# Phase Transformation Questions and Answers – Interstitial Diffusion

This set of Phase Transformation Multiple Choice Questions & Answers (MCQs) focuses on “Interstitial Diffusion”.

1. If plane (1) contains 5 B-atoms per metre square, calculate the number of atoms that will jump from plane (1) to (2) in 1s? (Assume that on average, an interstitial atom jumps 6 times per second)
a) 5
b) 6
c) 1
d) 2

Explanation: Here one can use the formula =1/6*(number of jumps per sec) *(number of B atoms) to obtain the result and in this case, it is 5 because on an average it jumps 6 times in a second.

2. Which of the following equation is related to Fick’s first law of diffusion?
a) J = D*(∂C/∂X)
b) J = D*(∂C/∂t)
c) J = D*(dC/dt)
d) J = D*(dC/dx)

Explanation: This equation is identical to that proposed by Fick in 1855 and is usually known as Fick’s first law of diffusion. D is known as the intrinsic diffusivity or the diffusion coefficient. The partial derivative has been used to indicate that the concentration gradient can change with time.

3. Assume that on average an interstitial B-atom jumps 10 times per second. The distance between the plane is given by 2m. Then, calculate the coefficient of diffusion of B atoms? (In m2/s)
a) 20/3
b) 40/3
c) 10/3
d) 6

Explanation: For this question one can use the formula, Diffusion coefficient = 1/6*(number of times atom jumps) *(square of the distance between the plane) and just substitute the values in this formula we get the coefficient of diffusion as 20/3.

4. The concentration of oxygen at the inner surface of the vessel is maintained at a level C depending on the pressure in the vessel, while the concentration at the outer surface is reduced to zero by the escape of oxygen to the surroundings. A steady state will eventually be reached when the concentration everywhere reaches a constant value. Provided D is independent of concentration there will be a single concentration gradient in the wall and the thickness of the wall is L, the flux is given by________________
a) DC/L
b) DL/C
c) CL/D
d) DC/L + K (some constant)

Explanation: Here in this equation the concentration gradient is given by (0-C)/L and the diffusion coefficient is D. Hence the product of this gives the flux.

5. In a hexagonal lattice on average, an interstitial atom jumps 6 times per second and that each jump is in a random direction, then the probability of the atom jumping to every one of the six adjacent sites is given by___________
a) 1
b) 1/6
c) 1/2
d) Cannot be predicted

Explanation: This cannot be predicted because in the hexagonal lattice the diffusion rates of atoms in the perpendicular and parallel directions (to the base plane) are not constant and they vary. Generally, in case of non-cubic lattices the jumping probability in different crystallographic directions is not in equal proportion and depends on direction.
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6. Particularly violent oscillation of an interstitial atom or some chance coincidence of the movement of the matrix and interstitial atoms will result in a jump.
a) True
b) False

Explanation: When the thermal energy of a solid increases the atoms starts to vibrate about their mean positions. When they acquire enough energy there is a chance that a particularly violent oscillations of an interstitial atom can make an attempt to jump from its mean position and this result in a jump.

7. The rest positions of the interstitial atoms are positions of____________
a) Minimum potential energy
b) Maximum potential energy
c) Minimum kinetic energy
d) Maximum internal energy

Explanation: The rest positions of the interstitial atoms are positions where these atoms have the lowest energy and they are in their comfort zone. In order to push or move an interstitial atom to a nearby or an adjacent lattice we require sufficient energy so that we can force that to that particular high energy position.

8. During decarburization of steel, the surface concentration is reduced to a very low value.
a) True
b) False

Explanation: During decarburization of steel the surface concentration is reduced to a very low value and carbon diffuses out of the specimen and this is how the carbon content is reduced while decarburization.

9. To move an interstitial atom to an adjacent interstice, the atoms of the parent lattice must be forced apart into higher energy positions. The work that must be done to accomplish this process causes____
a) An increase in free energy of system
b) A decrease in free energy of system
c) An increase in internal energy
d) A decrease in internal energy

Explanation: The work that must be done to accomplish this process causes an increase in the free energy of the system by ΔGm (m refers to migration). Gm is known as the activation energy for the migration of the interstitial atom. In any system in thermal equilibrium the atoms are constantly colliding with one another and changing their vibrational energy.

10. The activation enthalpy for interstitial diffusion increases as the size of the interstitial atom increases.
a) False
b) True

Explanation: The activation enthalpy for interstitial diffusion increases as the size of the interstitial atom increases. This is to be expected since smaller atoms cause less distortion of the lattice during migration.

11. On average, the fraction of atoms with an energy of ΔG or more than the mean energy is given by_____
a) Exp (-ΔG/RT)
b) Exp (RT/ΔG)
c) Exp (ΔG/RT)
d) Exp (RT/ΔG)

Explanation: Thus, if the interstitial atom is vibrating with a mean frequency v in the x direction it makes v attempts per second to jump into the next site and the fraction of these attempts that are successful is given by exp (-ΔGm/ RT).

12. Which of the following equation is related to Fick’s second law_________
a) J = D*(∂C/∂X)
b) (∂C/∂X) = D*(∂2C/∂X2)
c) J = D*(∂C/∂T)
d) ∂C/∂T=k*(∂C/∂X) (k some constant)

Explanation: These equations relate the rate of change of composition with time to the concentration profile C(x). Equation has a simple graphical interpretation as (∂2C/∂X2) is the curvature of the C versus x curve.

13. Diffusion coefficient of B-atom is given as 2.5m2/s and L value is given as 2m, calculate the relaxation time?
a) 0.161
b) 0.201
c) 0.321
d) 0.404

Explanation: The relaxation time can be calculated using the formula = L2/(π2*D), the amplitude of the concentration profile decreases exponentially with time and after a sufficiently long time approaches zero and this rate is determined by using the relaxation time.

14. After a time t=2*Ʈ (Ʈ is taken as relaxation time), the amplitude of concentration decreases by__
a) 1/e2
b) 1/e
c) 1/2
d) 1/3

Explanation: The amplitude of the concentration profile after a time t is given by A=A (max) * exp (-t/Ʈ), substituting the value of t=Ʈ gives the resulting solution as A (max)* 1/e2.

15. During carburization to obtain a twofold increase in penetration requires a __________
a) Fourfold decrease in time
b) Threefold increase in time
c) Fourfold increase in time
d) Twofold increase in time

Explanation: The thickness of a carburized layer can be calculated using the formula √(Dt). Thus, to obtain a twofold thickness either we need to make the value of D as 4D or t as 4t. So, we need a fourfold increase in time to obtain a twofold increase in penetration.

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