9-1

C H A P T E R 9

P H A S E E Q U I L I B R I A & P H A S E D I A G R A M S

9.1 COMPONENTS AND PHASES

9.2 ONE-COMPONENT SYSTEMS

9.3 TWO-COMPONENT SYSTEMS 9.3.1 Solubi l i ty in the Sol id State 9.3.2 Spec i f icat ion of Compos i t ion

9.4 BINARY ISOMORPHOUS SYSTEM 9.4.2 Determinat ion of Phases Present 9.4.3 Determination of Phase Compositions 9.4.4 Determinat ion of Phase Amounts 9.4.5 Solidification Under Equilibrium

Conditions 9.4.6 Non-Equi l ibr ium Sol id i f icat ion 9.4.7 Mechanica l Propert ies of

I somorphous A l loys

9-2

9.5 BINARY EUTECTIC SYSTEM 9.5.1 Sol id i f icat ion of Eutect ic A l loy 9.5.2 Sol id i f icat ion of Of f -Eutect ic A l loy 9.5.3 A l loys Without Eutect ic React ions 9.5.4 Mechanica l Propert ies of Eutect ic

A l loys

9.6 OTHER BINARY SYSTEMS 9.6.1 Invariant Reactions in Binary Systems 9.6.2 Complex B inary Phase Diagrams

9.7 IRON-IRON CARBIDE (FE-FE3 C) SYSTEM 9.7.1 Transformat ions in Eutecto id Stee ls 9 .7.2 Transformations in Hypoeutectoid Steels 9 .7.3 Transformations in Hypereutectoid Steels 9 .7.4 Mechanica l Propert ies of Stee ls

9-3

9.1 COMPONENTS AND PHASES

• Most engineering materials are mixtures of elements

and/or molecular compounds. Each element and/or

compound in the mixture is known as a component,

which is defined as a chemically distinct and essentially

indivisible substance; e.g. Fe, Si, NaCl, H2O.

• Material mixtures may be physical mixtures, in which the

components are unchanged chemically and remain as the

same identifiable entities. More often however, the

components interact chemically to form new constituents

or phases.

• A phase is a region of material that has the same

composition and structure throughout, and is separated

from the rest of material by a distinct interface. A phase

may contain one or more components.

• Some everyday examples of components and phases:

Material(s) present No. of components No. of phases Water 1 (H2O) 1 (liquid) Water & ice 1 (H2O) 2 (liquid & solid) Salt & water 2 (NaCl & H2O) 1 (salt solution) Excess salt & water 2 (NaCl & H2O) 2 (saturated solution &

solid salt)

9-4

• Note that the phases in a material refer not only to the

gaseous, liquid and solid states; within the same material,

regions of different composition, different crystal

structures, or crystalline as opposed to amorphous, are

considered different phases, e.g. BCC iron is a distinct and

separate phase from FCC iron.

• Microstructure is the structure of a material on the

microscopic scale. It is characterized by the phases present,

their relative amounts, the composition and structure of each

phase, and size, shape and distribution of the phases.

• The microstructure depends on the overall material

composition, the external temperature and pressure, and

thermal processing history of the material. The

microstructure of a material has a profound influence on its

properties.

• A phase diagram is a graphical representation of the

stable phases present, and the ranges in composition,

temperature, and pressure over which the phases are

stable.

• A phase diagram describes the equilibrium (lowest energy)

state of a system: the compositions, structures and

amounts of the equilibrium (stable) phases do not vary

with time.

9-5

9.2 ONE-COMPONENT SYSTEMS

• Unary (1 component) system; e.g. H2O (Fig. 9.2-1).

Fig. 9.2-1 Schematic phase diagram for H2O.

• The stable phase (whether ice, water or steam) depends on

the temperature and pressure.

• Phase boundaries separate the 3 different regions over

which each phase is stable; the boundaries also indicate

conditions under which 2 phases coexist.

• Under very restricted conditions, all 3 phases coexist (triple

point).

• The phase diagram identifies the stable phase(s) at any

given pressure and temperature.

9-6

9.3 TWO-COMPONENT SYSTEMS

• When two components are mixed, they may be

completely soluble, partially soluble or insoluble in each

other, or react to form a new compound (Fig. 9.3-1).

