# Phase Transformation Questions and Answers – Tracer Diffusion in Binary Alloys

This set of Phase Transformation online test focuses on “Tracer Diffusion in Binary Alloys”.

1. With increase in annealing time the penetration distance __________
a) Remains constant
b) Increases
c) Decreases
d) First decreases then increases

Explanation: Normally when the experiment is performed at a certain temperature, the diffusion takes place in the radioisotope impurities and the extent to which they diffuse depend on the random walk of atoms. As the annealing time increases the penetration distance will also start to increase.

2. Pre-exponential factor and the activation energy does not depend on ___
a) Elastic modulus of material
b) Lattice parameter
c) Interstitial atoms
d) Composition

Explanation: The pre-exponential factor and the activation energy depend on a number of factors, such as size of the interstitial atoms, elastic modulus of the material, lattice parameter and the crystal structure.

3. The slope of a ln(IR) vs x2 graph is given as -2.Calculate the value of the impurity coefficient of diffusion at time 3sec?(IR is the specific intensity)
a) 0.7869
b) 0.4167
c) 0.9865
d) 0.5769

Explanation: The slope of this graph gives the value of -1/4Dt. Hence relating the slope to the given values gives the value of D, which is the required one. So here -2 = 1/ (4*D*3) which when calculated gives the value of D as 0.9865.

4. Tracer method is followed to calculate the impurity diffusion coefficient utilizing radioisotopes, which are easy to detect.
a) True
b) False

Explanation: Here what matters is the concentration of the diffusing impurity element and in this case, it will be so small hence this method called tracer method is considered to calculate the impurity diffusion coefficient utilizing radioisotopes, because in this case it is easy to detect.

5. After the experiment for certain time t=2sec, at a desired temperature, the specimen is sliced at different known distances along the x direction and is given as 2m. Calculate the specific intensity if the impurity diffusion coefficient is given as 2m2/sec?
a) 0.987
b) 0.568
c) 0.219
d) 0.789

Explanation: After the experiment for certain time at a desired temperature, the specimen is sliced at different known distances along the x direction and the concentration of the radioisotopes is measured by measuring intensities of the emitted rays. Following the solution for thin film from Fick’s second law, we can write the relative intensity as I = (1/(√πDt))*exp (-x2/4Dt). D is the diffusion coefficient of impurity.
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6. Calculate the probability of exchanging positions between the vacancy and the tracer atom, if the coordination number is given as 12?
a) 1/12
b) 1/6
c) 1/2
d) 1/4

Explanation: We can say that the probability of exchanging positions between the vacancy and the tracer atom is 1/Z (Z is the coordination number). So, here substituting the value of Z as 12 we get 1/12 as the probability factor.

7. We can say roughly that the fraction of jumps that will give successful diffusion for the tracer atom is_______ (Z is the coordination number).
a) F = 1-(2/Z)
b) Z
c) 1/Z
d) 1-(Z/2)

Explanation: We can say roughly that the fraction of jumps that will give successful diffusion for the tracer atom is F= 1-2/z. Note here that we add the probabilities since these two steps are separate events. This is very rough estimation since we have not considered the possibilities of coming back of the tracer atom to its initial position after few or many jumps.

8. What is the correlation factor of a body centered cubic crystal structure?
a) 0.65549
b) 0.72149
c) 0.78145
d) 0.98765

Explanation: The correlation factor of a body centered cubic crystal structure is 0.72149. Correlation factor of simple cubic is 0.65549 and for FCC the correlation factor is 0.78145.

9. Calculate the distance travelled along the x direction at time t=3sec, if the impurity diffusion coefficient is given as 2m2/sec and the relative intensity as 1(m-1)? (Take the impurity diffusion coefficient as 2.5(m2/sec))
a) 0
b) 1.7
c) 2.8
d) 6.98

Explanation: After the experiment for certain time at a desired temperature, the specimen is sliced at different known distances along the x direction and the concentration of the radioisotopes is measured by measuring intensities of the emitted rays. Following the solution for thin film from Fick’s second law, we can write the relative intensity as I = (1/(√πDt))*exp (-x2/4Dt). D is the diffusion coefficient of impurity.

10. The measured tracer diffusion coefficient is exactly the same as the self-diffusion coefficient.
a) True
b) False

Explanation: The tracer diffusion coefficient is not exactly the same as the self-diffusion coefficient. They are related by a correlation factor, f. Sometimes, the tracer diffusion coefficient is stated as the same as self-diffusion coefficient, which is not really correct.

11. The diffusion coefficients are strongly dependent on ________
a) Crystal structure
b) Composition
c) Grain boundaries
d) Correlation factor

Explanation: The diffusion coefficients are composition dependent. There is a difference of about three orders of magnitude across the composition range and it doesn’t depend on the crystal structure or the grain boundaries.

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