[puccalie]

I had one question regarding to the packing factor. I am confusing with the relationship between packing factor and the crystal structure.

As I know the crystalline of TiO2 (anatase and rutile) are belongs to the tetragonal structure. This is also in agreement with the first pauling rule, in which the structural coordination can be estimated from the ratio of ionic radius between cation (Ti4+ = 0.42 A, for 4 coordination number)
and (O2- = 1.21 A, for 2 coordination number, and gives the ratio C/A = 0.34 which is fall to the tetragonal structure).

There are 3 kinds of packing density for various crystal structures: CCP (cubic close packed), HCP (hexagonal close packed) and BCC (body centered cubic). Some literature mention that TiO2 belong to the HCP (hexagonal close packed), which I could not understand how this could be since in my mind, the TiO2 structure actually is tetragonal.

Would anyone kindly help me to understand this ? How should I distinguish the packing density and the crystal arrangement?

[zephyrblows]

Well, firstly, what the ratio rules predict is the shape of the HOLES in which cations rest,
and NOT THE OVERALL STRUCTURE.

The holes in ionic crystals are the vacant spaces formed by relatively big anions.
Thus, a tetragonal hole is formed by 4 anions, each of which rests in a climax of the tetragon,
and 1 cation rests in the center of the tetragon.

However, according to my reference, the radii ratio is:
r (Ti4+) / r(O2-) = 61 pm / 140 pm (Pauling) = 0.44
Thus, IF WE TRUST the ratio rules, the holes should be octahedral, as they actually are:
The anions in rutile crystals are arrayed in hexagonal close packing structure, in which there are many octahedral holes, and the cations rest in every 1 out of 2 octahedral holes.

Nonetheless, WE'D BETTER NOT TRUST THE RATIOS RULES, because in many cases they are quite INACCURATE, even IN THIS CASE...

You may ask why, but I guess that's beyond my knowledge. What I know is that the REAL factors causing TiO2 structure are about covalent bonding properties and electric forces torting the overall structure.

If I typed anything wrong, please correct me.

[AWK]

http://ruby.colorado.edu/~smyth/min/tio2.html
Ti has CN=6