Fig. 9.3-1 Two component mixtures in the liquid state.

9-7

9.3.1 Solubil ity in the Solid State

• A solid solution is a homogeneous single phase formed by

the incorporation of solute atoms (either substituting for

solvent atoms or in interstitial sites) into a host crystal. The

original crystal structure is maintained, with solute atoms

uniformly and randomly dispersed throughout.

• If the solute and solvent atoms are

of similar size, a substitutional

solid solution, is formed, in

which the solute atoms substitute

for the solvent atoms (Fig. 9.3-2).

Fig. 9.3-2 Substitutional solid solution.

• If the solute atom is much smaller

than the solvent atom, an

interstitial solid solution is

formed, in which the solute atoms

reside in the interstitial spaces

between solvent atoms (Fig. 9.3-3).

Fig. 9.3-3 Interstitial solid solution.

• Unlimited solubility: the components form a substitutional

solid solution when mixed in any amounts. 9-8

• Limited solubility: solute atoms dissolve in the solvent to

an extent only; excess solute may combine with the

solvent to form a separate new phase. The solubility of

interstitial atoms is always limited (rule 1 below).

• The necessary (but not sufficient) conditions for unlimited

solubility are expressed by the Hume-Rothery rules: 1. Difference in atomic radii < 15%.

2. Must belong to the same group or adjacent groups in

the Periodic Table to prevent compound formation.

3. Valences must be the same.

4. Crystal structures must be the same.

9.3.2 Specification of Composition

Composition is specified in weight percent (wt%) or atom

percent (at%). In a system containing components A and

B, the composition of A is:

CA =

!

weight (mass) of Atotal weight

x 100 wt%

=

!

weight of Aweight of A + weight of B

x 100 wt%

CA =

!

no. of moles of Atotal no. of moles x 100 at%

=

!

no. of moles of Ano. of moles of A + no. of moles of B x 100 at%

9-9

9.4 BINARY ISOMORPHOUS SYSTEM

• In this system, there is complete solubility (isomorphous) of

2 components (binary) over the entire composition range

in both liquid and solid states; e.g. Cu-Ni (Fig. 9.4-1).

Fig. 9.4-1 The Cu-Ni phase diagram.

• Since most materials are used under constant pressure (i.e.

1 atm), the variables are now the temperature (vertical

axis) and composition of the alloy (horizontal axis). 9-10

• The left edge of the phase diagram represents pure Cu

(100wt%Cu-0wt%Ni), the right edge pure Ni (0wt%Cu-

100wt%Ni); at all other points, there are varying amounts

of Cu and Ni.

• There are three distinct phase fields: liquid L, solid solution

!, and 2-phase ! + L. Above the liquidus, the liquid phase

is stable, while below the solidus, the solid phase is stable.

In between these boundaries, liquid and solid coexist.

• Melting/solidification in pure Cu and Ni occurs

isothermally at unique melting temperatures. At all other

compositions containing both Cu and Ni,

melting/solidification occurs over a temperature range.

• The composition of an alloy is usually fixed, so the only

external variable is temperature; the effects of temperature

on the phases present, their compositions and their relative

amounts, are then of interest.

• Within single-phase fields (L or !), the temperature may be

varied without changing the equilibrium phase or its

composition.

• In 2-phase fields (! + L), changes in temperature are

accompanied by changes in the relative amounts and

compositions of ! and L (details later).

9-11

9.4.2 Determination of Phases Present

• To identify the phases present for an alloy of composition

C0 at temperature T0, locate the point on the phase

diagram (Fig. 9.4-1) with the coordinates C0, T0 (this point of

interest is known as the state point) and see which phase

field (single phase L, !, or 2-phase ! + L) the point lies in.

• For example, an alloy with composition 60wt%Ni-

40wt%Cu at 1100°C (point A) is a single-phase solid

solution of Cu in Ni, denoted as !, while a 35wt%Ni-

65wt%Cu alloy at 1250°C (point B) consists of both solid !

and liquid phases.

9.4.3 Determination of Phase Compositions

• Locate the state point on the phase diagram (Fig. 9.4-1).

• If the point lies in a single-phase field (e.g. point A), the

phase composition is identical to the overall alloy

composition C0.

