1. Phase Diagram-Ⅰ
Dr. Aneela Wakeel
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3. Basic of phase diagrams
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Phase diagrams are an important tool in the armory of an materials scientist
 In the simplest sense a phase diagram demarcates regions of existence of
various phases.
Phase diagrams are maps*
 Phase diagrams are also referred to as “EQUILIBRIUM PHASE DIAGRAMS”
This usage requires special attention: though the term used is “Equilibrium”, in
practical terms the equilibrium is NOT GLOBAL EQUILIBRIUM but
MICROSTRUCTURAL LEVEL EQUILIBRIUM
This implies that any microstructural information overlaid on a phase diagram is
for convenience and not implied by the phase diagram.
A phase diagram - graphical representation of the combinations
of temperature, pressure, composition, or
other variables for which specific phases exist at equilibrium.

4. Basic definitions
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5. Phase
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8. Microstructure
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The properties of an alloy depend not only on proportions of the phases
but also on how they are arranged structurally at the microscopic level.
Thus, the microstructure is specified by the number of phases, their
proportions, and their arrangement in space.
This is an alloy of Fe with 4
wt.% C.
There are several phases.
The long gray regions are
flakes of graphite.
The matrix is a fine mixture
of BCC Fe and
Fe3Ccompound.
These graphite flakes give
grey iron a distinctive gray
color when it is fractured,
and they are also involved in
many of the physical
properties of this iron alloy. Phase diagrams will help us to understand
and predict the microstructures like the
one shown in this page

9. Phase equilibria
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10. Phase diagrams
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Map demarcating regions of stability of various phases.
or
Map that gives relationship between phases in equilibrium in a system
as a function of T, P and composition

11. Solubility limit
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For many alloy systems and at some specific
temperature, there is a maximum
concentration of solute atoms that may dissolve
in the solvent to form a solid solution; this is
called a solubility limit.
The addition of solute in excess of this solubility
limit results in the formation of another solid
solution or compound that has a distinctly
different composition.
This solubility limit of sugar in water depends on the temperature of the water
and may be represented in graphical form on a plot of temperature along the
ordinate and composition (in weight percent sugar) along the abscissa, as shown
in Fig.

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 The solubility limit is represented
as the nearly vertical line in the
figure.
 For compositions and temperatures
to the left of the solubility line, only
the syrup liquid solution exists; to
the right of the line, syrup and solid
sugar coexist.
 The solubility limit at some
temperature is the composition
that corresponds to the intersection
of the given temperature coordinate
and the solubility limit line.
 For example, at the maximum
solubility of sugar in water is 65
wt%.
As Figure indicates, the solubility limit
increases slightly with rising
temperature.

13. Quiz- Problem 9.1:Solubility limit
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14. Solution
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16. One component (Or unary phase
diagram)
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 The simplest and easiest type of phase diagram
 For a one-component system, in which composition is held constant (i.e., the phase
diagram is for a pure substance); this means that pressure and temperature are the
variables. This one-component phase diagram (or unary phase diagram)
[sometimes also called a pressure–temperature (or P–T) diagram] is
represented as a two-dimensional plot of pressure (ordinate, or vertical axis) versus
temperature (abscissa, or horizontal axis). Most often, the pressure axis is scaled
logarithmically.
Pressure-temperature
phase diagram for H2O.

17. Phase diagram of Water
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Three phases Present: Solid,
Liquid, Gas
The three curves shown on the
plot (labeled aO, bO, and cO) are
phase boundaries; at any
point on one of these curves, the
two phases on either side of the
curve are in equilibrium (or
coexist) with one another.
That is, equilibrium between
solid and vapor phases is along
curve ao—likewise for the solid-
liquid, curve bo, and the liquid
vapor, curve co.
o
a
b
c
Also, upon crossing a boundary (as temperature and/or pressure is altered), one phase transforms
to another. For example, at one atmosphere pressure, during heating the solid phase transforms to
the liquid phase.

