CHAPTER 10: PHASE DIAGRAMS
ISSUES TO ADDRESS...
• When we combine two elements...
what equilibrium state do we get?
• In particular, if we specify...
--a composition (e.g., wt%Cu - wt%Ni), and
--a temperature (T)
then...
How many phases do we get?
What is the composition of each phase?
How much of each phase do we get?
1
Phase Diagrams
• Introduction and Motivation
– Use Phase Diagrams to choose/design heating cycles
for forming metal alloys
– Phase Diagrams represent equilibrium states, but can
also be used to guide the formation of materials under
non-equilibrium conditions
Phase Diagrams
• Phase diagrams
– You are used to thinking about phase diagrams in vapor-liquid
equilibrium
– In this course we will use phase diagrams to describe and
understand structure in metal alloys
– Why? Structure  Properties
• We will:
1.
2.
3.
4.
Learn some terminology
Learn how to interpret phase diagrams
Study some “simple” binary phase diagrams
Learn how structure evolves upon cooling
Phase Diagrams
• Phase diagrams – definitions
– Component – pure species
– System (more than one element)
• Book also uses solute/solvent nomenclature
(usually for binary mixtures)
• Solubility limit – maximum amount of solute you
can add to a solvent before the solute does not
dissolve into the solvent
– This often depends on temperature (Fig 10.1)
THE SOLUBILITY LIMIT
• Solubility Limit:
Max concentration for
which only a solution
occurs.
• Ex: Phase Diagram:
Water-Sugar System
Question: What is the
solubility limit at 20C?
Answer: 65wt% sugar.
If Co < 65wt% sugar: solution
If Co > 65wt% sugar: syrup + sugar.
Adapted from Fig. 9.1,
Callister 6e.
• Solubility limit increases with T:
e.g., if T = 100C, solubility limit = 80wt% sugar.
2
COMPONENTS AND PHASES
• Components:
The elements or compounds which are mixed initially
(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regions
that result (e.g., a and b).
AluminumCopper
Alloy
Adapted from
Fig. 9.0,
Callister 3e.
3
Phase Diagrams
• Phases
– Phase – a homogeneous portion of a system that has uniform
physical & chemical properties (i.e. composition)
– Again – you are familiar with two-phase systems (pure material –
VLE)
– Each phase may have different physical properties and same
chemical composition (example water + ice; iron FCC+BCC).
– In other cases, each phase may have different physical
properties and different chemical composition (example VLE
binary mixture)
EFFECT OF T & COMPOSITION (Co)
• Changing T can change # of phases: path A to B.
• Changing Co can change # of phases: path B to D.
• watersugar
system
Adapted from
Fig. 9.1,
Callister 6e.
4
Phase Diagrams
• Phase Equilibrium (10.5)
– Know all about this – a system with multiple phases is at
equilibrium (for a pure compound) when
• The T, P, and Gibbs free energy of each phase (chemical potential)
are the same
– Why does this matter? The phase diagrams of many simple
metals alloys are known
• However when real materials are processed an equilibrium state is
not reached (why would that be the case?)
PHASE DIAGRAMS
• Tell us about phases as function of T, Co, P.
• For this course:
--binary systems: just 2 components.
--independent variables: T and Co (P = 1atm is always used).
• Phase
Diagram
for Cu-Ni
system
Adapted from Fig. 9.2(a), Callister 6e.
(Fig. 9.2(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P.
Nash (Ed.), ASM International,
Materials Park, OH (1991).
5
Phase Diagrams
• Binary Isomorphous
Systems
– Simplest place to start – two
metals that are completely
soluble in one another (e.g.
Cu – Ni)
– Three regions in the
diagram – pure liquid, pure
solid (a – phase), and a
coexistence region
Phase Diagrams
• Binary Isomorphous
Systems
– How to read this thing
• Far left – pure copper, far
right – pure nickel
• Above the “liquidus” line a
one phase liquid is obtained,
below the “solidus” line a one
phase solid is obtained
– In between these lines there
is a two-phase region; a+L
• What phases are present at
point B and what are their
compositions?
