Post on 11-Jan-2016
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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.