18. Triple point
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All three of the phase boundary curves intersect at a common point, ( for this
system, at a temperature of 273.16 K and a pressure of 6.04 × 10-3 atm). This
means that at this point only, all of the solid, liquid, and vapor phases are
simultaneously in equilibrium with one another.
Appropriately, this, and
any other point on a P–T
phase diagram where
three phases are in
equilibrium, is called a
triple point; sometimes it
is also termed an
invariant point inasmuch
as its position is distinct,
or fixed by definite values
of pressure and
temperature

19. Examples
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20. Binary phase diagram
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Binary phase diagrams are maps that represent the relationships between
temperature and the compositions and quantities of phases at equilibrium,
which influence the microstructure of an alloy.
Another type of extremely common phase diagram is one in which temperature
and composition are variable parameters, and pressure is held constant—normally
1 atm.
Binary Isomorphous system-complete solid
solubility of the two
components (both in the liquid and solid
phases).
Three phase region can be identified on the
phase diagram:
Liquid (L) , solid + liquid (α +L), solid (α )
Liquidus line separates liquid from
liquid + solid
Solidus line separates solid from
liquid + solid

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22. Example- Binary isomorphous system
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Cu-Ni (the complete
solubility occurs because both Cu and Ni
have the same crystal structure, FCC,
similar radii, electronegativity and
valence).
Temperature is plotted along the ordinate, and
the abscissa represents the composition of the
alloy, in weight percent (bottom) and atom
percent (top) of nickel.
The composition ranges from 0 wt% Ni (100
wt% Cu) on the left horizontal extremity to 100
wt%Ni (0 wt% Cu) on the right.
Three different phase regions, or fields, appear
on the diagram, an alpha ( α) field, a liquid (L)
field, and a two-phase field. Each
region is defined by the phase or phases that
exist over the range of temperatures
and compositions delimited by the phase
boundary lines.

23. Interpretation of phase diagram
• For a given temperature and composition we
can use phase diagram to determine:
• 1) The phases that are present
• 2) Compositions of the phases
• 3) The relative fractions of the phases
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24. Phases present
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One just locates
the temperature–composition
point on the diagram and note the
phase(s) with
which the corresponding phase
field is labeled.
For example, an alloy of
composition 60 wt% Ni–40 wt%
Cu at would be located at point A
in Figure 9.3a;
since this is within the region,
only the single phase will be
present.
On the other hand, a 35 wt% Ni–
65 wt% Cu alloy at (point B) will
consist of both α
and liquid phases at equilibrium.

25. Determination of phase composition
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The first step in the determination of phase compositions (in terms of the
concentrations of the components) is to locate the temperature–composition point
on the phase diagram.
Single phase region
Two- phase region
For example, consider
the 60 wt% Ni–40 wt% Cu alloy at (point
A, Figure 9.3a). At this composition and
temperature, only the phase is present,
having a composition of 60 wt%
Ni–40 wt% Cu.

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27. Determination of phase amount
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The relative amounts (as fraction or as percentage) of the phases present at
equilibrium may also be computed with the aid of phase diagrams.
Two-phase region : Lever
rule
If the composition and temperature
position is located within a two-
phase region, things are more
complex. The tie line must be utilized
in conjunction with a procedure that
is often called the lever rule(or the
inverse lever rule)
Single phase region: (point Ain
Figure 9.3a), only the phase is present;
hence, the alloy is completely or 100% α

28. LEVER RULE
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Finding the amounts of phases in a two phase region:
1. Locate composition and temperature in diagram
2. In two phase region draw the tie line or isotherm
3. Fraction of a phase is determined by taking the length of the tie line to the
phase boundary for the other phase, and dividing by the total length of tie
line

29. Derivation of lever rule
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30. The lever rule
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33. Question
• Is it possible to have a
copper-nickel alloy
that, at equilibrium,
consists of an α phase
of composition 37 wt%
Ni-63 wt% Cu, and
also a liquid phase of
composition 20 wt%
Ni-80 wt% Cu? If so,
what will be the
approximate
temperature of the
alloy? If this is not
possible, explain why.
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34. Answer
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It is not possible to have a Cu-Ni alloy, which at equilibrium, consists of
a liquid phase of composition 20 wt% Ni-80 wt% Cu and an α phase of
composition 37 wt% Ni-63 wt% Cu.
From Figure , a single tie line does not exist within the α+ L region that
intersects the phase boundaries at the given compositions. At 20 wt%
Ni, the L-(α+ L) phase boundary is at about 1200°C, whereas at 37 wt%
Ni the (L + α)-αphase boundary is at about 1225°C.