• Tie lines and lever rule
Phase Diagrams
• Binary Isomorphous
Systems
– Point B – a+liquid phase
– Phase compositions – use tie
line
• Line parallel to x-axis drawn from
the point of interest (here B) to
the solidus and liquidus lines
• Draw vertical lines to x-axis from
the intercepts with the solidus,
liquidus lines
• Where green lines intercept the xaxis gives the composition of the
different phases
Phase Diagrams
• Binary Isomorphous
Systems
– Point B – a+liquid phase
– Now I know the phase
compositions – how much of
each phase is present?
– Use the inverse lever rule
S
WL 
RS
Or in words, the weight fraction of one phase is
determined by taking the length of tie line from the
overall alloy composition to the phase boundary for the
other phase, and dividing it both the total length of the
tie line
Phase Diagrams
• Binary Isomorphous
Systems
B
WL 
 0.45
A B
Wa  0.55
Liquid
1350
a+L
T, Kelvin
– Example: what is the
composition and phase
fractions for point C shown in
the Figure?
1400
C
1300

A
1250
B
a
1200
1150
20
25
30
35
40
45 50
Weight percent A
55
60
CL ~ 35.5 wt% A
Ca ~ 53.5 wt% A
Aside: pp 366-368, volume fractions, etc..
PHASE DIAGRAMS:
# and types of phases
• Rule 1: If we know T and Co, then we know:
--the # and types of phases present.
• Examples:
Cu-Ni
phase
diagram
Adapted from Fig. 9.2(a), Callister 6e.
(Fig. 9.2(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P.
Nash (Ed.), ASM International,
Materials Park, OH, 1991).
6
PHASE DIAGRAMS: composition of
phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
• Examples:
Cu-Ni
system
Adapted from Fig. 9.2(b), Callister 6e.
(Fig. 9.2(b) is adapted from Phase Diagrams
of Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
7
PHASE DIAGRAMS:
weight fractions of phases
• Rule 3: If we know T and Co, then we know:
--the amount of each phase (given in wt%).
• Examples:
Cu-Ni
system
S
43  35
 73wt %
WL   
R S 43  32
R
Wa  
R S
= 27wt%
Adapted from Fig. 9.2(b), Callister 6e.
(Fig. 9.2(b) is adapted from Phase Diagrams
of Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
8
THE LEVER RULE: A PROOF
• Sum of weight fractions: WL  Wa  1
• Conservation of mass (Ni): Co  WL CL  WaCa
• Combine above equations:
• A geometric interpretation:
moment equilibrium:
WLR  WaS
1 Wa
solving gives Lever Rule
9
EX: COOLING IN A Cu-Ni BINARY
• Phase diagram:
Cu-Ni system.
Cu-Ni
system
• System is:
--binary
i.e., 2 components:
Cu and Ni.
--isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100wt% Ni.
• Consider
Co = 35wt%Ni.
Adapted from Fig. 9.3,
Callister 6e.
10
CORED VS EQUILIBRIUM
PHASES
• Ca changes as we solidify.
• Cu-Ni case: First a to solidify has Ca = 46wt%Ni.
Last a to solidify has Ca = 35wt%Ni.
• Fast rate of cooling:
Cored structure
• Slow rate of cooling:
Equilibrium structure
11
Phase Diagrams
• Microstructure
development in
isomorphous
alloys
– How does structure
evolve in the solid
alloy as it is cooled
– Initial analysis:
assume cooling is
sufficiently slow that
phase equilibrium is
maintained
– Go from points a e
as you cool
Phase Diagrams
• Nonequilibrium
cooling
– What happens
during “real”
cooling
conditions?
– Much more
complicated
now
• Why solid
phases
cannot reequilibrate as
T is lowered
• See
segregation
within the
grains
MECHANICAL PROPERTIES: Cu-Ni System
• Effect of solid solution strengthening
on:
--Tensile strength (TS)
Adapted from Fig. 9.5(a), Callister 6e.
--Peak as a function of Co
--Ductility (%EL,%AR)
Adapted from Fig. 9.5(b), Callister 6e.
