Phase Diagrams -...

Chapter 9

Phase

Diagrams

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Dr. Mohammad Abuhaiba, PE 1

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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Dr. Mohammad Abuhaiba, PE

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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 the

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 the 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 Limit

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9.3 Phases

A phase: a 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 the particular 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 the

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

what 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

Isomorphous Systems

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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 and

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 the

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

Phases Present

Determination of Phase Compositions

Determination of Phase Amounts

Example Problem 9.1

Derive the lever rule

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9.8 Interpretation of Phase Diagrams

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Volume Fractions

Conversion between volume and 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. Growth requires that 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 Schematic

representation of

the development of

microstructure

during equilibrium

solidification of a 35

wt% Ni–65 wt% Cu

alloy.


On cooling from liquidus to 1250oC,

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-40%Ni.

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9.9 Development of

Microstructure in Isomorphous Alloys

Figure 9.5 Schematic

representation of the

development of

microstructure during

nonequilibrium

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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9.11 Binary Eutectic Systems

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Example Problem 9.2 Determination of Phases Present and

Computation of Phase Compositions

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

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

b. What is (are) the composition(s) of the

phase(s)?

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Example Problem 9.3

Relative Phase Amount Determinations—

Mass and Volume Fractions

For the lead–tin alloy in Example Problem

9.2, calculate the relative amount of each

phase present in terms of

a. mass fraction

b. volume fraction. At 150°C take the

densities of Pb and Sn to be 11.23 and

7.24 g/cm3, respectively.

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9.12 Development

of Microstructure in

Eutectic Alloys

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9.12 Development

of Microstructure in

Eutectic Alloys


Eutectic Alloys

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Eutectic Alloys

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Eutectic Alloys

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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 (Sec

3.6)

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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9.18 The IRON–IRON Carbide

(Fe–Fe3C) Phase Diagram


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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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 - 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

Determination of Relative Amounts of Ferrite,

Cementite, and Pearlite Microconstituents

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

just below the eutectoid, determine the following:

a. The fractions of total ferrite and cementite phases

b. The fractions of the proeutectoid ferrite and

pearlite

c. The fraction of eutectoid ferrite

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9.20 The Influence of Other Alloying Elements

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Home Work Assignment

1, 6, 11, 16, 21, 26, 32,

39, 44, 49, 54, 59, 65

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