Question

Arrange the following options in decreasing order:
A. The activation energy for lattice diffusion is \(Q_l\),
B. The activation energy for dislocation core is \(Q_d\),
C. The activation energy for grain boundaries is \(Q_g\),
D. The activation energy for surface is \(Q_s\).

• A. D \(>\) A \(>\) B \(>\) C
• B. A \(>\) C \(>\) B \(>\) D
• C. A \(>\) B \(>\) C \(>\) D
• D. B \(>\) C \(>\) D \(>\) A

Hint:

Activation energy for diffusion is generally highest in the lattice and lowest on the surface.

Answer 1

The Correct Option is B

Concept:
Diffusion becomes easier when the atomic path is less restricted. Therefore, activation energy is highest for lattice diffusion and lowest for surface diffusion.

Step 1: Lattice diffusion.
Lattice diffusion occurs through the regular crystal lattice. It requires the highest activation energy. \[ Q_l \text{ is highest} \] So, \[ A \text{ comes first} \]

Step 2: Grain boundary diffusion.
Grain boundaries are more open than the perfect lattice, so activation energy is lower than lattice diffusion. \[ Q_g<Q_l \] So, \[ C \text{ comes after } A \]

Step 3: Dislocation core diffusion.
Dislocation core diffusion is easier than grain boundary diffusion in this order. \[ Q_d<Q_g \] So, \[ B \text{ comes after } C \]

Step 4: Surface diffusion.
Surface diffusion is the easiest, so it has the lowest activation energy. \[ Q_s \text{ is lowest} \] So, \[ D \text{ comes last} \] Therefore, the decreasing order is: \[ A>C>B>D \] \[ \therefore \text{Correct Answer is (B)} \]