--Min. as a function of Co
Tensile strength: maximum stretching force that a material can stand
Ductility: capacity of being molded or shaped without breaking 12
BINARY-EUTECTIC SYSTEMS
2 components
has a special composition
with a min. melting T.
Cu-Ag
system
Adapted from Fig. 9.6,
Callister 6e. (Fig. 9.6 adapted
from Binary Phase Diagrams, 2nd ed., Vol. 1, T.B.
Massalski (Editor-in-Chief), ASM International,
Materials Park, OH, 1990.)
13
• Binary Eutectic mixtures
– These are another very common class of bimetallic alloys
– Two metals that are not totally miscible (e.g. copper-silver)
• Can only dissolve about 8 wt% of each metal into one another
• Now have two different “pure” solid metal phases (a and b)
EX: Pb-Sn EUTECTIC SYSTEM (1)
• For a 40wt%Sn-60wt%Pb alloy at 150C, find...
--the phases present:
a+b
--the compositions of
the phases:
Pb-Sn
system
Adapted from Fig. 9.7,
Callister 6e. (Fig. 9.7 adapted
from Binary Phase Diagrams, 2nd ed., Vol. 3, T.B.
Massalski (Editor-in-Chief), ASM International,
Materials Park, OH, 1990.)
14
EX: Pb-Sn EUTECTIC SYSTEM (2)
• For a 40wt%Sn-60wt%Pb alloy at 150C, find...
--the phases present: a + b
--the compositions of
the phases:
Ca = 11wt%Sn
Cb = 99wt%Sn
--the relative amounts
of each phase:
Pb-Sn
system
Adapted from Fig. 9.7,
Callister 6e. (Fig. 9.7 adapted
from Binary Phase Diagrams, 2nd ed., Vol. 3, T.B.
Massalski (Editor-in-Chief), ASM International,
Materials Park, OH, 1990.)
15
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-I
• Co < 2wt%Sn
• Result:
--polycrystal of a grains.
Adapted from Fig. 9.9,
Callister 6e.
16
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-II
• 2wt%Sn < Co < 18.3wt%Sn
• Result:
--a polycrystal with fine
b crystals.
Pb-Sn
system
Adapted from Fig. 9.10,
Callister 6e.
17
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-III
• Co = CE
• Result: Eutectic microstructure
Lead-rich α-solid soln (dark)
+ tin-rich β-solid soln (light)
Lamellae structure
--alternating layers of a and b crystals.
Pb-Sn
system
Adapted from Fig. 9.12, Callister 6e.
(Fig. 9.12 from Metals Handbook, Vol.
9, 9th ed., Metallography and
Microstructures, American Society
for Metals, Materials Park, OH, 1985.)
Adapted from Fig. 9.11,
Callister 6e.
18
MICROSTRUCTURES
IN EUTECTIC SYSTEMS-IV
• 18.3wt%Sn < Co < 61.9wt%Sn
• Result: a crystals and a eutectic microstructure
Pb-Sn
system
Adapted from Fig. 9.14,
Callister 6e.
19
Phase Diagrams
• Binary Eutectic mixtures
– Point E is something new – this is called the invariant (or
eutectic) point
– What happens when you change temperature at the invariant
point?
cooling, heating
LCE 
a CaE   b CbE 
This is called a eutectic reaction
Upon cooling it is similar to
solidification, however now two
phases are formed
Line BG is also referred to as the
eutectic isotherm
Phase Diagrams
• Microstructure development in
Eutectic Alloys
– Case 1 – low tin content (Pb-Sn alloy)
– Looks pretty similar to before (what is
different?)
– Again, assuming slow cooling
Phase Diagrams
• Microstructure development in Eutectic
Alloys
– Case 2 – tin content above solid-solution
max. tin loading
– More going on here
– Notice b phase formation at lower T
– Equilibrium cooling
Phase Diagrams
• Microstructure development in Eutectic Alloys
– Case 3 – Solidification at the eutectic composition
– Go through eutectic point at 183 C
cooling, heating
L61.9wt %Sn 
a 18.3wt %Sn  b 97.8wt %Sn
• Microstructure development in Eutectic Alloys
– Case 4 – Not eutectic composition, but cross eutectic
isotherm
– Two different types of a structural domains – why?