• When the point lies in a 2-phase field (e.g. point B), the

phase compositions differ from each other and also from

the original overall alloy composition C0. The composition

of each phase depends on the temperature.

9-12

• To find the composition of each phase in any 2-phase field:

1. Extend an isotherm (known as the tie line) at

temperature T0, through the state point, and across the

2-phase field.

2. Note the intersections between the tie line and the

phase boundaries on either side.

3. The compositions of the phases are given by the

horizontal coordinates (on the composition axis) of

these intersections.

• For example, point B (Fig 9.4-2) is located in the 2-phase (! +

L) field; the compositions of the liquid L phase and the

solid ! phase are CL and C!, respectively.

Fig. 9.4-2 Determining phase compositions in any 2-phase field.

9-13

9.4.4 Determination of Phase Amounts

• Locate the state point on the phase diagram (Fig. 9.4-1).

• If the point lies in a single-phase field (e.g. point A), the

amount of the single phase is 100%.

• If the point lies in a 2-phase field (e.g. point B), the relative

amounts of the phases are calculated by the lever rule:

1. Draw a tie-line through the state point.

2. Locate the overall alloy composition C0 on the tie line.

3. The tie line may be thought of as a ‘lever’ pivoted at

alloy composition C0 (Fig. 9.4-3 & 9.4-4). The mass fraction of

any phase is proportional to the length of the opposite

lever arm.

Mass fraction =

!

Mass of phaseTotal mass

=

!

Opposite lever arm

Total lever length

Mass fraction of ! phase, ƒ! =

!

M"Mo

=

!

Co " CLC# " CL

Mass fraction of L phase, ƒL =

!

MLMo

=

!

C" # CoC" # CL

9-14

Fig. 9.4-3 Determine phase amounts in any 2-phase field using the lever rule.

Fig. 9.4-4 Schematic illustration of the lever rule.

9-15

Worked Example

Determine the phases, their compositions and relative amounts in a 40

wt%Ni-60wt%Cu alloy at 1300°C, 1270°C, 1250°C, and 1200°C.

Fig. 9.4-5 Tie lines and phase compositions for

a 40 wt%Ni-60wt%Cu alloy at several temperatures.

Tempera-ture Phase

Compo-sition

(wt%Ni)

Amount (%) Remarks

1300 L 40 100 Read directly

L 37 77

1270

! 50 23

Draw tie-line – read from intersection with liquidus (for L) and solidus (for !) Use lever rule for phase amounts (Fig. 9.4-6)

L 32 38 1250

! 45 62 As above

1200 ! 40 100 Read directly

9-16

Using the lever rule:

At 1270°C,

Mass fraction of L, ƒL =

!

C" # Co

C" # CL =

!

50 " 4050 " 37 = 0.77 (77%)

Mass fraction of !, ƒ! =

!

Co " CLC# " CL

=

!

40 " 3750 " 37 = 0.23 (23%)

(or simply, 1- ƒL = 1- 0.77 = 0.23)

At 1250°C (Fig. 9.4-6),

Fig. 9.4-6 Tie line at 1250°C for determining phase amounts using lever rule.

Mass fraction of L, ƒL =

!

C" # Co

C" # CL =

!

45 " 4045 " 32 = 0.38 (38%)

Mass fraction of !, ƒ! =

!

Co " CLC# " CL

=

!

40 " 3245 " 32 = 0.62 (62%)

(or simply, 1- ƒL = 1- 0.38 = 0.62)

9-17

9.4.5 Solidification Under Equilibrium Conditions

Consider the cooling of an alloy of composition 35 wt%Ni-

65wt% Cu from 1300°C (Fig. 9.4-7):

• Point a: 100% liquid L

Phase: L (35 wt% Ni = alloy composition, C0)

• Point b: solidification starts at the liquidus temperature

Phases: L (35%Ni) + ! (46%Ni)

Amounts: <100% L + > 0% !

• Point c: the proportion of ! increases, the compositions of

L and ! change with temperature, following the

liquidus and solidus respectively

Phases: L (32%Ni) + ! (43%Ni)

Amounts: 73% L + 27% !

