Question

The following are the activation energies for diffusion of carbon and iron at 773 K in polycrystalline BCC iron: P = Activation energy for diffusion of carbon in BCC iron through the lattice
Q = Activation energy for diffusion of iron in BCC iron through the lattice
R = Activation energy for diffusion of iron in BCC iron along the grain boundary
Which one of the following statements is correct?

• A. R less than P less than Q
• B. R less than Q less than P
• C. Q less than P less than R
• D. P less than R less than Q

Hint:

Remember: Grain boundary diffusion is the fastest (lowest activation energy), interstitial diffusion is faster than substitutional diffusion, and substitutional lattice diffusion always requires the highest energy.

Answer 1

The Correct Option is A

Step 1: Recall concept of diffusion activation energy.
- Interstitial diffusion (like carbon in BCC iron) requires lower activation energy compared to substitutional diffusion (like iron atoms in BCC iron lattice).
- Grain boundary diffusion always has the lowest activation energy because grain boundaries provide fast, short-circuit diffusion paths.
Step 2: Compare the three cases.
- R = Diffusion of iron along grain boundaries → lowest activation energy.
- P = Diffusion of carbon (interstitial) through lattice → moderate activation energy.
- Q = Diffusion of iron (substitutional) through lattice → highest activation energy.
Step 3: Arrange in increasing order.
Thus, \[ R \; \text{less than} \; P \; \text{less than} \; Q \] Step 4: Match with options.
Option (A) matches this sequence correctly. \[ \boxed{\text{Correct Answer = (A) R less than P less than Q}} \]