Question

Match the lattice planes and directions (in Column I) with the corresponding Miller indices (in Column II):

• A. P-2, Q-4, R-1, S-3
• B. P-3, Q-1, R-4, S-2
• C. P-2, Q-4, R-3, S-1
• D. P-3, Q-4, R-2, S-1

Hint:

For Miller indices: directions $[uvw]$ correspond to vector coordinates, while planes $(hkl)$ are determined by intercepts on the axes and then taking reciprocals. Always visualize the geometry inside the unit cell for matching.

Answer 1

The Correct Option is C

Step 1: Analyze direction (P).
In the figure, vector (P) points from origin $(0,0,0)$ to $( -1, 1, 2 )$ type direction. This corresponds to $[\bar{1}12]$. \[ \Rightarrow P \;=\; 2 \]
Step 2: Analyze plane (Q).
(Q) is a vertical plane cutting through $a$ and $b$ axes but parallel to $c$-axis. This matches $[\bar{1}10]$. \[ \Rightarrow Q \;=\; 4 \]
Step 3: Analyze plane (R).
(R) shows a plane cutting across both $a$ and $b$ axes at 2 units and 1 unit respectively while extending along $c$. This corresponds to $[\bar{2}21]$. \[ \Rightarrow R \;=\; 3 \]
Step 4: Analyze direction (S).
(S) is along body diagonal direction $( -1,1,1 )$. This corresponds to $[\bar{1}11]$. \[ \Rightarrow S \;=\; 1 \]

Step 5: Final matching.
\[ P-2,\; Q-4,\; R-3,\; S-1 \] Final Answer: \[ \boxed{\text{(C) P-2, Q-4, R-3, S-1}} \]