Question

The bcc unit cell of a substitutional alloy has atoms of element A at the corners of the unit cell and an atom of element B at the center of the unit cell. Write the formulas in terms of A and B. List element A first for both answers.
1. What is the formula of the alloy?
2. What would the formula of the alloy be if the positions of the two elements were reversed in the unit cell?

Answer 1

1)

In bcc unit cell :

• Each atom at a corner is shared between eight adjacent unit cells , hence contribution of the corner atom in the unit cell is 1/8
• Center atom is fully owned by the unit cell , hence contribution of the center atom to the unit cell is 1.

therefore,

total number of A present in a unit cell = $contribution \times number \ of \ atoms \ in \ unit \ cell$

= $\dfrac{1}{8}\times 8=1$

total number of B present in a unit cell =$contribution \times number \ of \ atoms \ in \ unit \ cell$

= $1\times 1=1$

hence formula of the alloy will be AB

2) as the ratio of A and B is 1:1 so when we interchange the positions of A and B formula will remain same i.e. AB