Eutectic microconstituents
50-50 wt % Pb-Sn alloy
Primary α (large dark regions)
+ lamellar eutectic structure
(lead-rich α+ tin-rich β)
Phase Diagrams
• Example – calculation of phases/phase fractions in a
binary eutectic alloy
– Consider the phase diagram below – what are the phase
fractions and compositions at C4’ at the eutectic isotherm?
You know how to solve this, it is just a bit
more involved than the last example:
Phases: a, b
Microstructures: Eutectic (a,b), “primary” a
Why no “primary” b? – C4’ is fixed, and so
came down through the a+L field
Fractions we need:
Fraction of eutectic
Fraction of a – both in the eutectic and
“primary” phase
Fraction of b
Phase Diagrams
• Example – calculation of phases/phase fractions in a
binary eutectic alloy
– Consider the phase diagram below – what are the phase
fractions and compositions at C4’ at the eutectic isotherm?
Eutectic fraction
We  WL 
P
C  18.3
 4'
P  Q 61.9  18.3
Primary a fraction
Wa ' 
Q
61.9  C4'

P  Q 61.9  18.3
Total a fraction
Wa 
QR
97.8  C4'

P  Q  R 97.8  18.3
Total b fraction
Wb 
P
C  18.3
 4'
P  Q  R 97.8  18.3
Phase Diagrams
• Example – calculation of phases/phase fractions in a
binary eutectic alloy
– Consider the phase diagram below – what are the phase
fractions and compositions at C4’ at the eutectic isotherm?
you know C4’ !
(~32.5 wt% Sn)
Eutectic fraction
We  WL 
P
C  18.3
 4'
= 0.33
P  Q 61.9  18.3
Primary a fraction
Wa ' 
Q
61.9  C4'
= 0.67

P  Q 61.9  18.3
Total a fraction
Wa 
QR
97.8  C4'

= 0.82
P  Q  R 97.8  18.3
Total b fraction
Wb 
P
C  18.3
 4'
= 0.18
P  Q  R 97.8  18.3
• Example – calculation of phases/phase fractions in a binary
eutectic alloy
– Consider the phase diagram below – what are the phase
fractions and compositions at C4’ at the eutectic isotherm?
Couple of points
The eutectic and primary a fractions tell you how
much of the different microstructures are present
The a and b fractions tell you how much of each
phase are present
At the eutectic point there are three phases (a, b,
and the eutectic) present.
At the left of the Eutectic point, on the eutectic
isotherm, there are 2 phases (primary α and
eutectic)
There are now also different microstructures –
here two types of a phases!
The a phase in the eutectic is 18.3wt% Sn, b
phase in the eutectic is 97.8wt% Sn!
At the right of the Eutectic point, on the eutectic
isotherm, there are 2 phases (primary β and
eutectic)
Phase Diagrams
• Mixtures with intermediate phases/compounds
– Binary isomorphous and eutectic mixtures are very simple
• Have only two solid phases – these are often referred to as
terminal solid solutions since they are in the “A” or “B” rich
regions of the phase diagram
– Many other alloys form intermediate solid solutions at other
compositions besides the extremities
– Good example – copper/zinc system
•
•
•
•
Six different solid solutions (diagram next page)
This is more representative of real solids
Important point – still only single- or two-phase regions present
Commercial brass – 70/30 Cu/Zn, single a-phase
Phase Diagrams
• Mixtures with intermediate phases/compounds
– Good example – copper/zinc system
Phase Diagrams
• Mixtures with intermediate phases/compounds
– Intermetallic compounds – in some systems discrete
compounds (i.e. well-defined stoichiometries) form instead of
solid solutions
– Example Mg2Pb
Phase Diagrams
• Eutectoid and peritectic reactions
– Besides the eutectic point, other invariant points involving
three phases can be found in binary alloy systems
– Go back to Zn-Cu system
• One solid phase going to two solid phases -- eutectoid
cooling, heating
 
   
• Eutectoid isotherm
• Difference with eutectic?