35. Problem
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36. Solution
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37. Problem 9:12
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38. Solution
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39. Binary isomorphous system (Cu-Ni Phase
diagram)
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40. Solution
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41. Concept check
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43. Development of microstructure in
isomorphous alloys
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Equilibrium cooling
In this case the cooling
occurs very slowly and
phase equilibrium is
continuously
Maintained.
specifically an alloy
of composition 35 wt% Ni–65
wt% Cu as it is cooled from
1300℃

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a
Composition at point a:
Completely liquid (35
wt% Ni- 65wt%Cu)
b
(point b, ).At this
point, the first solid
begins to form, which has
a composition dictated by
the tie line drawn at this
temperature [i.e., 46 wt%
Ni–54 wt% Cu, noted as
(46 Ni)]; the composition
of liquid is still
approximately 35 wt% Ni–
65 wt% Cu [L(35 Ni)],
which is different from
that of the solid .

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a:1300℃ ( L phase.35wt%Ni-
65wt%Cu)
b:1260℃ (46wt%Ni,α Phase)
c:1250℃ (Lphase,32wt%Ni-
68wt%Cu). ( αphase,43wt%Ni-
57wt%Cu)
d: 1220℃(L phase,24wt%Ni-
76wt%Cu). (α phase, 35wt%Ni-
65wt%Cu)
e:1185℃ (α phase, 35wt%Ni-
65wt%Cu)

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47. Mechanical properties of isomorphous
alloy
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For all temperatures and compositions below the melting temperature of the
lowest-melting component, only a single solid phase will exist. Therefore,
each component will experience solid-solution strengthening, or
an increase in strength and hardness by additions of the other component.
The ductility
(%EL)–composition
behavior, which is
just the opposite of
tensile strength; that
is,
ductility decreases
with additions of the
second component,
and the curve
exhibits
a minimum.

48. Binary Eutectic systems
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Three single phase regions
(α- solid solution of Ag in Cu
matrix, β= solid solution of
Cu in Ag matrix, L - liquid)
The solubility limit for α Phase-
line CBA, which increase with
temperature to max (8wt%Ag
at 779℃) at point B, and
decreases back to zero at the
melting temperature of copper
at 1085℃. The solubility limit
for β phase- line HGF, which
increases with temperature to
max(8.8wt% Cu at 779℃)

49. Binary Eutectic systems
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Solvus line separating α
the α+β region and Solidus line
separating the α and α+L region.
Solvus line and
solidus line for β
phase
Line BEG Which represent
the lowest temperature at
which liquid phase may
exist for any Cu-Ag system
Line BEG can be said as
solidus line because it lies
between maximum solubility
positions.

50. Eutectic Point
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Three two-phase regions (α+
L, β+L, α+β)
AE or EF –Liquidus line
Melting temp of Cu is reduced
by adding Ag or similarly by
addition of Cu in Ag.
Both Liquidus lines meet at
point E which is invariant
point
Composition at E point: 71.9
wt% Ag at 779℃
Eutectic reaction

51. Binary Eutectic systems (General
rules)
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 Eutectic reaction– transition between liquid and mixture of two solid phases,
α+ β at eutectic concentration.
 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.

52. Example (Pb-Sn)
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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. Figure 9.8
indicates that an alloy of this
composition is completely molten at
about 185℃, which makes this
material especially attractive as a
low-temperature solder, since it is
easily melted.

53. Problem 9.2
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At 100℃ what is the maximum solubility (a)of Pb in Sn? (b) of Sn in Pb

54. Solution (P9.2)
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