Question:
Which of the following statement is correct for fcc lattice?
Which of the following statement is correct for fcc lattice?
Show Hint
In fcc lattice:
\[
\text{Octahedral voids}=4
\]
and
\[
\text{Tetrahedral voids}=8
\]
Also,
\[
\text{PE of fcc}=\text{PE of hcp}=74\%
\]
Updated On: Jun 22, 2026
- There are equal number of octahedral and tetrahedral voids in a unit cell.
- The tetrahedral voids are present at the edge centers.
- Octahedral voids are present at the body center and edge centers.
- Its packing efficiency (PE) is higher than hcp lattice PE.
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Recall the structure of fcc lattice.
In an fcc lattice: Atoms are present at corners and face centers The packing efficiency of fcc lattice is \[ 74\% \] which is equal to that of hcp lattice.
Step 2: Analyze option (1).
For fcc lattice: \[ \text{Number of octahedral voids}=4 \] \[ \text{Number of tetrahedral voids}=8 \] Thus, they are not equal.
Hence, option (1) is incorrect.
Step 3: Analyze option (2).
Tetrahedral voids in fcc are located inside the unit cell at positions such as \[ \left(\frac14,\frac14,\frac14\right) \] They are not located at edge centers.
Hence, option (2) is incorrect.
Step 4: Analyze option (3).
In fcc lattice: Octahedral voids occur at body center and edge centers Thus, option (3) is correct.
Step 5: Analyze option (4).
Packing efficiency of fcc and hcp lattices are equal: \[ 74\% \] Therefore, fcc packing efficiency is not higher than hcp packing efficiency.
Hence, option (4) is incorrect.
Step 6: Final conclusion.
Therefore, the correct statement is \[ \boxed{\text{Octahedral voids are present at the body center and edge centers}} \]
In an fcc lattice: Atoms are present at corners and face centers The packing efficiency of fcc lattice is \[ 74\% \] which is equal to that of hcp lattice.
Step 2: Analyze option (1).
For fcc lattice: \[ \text{Number of octahedral voids}=4 \] \[ \text{Number of tetrahedral voids}=8 \] Thus, they are not equal.
Hence, option (1) is incorrect.
Step 3: Analyze option (2).
Tetrahedral voids in fcc are located inside the unit cell at positions such as \[ \left(\frac14,\frac14,\frac14\right) \] They are not located at edge centers.
Hence, option (2) is incorrect.
Step 4: Analyze option (3).
In fcc lattice: Octahedral voids occur at body center and edge centers Thus, option (3) is correct.
Step 5: Analyze option (4).
Packing efficiency of fcc and hcp lattices are equal: \[ 74\% \] Therefore, fcc packing efficiency is not higher than hcp packing efficiency.
Hence, option (4) is incorrect.
Step 6: Final conclusion.
Therefore, the correct statement is \[ \boxed{\text{Octahedral voids are present at the body center and edge centers}} \]
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