Question:
In the structure of A\(_x\)B\(_y\), cations (A) occupy all the tetrahedral voids while anions (B) form fcc lattice. What is the ratio of x and y?
In the structure of A\(_x\)B\(_y\), cations (A) occupy all the tetrahedral voids while anions (B) form fcc lattice. What is the ratio of x and y?
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In fcc lattice, number of tetrahedral voids = 2 × number of atoms in unit cell.
Updated On: Jun 20, 2026
- 3:1
- 1:1
- 1:2
- 2:1
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The Correct Option is D
Solution and Explanation
Step 1: Understand fcc lattice of anions.
In an fcc lattice, the number of atoms per unit cell is 4. Here, anions (B) form the fcc lattice, so total B atoms per unit cell = 4.
Step 2: Determine tetrahedral voids in fcc.
An fcc unit cell contains 8 tetrahedral voids. If all tetrahedral voids are occupied by cations (A), then number of A atoms = 8.
Step 3: Write atomic ratio.
Thus: \[ A : B = 8 : 4 \]
Step 4: Simplify ratio.
Dividing both by 4: \[ A : B = 2 : 1 \]
Step 5: Interpret structure.
This corresponds to anti-fluorite type structure where cations fully occupy tetrahedral voids in an fcc anion lattice.
Step 6: Final conclusion.
Hence the ratio of x and y is 2:1.
Final Answer: \[ \boxed{2:1} \]
In an fcc lattice, the number of atoms per unit cell is 4. Here, anions (B) form the fcc lattice, so total B atoms per unit cell = 4.
Step 2: Determine tetrahedral voids in fcc.
An fcc unit cell contains 8 tetrahedral voids. If all tetrahedral voids are occupied by cations (A), then number of A atoms = 8.
Step 3: Write atomic ratio.
Thus: \[ A : B = 8 : 4 \]
Step 4: Simplify ratio.
Dividing both by 4: \[ A : B = 2 : 1 \]
Step 5: Interpret structure.
This corresponds to anti-fluorite type structure where cations fully occupy tetrahedral voids in an fcc anion lattice.
Step 6: Final conclusion.
Hence the ratio of x and y is 2:1.
Final Answer: \[ \boxed{2:1} \]
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