• Point d: solidification is almost complete at the solidus

temperature

Phases: L (24%Ni) + ! (35%Ni)

Amounts: > 0% L + < 100% !

• Point e: 100% solid !

Phase: ! (35%Ni = alloy composition, C0)

9-18

Fig. 9.4-7 The development of microstructure during the equilibrium solidification of a 35 wt% Ni-65 wt% Cu alloy.

9-19

9.4.6 Non-Equil ibrium Solidification • During solidification, the composition of ! and L changes

constantly according to the solidus and liquidus as the

temperature drops. These changes are accomplished by

diffusion. Since diffusion in solids is usually very slow, in

most practical situations, cooling is too fast for the

diffusing atoms to establish equilibrium phases and

compositions in the solid state (Fig. 9.4-8). • Point a’: 100% liquid L

Phase: L (35%Ni = alloy composition, C0) • Point b’: solidification starts at the liquidus temperature

Phases: L (35%Ni) + ! (46%Ni) • Point c’: the diffusion in liquid L is assumed to be rapid

enough for the composition of L to follow the

liquidus; however, the composition of the ‘new’

layer of ! (40%Ni) formed is different from the

‘old’ ! (46%Ni) formed earlier at point b’. Since

diffusion is too slow for the ‘old’ ! to reach the

‘new’ ! composition of 40%Ni, the overall !

composition is higher than the solidus and does

not follow the solidus

Phases: L (29%Ni) +

! (40%Ni!C!!46%Ni; overall C!"42%Ni) 9-20

Fig. 9.4-8 The development of microstructure during the non-equilibrium solidification of a 35 wt% Ni-65 wt% Cu alloy.

A cored structure is obtained after solidification.

9-21

• Point d’: because of the shift in the solidus, more liquid

remains than in the equilibrium case

Phases: L (24%Ni) +

! (35%Ni!C! !46%Ni; overall C!"38%Ni)

• Point e’: solidification is almost complete

Phases: L (21%Ni) +

! (31%Ni!C!!46%Ni; overall C!"35%Ni)

• Point f’: 100% solid !

Phase: # with cored structure as a result of

segregation (i.e. the non-equilibrium

variation in composition within a phase)

(31%Ni!C!!46%Ni; overall C!"35%Ni"Co)

• The shift of the solidus from the equilibrium depends on

the cooling rate. Faster cooling results in greater deviation.

• The component with the higher melting point segregates

at the centre of the solid while regions between the grains

are rich in the lower-melting point component. This

coring phenomenon causes hot shortness, where regions

around the grain boundaries melt before the equilibrium

solidus temperature of the alloy is reached.

9-22

9.4.7 Mechanical Properties of Isomorphous Alloys

• Since isomorphous alloys form a single solid phase at all

compositions, each component will experience solid-

solution strengthening by additions of the other

component [note that grain-size strengthening is also possible in polycrystals].

• At some intermediate composition, the strength of the

alloy will be a maximum, but its ductility will exhibit the

opposite trend (Fig. 9.4-9).

Fig. 9.4-9 For the copper-nickel system, (a) solid solution strengthening with alloying addition, but (b) opposite trend in ductility.

9-23

9.5 BINARY EUTECTIC SYSTEM

• In this system, the two components are only partially

soluble in the solid state; e.g. Pb-Sn (Fig. 9.5-1)

Fig. 9.5-1 The Pb-Sn phase diagram.

• Sn is soluble in Pb up to maximum 18.3 wt% at 183°C,

while Pb is soluble in Sn up to 2.2 wt%, forming single-

phase solid solutions ! and " respectively.

• For all other intermediate alloy compositions, a 2-phase

mixture of ! + " exists. 9-24

• The solvus separates the single phase solid regions (! or ")

from the 2-phase ! + " solid region. The solvus corresponds

to the solubility limit of Pb in Sn and vice versa.

• At the eutectic point, E (Fig. 9.5-1), !, " and L coexist in

equilibrium. The eutectic point is invariant; i.e. it exists only

at a specific temperature and alloy composition that

cannot be varied. The eutectic point is similar to the triple

point in one-component systems.

