Structures of AX,AX2 and ABX3 type compounds

The simple structures come from the arrangement of the anions (though sometimes the cations) in the positions of the spheres in the fcc or hcp lattices, and the cations go into some or all of the octahedral and tetrahedral holes within the lattices.

Structures based on face centered cubic lattices

The Rock Salt structure

This the structure adopted by Sodium Chloride, NaCl. It is based on the fcc array of the large chloride anions, and the sodium cations occupy all the octahedral holes in the fcc lattice. However, it could also be seen as an fcc array of sodium ions, with the anions in all the octahedral holes.

Each ion is octahedrally coordinated by six counterions, and so this structure has so-called (6,6)-coordination, where the first number refers to the coordination of the cation and the second to the anion.

The structure beyond the first coordination sphere can also be visualized.

The Rock Salt, or NaCl, structure
	The sodium cations (green) occupy the octahedral holes in the fcc lattice of chloride anions (red).

The extended coordination of the ions can be seen by considering the coordination of the sodium ion at the center of the unit cell. It has six nearest neighbours, which are the oppositely charged chloride anions, octahedrally arranged at the centers of the faces of the cube. The next nearest neighbours are 12 sodium cations, sited on the middle of each of the edges of the cube. Beyond that, there are 8 chloride anions situated at the corners of the cube.

The Sphalerite structure

This is the structure adopted by Zinc Sulphide, ZnS, and is also known as the zinc blende structure.

Here there is an fcc array of sulphide anions, and the zinc cations occupy half the tetrahedral holes. There are two tetrahedral holes for each atom in the fcc array, and so the stoichiometry of the compound dictates that only half of them be occupied, so that there are the same number of cations as anions.

The cations are tetrahedrally coordinated by anions, and the anions are surrounded by eight tetrahedral sites, of which half are occupied, and hence the anions are also four-coordinate. The zinc blende structure therefore has (4,4)-coordination.

The Sphalerite, or Zinc Blende, structure
	The zinc cations (green) occupy half of the tetrahedral holes in the fcc lattice of sulphide anions (red).

The Fluorite structure

This is the structure adopted by Calcium Fluoride, CaF₂.

There is now an fcc array of calcium cations, and the fluoride anions occupy all of the tetrahedral holes. There are two tetrahedral holes for each atom in the fcc array, and so the stoichiometry of the compound dictates that both of the tetrahedral holes be occupied for each of the cationic fcc sites.

The anions are tetrahedrally coordinated by cations, and the cations are surrounded by eight tetrahedral sites, all of which are occupied, and hence the cations are eight-coordinate. The fluoride structure therefore has (8,4)-coordination.

The Fluorite, CaF2, structure
	The fluoride anions (green) occupy all of the tetrahedral holes in the fcc lattice of calcium cations (red).

The antifluorite structure is that adopted by compounds with the stoichiometry A₂B, where A is the cation and B is the anion. Examples include potassium oxide, K₂O. Here, the fcc array of oxide ions has potassium ions in all the tetrahedral holes, and there is a (4,8)-coordination.

Structures based on other cubic lattices

The Caesium Chloride structure

This is the structure adopted by Caesium Chloride, CsCl, and also by CsBr and CsI. It is formed when the anion and cation have similar sizes.

This is based on a simple cubic lattice of anions. In this the anions are not close packed, but the unit cell is a simple cube with an ion at the each of the corners. The cations are located at the center of the anionic cube.

Similarly, the structure can be considered as a simple cubic array of cations with the anions at the center of the cubes. It is fully understood as interleaved simple cubic lattices of cations and anions.

The Caesium Chloride Structure
	The simple cubic array of chloride anions (red) has a cesium cation (green) at the center of the cube. There is an interleaved arrangement of simple cubic anionic and cationic arrays.

