DMCB 2423 - Tutorial CHPT 9 - Answer

DMCB 2423 MATERIALS SCIENCE
SEMESTER III 2019/2020
TUTORIAL 9
PHASE DIAGRAM
1. What is a metal alloy?

Answer:
Metal alloy is a metallic substance that is composed of two or more elements.
2. Define the following terms:

a. Solid solution
b. Solidus line and liquidus line
c. Solubility limit
Answer:
a. Solid solution is a homogeneous crystalline phase that contains two or more
chemical species. Both substitutional and interstitial solid solutions are
possible. Substitutional solid solution is a solid solution wherein the solute
atoms replace or substitute for the host atoms. Interstitial solution is a solid
solution wherein relatively small solute atoms occupy interstitial position
between the solvent or host atoms.
b. Solidus line Solidus line is on a phase diagram, the locus of points at which
solidification is complete upon equilibrium cooling, or at which melting begins
upon equilibrium heating. Liquidus line is on a binary phase diagram, the line
or boundary separating liquid and liquid + solid phase regions. For an alloy,
the liquidus temperature is the temperature at which a solid phase first form
under conditions of equilibrium cooling.
c. Solubility limit is the maximum concentration of solute that may be added

without forming a new phase.
3. Explain the function of lever rule and tie line in a diagram phase
Answer:
Function of lever rule is to compute the relative amounts in a complex of two-
phases alloy at equilibrium.
The tie line function is to compute the equilibrium concentrations of the two
phases by extension across the two-phase region and terminate at the phase
boundary lines on either side.
4. Explain the binary diagrams and ternary diagrams.

Answer:
Binary diagrams (binary phase diagrams) represent the relationships between
temperature and the compositions and quantities of phases at equilibrium, which
influence the microstructure of an alloy and consist of two components. Many
microstructures develop from phase transformations, the changes that occur when
the temperature is altered (ordinarily upon cooling). This may involve the
transition from one phase to another, or the appearance or disappearance of a
1
phase. Binary phase diagrams are helpful in phase transformations and the
resulting microstructures, which may have equilibrium or non-equilibrium
character. Ternary diagrams consist of three components. composition–
temperature phase diagram in its entirety is depicted by a three dimensional
model.
5. A 65 wt. % Ni – 35 wt. % Cu alloy (refer to Figure 1)is heated to a temperature

within the α + liquid phase region. If the composition of the αphase is 70 wt %
Ni, determine:
a. The temperature of the alloy.
In order to determine the temperature of a 65 wt % Ni – 35 wt % Cu alloy
for which α and liquid phases are present with the αphase is 70 wt % Ni,
we need to construct a tie line across the α + L phase region of Figure 1
that intersects the solidus line at 70 wt% Ni; this is possible at about 1340
o
C.
b. The composition of the liquid phase.
The composition of the liquid phase at this temperature is determined from
the intersection of this tie line with liquidus line, which responds to about
59 wt.% Ni.
c. The weight fractions of both phases.
The weight fraction of the two phases are determined using the lever rule,
with C0 = 65 wt.% Ni, CL = 59 wt.% Ni and Cα = 70 w.t% Ni, as
C0−C L 65−59
Wα= = =0.55
C α −C L 70−59
Cα −C0 70−65
W L= = =0.45
C α −C L 70−59
d. Explain the terms of “solidus line” and “liquidus line”.
Solidus line is on a phase diagram, the locus of points at which
solidification is complete upon equilibrium cooling, or at which melting
begins upon equilibrium heating.
Liquidus line is on a binary phase diagram, the line or boundary
separating liquid and liquid + solid phase regions. For an alloy, the
liquidus temperature is the temperature at which a solid phase first form
under conditions of equilibrium cooling.
Figure 1. The
copper-nickel
phase diagram
2
Last solid (~ 83 wt% Ni, ~1390 oC)
First liquid (~ 65 wt% Ni),

