Question

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?

• A. $ A_4B_2 $
• B. $ A_2B_4 $
• C. $ A_2B_2 $
• D. $ A_4B_4 $

Hint:

Number of tetrahedral voids is twice the number of atoms in the unit cell.

Answer 1

The Correct Option is A

In an  A_xB_y  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.