Chapter 9site.iugaza.edu.ps/mhaiba/files/2010/02/CH9-phase-diagrams-2015.pdf · Given composition...

Chapter 9

Phase

Diagrams

12/12/2015 11:23 AM

Mohammad Suliman Abuhaiba, Ph.D., PE1

Assignment1, 6, 11, 16, 21, 27, 39, 44,

49, 54, 59, 65

Due Tuesday 01/12/2015Exam #5 on Ch9: Tuesday 8/12/2015

12/12/2015 11:23 AM

Mohammad Suliman Abuhaiba, Ph.D., PE

2

Learning Objectives

1. Isomorphous and eutectic phase

diagrams:

a. label various phase regions

b. Label liquidus, solidus, and solvus lines

2. Given a binary phase diagram at

equilibrium, composition of an alloy, its

temperature, determine:

a. phases present

b. compositions of phases

c. mass fractions of phase

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Learning Objectives

3. For some given binary phase

diagram upon heating or cooling,

locate temperatures & compositions

and write reactions of:

Eutectic

Eutectoid

Peritectic

congruent phase transformations

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Learning Objectives

4. Given composition of an Fe–C alloy

containing between 0.022 & 2.14 wt% C:

a. Is alloy hypoeutectoid or

hypereutectoid?

b.name proeutectoid phase

c.compute mass fractions of

proeutectoid phase and pearlite

d.schematic diagram of microstructure at

a temperature just below eutectoid

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Why Study Phase Diagrams?

Design & control of HT procedures

Strong correlation between

microstructure & mechanical properties

Development of microstructure of an

alloy is related to char of its phase

diagram

Phase Diagram (PD) provides valuable

info about melting, casting, crystallization,

and other phenomena

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9.2 Solubility LimitFigure 9.1: Solubility of Sugar (C12H22O11 in a

sugar-water syrup

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9.3 Phases

A phase: physically distinct &

homogenous portion in a

material.

Each phase is a homogenous part

of total mass & has its own

characteristics and properties.

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9.3 Phases

Phase Characteristics:

Same structure or atomic arrangement

Same composition & properties

Definite interface between phase and

any surrounding or adjoining phases

Two types of alloys:

single phase

multiple phases

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9.3 Phases

Alloying consists of two basic forms:

1. Solid solutions

2. Inter-metallic compounds

Solid Solutions (SS): solid material in

which atoms or ions of elements

constituting it are dispersed

uniformly.

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9.3 Phases

A SS is not a mixture

A mixture contains more than one

type of phase whose char are

retained when mixture is formed.

Components of SS completely

dissolve in one another and do

not retain their individual char.

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9.3 Phases

Properties are controlled by creating

point defects such as substititional &

interstitial atoms.

Solute: minor element that is added

to solvent (major element)

When crystal structure of solvent is

maintained during allying, alloy is

called a Solid Solution.

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9.6 One Component (Unary) Phase Diagrams

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9.7 Binary Isomorphous Systems

A phase diagram (PD) shows

relationships among temperature,

composition, and phases present in a

particular alloy system under

equilibrium conditions

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From PD, we can predict:

how a material will solidify under

equilibrium conditions

phases for diff temp and comp.

Equilibrium means that state of a

system remains constant over an

indefinite period of time.

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9.7 Binary

IsomorphousSystems

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Only one solid phase forms, the two

components in the system display

complete solid solubility

Liquidus temperature

Solidus temperature

Freezing range: pure metals & alloys

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When temperature of molten metal

is reduced to freezing point:

Energy of latent heat of solidification is

given off while temperature remains

constant.

Eventually, solidification is complete

and solid metal continues cooling to RT.

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Cooling curve for

solidification of pure

metals

Alloys solidify over a

range of temperatures

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9.8 Interpretation of Phase Diagrams

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% 100

opposite arm of leverPhase

total length of tie line

Example Problem 9.1

Derive the lever rule

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9.8 Interpretation of Phase Diagrams

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Volume & mass fractions

9.9 Development of Microstructure in Isomorphous Alloys

The completely solidified alloy in the phase

diagram shown is a solid solution because:

Alloying element (Cu, solute) is

completely dissolved in host metal (Ni,

solvent)

Each grain has same composition

Atomic radius of Cu is 0.128nm & that of

Ni is 0.125nm,

Both elements are FCC; HRRs are obeyed.

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Two conditions required for growth of solid a:

1. Latent heat of fusion (DHf), which evolves

as liquid solidifies, be removed from solid

liquid interface.

