Interstitial holes

Closed-packed structures have gaps between the spheres call interstitial holes. There are two types, the first are octahedral holes:

The second type are tetrahedral holes:

Two rules:


For N spheres there are N octahedral holes
For N spheres there are 2N tetrahedral holes


The relative sizes of the holes are:

Octahedral: 0.414r
Tetrehedral: 0.225r


Other (smaller) atoms are able to fit into these interstitial holes. A common example is adding carbon to iron to produce steel. Many atoms are too big for the holes and cause the original structure to stretch, but this stretching can still be a uniform making a uniform structure.

So long as the holes are formed in a consistent pattern, such as "all octahedral" or "every other tetrahedral" then it is still a uniform pattern which can modelled with a unit cell - or two overlapping unit cells.

Holes can also be filled randomly with neutral atoms to create a "non-stoichiometric compound".

In close-packed solids, tetrahedral holes can be divided equally into two sets, denoted T and T', which point in opposite directions. In the hcp arrangement they share a common face and are too close to be occupied simultaneously, so in hcp you won't see more than half the tetrahedral holes filled at once.