Question

In bcc lattice containing X and Y type of atoms, X type of atoms are present at the corners and Y type of atoms are present at the centers. In its unit cell, if three atoms are missing in the corners, the formula of the compound is:

• A. \( X_5Y_8 \)
• B. \( X_8Y_5 \)
• C. \( X_3Y_5 \)
• D. \( X_5Y_3 \)

Hint:

In calculations involving defects or missing atoms in crystal lattices, account for the fraction each atom in a particular position (corners, faces, etc.) contributes to the unit cell.

Answer 1

The Correct Option is A

In a bcc lattice with X atoms at the corners and Y atoms at the center, each corner atom contributes \(\frac{1}{8}\) of an atom to the unit cell and the center atom contributes entirely. Normally, there would be 1 Y atom and \(8 \times \frac{1}{8} = 1\) X atom per unit cell. However, with three X atoms missing, \(1 - 3 \times \frac{1}{8} = \frac{5}{8}\) contributions from X atoms remain. Thus, the formula becomes approximately \( X_{5}Y_{8} \).