Question

Calculate the theoretical volume change in percentage accompanying a polymorphic transformationin a pure metal from the FCC to BCC crystal structure. Assume the hardsphere atomicmodel and that there is no change in atomic volume before and after the transformation.

(a) +8.8% (b) -0.88% (c) +4.42% (d) -0.44%  

Answer 1

Correct option  (a) +8.8%

Explanation:

In FCC crystal structure unit cell =4R/√2

In BCC crystal structure unit cell a =  4R/√3

The volume per atom of FCC crystal lattice

V_FCC = a³/4 = 5.66 R³ 

The volume per atom of BCC crystal lattice

V_BCC = a³/2 = 6.16 R³

The change in volume associated with the transformation from the FCC to BCC crystal structure, assuming no change in atomic radius, is

Comments

Can anyone help me to understand why In FCC crystal structure unit cell =4R/√2?