Important Structures of AB2 compounds

AB2 compounds have many different structures but many of them belong to one of the following 5 types.

Fluorite (CaF2) The fluorite structure is very unique in so far as the close-packed ions are the cations and not the anions. In normal cases, the anion is the larger ion but in the case of CaF2, Ca is larger than F hence the structure is based on a cubic close-packing of the Ca2+ ions. There are 8 tetrahedral - holes in the unit cell of CaF2 and they are all occupied by F ions. One can notice that the only difference between fluorite and sphalerite (ZnS) is that in sphalerite only 4 of the tetrahedral holes are filled. Every fluorine anion is surrounded tetrahedrally by 4 calcium cations and every calcium cation is surrounded cubically by 8 flourine ions. In other words in the fluorite structure a (8,4)-coordination is observed. Antifluorite The antifluorite structure gets its name from the fluorite structure because it’s just the opposite i.e. the cations occupy the tetrahedral holes as compared to the anions in the fluorite structure. In this structure a cubic close-packing of the anions is observed. For example in K2O the cubic close-packing is made by oxide and the potassium occupy all 8 tetrahedral holes. The oxygen anions are surrounded by 8 potassium cations in a cubic way and the potassium cations are surrounded tetrahedrally by 4 oxygen ((4,8)-coordination).

Cadmium Chloride (CdCl2)

- In CdCl2 we have a cubic close-packed array of Cl ions. One knows that the number of tetrahedral and octahedral holes is determined by the ion that is close-packed. For n chloride ions there are n octahedral holes and 2n tetrahedral holes, but since there are 2 chloride ions in CdCl2 it implies that there are 2n octahedral holes therefore Cd cations can only fill half of the available octahedral holes. The octahedral holes in every second layer keep empty. Thus CdCl2 forms sheets or layers. If we number the layers 1,2,3,4,5,…every even numbered layer will be empty and the only interaction that will be present is the Van der Waal’s interaction between the chloride ions of adjacent occupied chlorine layers. Every Cd cation is surrounded by 6 chloride ions in an octahedral way and every chloride forms with 3 Cd cations a trigonal pyramid. The coordination of the cations and anions is (6,3).

Cadmium Iodide (CdI2 )

In CdI2 the iodide ions are hexagonal close packed. This is the only difference to CdCl2. Again every second layer is occupied by Ca, resulting in a sheet structure, as descussed above. The coordination number of the cations and anions is (6,3).

Rutile (TiO2)

In TiO2 there is no close-packing of both the cations and anions. Ti cations are octahedrally surrounded by oxygen anions and the oxygen anions are surrounded by 3 Ti cations in a trigonal planar orientation hence the coordination between the cations and anions is (6,3). In the unit cell of TiO2 there are 8 Ti cations on the corners and 1 in the center which is surrounded by 6 oxide ions. Of these 6 oxide ions, 2 are located inside the unit cell, 2 on the top face and the other 2 on the bottom face. Questions

1) Draw the unit cell of TiO2. 2) Explain the difference between the sphalerite and fluorite structures with the aid of a sketch. References:

• Inorganic Chemistry, 3rd edition, Shriver and Atkins.

• Inorganic Structural Chemistry, (Inorganic Chemistry A Textbook Series), Ulrich Mueller.

• Structural Inorganic Chemistry, 4th edition, A.F. Wells