All ionic compounds, and therefore most solids, are crystals. That is, they consist of a regular, infinitely repeated array of anions and cations: a crystal structure. The arrangement of this crystal structure is not the same for all ionic compounds; rather, it varies depending on the nature (principally the size) of the ions which form the compound. The crystal structures of many ionic solids can be rationalized into about eight principal types.

First it is best to review the basics of crystallography. The structures of all crystalline solids are described by a regular array of atoms (or ions). For every structure there is a smallest possible set of atoms, the unit cell, which when infinitely reproduced completely describes the structure. The unit cell is in turn described by a Bravais lattice, an array of points in 3-D space which has the property that every point has an identical surrounding arrangement of points. The Bravais lattice is a mathematical abstraction, and a central concept not only in crystal chemistry but in geometry too, so you will often find basic crystallography treated as more of a mathematical than a chemical subject.

There are seven shapes of unit cell, as defined by the angles and relative lengths within the 3-D Bravais lattice: these shapes are cubic, hexagonal, tetragonal, rhombohedral, orthorhombic, monoclinic and triclinic. For definitions please see the nodes in each case. The lattice points defining a unit cell can take one of four types of centering systems: primitive (present only at the vertices), c-centred (present at the vertices and two opposing faces), body-centred (the vertices and the centre), and face-centred (the vertices, all faces and the centre). Some of the seven shapes can have more than one of these systems, so that there are a total of fourteen distinct Bravais lattices.

The above material is well covered on E2, but dispersed over a number of un-indexed nodes: see lattice, Bravais lattice, unit cell, crystal, crystallographic groups, crystal classes, crystal systems.

It is often feasible to idealize atoms and ions as hard spheres, just like a baseball or tennis ball. Many elemental solids can be described by arrangements of such atoms in one of the fourteen types above: for example, nickel and copper have a face-centred cubic arrangement, iron is body-centred cubic under standard conditions, and magnesium and zinc are hexagonal. However it is also possible to describe many binary ionic solids by a simple expansion of this system.

An important concept in simple ionic structures is holes: the empty space between atoms or ions in their crystallographic arrangement. It's quite easy to visualize that, if you pack spheres together as closely as possible, you cannot get them to fill all the space. When atoms are packed with an optimum level of efficiency - occupying the most possible space- it is called close packing.

As it happens, two Bravais lattices which both show close packing are face-centred cubic (which is also called cubic close packed), and hexagonal. It can be shown mathematically that cubic close packing, and less straightforwardly that hexagonal close packing, both have an efficiency of 74%. These are the most important lattice types for simple ionic crystallography. The atoms in these arrangements leave between them two important types of hole: tetrahedral and octahedral. A tetrahedral hole is the space between four atoms which describe a tetrahedron; n close-packed atoms leave 2n tetrahedral holes. An octahedral hole is the space between six atoms describing an octahedron; n close-packed atoms leave n octahedral holes. Many ionic solids have crystal structures which can be rationalized as a cubic close packed (CCP) or hexagonal close packed (HCP) arrangement of one type of ion, with the counterions occupying a certain proportion of the holes.

The actual structure adopted by a particular compound depends principally on the relative sizes of the ions. If the anions and cations have very different sizes, it will be possible to fit one into the holes in the close-packed arrangement of the other, otherwise close-packing may not be possible. On the other hand, there is a considerable degree of variation, in some cases even in the same compound.

The main crystal structures for simple ionic compounds are as follows, with examples of compounds which adopt them:

  • Rock-salt: CCP arrangement of the anion with the cation in all 13 octahedral holes. Named after NaCl, also adopted by KBr, CaO, ScN, and many others.
  • Fluorite: CCP arrangement of the cation with the anion in all 8 tetrahedral holes. Named after fluorite, CaF2, also adopted by BaCl2, PbO2 and others. The reverse, antifluorite, is adopted by K2O, Na2S. and others.
  • Zinc blende: CCP arrangement of the anion with the cation in half of the 8 tetrahedral holes. Named after the blende form of zinc sulphide, ZnS; also adopted by CuCl, CdS and others.
  • Wurtzite: HCP arrangement of the anion with the cation in half the tetrahedral holes. Named after the wurtzite form of ZnS; also adopted by ZnO, SiC and others.
  • Nickel arsenide: HCP arrangement of the anion with the cation in all the octahedral holes. Also adopted by FeS, PtSn and others.
  • Rutile: HCP arrangement of the anion with the cation in half the octahedral holes. Named after the rutile form of titanium oxide, TiO2, and also adopted by WO2, MgF2 and others.
  • Cadmium iodide: HCP arrangement of the anion with the cation in the tetrahedral holes of alternate layers.
  • Caesium chloride: Primitive cubic arrangement of one type of ion with the counterion at the body centre. This structure is not close-packed, but consists of interlocking cubes of each type of ion.

Reference: Shriver, D.F. and Atkins, P.W. Inorganic Chemistry (third edition). 2001, Oxford University Press.