In a $ A_xB_y $ crystal structure, $ A^{+y} $ ions occupy all the tetrahedral voids and $ B^{-x} $ ions make BCC unit cell. What is the formula of the compound?
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- $ A_4B_2 $
- $ A_2B_4 $
- $ A_2B_2 $
- $ A_4B_4 $
The Correct Option is A
Solution and Explanation
In an AxBy crystal structure, A+y ions occupy all the tetrahedral voids, and B-x ions form a body-centered cubic (BCC) unit cell. To determine the formula of the compound, we need to analyze the occupation of the ions within the structure:
Step 1: BCC unit cell structure with B-x ions
In a BCC lattice, there are 2 atoms per unit cell. So, we have 2 B atoms for the crystal structure.
Step 2: Tetrahedral voids in BCC structure
The BCC lattice contains 8 tetrahedral voids per unit cell. Given that A+y ions occupy all these voids, we have 8 A atoms within the unit cell.
Step 3: Determining the empirical formula
The structure consists of 8 A atoms and 2 B atoms. Simplifying this ratio gives:
A8B2 = A4B1.
Correct formula: A4B2.
Therefore, the correct option for the given crystal structure is A4B2.
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