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An alloy of overall composition, X<sub>B</sub> = 0.7 was equilibrated at temperature T<sub>1</sub>. Microstructural analysis showed two phases, (α and β, and that the phase fraction of β was 0.75. Given that the equilibrium composition of β at Ti is 0.9 as shown in the phase diagram below, the maximum solubility of B in α (in mole fraction) at this temperature is . . . . . . . .<br><img src="/images/question-image/metallurgical-engineering/physical-metallurgy/1684342374-M2-B-7-135.PNG" title="Physical Metallurgy mcq question image" alt="Physical Metallurgy mcq question image">
A
0.05
B
0.10
C
0.50
D
0.85
Correct Answer:
0.10
In the hypothetical phase diagram, the melting point of each pure component is. 1000 K and the eutectic temperature is 800 K. The eutectic is located at the equi-atomic composition. The maximum solid solubility in α-phase is given by the mole fraction, Ne = 0.1.
The freezing range (in K) of the alloy with composition, Ne = 0.1 is
A
100
B
130
C
160
D
190
The diffusion couple shown below is made from two A-B alloys. The initial compositions of the two alloys are indicated in the diagram. The centreline is at x = 0. The couple is held at an elevated temperature for 40 hours. Diffusivity; D = 3 × 10
-11
m
-2
s
-1
. Assume the diffusion couple to be infinitely long.
Which of the parameters give the composition profile in the following form?
$$C\left( {x,t} \right) + {c_1} + {c_2}\,erf\left( {\frac{1}{{2\sqrt {Dt} }}} \right)$$
A
c<sub>1</sub> = 0.45, c<sub>2</sub> = 0.05
B
c<sub>1</sub> = 0.5, c<sub>2</sub> = 0.4
C
c<sub>1</sub> = -0.05, c<sub>2</sub> = 0.45
D
c<sub>1</sub> = 0.1, c<sub>2</sub> = 0.9
Match the heat treatment for an eutectoid steel shown in the TTT diagram below (as P, Q, R and S) with the resulting microstructure listed below:
1. Fine pearlite
2. martensite
3. Bainite
4. Coarse pearlite
A
P-1, Q-2, R-4, S-3
B
P-4, Q-1, R-3, S-2
C
P-2, Q-1, R-3, S-4
D
P-1, Q-4, R-3. S-2
A simplified energy band-diagram of an intrinsic semiconductor at thermal equilibrium (300 K) is shown. In the accompanying table, which one of the four cloumns correctly represents the listed parameters? Assume same effective mass for electrons and holes.
A
<table class="table-style-1"> <tr> <td rowspan="2">Parameter</td> <td colspan="4">Energy-difference</td> </tr> <tr> <td><strong>Column 1</strong></td> <td><strong>Column 2</strong></td> <td><strong>Column 3</strong></td> <td><strong>Column 4</strong></td> </tr> <tr> <td>Band-gap</td> <td>ΔE<sub>2</sub></td> <td>ΔE<sub>1</sub></td> <td>ΔE<sub>2</sub></td> <td>ΔE<sub>1</sub></td> </tr> <tr> <td>Electron affinity</td> <td>$$\frac{{\Delta {E_1}}}{2}$$</td> <td>ΔE<sub>2</sub> - ΔE<sub>1</sub></td> <td>$$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE<sub>2</sub> - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr> <tr> <td>Work function</td> <td>ΔE<sub>1</sub> + ΔE<sub>2</sub></td> <td>ΔE<sub>2</sub> - $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> <td>ΔE<sub>1</sub> - $$\frac{{\Delta {E_2}}}{2}$$</td> <td>ΔE<sub>2</sub> + $$\left( {\frac{{\Delta {E_1}}}{2}} \right)$$</td> </tr></table> Column 1
B
Column 2
C
Column 3
D
Column 4
Thin layer of material B (of total amount m) is plated on the end faces of two long rods of material A. These are then joined together on the plated side (see the figure below) and heated to a high temperature. Assuming the diffusion coefficient of B in A is D, the composition profile CB along the rod axis x after a time t is described by
A
$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\exp \left$$
B
$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}erf\left$$
C
$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}\left$$
D
$${C_B} = \frac{m}{{2\sqrt {\pi Dt} }}t$$
A furnace wall consists of four layers of different materials, M
1
, M
2
, M
3
and M
4
. If the layers are of equal thickness and the steady state temperature profiles is as shown below, then the material with the lowest thermal conductivity is
A
M<sub>1</sub>
B
M<sub>2</sub>
C
M<sub>3</sub>
D
M<sub>4</sub>
From a 2 m × 1.2m sheet, squares are Cut out from each of the four comers as shown in the figure and then the sides are bent to form an open box. The maximum possible volume (in m
3
) of the box is
A
0.14
B
0.26
C
0.54
D
0.82
A furnace wall is made of three materials (I, II and III) of equal thickness and having thermal conductivity k
1
k
2
and k
3
respectively. The steady state temperature profile inside each material is shown in the figure. Thermal conductivities of the materials will vary as
A
k<sub>1</sub> > k<sub>2</sub> > k<sub>3</sub>
B
k<sub>2</sub> > k<sub>1</sub> > k<sub>3</sub>
C
k<sub>3</sub> > k<sub>1</sub> > k<sub>2</sub>
D
k<sub>3</sub> > k<sub>2</sub> > k<sub>1</sub>
A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below. The miller idices of Peak A is
A
210
B
220
C
222
D
310
A square of 9 mm
2
area is subjected to simple shear displacement √3 mm along x-direction, as shown below: The strain imparted will be
A
$$\frac{1}{3}$$
B
$$\frac{1}{{\surd 3}}$$
C
$${\surd 3}$$
D
3
