Chapter 9 phase diagrams 1

Phase Diagrams
Chapter reading 9
 Definitions and basic concepts

 Phases and microstructure
 Phase equilibria
 One component phase diagrams
 Binary phase diagrams
 The iron-carbon system (steel and cast iron)

MSE-211-Engineering Materials

1

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Phase Diagrams
Background/Importance
Many material systems and alloy systems exist in more than one
phases depending on the conditions of temperature, pressure and
compositions. Each phase will have different microstructure which
is related to the mechanical properties. The development of
microstructure is related to the characteristics of phase diagrams.
Thus the knowledge and understanding of the phase diagrams is very
important for engineers . Proper knowledge and understanding of
phase diagrams will lead to design and control of heating procedures
for developing the required microstructure and properties.


2

Definitions and basic concepts
Component - chemically recognizable species (Fe and C in

carbon steel, H2O and NaCl in salted water). A binary
alloy contains two components, a ternary alloy – three, etc.
The chemical elements which make up the alloy
Solvent : primary atomic species. Host atoms
Solute : the impurities. Normally the minor component
System : Specific body of material under consideration
(e.g., a ladle of molten steel)


3

Solubility limit: Maximum concentration of solute
atoms that may dissolve in the solvent to form a solid
solution. Example : water-sugar solution
Sugar/Water Phase Diagram
Solubility
Limit

80

What is the solubility limit for
sugar in water at 20 ºC
Ans: 65 wt% sugar

L
(liquid)

60

L

40

(liquid solution
i.e., syrup)

0

+
S
(solid
sugar)

At 20ºC, if C < 65 wt% sugar: syrup
At 20ºC, if C > 65 wt% sugar:
syrup + sugar

20
40
60 65 80
100
C = Composition (wt% sugar)

Sugar

20

Water

Temperature (ºC)

10 0


4

Phase (solid, liquid, gas): a homogeneous portion of a
system that has uniform physical and chemical
characteristics.
Two distinct phases in a system have distinct physical
or chemical characteristics (e.g. water and ice) and
are separated from each other by definite phase
boundaries. A phase may contain one or more
components.
A single-phase system is called homogeneous,
Systems with two or more phases are mixtures or
heterogeneous systems.


5

Effect of Temperature & Composition
• Altering T can change # of phases: path A to B.
• Altering C can change # of phases: path B to D.
B (100ºC,C = 70) D (100ºC,C = 90)
1 phase

watersugar
system

Adapted from Fig. 9.1,
Callister & Rethwisch 8e.

Temperature (ºC)

100

L

80

60
40

(liquid)

L

+
S

i.e., syrup)

(solid
sugar)

(liquid solution

20
00

2 phases

A (20ºC,C = 70)
2 phases

20
40
60 70 80
100
C = Composition (wt% sugar)

6

Phase Equilibrium
Equilibrium
A system is at equilibrium if its free energy is at a minimum
under some specified combination of temperature, pressure,
and composition. On a macroscopic sense this means the
system is stable and its characteristics donot change over time.
Under conditions of a constant temperature and pressure
and composition, the direction of any spontaneous
change is toward a lower free energy.


7

Phase Equilibrium
Metastable state: Equilibrium is the state that is achieved given sufficient
time. It is often the case in solid systems that they never achieve complete
equilibrium state because the rate to approach equilibrium is extremely
slow; such a system is said to be in a non-equilibrium or metastable state.
A system at a metastable state is trapped
in a local minimum of free energy that is
not the global one.
A metastable state or microstructure may persist
indefinitely, experiencing
only extremely slight and almost negligible changes as
time progresses. Often, metastable structures are of more
practical significance than equilibrium ones.


8

Phase Diagrams
Phase Diagram–a graphic representation showing the phase
or phases present for a given composition, temperature and
pressure. Also termed equilibrium diagrams.

A phase diagrams show what phases exist at equilibrium and
what phase transformations we can expect when we change
one of the parameters of the system (T, P, composition).
We will discuss phase diagrams for binary alloys only and
will assume pressure to be constant at one atmosphere.
Phase diagrams for materials with more than two components
are complex and difficult to represent

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ONE-COMPONENT (OR UNARY)
PHASE DIAGRAMS

Example of water: Three different phases. Phase boundaries: aO, bO, cO.
The two phases on either side of the boundary are in equilibrium.

For
details
Read page
86-87


10

Unary Systems
Single component system

Consider 2 elemental metals separately:
Cu has melting T = 1085oC
(at standard P = 1 atm)
Ni has melting T = 1453oC

What happens when Cu and Ni
are mixed?