Eutectic: 1 liquid phase  2 solid phases
Eutectoid: 1 solid phase  2 solid phases
Phase Diagrams
• Eutectoid and peritectic reactions
• One solid phase going to one liquid phase and one
solid phase -- peritectic
cooling, heating
  L 
  
Important point: eutectic, eutectoid,
and peritectic are phase transitions
involving three phases
It is essentially nomenclature
Phase Diagrams
• Phase transformations
– What we have been talking about are called phase
transformations
• Congruent transformations – phase transformations in which
there is no change in composition of the phases involved
– These include melting of pure materials
– Allotropic transformations (polymorphism, example carbon
graphite-> diamond ->other forms)
• Phase transformations where the composition of the phases
involved change – incongruent transformations
– These include eutectic/eutectoid reactions, and melting of an
alloy in an isomorphous system
Phase Diagrams
• Phase transformations
– Intermediate phases are often
categorized based on whether
they melt congruently or
incongruently
– Figure below shows both –
what are examples of each?
Phase Diagrams
• Label Eutectic, Eutectoid, Peritectic points and
congruent phase transitions
Eutectic points
(~1450 C, 18 wt%V)
L  bHf + HfV2
(~1520 C, 39 wt%V)
L  HfV2 + sol. soln
Eutectoid points
(~1190 C, 6 wt%V)
bHf  aHf + HfV2
Congruent melting
(~1550 C, 36 wt%V)
L  HfV2 (cooling)
Ceramic phase diagrams
– Can observe all the same phenomena for
ceramics as you do for metals
Example: silica-alumina system
cristoballite
mullite: intermediate
compound
3Al2O32SiO2
APPLICATION: REFRACTORIES
• Need a material to use in high temperature furnaces.
• Consider Silica (SiO2) - Alumina (Al2O3) system.
• Phase diagram shows:
mullite, alumina, and crystobalite (made up of SiO2)
tetrahedra as candidate refractories.
2200
T(°C)
2000
3Al2O3-2SiO2
Liquid
(L)
1800
1400
0
alumina + L
mullite
+L
crystobalite
+L
1600
mullite
mullite
+ crystobalite
20
alumina
+
mullite
Adapted from Fig.
12.27, Callister 6e.
(Fig. 12.27 is adapted
from F.J. Klug and R.H.
Doremus, "Alumina
Silica Phase Diagram in
the Mullite Region", J.
American Ceramic
Society 70(10), p. 758,
1987.)
40
60
80
100
Composition (wt% alumina)
25
Phase Diagrams
• Ternary phase diagrams
– Can also have three-component systems
– These get messy – why?
– Hard to visualize (need 3D-plots)– See Phase program
• Something very useful – Gibbs phase rule
– After all, equilibrium phase diagrams should be governed by
thermodynamics
– Gibbs phase rule: for a system with C components, P phases
and N non-compositional variables (T and P), the number of
degrees of freedom (F) is given by:
F  C  N P
Phase Diagrams
• Gibbs phase rule
– What does this tell you? For all the phase diagrams (binary
mixtures, fixed pressure P) it says
F  C 1 P
F  3P
This is 1 because P is fixed
Now assuming a 2-component system
Ok, now what? This tells you for a binary mixture that is one phase (P = 1) that
two parameters must be specified (temperature and composition) to fix the position
of the system on the phase diagram
For two phases (P = 2) only one need be specified – if for instance T is specified
this “fixes” the composition
For three phases (P = 3) it is an invariant point (example eutectic point)
Let’s try it out…
Phase Diagrams
• Gibbs phase rule
– Our old friend the Cu-Ag
system
– Consider the a + L region
• If we fix T then we have
fixed the composition of the
two phases
• If we choose the
composition of one phase,
we have chosen the other
composition as well as the
temperature
• Iron-Carbon System
– This is a very important binary alloy system – steel!
