Diffusion in Solids - Physical Metallurgy - Metallurgical Engineering Previous Year Questions

1

2007 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2007

The carbon concentration profile \( C(x,t) \) during decarburization is given by: \( C(x,t) = L + M \, \mathrm{erf}\left( \frac{x}{2\sqrt{Dt}} \right) \) where \( x \) is the distance from the surface, \( t \) is time, \( D \) is the diffusion coefficient of carbon in austenite, and \( L \) and \( M \) are constants. If the furnace atmosphere is free of carbon and maintained at 927°C, approximately how long does it take for a steel with an initial carbon concentration of 1.2 % to attain a carbon concentration of 0.8 % at a distance of 0.5 mm below the surface? [Given: \( D = 1.28 \times 10^{-11} \, \mathrm{m^2\,s^{-1}} \) at 927 °C; erf(0) = 0; erf(0.65) = 0.64; erf(0.69) = 0.667; erf(0.7) = 0.678; erf(∞) = 1]

A

30 hours

B

3 hours

C

3 minutes

D

30 seconds

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2

2008 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2008

The activation energy for diffusion in kJ mol^-1 is

A

138

B

148

C

158

D

168

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3

2008 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2008

The diffusivity of carbon in γ-iron at 1373 K in m²s^-1 is

A

3.4 × 10^-11

B

4.4 × 10^-11

C

5.4 × 10^-11

D

6.4 × 10^-11

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4

2009 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2009

Fick’s first law relates

A

flux of atoms and the concentration gradient

B

amount of gas dissolved in the molten metal and the partial pressure

C

applied normal stress and the orientation of slip system

D

heat flux and the temperature gradient

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5

2009 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2009

A 0.2 wt % C steel is carburized at 1200 K for 4 hours to obtain 0.8 wt % C at a depth of 0.20 mm. Instead, if the carburizing is performed for 8 hours at the same temperature, then 0.8 wt % C will be achieved at a depth of

A

0.23 mm

B

0.55 mm

C

0.28 mm

D

0.40 mm

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6

2010 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2010

Which of the parameters give the composition profile in the following form? \(C(x,t) = C_1 + C_2 erf\left(\frac{x}{2\sqrt{Dt}}\right)\)

A

\(C_1 = 0.45, C_2 = 0.05\)

B

\(C_1 = 0.5, C_2 = 0.4\)

C

\(C_1 = -0.05, C_2 = 0.45\)

D

\(C_1 = 0.1, C_2 = 0.9\)

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7

2012 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2012

A 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 c_B along the rod axis x after a time t is described by

A

\(c_B = \frac{m}{2\sqrt{\pi Dt}} \exp\left[-\frac{x^2}{4Dt}\right] \)

B

\(c_B = \frac{m}{2\sqrt{\pi Dt}} \text{erf}\left[-\frac{x^2}{4Dt}\right] \)

C

\(c_B = \frac{m}{2\sqrt{\pi Dt}} \left[1 - \text{erf}\left(-\frac{x^2}{4Dt}\right)\right] \)

D

\(c_B = \frac{m}{2\sqrt{\pi Dt}} t \)

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8

2013 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2013

What is the depth (in μm) from the surface of the specimen at which a composition of 0.4 wt.% C is obtained after carburizing at 870°C for 10 h?

A

15

B

84

C

113

D

875

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9

2013 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2013

How long (in h) will it take to double the depth at which 0.4 wt.% C is reached?

A

40

B

20

C

18

D

14

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10

2018 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2018

A copper-aluminium diffusion couple develops a certain concentration profile after an isothermal treatment at 600°C for 10 hours. The time required to achieve the same concentration profile at 500°C is ________ (in hours to 1 decimal place)

Given: The interdiffusion coefficient for copper in aluminium at 500°C and 600°C are \(4\times10^{-14}\) m²s⁻¹ and \(8\times10^{-13}\) m²s⁻¹.

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11

2019 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2019

The fastest diffusing element in iron at 1100 °C is ____________.

A

Ni

B

Co

C

Cr

D

C

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12

2020 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2020

Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]
Assertion [a]: The rate of homogenization in a dilute substitutional solid solution of B in A is controlled by the diffusivity of B.
Reason [r]: Atomic migration cannot occur along dislocations and grain boundaries.

A

Both [a] and [r] are true and [r] is the correct reason for [a].

B

Both [a] and [r] are true but [r] is not the correct reason for [a].

C

Both [a] and [r] are false.

D

[a] is true but [r] is false.

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13

2021 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2021

A thick steel plate containing 0.1 wt.% C is carburized at 950 °C. The plate’s surface carbon concentration is maintained at 1.1 wt.% C. After 9 hours, the depth (in mm) below the surface at which the carbon concentration is 0.6 wt.% C will be: ______ (round off to 2 decimal places).
Given: Diffusivity of carbon in \( \gamma \)-Fe at 950 °C = \( 1.6 \times 10^{-11} \) m² s^-1
Error function table:

z	0.35	0.40	0.45	0.50	0.55	0.60
erf(z)	0.3794	0.4284	0.4755	0.5205	0.5633	0.6039

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14

2023 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2023

For self-diffusion in polycrystalline copper with a lattice diffusion coefficient \(D_L\), grain boundary diffusion coefficient \(D_{GB}\), and surface diffusion coefficient \(D_S\), the correct relationship is

A

\(D_S > D_{GB} > D_L\)

B

\(D_L > D_S > D_{GB}\)

C

\(D_{GB} > D_S > D_L\)

D

\(D_{GB} = D_S = D_L\)

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15

2024 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2024

During carburization of a steel at \( 950 \, ^\circ C \), carbon concentration is measured as \( 0.8 \, wt \% \) at a depth of \( 0.3 \, mm \) after one hour. The time required to get the same carbon concentration at a depth of \( 0.6 \, mm \) at the same carburization temperature is _____ \( hours \).
(Round off to the nearest integer).

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16

2025 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2025

The following are the activation energies for diffusion of carbon and iron at 773 K in polycrystalline BCC iron:
P = Activation energy for diffusion of carbon in BCC iron through the lattice
Q = Activation energy for diffusion of iron in BCC iron through the lattice
R = Activation energy for diffusion of iron in BCC iron along the grain boundary
Which one of the following statements is CORRECT?

A

R < P < Q

B

R < Q < P

C

Q < P < R

D

P < R < Q

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17

2026 · Metallurgical Engineering · Physical Metallurgy · Diffusion in Solids

Metallurgical Engineering (MT) 2026

During carburizing of a steel, the surface concentration is kept constant at 1.4 wt.% carbon. Diffusivity of carbon for the steel at 950 °C is 6.25 × 10⁻¹¹ m²/s. At 950 °C, the time required to carburize the steel with an initial composition of 0.2 wt.% carbon to 0.8859 wt.% carbon at a depth of 0.2 mm is ______ seconds (approximate to the nearest integer).
Use the nearest value of the error function from the table given below for your calculation.

z	erf (z)
0.3	0.3286
0.4	0.4284
0.5	0.5205

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