Single-phase system: homogeneous system

• Systems with two or more phases: mixtures or heterogeneous systems

• Equilibrium: The free energy of a

system is at a minimum undersome specified combination of

temperature, pressure, and

composition; the characteristics of

the system do not change (or the

system is stable).

• Phase equilibrium: a constancy

with time in the phase

characteristics of a system (sugar–

water syrup in contact with solid

sugar at 20 °C).

• Metastable state (Non-equilibrium)


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MSE 3300 / 5300 UTA Spring 2015 Lecture 14 - 4

Phase Equilibria: Solubility Limit

Question: What is the

solubility limit for sugar inwater at 20°C?

Answer: 65 wt% sugar . At 20°C, if C < 65 wt% sugar: syrup

At 20°C, if C > 65 wt% sugar: syrup + sugar

65

• Solubility Limit:Maximum concentration forwhich only a single phase

solution exists.

Sugar/Water Phase Diagram

S

u g a r

T e m

p e r a t u r e ( ° C )

0 20 40 60 80 100 C = Composition (wt% sugar)

L(liquid solution

i.e., syrup)

SolubilityLimit L

(liquid)

+S

(solidsugar)20

4 0

6 0

8 0

10 0

W

a t e r

Adapted from Fig. 9.1,

Callister & Rethwisch 9e.

• Solution – solid, liquid, or gas solutions, single phase• Mixture – more than one phase


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• Components:

The elements or compounds which are present in the alloy(e.g., Al and Cu)

• Phases:The physically and chemically distinct material regions

that form (e.g., α and β).

Aluminum-

Copper

Alloy

Components and Phases

α

(darkerphase)

β (lighter

phase)

Adapted from chapter-

opening photograph,

Chapter 9, Callister,

Materials Science &

Engineering: An

Introduction, 3e.


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70 80 1006040200

T e m p e r a t u r e ( ° C

)

C = Composition (wt% sugar)

L(liquid solution

i.e., syrup)

20

100

40

60

80

0

L (liquid)+S

(solidsugar)

Effect of Temperature & Composition

• Altering T can change # of phases: path A to B.

• Altering C can change # of phases: path B to D.

water-

sugar

system

Fig. 9.1, Callister &

Rethwisch 9e.

D (100°C,C = 90)2 phases

B (100°C,C = 70)1 phase

A (20°C,C = 70)2 phases


7/22MSE 3300 / 5300 UTA Spring 2015 Lecture 14 -

2. One-component (or Unary)

Phase Diagrams

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3. Binary Isomorphous Systems

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• Binary Isomorphous Systems: copper–nickel system

• Isomorphous: the complete liquid and solid solubility of the two components


9/22MSE 3300 / 5300 UTA Spring 2015 Lecture 14 - 9

Criteria for Solid Solubility

CrystalStructure

electroneg r (nm)

Ni FCC 1.9 0.1246

Cu FCC 1.8 0.1278

• Both have the same crystal structure (FCC) and havesimilar electronegativities and atomic radii (W. Hume –

Rothery rules) suggesting high mutual solubility.

Simple system (e.g., Ni-Cu solution)

• Ni and Cu are totally soluble in one another for all proportions.



Phase Diagrams

• Indicate phases as a function of T , C , and P .

• For this course: - binary systems: just 2 components.

- independent variables: T and C (P = 1 atm is almost always used).

PhaseDiagram

for Cu-Ni

system

• 2 phases:

L (liquid) α (FCC solid solution)

• 3 different phase fields:

L

L + α α

L (liquid)

α

(FCC solidsolution)



Cu-Ni

phase

diagram

Isomorphous Binary Phase Diagram

• Phase diagram:

Cu-Ni system.

• System is:

Fig. 9.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary

Nickel Alloys, P. Nash, Editor, 1991. Reprinted

by permission of ASM International, Materials

Park, OH.)

-- binaryi.e., 2 components:

Cu and Ni.

-- isomorphousi.e., complete

solubility of one

component in

another; α phase

field extends from0 to 100 wt% Ni.

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600

T (°C)

L (liquid)

α

(FCC solidsolution)



wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600T (°C)

L (liquid)

α (FCC solid

solution)

Cu-Ni

phase

diagram

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Phase Diagrams:Determination of phase(s) present

• Rule 1: If we know T and C o, then we know:-- which phase(s) is (are) present.

