# Phase Transformation Questions and Answers – Atomic Mechanism of Diffusion

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

1. The mean vibrational energy possessed by each atom at 300K is given by__________ (In joules)
a) 4.14*10-23
b) 1.242*10-20
c) 1.242*10-23
d) 1.242*10-21

Explanation: The mean vibrational energy possessed by each atom is given by 3 KT, and therefore it increases in proportion to the absolute temperature and in this case take the value of T as 300K and substitute in the equation and we get the answer as 1.242*10-20.

2. Which of the following atoms use the vacancy mechanism to diffuse?
a) Large atoms
b) Surface atoms
c) Substitutional atoms
d) Small interstitial atoms

Explanation: Substitutional atoms usually diffuse by a vacancy mechanism whereas the smaller interstitial atoms migrate by forcing their way between the larger atoms.

3. Vibrational energy is increased by increasing the amplitude of the oscillations.
a) True
b) False

Explanation: Since the mean frequency of vibration is approximately constant the vibrational energy is increased by increasing the amplitude of the oscillations.
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4. When considering the flux of particles (atoms, molecules, ions etc.) in a one-dimensional system caused by a concentration gradient, the flux can be expressed as ____________
a) J = dm/dt
b) J = dm/(dt*A)
c) J = dm/dx
d) J = dm/(dx*A)

Explanation: J = dm/dt*A = – D*(ΔC/∆x)
Where J (mol/m2 s) is the flux, dm (mol) is the change in the amount of matter in small time dt (seconds), A (m2) is the area, D (m2/s) is the diffusion coefficient, C (mol/m3) is the concentration of the particles, and x (m) is the position parameter. The negative sign stems from the fact that diffusion occurs in the direction opposite to the increasing concentration gradient.

5. Fick’s first law can be directly applied only in a steady-state condition, where the composition does not change with time.
a) True
b) False

Explanation: Fick’s first law can be directly applied only in a steady-state condition, where the composition does not change with time. In addition, there should not be any external driving forces present other than the concentration gradient.

6. The movement of atom from copper to Nickel is an example of________
a) Intra diffusion
b) Inter diffusion
c) Self diffusion
d) Mixed diffusion

Explanation: Atoms move from higher to lower concentration region. If this movement is from one element to another e.g. Cu to Ni, then it is termed as Inter-diffusion. If the movement is within similar atoms as in pure metals, it is termed self-diffusion.

7. Usually the concentration of interstitial atoms is_________
a) So low that only a fraction of available site is occupied
b) Very high that entire fraction is occupied
c) Low but most of the fraction of available site is occupied
d) High but most of the available sites are vacant

Explanation: Usually the concentration of interstitial atoms is so low that only a small fraction of the available sites is occupied. This means that each interstitial atom is always surrounded by vacant sites and can jump to another position as often as its thermal energy permits it to overcome the strain energy barrier to migration.

8. The distance between two adjacent atoms in an octahedral site is given by _____ (if the sides of the unit cell are of length a, FCC material)
a) a/√2
b) a/2
c) 3a/√2
d) 2a

Explanation: In FCC materials the interstitial sites are midway along the cube edges or, equivalently, in the middle of the unit cell. These are known as octahedral sites since the six atoms around the site form an octahedron.

9. The diffusion coefficient is given as 16(m2/s) and the concentration gradient is given as 2(mol/m^4), the flux of the particle is given by _____
a) 8
b) 32
c) -32
d) -8

Explanation: The flux of particles (atoms, molecules, ions etc.) in a one-dimensional system caused by a concentration gradient is given by (– Diffusion coefficient *concentration gradient).

10. The mean vibrational energy of a particle is given by 1.656*10-20. Calculate the temperature at which the particle attains this vibrational energy?
a) 900K
b) 400K
c) 300K
d) 500K

Explanation: The mean vibrational energy possessed by each atom is given by 3 KT, and therefore it increases in proportion to the absolute temperature. Here its value is given as 1.656*10-20, so equate it with 3KT, finally we get T=1.656*10-20/3K (K is Boltzmann constant) so we get T as 400K.

11. State the reason behind the following
The diffusion coefficient for carbon in fee-Fe at 1000 °C is 2.5 X 10-11 (m2*s-1) at 0.15 wt% C, but it rises to 7.7 x 10-11 (m2*s-1) in solutions containing 1.4 wt % C.
a) Melting point of carbon
b) C atom strain Fe lattice
c) Melting point of Fe atom
d) Shrinking of C atom

Explanation: The reason for the increase of D that is the diffusion coefficient with concentration is that the C atoms strain the Fe lattice thereby it always try to make the diffusion easier as the amount of strain increases.

12. For a random walk during a diffusion process, at time t the average atom will have advanced a radial distance r from the origin and it is given by_________
a) 3.6/√Dt
b) 2.4/√Dt
c) 4.8√Dt
d) 1.2√DT

Explanation: For a random walk during a diffusion process, at time t the average atom will have advanced a radial distance r from the origin and it is given by 2.4/√Dt. It will be seen that the distance √(Dt) is a very important quantity in diffusion problems because only a very few of the atom jumps provide a useful contribution to the total diffusion distance.

13. After 2s, the average atom has an advanced radial distance of 3m from the origin, then calculate the diffusion coefficient__________ (in m2/s)
a) 0.32
b) 0.48
c) 0.69
d) 0.96

Explanation: For a random walk during a diffusion process, at time t the average atom will have advanced a radial distance r from the origin and its diffusion coefficient is given by 5.76/(t*r2).

14. Assume that 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) 1/6
b) 1/3
c) 1
d) 1/2

Explanation: Assume that on average an interstitial atom jumps k times per second and that each jump is in a random direction, then there is an equal probability of the atom jumping to every one of the six adjacent sites.

15. During a diffusion process, at time 1s the average atom will have advanced a radial distance r from the origin and it is given by_________ (D = 2.5*10-11 (m2/s))
a) 48000m
b) 45000m
c) 36000m
d) 24000m

Explanation: For a random walk during a diffusion process, at time t the average atom will have advanced a radial distance r from the origin and it is given by 2.4/√Dt and just substitute the value of D and t in the formula, we get the value of r as 48000m.

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