GATE MT Diffusion in solids PYQs & Answers

Questions 1–10 of 10. Imported answers require independent review unless marked reviewed.

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 0.859 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	0.3268
0.4	0.4284
0.5	0.5205

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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?

Your answerChoose one option.

R < P < Q

R < Q < P

Q < P < R

P < R < Q

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During carburization of a steel at 950 °C, carbon concentration is measured as 0.8 wt.% at a depth of 0.3

after one hour. The time required to get the same carbon concentration at a depth of 0.6

at the same carburization temperature is _____

. (Round off to the nearest integer).

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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

Your answerChoose one option.

D_S > D_GB > D_L

D_L > D_S > D_GB

D_GB > D_S > D_L

D_GB = D_S = D_L

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The concentration

of a solute (in units of atoms·mm⁻³) in a solid along

direction (for

) follows the expression

where

is in mm,

and

are in units of atoms·mm⁻⁵ and atoms·mm⁻⁴, respectively. Assuming

, the magnitude of flux at

mm is _____ ×

atoms·mm⁻²·s⁻¹ (answer rounded off to the nearest integer).

Given: diffusion coefficient of the solute in the solid is 3 ×

mm²·s⁻¹.

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A hypothetical binary eutectic phase diagram of A – B is shown below. An alloy with 5 wt.% B solidifies with no convection. Assuming steady state, the critical temperature gradient (in K mm⁻¹) required to maintain planar solidification front is: __________ (round off to nearest integer). Given: Diffusivity of B in liquid =

m² s⁻¹ Velocity of solidification front = 4 μm s⁻¹

Diagram for Metallurgical Engineering question 50

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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 γ-Fe at 950 °C =

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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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.

Your answerChoose one option.

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

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

Both [a] and [r] are false

[a] is true but [r] is false

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

Your answerChoose one option.

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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

and

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GATE MT Diffusion in solids PYQs

How to practice Diffusion in solids

Question 60

Question 43

Question 55

Question 20

Question 56

Question 50

Question 51

Question 38

Question 13

Question 25