Palladium metal has a face-centered cubic crystalline structure in which there are two tetrahedron-shaped gaps and one octahedron-shaped gap per palladium atom. The metallic radius of palladium is 137 pm. Estimate the largest possible size of dopant atoms that could fill interstices in palladium metal to form an interstitial alloy without perturbing the crystal lattice.
I know how fcc looks, how to calculate the metal radius, side and diagonal. I don't know how to calculate the volume of the gaps. How to do it for the tetrahedron shaped and how for the octahedron shaped gap?