11

Binary Isomorphous Systems
Binary: 2 components
Isomorphous system - complete solid solubility of the
two components (both in the liquid and solid phases).
3 different phase fields
Liquid(L)
Solid + liquid(L + α)

Solid(α)
Liquidus line separates liquid
from liquid + solid

Solidus line separates solid from
liquid + solid

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Example of isomorphous system: Cu-Ni


13

In one-component system melting occurs at a well-defined
melting temperature. In multi-component systems melting
occurs over the range of temperatures, between the solidus
and liquidus lines. Solid and liquid phases are in
equilibrium in this temperature range.
50/50 wt % composition in Cu-Ni melting begins at 1280 C


14



15

Interpretation of Phase Diagrams
From binary phase diagrams we can determine

(1) The phases that are present
(2) The composition of phases
(3) The percentage and fraction of the phases


16

Determination of Phases Present
• Rule 1: If we know T and Co, then we know:
-- which phase(s) is (are) present.

A(1100ºC, 60 wt% Ni):
1 phase: a

B (1250ºC, 35 wt% Ni):
2 phases: L + a

1600

L (liquid)
B (1250ºC,35)

• Examples:

T(ºC)
1500
1400
1300

Cu-Ni
phase
diagram

a

1200
A(1100ºC,60)

1100
1000

0

20

40


60

80

100

wt% Ni
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Determination of Phase Composition
Finding the composition in a two phase region:

1. Locate composition and temperature in diagram
2. In two phase region draw the tie line or isotherm
3. Note intersection with phase boundaries. Read
compositions at the intersections.
The liquid and solid phases have these compositions.


18

Determination of Phase Composition

Point B: T=1250 oC ,35 wt% Ni–
65 wt% Cu
Composition of Liquid phase:
CL=31.5wt% Ni –68.5%Cu

Composition of α phase:
Cα=42.5wt% Ni‐57.5wt%Cu

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Determination of Phase Amounts
Phase weight fractions or %

For single phase weight fraction of a phase is 1 or 100%.
For two phase region Lever Rule
 Locate composition and temperature in diagram
 Construct a tie line in two phase region at alloy temperature

 Fraction of a phase is determined by taking the length of the
tie line from the overall alloy composition to the phase
boundary for the other phase, and dividing by the total length
of tie line.

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Determination of Phase Amounts

Mass Fraction

𝐶 𝑜 = 35 𝑤𝑡. %, 𝐶 𝐿 = 31.5 𝑤𝑡. %
𝐶 𝛼 = 42.5𝑤𝑡. %,
𝑊 𝐿 = 𝐶 𝛼 − 𝐶 𝑜 𝐶 𝛼 − 𝐶 𝐿 = 0.68

𝑊𝛼 = 𝐶 𝑜 − 𝐶 𝐿 𝐶 𝛼 − 𝐶 𝐿 = 0.32

21

Development of microstructure in isomorphous alloys
Equilibrium Cooling: Very slow cooling to allow phase equilibrium
to be maintained during the cooling process.


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23

Mechanical Properties of Isomorphous Alloys
Solid solution strengthening

-- Ductility (%EL)

400
TS for
pure Ni

300
TS for pure Cu
200
0 20 40
Cu

60 80 100
Ni

Composition, wt% Ni

Elongation (%EL)

Tensile Strength (MPa)

-- Tensile strength (TS)

60

%EL for pure Cu
%EL for
pure Ni

50

40
30
20
0 20
Cu


40

60

80 100
Ni

Composition, wt% Ni

2424

Binary Eutectic Systems
Eutectic Systems
In a eutectic reaction, when a liquid solution of fixed composition, soldifies
at a constant temperature, forms a mixture of two or more solid phases
without an intermediate pasty stage. This process reverses on heating.
Systems exhibiting this behavior are known as “Eutectic systems”.

In a eutectic system there is always a specific alloy , known as eutectic
composition, that freezes at a lower temperature than all other compositions.
At ‘eutectic temperature’, two solids form simultaneously from a single
liquid phase. The eutectic temperature and composition determine a
point on the phase diagram known as ‘eutectic point’.

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Three single phase regions
(α - solid solution of Ag in Cu
matrix,
β = solid solution of Cu in Ag
marix, L - liquid)

•Three two-phase regions (α + L, β +L, α +β)

•Solvus line separates one solid solution from a
mixture of
solid solutions. The Solvus line shows limit of
solubility

26


Eutectic or invariant point - Liquid and two solid
phases co-exist in equilibrium at the eutectic composition
CE and the eutectic temperature TE.
Eutectic isotherm - the horizontal solidus line at TE.


