# Phase Transformation Questions and Answers – Substitutional Diffusion

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

1. In a substitutional diffusion, the diffusion coefficient can be related to the jump frequency by the equation_______ (α=distance between the planes, Ʈ=jump frequency, f=correlation factor)
a) D = (1/6)*α2
b) D = (1/2)*α2
c) D = f*(1/6)*α2
d) D = f*(1/2)*α2

Explanation: The same way we calculate for interstitial diffusion, but a slight change because once an atom has jumped into a vacancy the next jump is not equally probable in all directions, but is most likely to occur back into the same vacancy. Such jumps do not contribute to the diffusive flux and therefore the equation is multiplied by a correlation factor.

2. In FCC metal, the value of α (jump distance) is given by____________ (a is the length of a side of cubic lattice)
a) a
b) √2a
c) a/√2
d) 2a

Explanation: The distance between the two adjacent atoms in an octahedral site gives the value of the jump distance and for FCC it is a/√2 and this can be calculated easily if one assumes the octahedral site to be present at the edge center.

3. What is the number of nearest neighbours present in FCC metals?
a) 12
b) 8
c) 6
d) 10

Explanation: The coordination number gives the total number of nearest neighbors for a lattice, here in FCC the coordination number is 12 hence the total number of nearest neighbors present in a FCC metal is 12.
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4. Consider the atomic jump. An atom next to a vacancy can make a jump provided it has enough thermal energy to overcome the activation energy barrier to migration. However, most of the time the adjacent site will not be vacant and the jump will not be possible. The probability that an adjacent site is vacant is given by_________. (X is the probability that any one site is vacant, z is the number of nearest neighbours)
a) X*z
b) X/z
c) X+z
d) X-z

Explanation: The probability that an adjacent site is vacant is given by z*X, where z is the number of nearest neighbours and X is the probability that any one site is vacant, which is just the mole fraction of vacancies in the metal. Combining all these probabilities gives the probability of a successful jump.

5. Which of the following is known as Darkens equation?
a) D’ = Dв*XA + DA*Xв
b) D’ = Dв*Xв + DA*XA
c) D’ = Dв*XA
d) D’ = Dв*Xв

Explanation: Interdiffusion coefficient D’ for substitutional alloys depends on DA and Dв whereas in interstitial diffusion Dв alone is needed. This equation was first derived by Darken, hence it is known by his name.

6. When atoms migrate by the vacancy process the jumping of an atom into a vacant site can equally well be regarded as the jumping of the vacancy onto the atom.
a) False
b) True

Explanation: When atoms migrate by the vacancy process the jumping of an atom into a vacant site can equally well be regarded as the jumping of the vacancy onto the atom. In other words one can say that, if there is a net flux of atoms in one direction there is an equal flux of vacancies in the opposite direction.

7. Vacancy diffusion is slower than interstitial diffusion, because_______
a) Bonding of Interstitial to the surrounding atom is weaker
b) Bonding of Interstitial to the surrounding atom is stronger.
c) More vacancy sites than interstitial sites
d) Intermolecular forces are stronger in interstitials

Explanation: There are mainly two reason for this. The first one, the weak bonding of interstitial to surrounding atoms and the second one is due to many more interstitial sites than vacancy sites to jump to.

8. Correlation factor in interstitial diffusion is _____
a) 0.45
b) 0.78
c) 0
d) 1

Explanation: Correlation factor in interstitial diffusion is 1, since we consider that the concentration of interstitial atoms is very low to make random jump possible because of availability of free sites to jump.

9. Correlation factor of a simple cubic crystal structure is _______
a) 0.65549
b) 0.72149
c) 0.78145
d) 0.932

Explanation: The correlation factor of a simple cubic crystal structure is 0.65549, 0.72149 and 0.78145 are the correlation factors of BCC and FCC respectively.

10. In general it is found that in any given couple, atoms with the lower melting point possess a higher D. (Diffusion Coefficient).
a) True
b) False

Explanation: In general, it is found that in any given couple, atoms with the lower melting point possess higher D. The exact value of D, however, varies with the composition of the alloy.

11. If the mole fraction of A and B are given as 1/3 and 2/3 respectively and their respective diffusion coefficient are 6 and 3. Calculate the inter-diffusion coefficient (in m2/s)
a) 3
b) 4
c) 6
d) 1

Explanation: The inter-diffusion coefficient is given by, D’ = DB*XA + DA*XB, (where XA, XB are the mole fractions of A and B and Dᴀ, Dв are their respective diffusion coefficient. Substituting their respective values, we get, D’ = 2 + 2 = 4.

12. If the inter-diffusion coefficient is given as 3m2/s and the L value is given as 2m. Calculate the relaxation time?
a) 0.449
b) 0.567
c) 0.789
d) 0.345

Explanation: The relaxation time can be calculated using the formula = L2/(π2*D) (Here D is the inter diffusion coefficient. Just substitute the values in this equation T= 22/ π2*3 = 0.449 sec.

13. Calculate the value of D at 1768K from the given parameters? (In 10-6 m2/s)
Self-diffusion
D° = 83mm2/s
Q = 283.4 KJ/mol
a) 0.29
b) 0.35
c) 0.49
d) 0.67

Explanation: This can be calculated using the equation D° = D*exp (-Q/RT). This equation is similar to that in interstitial diffusion except that the value of activation energy for self-diffusion has an extra term.

14. Calculate the total flux of A-atoms across a stationary plane with respect to the specimen from the following parameters?
Diffusive flux is given as 3 (moles/m2s)
Flux due to velocity of the lattice is given as 4(moles/m2s)
a) 7
b) 1
c) 12
d) 8

Explanation: The total flux is the sum of diffusive flux (due to diffusion related to lattice) and velocity flux (due to the velocity of the lattice in which diffusion is occurring). So the total flux is given as 3+4=7.

15. T/Tm is known as____________
a) Homologous temperature
b) Analogous temperature
c) Hector temperature
d) Hetero temperature

Explanation: An immediate consequence of these correlations is that the diffusion coefficients of all materials with a given crystal structure and bond type will be approximately the same at the same fraction of their melting temperature.

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