The anions, at the corners of the cube, are coordinated to eight cations at the centers of each of the surrounding cubes, and the cations are surrounded by the eight anions at the corners of the cube. The cesium chloride structure therefore has (8,8)-coordination.

The Perovskite Structure

This is the structure adopted by Calcium Titanate, CaTiO₃. It is the template for many compounds of the formula ABX₃.

In this structure, there is a simple cubic array of B atoms (Ti), with the A atoms (Ca) occupying the center of the cube, as in CsCl, and the X atoms (O) being sited at the center of the 12 edges of the simple cube.

Therefore, the central A ion is coordinated by 12 X ions; the B ion is octahedrally coordinated by 6 X ions; and the X ion is linearly coordinated by 2 B ions.

The Perovskite Structure
	The simple cubic array of titanium cations (red) has a calcium cation (blue) at the center of the cube, and oxide anions (green) at the center point of each of the edges of the cube of Ti ions.

This is the prototype structure for compounds of the formula A²⁺B⁴⁺(O^2-)₃, as in perovskite itself, A³⁺B³⁺(O^2-)₃, and also in mixed oxides of formula A(B_0.5B’_0.5)O₃, or A₂BB’O₆.

Structures based on hexagonal close packed lattices

The Wurtzite Structure

This is another structure adopted by Zinc Sulphide, ZnS, the difference from Zinc Blende being that the ions now occupy the sites in an hcp lattice.

Here there is an hcp array of sulphide anions, and the zinc cations occupy half the tetrahedral holes. There are two tetrahedral holes for each atom in the hcp array, and so the stoichiometry of the compound dictates that only half of them be occupied, so that there are the same number of cations as anions.

The Wurtzite, ZnS, Structure
	The zinc cations (red) occupy half of the tetrahedral holes in the hcp lattice of sulphide anions (green).

The cations are tetrahedrally coordinated by anions, and the anions are also tetrahedrally coordinated by cations. The Wurtzite structure therefore has (4,4)-coordination.

The local coordination of the ions at the next nearest neighbour level is the same in Wurtzite as Sphalerite, each ion being tetrahedrally coordinated by its counterions, but the coordination differs at the next nearest neighbour level.

The Nickel Arsenide Structure

This is the structure of NiAs, and is based on a distorted hcp array of Arsenide anions. By contrast with the wurtzite structure, however, which is also of formula AB, the cations now occupy all the octahedral sites rather than half the tetrahedral holes. There is one octahedral hole for each hcp lattice site, and so the AB stoichiometry is preserved.

The Nickel-Arsenide, NiAs, Structure
	The hcp array of As anions (red) has Ni cations (green) in the octahedral holes.

The local coordination of the anions and cations are different in this structure.

This structure is also adopted by NiS, FeS, and other sulphides. It is common where there are soft anions and soft cations, suggesting a degree of covalency.

The local coordination in the NiAs structure
AsNi6: The local coordination of cations around the anion. There are 6 Ni (green) arranged in a trigonal prism around the central As (red).	NiAs6: The local coordination of anions around the cation. There are 6 As (red) octahedrally arranged around the Ni (green).

In this structure, whilst the anions are based on an hcp lattice, they do not actually touch each other, and so the compound is not metallic.

The Rutile Structure

This is the structure adopted by Titanium Oxide, TiO₂.

Here, the anions occupy the hcp lattice, and the cations occupy half of the octahedral holes.

This results in the oxide ions being octahedrally arranged around the titanium cation, and the oxide ions themselves have titanium ions arranged in a planar triangle around them.

The Rutile, TiO2, Structure
The Rutile Unit Cell	The extended structure
The Ti cation (red) is octahedrally surrounded by O anions (green): the O anion has a planar triangle of Ti cations around it.	The TiO6 octahedra stack vertically throughout the structure.

The local arrangement of the anions and cations leads to the (6,3)-coordination in this structure.

The TiO₆ octahedra are edge-sharing, and this results in chains of octahedra which run throughout the 3D-structure.