Deriving a simplified expression for geometrical structure factor

I am interested in deriving a simplified expression for the geometrical structure factor $F_{hkl}$ for the alloy $Cu_3Au$. At high temperatures, there is an order-disorder phase transition, but lets assume that it is at low temperature.

The Au atom is at <0,0,0> and the Cu atoms are at <0.5, 0.5, 0>, <0.5, 0, 0.5>, <0, 0.5, 0.5> in a simple cubic unit cell. How do I find simplified expressions for the structure factor here?

What I want to do is compare this structure factor to that of the alloy when it undergoes the phase transition (placing the atoms at random positions), but first I’d need to find $F_{hkl}$ for the simple structure.