– Turns out carbon has a fairly low solubility in iron – this has all
sorts of technological implications
a ferrite: BCC
 austenite: FCC
 ferrite: BCC
Note: diagram
–only goes to 6.7
wt% C
–– all steels/cast
iron have carbon
contents below
this
Phase Diagrams
• Iron-Carbon System
– Carbon is an interstitial impurity
in Fe
– Forms solid solutions with the a,
,  phases
– Also forms iron carbide (Fe3C)
known as cementite
– Phase diagram has features we
have seen before
• Eutectic
• Eutectoid
Phase Diagrams
• Iron-Carbon System
– Are there any eutectic points on this phase diagram?
cooling, heating
L 
   2.14 wt %C   Fe3C 6.7 wt %C 
Phase Diagrams
• Iron-Carbon System – microstructure evolution
– Pearlite formation
• When one crosses the eutectoid point
cooling, heating
 0.76wt %C  
  a 0.022wt %C   Fe3C 6.7 wt %C 
• Pearlite – alternating layers of Fe3C and a ferrite
• Why do you get this structure – phases formed
have different C contents – need C diffusion
Phase Diagrams
• Iron-Carbon System – microstructure evolution
• Hypoeutectic alloys
• Go from austenite  ferrite + cementite but go through the a   2phase region to get there
•
Note that at point d the a phase has started to
form
• It usually nucleates at grain boundaries
• As ferrite domains increase in size they
coalesce (spherical  lamellar type
domains)
• Again see pearlite type structure at f, but
now there are 2 “types” of ferrite domains
• Proeutectoid ferrite
• Eutectoid ferrite
Phase Diagrams
• Hypoeutectic alloys
• What are the relative amounts of eutectoid and proeutectoid ferrite?
– You already know how to do this – lever rule (with a twist)
Fraction of pearlite
T
Wp 
T U
Fraction of proeutectoid a
Wa ' 
U
T U
Phase Diagrams
• Hypereutectic alloys – go down in T from
other side (i.e. C-rich) of eutectoid point
• Again, note the minor phase (here Fe3C)
nucleates at the grain boundaries
• Now have two type of cementite Fe3C
– That formed before the eutectoid
(proeutectoid Fe3C)
– That formed at the eutectoid
HYPOEUTECTIC & HYPEREUTECTIC
Adapted from Fig. 9.7,
Callister 6e. (Fig. 9.7
adapted from Binary
Phase Diagrams, 2nd
ed., Vol. 3, T.B. Massalski
(Editor-in-Chief), ASM
International, Materials
Park, OH, 1990.)
(Figs. 9.12 and
9.15 from Metals
Handbook, 9th ed.,
Vol. 9,
Metallography and
Microstructures,
American Society
for Metals,
Materials Park,
OH, 1985.)
Adapted from
Fig. 9.15, Callister 6e.
Adapted from Fig. 9.12,
Callister 6e.
Adapted from Fig. 9.15,
Callister 6e. (Illustration
only)
20
IRON-CARBON (Fe-C) PHASE
DIAGRAM
(Adapted from Fig. 9.24, Callister 6e.
(Fig. 9.24 from Metals Handbook, 9th ed.,
Vol. 9, Metallography and
Microstructures, American Society for
Metals, Materials Park, OH, 1985.)
Adapted from Fig. 9.21,Callister 6e. (Fig. 9.21
adapted from Binary Alloy Phase Diagrams, 2nd ed.,
Vol. 1, T.B. Massalski (Ed.-in-Chief), ASM
International, Materials Park, OH, 1990.)
21
HYPOEUTECTOID STEEL
Adapted from Figs.
9.21 and 9.26,Callister
6e. (Fig. 9.21 adapted
from Binary Alloy
Phase Diagrams, 2nd
ed., Vol. 1, T.B.
Massalski (Ed.-inChief), ASM
International, Materials
Park, OH, 1990.)
Adapted from
Fig. 9.27,Callister
6e. (Fig. 9.27 courtesy Republic Steel Corporation.)
22
HYPEREUTECTOID STEEL
Adapted from Figs.
9.21 and 9.29,Callister
6e. (Fig. 9.21 adapted
from Binary Alloy
Phase Diagrams, 2nd
ed., Vol. 1, T.B.