• When an alloy of eutectic composition, CE, is cooled through

the eutectic temperature, a eutectic reaction occurs:

L heating! " " " " "

cooling" # " " " " " " " ! + "

• During the eutectic reaction, melting/solidification occurs

isothermally at one temperature instead of over a range of

temperatures, as seen in other alloy compositions.

• An alloy of eutectic composition, CE,, melts/solidifies at a

temperature lower than the melting points of either

component. The eutectic isotherm represents the lowest

temperature at which the liquid phase exists.

• The composition of a hypoeutectic alloy is lower than the

eutectic composition, CE,, while that of a hypereutectic

alloy is higher than the eutectic composition.

9-25

9.5.1 Solidification of Eutectic Alloy

Consider the cooling of an alloy of eutectic composition

61.9 wt% Sn (Fig. 9.5-2):

Fig. 9.5-2 The development of microstructure in a eutectic alloy.

• Point h: 100% liquid L

Phase: L (61.9%Sn = eutectic composition, CE)

• Eutectic point: eutectic reaction

L (61.9%Sn) 183°C! " ! ! ! ! ! (18.3%Sn) + " (97.8%Sn)

• Point i: 100% solid (overall composition = CE = 61.9%Sn)

Phases: eutectic ! (18.3%Sn) + " (97.8%Sn) lamellae

9-26

• During the eutectic reaction, Pb and Sn atoms must be

redistributed via diffusion to form simultaneously a high Pb-

low Sn ! phase and a low Pb-high Sn " phase.

• Alternating layers (lamellae) of ! and " are formed because

such a structure requires Pb and Sn atoms to diffuse only

over relatively short distances (Figs. 9.5-3 and 9.5-4).

Fig. 9.5-3 Simultaneous diffusion of Pb and Sn atoms to form eutectic lamellae.

Fig. 9.5-4 The eutectic lamellae structure in the Pb-Sn system.

Fig. 9.5-5 Schematic illustration of various

eutectic structures: (a) lamellar, (b) rodlike,

(c) globular, and (d) acicular.

9-27

9.5.2 Solidification of Off-Eutectic Alloy

Consider the cooling of an alloy of hypoeutectic

composition 40 wt% Sn (Fig. 9.5-6):

Fig. 9.5-6 The development of microstructure in a hypoeutectic alloy.

• Point j: 100% liquid L

Phase: L (40%Sn = overall composition)

• Point k: ! solidifies and increases in proportion as the alloy

cools; the compositions of L and ! increase with

decreasing temperature, following the liquidus

and solidus respectively

Phases: L (47%Sn) + ! (16%Sn)

9-28

• Point l: Phases: L (61.9%Sn) + ! (18.3%Sn)

• Just below the eutectic temperature, the remaining L

undergoes the eutectic reaction and transforms to the

eutectic ! + " lamellae.

• Point m: 100% solid (overall composition = 40%Sn)

Phases: proeutectic ! (18.3%Sn) +

eutectic ! (18.3%Sn) + " (97.8%Sn) lamellae

• The ! that forms prior to the eutectic reaction is known as

proeutectic or primary !, to distinguish it from the

eutectic ! lamellae formed during the eutectic reaction.

• To determine the relative amount of proeutectic !, the lever

rule is applied in the 2-phase ! + L region at point l, just

above the eutectic temperature, using the composition of

! at one end of the tie-line and the eutectic composition,

CE, at the other end.

• To determine the relative amount of eutectic ! (i.e. !

mixed in the eutectic ! + " lamellae), the lever rule is first

applied in the 2-phase ! + " region at point m, just below

the eutectic temperature, using the composition of ! at

one end of the tie-line and the composition of " at the

other end. This gives the total amount of !; therefore,

eutectic ! = total ! – proeutectic !.

9-29

Worked Example

Determine the phases, their compositions and relative amounts in a 30

wt%Sn-70wt%Pb alloy at 300°C, 200°C, 184°C and 182°C and 0°C.

Total ! @ 182°C = 86%, proeutectic ! (from 184°C) = 74%;

$ eutectic ! @ 182°C = 86-74 = 12% 9-30

9.5.3 Alloys Without Eutectic Reactions

• Only alloys with compositions exceeding either maximum

solid solubility limits at the eutectic temperature; i.e. 18.3

wt% Sn < C0 < 97.8 wt% Sn, undergo the eutectic reaction

during solidification.

