# Difference between BCC and SC

u_know_who
Hello, while studying crystalline solid structure one thing i don't understand. What does the "basis" means. Lattice seems clear but the basis comes along with problem. The problem arise in this case :

CsCl structure is not BCC (Body Centered Cubic). It is SC (Simple Cubic) with two basis.

That what says in the book.

My question is, if i consider CsCl is not BCC and it can be represented by SC with two basis (CS+ and Cl-) then why can't we imagine or consider original BCC structure as a combination of SC with two basis (two Fe atoms). But it is clearly declared that BCC is an unique Bravis lattice.

Can anyone clear me out?

Because the iron atoms are symmetry equivalent with respect to translations while a Cs and a Cl atom are clearly not. The same holds already in molecular physics Fe_2 molecule has symmetry group $\text{D}_{\infty h}$ while CsCl has only $\text{C}_{\infty v}$.

Useful nucleus
There is nothing wrong at all in considering BCC as simple cubic with two atoms as a basis. Similarly, FCC is a simple cubic with four atoms as a basis.

However, CsCl CANNOT be BCC because BCC sites are not occupied by the same species.

Chapter 4 in Solid State Physics by Ashcroft and Mermin gives a crystal clear explanation for these details.

There is nothing wrong at all in considering BCC as simple cubic with two atoms as a basis. Similarly, FCC is a simple cubic with four atoms as a basis.

However, CsCl CANNOT be BCC because BCC sites are not occupied by the same species.

Chapter 4 in Solid State Physics by Ashcroft and Mermin gives a crystal clear explanation for these details.
Yes, but you are considering then only a sub-group of the full crystallographic group and thus loose information.

Useful nucleus
Can you elaborate more on this, please?

xiyangxixia
The crystal must at least two basis if they are SCC. Similarly, FCC at least four basis.