Deriving fractional atomic coordination numbers

[SSJ2]

hi guys

i was wondering how the coordination numbers for the atomic positions of atoms in crystals such as NaCl are derived

...more specifically why is Na at (0,0,0) and Cl at (1/2,1/2,1/2) and not
(0,0,0) and (1/4,1/4,1/4)

of course this is in fractional coordinates

 

[mathman]

hi guys

i was wondering how the coordination numbers for the atomic positions of atoms in crystals such as NaCl are derived

...more specifically why is Na at (0,0,0) and Cl at (1/2,1/2,1/2) and not
(0,0,0) and (1/4,1/4,1/4)

of course this is in fractional coordinates

What are the units?

 

[SSJ2]

why do the units matter...NaCl has at halite structure...or the atomic positions of (0,0,0) and(.5,.5,.5) in fractional coordinates for the unit cell

maybe i didnt explain clearly enough... let me try again

So I know that the NaCl unit cell is based on a FCC lattice with a basis of Na Cl atoms at fractional coordinates (0,0,0) and (1/2,1/2,1/2) respectively

the zincblend (ZnS) unit cell (specifically the sphalerite not wurtzite) i know is also based on a fcc lattice but instead has a basis of Zn at (0,0,0) and S at (1/4,1/4,1/4) respectively which makes it tetrahedraly coordinated instead

i was wondering fundamentally why the S is at 1/4,1/4,1/4 and not 1/2,1/2,1/2 like Cl

i.e. the atomic positions...i was wondering if there was a way to derive this based on the lattice parameters.

 

[mathman]

I am not familiar with the terminology here. You talk about fractions of unit cells. Could you be more specific.

 

[SSJ2]

hmm, i guess in the end i was wondering how the position of the atoms in a fcc structure are determined. i know the lattice parameters are determined experimentally. But how are the positions of the atoms determined