27


Cu-Ag
system

T(ºC)

Ex.: Cu-Ag system

1200

L (liquid)
1000

• TE : No liquid below TE
• CE : Composition at
temperature TE

• Eutectic reaction
L(CE)

L(71.9 wt% Ag)

TE 800

a

8.0

71.9 91.2

a+b

400

0

heating

L +b b

779ºC

600

a(CaE) + b(CbE) 200

cooling

L+a

20

40

60 CE 80

100

C , wt% Ag
a(8.0 wt% Ag) + b(91.2 wt% Ag)

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General Rules
Eutectic reaction – transition between liquid and mixture of
two solid phases, α + β at eutectic concentration CE.
• The melting point of the eutectic alloy is lower than that
of the components (eutectic = easy to melt in Greek).
• At most two phases can be in equilibrium within a phase
field.
• Three phases (L, α, β) may be in equilibrium only at a few
points along the eutectic isotherm.
• Single-phase regions are separated by 2-phase regions.


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On occasion, low-melting-temperature alloys are prepared having
near-eutectic compositions. A familiar example is the 60–40 solder,
containing 60 wt% Sn and 40 wt% Pb. Completely melted at 185 C.
Attractive as low temperature solder.


30


Compositions and relative amounts of phases are determined from
the same tie lines and lever rule, as for isomorphous alloys.


31

For a 40 wt% Sn-60 wt% Pb alloy at 150ºC, determine:
-- the phases present
the phase compositions


32

Eutectic, Eutectoid and Pertectic Reactions
• Eutectic - liquid transforms to two solid phases
L cool a + b
(For Pb-Sn, 183ºC, 61.9 wt% Sn)
heat

• Eutectoid – one solid phase transforms to two other
solid phases
intermetallic compound
- cementite
S2
S1+S3
 cool a + Fe3C (For Fe-C, 727ºC, 0.76 wt% C)
heat

• Peritectic - liquid and one solid phase transform to a
second solid phase
S1 + L
S2
 +L

cool
heat



(For Fe-C, 1493ºC, 0.16 wt% C)

33

Eutectoid & Peritectic
Cu-Zn Phase diagram

Eutectoid transformation 

Peritectic transformation  + L

+



Adapted from Fig. 9.21,
Callister & Rethwisch 8e.

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Iron-Iron Carbide Phase Diagram


35

Phases in Fe–Fe3C Phase Diagram

α-ferrite - solid solution of C in BCC Fe
• Stable form of iron at room temperature.
• The maximum solubility of C is 0.022 wt% at 727 °C
• Transforms to FCC γ-austenite at 912 °C
γ-austenite - solid solution of C in FCC Fe
• The maximum solubility of C is 2.14 wt % at 1147 °C .
• Transforms to BCC δ-ferrite at 1395 °C
• Is not stable below the eutectic temperature
(727 ° C) unless cooled rapidly


36

Phases in Fe–Fe3C Phase Diagram

δ-ferrite solid solution of C in BCC Fe
• The same structure as α-ferrite
• Stable only at high T, above 1394 °C
• Melts at 1538 °C

Fe3C (iron carbide or cementite)

Interstitial solution of Fe in C with maximum solubility
of 6.67 wt% C. It is satble at room temperature.
Crystalline structure is orthorhombic.
Fe-C liquid solution

37

A few comments on Fe–Fe3C system
C is an interstitial impurity in Fe. It forms a solid solution
with α, γ, δ phases of iron
Maximum solubility in BCC α-ferrite is limited (max.
0.022 wt% at 727 °C) - BCC has relatively small interstitial
positions
Maximum solubility in FCC austenite is 2.14 wt% at 1147
°C - FCC has larger interstitial positions.
Mechanical properties: Cementite is very hard and brittle
-can strengthen steels. Ferrite and austenite are relatively
soft phases.
Magnetic properties: α -ferrite is magnetic below 768
°C, austenite is non-magnetic.

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Classification. Three types of ferrous alloys:

• Iron: less than 0.008 wt % C in α−ferrite at room T
• Steels: 0.008 - 2.14 wt % C (usually < 1 wt % )
α-ferrite + Fe3C at room T
• Cast iron: 2.14 - 6.7 wt % (usually < 4.5 wt %)


39


40

Development of Microstructure in
Iron - Carbon alloys
Microstructure depends on composition (carbon
content) and heat treatment. Here we consider slow cooling in
which equilibrium is maintained

Microstructure of eutectoid
steel


41

Development of Microstructure in
Iron - Carbon alloys
Microstructure of eutectoid steel

When alloy of eutectoid composition (0.76 wt % C) is cooled
slowly it forms perlite, a lamellar or layered structure of two
phases: α-ferrite and cementite (Fe3C).

Mechanically, pearlite has properties intermediate to soft,
ductile ferrite and hard, brittle cementite

In the micrograph, the dark areas are
Fe3C layers, the light phase is αferrite


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At room temperature steel is Ferrite with patches of Pearlite.


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