What is the basis in crystalline solid structures?

[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?

 

[DrDu]

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.

 

[DrDu]

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.

 

[DrDu]

If you treat e.g. iron using an enlarged unit cell, you resign to make use of the fact that the two iron atoms in your basis are symmetry equivalent.