Iron and vanadium both have the BCC crystal structure and V forms a substitutional solid solution for concentrations up to approximately 20 wt% V at room temperature. Compute the unit cell edge length for a 92 wt% Fe-8 wt% V alloy.

The unit cell edge length for the alloy is 0.288 nm

Explanation:

Given;

concentration of vanadium, Cv = 8 wt%

concentration of iron, Cfe = 92 wt%

density of vanadium = 6.11 g/cm³

density of iron = 7.86 g/cm³

atomic weight of vanadium, Av = 50.94 g/mol

atomic weight of iron, Afe= 55.85 g/mol

Step 1: determine the average density of the alloy

Step 2: determine the average atomic weight of the alloy

Step 3: determine unit cell volume

for a BCC crystal structure, there are 2 atoms per unit cell; n = 2

Step 4: determine the unit cell edge length

Vc = a³

= 0.288 nm

Therefore, the unit cell edge length for the alloy is 0.288 nm