2. Diffusion must occur so that compositions

of solid and liquid phases follow solidus

and liquidus curves during cooling.

DHf is removed over a range of

temperatures so that cooling curves shows

a change in slope

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9.9 Development of Microstructure in

Isomorphous Alloys

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Figure 9.4: Development of

microstructure

during equilibrium

solidification of a 35

wt % Ni–65 wt % Cu

alloy


On cooling from liquidus to 1250 oC,

some Ni atoms must diffuse from 1st solid

to new solid, reducing Ni in 1st solid.

Additional Ni atoms diffuse from

solidifying liquid to new solid.

Meanwhile, Cu atoms have

concentrated – by diffusion – into

remaining liquid.

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The process must continue until we

reach solidus temperature, where

last liquid to freeze, which contains

Cu-28%Ni, solidifies and forms a solid

containing Cu-35 %Ni.

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9.9 Development of

Microstructure in Isomorphous Alloys

Figure 9.5: Development of

microstructure

during non-

equilibrium

solidification of a

35 wt% Ni–65 wt%

Cu alloy

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9.10 Mechanical Properties of Isomorphous Alloys

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9.11 Binary Eutectic Systems

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Composition (wt % Ag)

Tem

pe

ratu

re (

°C

)

AgCu

9.11 Binary Eutectic Systems

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Example Problem 9.2For a 40 wt% Sn–60 wt% Pb alloy at 150°C,

a. what phase(s) is (are) present?

b. What is (are) composition(s) of phase(s)?

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Example Problem 9.3

For lead–tin alloy in Example Problem 9.2,

calculate relative amount of each phase

present in terms of

a. mass fraction

b. volume fraction. At 150°C take densities

of Pb & Sn to be 11.23 & 7.24 g/cm3,

respectively.

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12/12/2015 11:23 AM

Mohammad Suliman Abuhaiba,

Ph.D., PE

35

9.12 Development

of Microstructure in Eutectic Alloys

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9.12 Development

of Microstructure in

Eutectic Alloys

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Mohammad Suliman Abuhaiba,

Ph.D., PE

37

9.12 Development

of Microstructure in Eutectic Alloys


Eutectic Alloys

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Eutectic Alloys

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Figure 9.14: microstructure of a

Pb–Sn alloy of eutectic

composition.

Alternating layers of a

lead-rich a-phase solid solution (dark layers),

and a tin-rich b-phase solid solution (light

layers)

Source: Metals Handbook, 9th edition, Vol. 9,

Metallography and Microstructures, 1985.

Reproduced by permission of ASM International,

Materials Park, OH.


Eutectic Alloys

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Figure 9.15:Schematic

representation of

formation of eutectic

structure for lead–tin

system. Directions of

diffusion of tin & lead

atoms are indicated

by blue & red arrows

9.12 Development of Microstructure in Eutectic Alloys

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9.12 Development of Microstructure in Eutectic Alloys

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9.13 Equilibrium Diagrams Having Intermediate Phases or Compounds

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9.13 Equilibrium Diagrams Having Intermediate Phases or Compounds

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9.14 Eutectoid and Peritectic Reactions

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9.15 Congruent Phase Transformations

Congruent

transformations:

no compositional

alterations

allotropic

transformations

melting of pure

materials

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9.15 Congruent Phase Transformations

Incongruent

transformations: at least one of the

phases will

experience a change

in composition

Eutectic &

eutectoid reactions

melting of an alloy

that belongs to an

isomorphous system

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9.18 The IRON–IRON Carbide(Fe–Fe3C) Phase Diagram


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9.19 Development

of Microstructure in Iron Carbon Alloys

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9.19 Development of Microstructure in Iron Carbon Alloys

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Figure 9.28; Schematic

representation of the

formation of pearlite from

austenite; direction of

carbon diffusion

indicated by arrows.

9.19 Development of Microstructure

in Iron Carbon AlloysHypo-eutectoid Alloys

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Development of

Microstructure

in Iron Carbon

AlloysHypo-eutectoid

Alloys

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9.19 Development of Microstructure in Iron Carbon

Alloys - Hypo-eutectoid Alloys

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9.19 Development of Microstructure in Iron Carbon

Alloys - Hyper-eutectoid Alloys

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EXAMPLE PROBLEM 9.4

For a 99.65 wt% Fe–0.35 wt% C alloy at a

temperature just below the eutectoid,

determine the following:

a. Fractions of total ferrite & cementite

phases

b. Fractions of pro-eutectoid ferrite &

pearlite

c. Fraction of eutectoid ferrite

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Influence of Other Alloying Elements

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