• Alloys within the solubility limit at room temperature form

a single-phase solid solution, with microstructure and

solidification characteristics identical to the isomorphous

alloys (Fig. 9.5-7).

Fig. 9.5-7 Solidification in an alloy of composition C1, which lies within the room-temperature solubility limit This alloy does not undergo a eutectic reaction.

9-31

• Alloys exceeding the solubility limit at room-temperature,

but within the maximum solubility limit at the eutectic

temperature forms a two-phase microstructure that has a

different morphology (size/shape/distribution) from the

two-phase microstructure containing the eutectic.

Fig. 9.5-8 Solidification and precipitation in an alloy of composition C2. This alloy does not undergo a eutectic reaction.

9-32

Consider the cooling of an alloy of composition C2 wt% Sn

(Fig. 9.5-8):

• Point d: 100% liquid L

Phase: L (C2%Sn = overall composition)

• Point e: ! solidifies and increases in proportion as the alloy

cools; the compositions of L and ! increase with

decreasing temperature, following the liquidus

and solidus respectively

Phases: L + !

• Point f: 100% solid ! (C2%Sn = overall composition)

• Point g: solid solubility of ! is exceeded upon crossing the

solvus; " particles precipitate within !. " does not

form lamellae with !, but is dispersed within a

matrix of !

100% solid (overall composition = C2%Sn)

Phases: ! + " (non-lamellae dispersion)

• Because the solubility of ! drops with temperature, the

mass fraction of " increases, with the " precipitates

growing in size as the alloy cools. The compositions of !

and " will change with decreasing temperature, following

their respective solvus.

9-33

9.5.4 Mechanical Properties of Eutectic Alloys

• The boundary between the two phases (also known as

interphase boundary) is an obstacle to dislocation motion –

the greater the number of boundaries, the greater the

strengthening effect.

• The maximum number of interphase boundaries in a

slowly solidified eutectic alloy occurs when the

microstructure is wholly eutectic; thus, the larger the

amount of eutectic, the stronger the alloy (Fig. 9.5-9).

Fig. 9.5-9 The effect of composition and strengthening mechanism

on the strength of lead-tin alloys.

9-34

9-35

9.6 OTHER BINARY SYSTEMS

9.6.1 Invariant Reactions in Binary Systems

Fig. 9.6-1 Some important three-phase reactions in binary systems. All invariant reactions are reversible if cooling/heating is carried out under equilibrium conditions.

9.6.2 Complex Binary Phase Diagrams

• The solid solutions ! and # are called terminal solid

solutions because they appear at the ends (terminus) of

the phase diagram (Fig. 9.6-2).

• The components in a binary system may react chemically

to form intermediate phases, which are single phases

formed at alloy compositions away from the ends of the

phase diagram. 9-36

Fig. 9.6-2 The Cu-Zn phase diagram.

• Intermediate solid solutions exist over a range of

compositions; i.e., ", $, %, & (Fig. 9.6-2). Intermediate com-

pounds have fixed compositions, shown as straight lines

on the phase diagram; e.g. Mg2Ni and MgNi2 (Fig. 9.6-3).

Fig. 9.6-3 The Mg-Ni phase diagram.

9-37

9.7 IRON-IRON CARBIDE (FE-FE3C) SYSTEM

Fig. 9.7-1 Fe-Fe3C phase diagram.

• This system forms the basis for steels and cast irons.

• Fe3C is an intermediate compound of iron and carbon, and

is represented by a straight line at the right terminus of the

phase diagram.

• Although Fe3C forms one terminus of the phase diagram,

by convention and for convenience, the composition is still

measured in terms of wt% C; 6.67 wt% C = 100 wt% Fe3C.

9-38

• Peritectic reaction at 1493°C (important for casting):

% + L heating! " " " " "

cooling" # " " " " " " " $

• Eutectic reaction at 1147°C (important for cast irons):

L heating! " " " " "

cooling" # " " " " " " " $ + Fe3C

• Eutectoid reaction at 727°C (important for the heat

treatment of steels):

$ heating! " " " " "

cooling" # " " " " " " " ! + Fe3C

• Ferrite (!): solid solution of carbon in BCC iron (max.

solubility = 0.022 wt% C at 727°C); soft and ductile.