Massalski (Ed.-inChief), ASM
International, Materials
Park, OH, 1990.)
Adapted from
Fig. 9.30,Callister
6e. (Fig. 9.30
copyright 1971 by United States Steel Corporation.)
23
ALLOYING STEEL WITH MORE
ELEMENTS
• Teutectoid changes:
Adapted from Fig. 9.31,Callister 6e. (Fig. 9.31
from Edgar C. Bain, Functions of the Alloying
Elements in Steel, American Society for
Metals, 1939, p. 127.)
• Ceutectoid changes:
Adapted from Fig. 9.32,Callister 6e. (Fig. 9.32
from Edgar C. Bain, Functions of the Alloying
Elements in Steel, American Society for
Metals, 1939, p. 127.)
24
SUMMARY
• Phase diagrams are useful tools to determine:
--the number and types of phases,
--the wt% of each phase,
--and the composition of each phase
for a given T and composition of the system.
• Alloying to produce a solid solution usually
--increases the tensile strength (TS)
--decreases the ductility.
• Binary eutectics and binary eutectoids allow for
a range of microstructures.
26
Example Handouts
Phase Diagrams
• Example – calculation of phases/phase fractions in a
binary eutectic alloy
– Consider the phase diagram below – what are the phase
fractions and compositions at C4’ at the eutectic isotherm?
You know how to solve this, it is just a bit
more involved than the last example:
Phases: a, b
Microstructures: Eutectic (a,b), “primary” a
Why no “primary” b? – C4’ is fixed, and so
came down through the a+L field
Fractions we need:
Fraction of eutectic
Fraction of a – both in the eutectic and
“primary” phase
Fraction of b
Phase Diagrams
• Example – calculation of phases/phase fractions in a
binary eutectic alloy
– Consider the phase diagram below – what are the phase
fractions and compositions at C4’ at the eutectic isotherm?
Eutectic fraction
Primary a fraction
Total a fraction
Total b fraction
Phase Diagrams
• Example – calculation of phases/phase fractions in a binary
eutectic alloy
– Consider the phase diagram below – what are the phase
fractions and compositions at C4’ at the eutectic isotherm?
Couple of points
The eutectic and primary a fractions tell
you how much of the different
microstructures are present
The a and b fractions tell you how much of
each phase are present
Still only two phases (a,b) present!
There are now also different
microstructures – here two types of a
phases!
The a phase in the eutectic is 18.3wt% Sn,
b phase in the eutectic is 97.8wt% Sn!
Phase Diagrams
• Label Eutectic, Eutectoid, Peritectic points and
congruent phase transitions
Eutectic points
Eutectoid points
Congruent melting
Phase Diagrams
• Binary Isomorphous
Systems
– Point B – a+liquid phase
– Phase compositions – use tie
line
• Line parallel to x-axis drawn from
the point of interest (here B) to
the solidus and liquidis lines
• Draw vertical lines to x-axis from
the intercepts with the solidus,
liquidis lines
• Where green lines intercept the xaxis gives the composition of the
different phases
Phase Diagrams
• Binary Isomorphous
Systems
– Point B – a+liquid phase
– Now I know the phase
compositions – how much of
each phase is present?
– Use the inverse lever rule
S
WL 
RS
Or in words, the weight fraction of one phase is
determined by taking the length of tie line from the
overall alloy composition to the phase boundary for the
other phase, and dividing it both the total length of the
tie line
Phase Diagrams
• Binary Isomorphous
Systems
Liquid
1350
a+L
T, Kelvin
– Example: what is the
composition and phase
fractions for point C shown in
the Figure?
1400
C
1300

1250
a
1200
1150
20
Aside: pp 366-368, volume fractions, etc..
25
30
35
40
45 50
Weight percent A
55
60
ANNOUNCEMENTS
Reading: Chapter 10
HW # 6: Due Monday March 5th
10.1; 10.5; 10.7; 10.8; 10.12; 10.13; 10.22;
10.26; 10.27; 10.32; 10.41; 10.44
0