~1355 oC
6. Based on Figure 1, a 75 wt. % Ni – 25 wt. % Cu alloy is slowly heated from

temperature of 1300 oC (1573 K).
a. At what temperature does the first liquid phase form?
About 1355 oC.
b. What is the composition of this liquid phase?
About 59 wt.% Ni.
c. At what temperature does complete melting of the alloy occur?
About 1390 oC.
d. What composition of the last solid remaining prior to complete melting?
About 83 wt.% Ni.
7. Figure 2 shows a copper-nickel phase diagram. Cu-Ni alloy of composition 40

wt.% Ni - 60 wt.% Cu is heated within the a + liquid phase region. If the
composition of the a phase is 50 wt. % Ni, determine:
a. The temperature of the alloy: T = 1270 oC
b. The composition of the liquid phase. Cliquid = 30 wt% Ni
c. The weight percentage of both phase.
Given: Co = 40 wt.% Ni & Cα = 50 wt% Ni
C  C o 50  40
Wliquid  x100  x100  50 %
C  C liquid 50  30
3
Composition (at% Ni)

0 20 40 60 80 100
1600
2800
1500
Liquid 1453oC
2600
Temperature (oC)
Temperature (oF)
1400
2400
1300 a + L
1200 a 2200
1100 2000
1085oC
1000
0 20 40 60 80 100
(Cu) (Ni)
Composition (wt.% Ni)
Figure 2. The copper-nickel
phase diagram
8. Calculate the wt. % q in Al-55 Cu alloy that is slowly cooled from 548 to
27oC. Assume the solid solubility of Cu in Al at 27oC is 0.02 wt. % and that
the q phase contains 54.0 wt % Cu.
5.0−0.02
q wt %= x 100 %
54.02−0.02
4.98
¿ x 100 %
53.98
=9.2 %
9. A plain-carbon steel contains 93 wt.% ferrite and 7 wt.% Fe 3C. What is its
average carbon content in weight percent?
The average weight percent carbon is calculated based upon the tie line shown
below.
4
The average weight percent carbon is calculated based upon the tie line shown
below.
6.67−x
0.93=
6.67−0.02
x=6.67−0.93(6.67−0.02)
¿ 0.49 % C
10. A lead–tin alloy of composition 30 wt.% Sn–70 wt.% Pb is slowly heated from a
temperature of 150 °C (300 °F) as shown in Figure 3.
Figure 3. The lead-tin alloy phase diagram
5
a. The first liquid forms at the temperature at which a vertical line at this
composition intersects the eutectic isotherm--i.e., at 183 C.
b. The composition of this liquid phase corresponds to the intersection with the
( + L)–L phase boundary, of a tie line constructed across the  + L phase
region just above this eutectic isotherm--i.e., CL = 61.9 wt.% Sn.
c. Complete melting of the alloy occurs at the intersection of this same vertical
line at 30 wt.% Sn with the ( + L)–L phase boundary--i.e., at about 260 C.
d. The composition of the last solid remaining prior to complete melting
corresponds to the intersection with –( + L) phase boundary, of the tie line
constructed across the  + L phase region at 260 C--i.e., C is about 13 wt.%
Sn.

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DMCB 2423 MATERIALS SCIENCE

SEMESTER III 2019/2020

1. What is a metal alloy?

2. Define the following terms:

c. Solubility limit is the maximum concentration of solute that may be added

4. Explain the binary diagrams and ternary diagrams.

5. A 65 wt. % Ni – 35 wt. % Cu alloy (refer to Figure 1)is heated to a temperature

Last solid (~ 83 wt% Ni, ~1390 oC)

First liquid (~ 65 wt% Ni),

6. Based on Figure 1, a 75 wt. % Ni – 25 wt. % Cu alloy is slowly heated from

7. Figure 2 shows a copper-nickel phase diagram. Cu-Ni alloy of composition 40

Composition (at% Ni)

Figure 3. The lead-tin alloy phase diagram

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