• Examples:

A(1100°C, 60 wt% Ni):

1 phase: α B (1250°C, 35 wt% Ni):

2 phases: L + α

B

( 1 2 5 0 º C , 3

5 )

A(1100ºC,60) Fig. 9.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary



Park, OH.)


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Determination of Phase

Composition

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1. A tie line is constructed

across the two-phase

region at the temperature of

the alloy.

2. The intersections of the tie

line and the phaseboundaries on either side

are noted.

3. Perpendiculars are dropped

from these intersections to

the horizontal compositionaxis, from which the

composition of each of the

respective phases is read.


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wt% Ni20

1200

1300

T (°C)

L (liquid)

α

(solid)

30 40 50

Cu-Ni

system

Phase Diagrams:Determination of phase compositions

• Rule 2: If we know T and C 0, then we can determine:-- the composition of each phase.

• Examples: T A

A

35 C 0 32 C L

At T A = 1320°C:

Only Liquid (L) presentC L = C 0 ( = 35 wt% Ni)

At T B = 1250°C:

Both α and L present

C L = C liquidus ( = 32 wt% Ni)

C α = Csolidus ( = 43 wt% Ni)

At T D = 1190°C:

Only Solid (α ) present

C α = C 0 ( = 35 wt% Ni)

Consider C 0 = 35 wt% Ni

DT D

tie line

4 C α 3

Fig. 9.3(b), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary



Park, OH.)

BT B


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Determination of Phase Amounts:

Lever Rule

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• Rule 3: If we know T and C 0, then can determine:

-- the weight fraction of each phase.

• Examples:

At T A : Only Liquid (L) present

W L = 1.00, W α = 0 At T D : Only Solid (α ) present

W L = 0, Wα = 1.00

Phase Diagrams:Determination of phase weight fractions

wt% Ni

20

1200

1300

T (°C)

L (liquid)

α

(solid)

3 0 4 0 5 0

Cu-Ni

system

T A A

35 C 0

32 C L

BT B

DT D

tie line

4 C α 3

R S

At T B : Both α and L present

= 0.27

W L = S R +S

W α = R

R +S

Consider C 0 = 35 wt% Ni

Fig. 9.3(b), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary



Park, OH.)


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• Tie line – connects the phases in equilibrium with

each other – also sometimes called an isotherm

The Lever Rule

What fraction of each phase?

Think of the tie line as a lever

(teeter-totter)

M L M α

R S

wt% Ni

20

1200

1300

T (°C)

L (liquid)

α

(solid)

3 0 4 0 5 0

BTB

tie line

C 0 C L C α

S R

Adapted from Fig. 9.3(b),



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Equilibrium Colling

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wt% Ni20

120 0

130 0

3 0 4 0 5 0110 0

L (liquid)

α

(solid)

T (°C)

A

35 C 0

L: 35 wt%Ni

Cu-Nisystem

• Phase diagram:

Cu-Ni system.

Adapted from Fig. 9.4,


• Consider

microstuctural

changes that

accompany thecooling of a

C 0 = 35 wt% Ni alloy

Ex: Cooling of a Cu-Ni Alloy

46 35

43 32

α : 43 wt% Ni

L: 32 wt% Ni

Bα : 46 wt% Ni L: 35 wt% Ni

C

EL: 24 wt% Ni

α : 36 wt% Ni

24 36 D

α : 35 wt% Ni


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Nonequilibrium Colling

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Equilibrium Nonequilibrium


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• Slow rate of cooling: Equilibrium structure

• Fast rate of cooling: Cored structure

First α to solidify: 46 wt% Ni

Last α to solidify:

< 35 wt% Ni

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• C α changes as we solidify.

• Cu-Ni case: First α to solidify has C α = 46 wt% Ni.Last α to solidify has C α = 35 wt% Ni.

Equilibrium vs Cored Structures

Uniform C α : 35 wt% Ni


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Summary

1. Definitions and basic concepts: phases, phase

equilibrium, phase diagrams

2. One-component phase diagrams

3. Phase diagrams: Binary isomorphous systems

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MSE 3300-Lecture Note 14-Chapter 09 Phase Diagrams