• Austenite ($): solid solution of carbon in FCC iron (max.

solubility = 2.14 wt% C at 1147°C); tough and ductile.

• Cementite (Fe3C): intermediate compound of 4 C and 12

Fe atoms (6.67 wt%C); orthorhombic crystal structure with

metallic-covalent bonding, hard and brittle.

• Pearlite: 2-phase mixture of alternating layers (lamellae) of

ferrite and cementite (! + Fe3C) formed simultaneously

during the eutectoid reaction.

• The terms ferrite, austenite, cementite and pearlite are

used in the Fe-Fe3C system only.

9-39

9.7.1 Transformations in Eutectoid Steels

Consider the cooling of a eutectoid steel (0.76 wt% C)

from 800°C (Fig. 9.7-2).

Fig. 9.7-2 The development of microstructure in a eutectoid steel.

• Point a: 100% $ (0.76%C)

• Eutectoid point: eutectoid reaction:

$ (0.76%C) 727°C! " ! ! ! ! ! (0.022%C) + Fe3C (6.67%C)

• Point b: 100% pearlite

eutectoid ! (0.022%C) + Fe3C (6.67%C) lamellae

9-40

• During the eutectoid reaction, C atoms must be

redistributed by diffusion such that $ (0.76%C) is

transformed to low-C ! (0.022%C) and high-C Fe3C

(6.67%C) simultaneously.

• Alternating layers (lamellae) of ! and Fe3C are formed

because such a structure requires C atoms to diffuse only

over relatively short distances (Figs. 9.7-3 and 9.7-4).

Fig. 9.7-3 Schematic

representation of pearlite formation (arrows indicate

direction of C diffusion).

Fig. 9.7-4 Pearlite in

eutectoid steel, consisting of alternating layers of #

(light phase) and Fe3C (thin layers that look dark).

9-41

9.7.2 Transformations in Hypoeutectoid Steels

• Consider the cooling of a hypoeutectoid steel of

composition C0 (< 0.76 wt% C) from 875°C.

• Point c: all $ (compositionC0)

• Point d: proeutectoid !

forms along $ boundaries

and increases in pro-

portion as the steel

cools; the compositions

of ! and $ increase with

decreasing temperature,

according to the solvus.

Phases: ! (0.022%C) +

$ (0.3%C)

• Point e: Phases: ! (0.022%C) + $ (0.76%C) • Just below the eutectoid temperature, the remaining $

(0.76%C) undergoes the eutectoid reaction and transforms

to the eutectoid ! + Fe3C pearlite. • Point f: Phases: proeutectoid ! (0.022%C) +

eutectoid ! (0.022%C) +

Fe3C (6.67%C) }pearlite

9-42

9.7.3 Transformations in Hypereutectoid Steels

• Consider the cooling of a hypereutectoid steel of

composition C1 (> 0.76 wt% C) from 915°C.

• Point g: all $ (composition C1)

• Point h: proeutectoid Fe3C

forms along $ boundaries

and increases in

proportion as the steel

cools; the composition of

Fe3C remains constant but

that of $ decreases with

temperature, according to

the solvus.

Phases: $ (1.0%C) +

Fe3C (6.67%C)

• Just below the eutectoid temperature, the remaining $

(0.76%C) undergoes the eutectoid reaction and transforms to the eutectoid ! + Fe3C pearlite.

• Point i: Phases: proeutectoid Fe3C (6.67%C) +

eutectoid ! (0.022%C) +

Fe3C (6.67%C) }pearlite

9-43

9.7.4 Mechanical Properties of Steels

• The interphase boundary between ferrite and cementite is

an obstacle to dislocation movement – the greater the

number of boundaries, the greater the strengthening.

• In addition, cementite, which contains complex metallic-

covalent bonding, does not undergo plastic deformation at

room temperatures, such that dislocation movement can

occur only within the ferrite phase. Therefore, the more

cementite a steel contains (i.e. the higher the carbon

content), the higher its strength (Fig. 9.7-7).

Fig. 9.7-7 (a) Variation of strength and hardness, (b) ductility and impact energy

with carbon content for plain carbon steels with fine pearlite structure.