Confusing on Bravais lattice and base vectors

[KFC]

Hi there,
I know that primitive cell is not unique and there are more than one way to define the primitive vectors but my question is when we said "primitive vectors" do we have to construct the Bravais lattice with choosing a proper basis first? My reasoning is suppose the crystal consist of different type of atoms such that the atoms might not be arranged in a way of translational invariance, it seems not making sense to define primitive cell in that case, is that correct? Please point it out if I am wrong, thanks.

 

[sam_bell]

I find you're question confusing. But I think the following will suffice:

(i) A glass has no long-range positional ordering.
(ii) A quasi-crystal has long-range positional ordering, but you can't define a unit cell.
(iii) A disordered alloy (like 50/50 CuAu) consists of well-defined site positions, but randomly (or maybe short-range correlated) atomic occupations on each site. If you ignore the site occupancies, you can still talk of a unit cell.

and ..

(iv) A true crystal; in which case there is a definite, periodically repeated unit cell. In this case all the atoms in the unit cell define the basis, and you can choose any point in one of the unit cells to define the Bravais lattice. If you choose the smallest unit cell possible, then you have a primitive cell and primitive Bravais vectors.

sam bell