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. \( R<P<Q \)
• B. \( R<Q<P \)
• C. \( Q<P<R \)
• D. \( P<R<Q \)

Hint:

In materials science, diffusion along grain boundaries usually requires lower activation energy compared to diffusion through the bulk lattice. Diffusion of smaller atoms, such as carbon, is generally easier than diffusion of larger atoms like iron.

Answer 1

The Correct Option is D

The activation energy for diffusion is a critical factor in determining how easily atoms or ions move through a material. In general, diffusion of a smaller atom (such as carbon) in the lattice structure is easier than the diffusion of a larger atom (like iron) in the same lattice. Additionally, diffusion along grain boundaries typically requires less energy than diffusion through the lattice. 
Now, let’s break down the options: 
- P is the activation energy for diffusion of carbon in the BCC lattice. Since carbon atoms are smaller, they diffuse more easily than iron atoms. 
- Q is the activation energy for diffusion of iron in the BCC lattice. Iron atoms are larger, so this requires more energy than the diffusion of carbon through the lattice. 
- R is the activation energy for diffusion of iron along the grain boundary. Diffusion along the grain boundary is typically easier than in the lattice, which means R is lower than Q. 
Thus, the correct order of activation energies is: \[ P<R<Q \] Hence, Option D is the correct answer. 
Step 1: Analyzing each option - Option (A): \( R<P<Q \) - This is incorrect because the diffusion of carbon (P) through the lattice is easier than the diffusion of iron along the grain boundary (R), and thus P<R. 
- Option (B): \( R<Q<P \) - This is also incorrect because it places Q before P, which contradicts the general rule that carbon diffuses more easily than iron in the lattice. 
- Option (C): \( Q<P<R \) - This is incorrect because it incorrectly places P before Q. The activation energy for carbon diffusion is lower than for iron, but not in this order. 
- Option (D): \( P<R<Q \) - Correct: This order is consistent with the expected activation energies for diffusion, with carbon diffusing easiest, followed by diffusion along grain boundaries, and the hardest being the diffusion of iron through the lattice. 
Step 2: Conclusion The correct order is \( P<R<Q \), making Option D the correct answer.