From a pile of spheres to a named structure
In the last guide you learned the universal toolkit of the ionic solid: the larger ions stack in close packing, and the smaller ones tuck into the tetrahedral and octahedral holes left between them. That sounds like a recipe for endless variety, but the opposite is true. Almost every common ionic crystal is just one of a short list of arrangements — and chemists name each by a single famous compound that wears it. Learn the handful here and you can read the architecture of thousands of solids at a glance.
Every structure type below is defined by its [[inorg-unit-cell|unit cell]] — the smallest box that, repeated in all directions, rebuilds the whole crystal. Two numbers will recur as we go, and they are the whole game. The first is the [[inorg-coordination-number|coordination number]]: how many nearest neighbours of opposite charge surround each ion. The second is Z, the number of formula units inside one unit cell, which you reach by the fractional bookkeeping from last time (a corner ion counts 1/8, an edge ion 1/4, a face ion 1/2, an interior ion a full 1). Quote a structure's cation and anion coordination and its Z, and you have described it completely.
The two 1:1 cubics: rock salt and cesium chloride
Start with the most famous structure in all of inorganic chemistry. In the [[inorg-rock-salt-structure|rock salt structure]] the chloride ions sit in cubic close packing — a face-centred cubic array — and the sodium ions fill every one of the octahedral holes. The result is gorgeously symmetric: each Na+ is surrounded by six Cl- at the corners of an octahedron, and each Cl- by six Na+ in turn, so we call it 6:6 coordinate. Counting shared ions gives Z = 4 (four NaCl per cubic cell). A huge family of size-matched 1:1 compounds copies it — most alkali halides (LiCl, KBr), the silver halides, and oxides like MgO, where the doubled charges of Mg2+ and O2- make the same structure melt near 2850 degrees Celsius instead of NaCl's 801.
Now make the cation bigger. When the positive ion is large enough to touch eight anions at once, the crystal prefers the [[cesium-chloride-structure|cesium chloride structure]]. Picture eight chloride ions at the corners of a simple cube with one cesium dropped into the exact centre, touching all eight equally: coordination 8, and by symmetry each chloride is surrounded by eight cesiums too, so this is 8:8 coordinate. The unit cell holds just one CsCl (Z = 1). Watch the common trap: this is NOT body-centred cubic in the strict sense, because the corner and centre ions are different species, and the anions here are simple-cubic, not close-packed. CsCl, CsBr and CsI take this form — and squeeze rock-salt KCl under enough pressure and it flips into it, proof that size, not just charge, sets the coordination.
Drop the cation the other way — make it small — and a 1:1 compound abandons close-packed counting altogether for four neighbours. In [[zinc-blende-and-wurtzite|zinc blende]] (the mineral sphalerite, ZnS) the sulfide ions form a cubic close-packed array and the zinc ions fill exactly half of the tetrahedral holes, in an alternating pattern. Each ion is tetrahedrally surrounded by four of the other — 4:4 coordinate, Z = 4. Its twin, wurtzite, is the same local idea built on a hexagonal close-packed array instead (the only difference is ABCABC versus ABAB stacking). Tellingly, the zinc blende framework is just the diamond structure with two kinds of atom, which is why it shows up in the semiconductors GaAs and GaN. The tetrahedral, directional bonding here signals real covalent character — so a strictly ionic point-charge model fits these less well than it fits rock salt.
Counting the unit cell: how Z really comes out
Naming a structure is one thing; proving its formula from the box is the skill that turns recognition into understanding. Let us do the rock salt cell out loud, because the same fractional bookkeeping works on every cubic structure. The trick is that most ions sit on a shared boundary of the cell, so each cell only owns a fraction of them, and the fractions are fixed entirely by where the ion sits.
- Count the chlorides. Eight sit at the cube corners (each shared by 8 cells: 8 times 1/8 = 1) and six on the face centres (each shared by 2 cells: 6 times 1/2 = 3). Total chlorides = 1 + 3 = 4.
- Count the sodiums. Twelve sit at the edge midpoints (each shared by 4 cells: 12 times 1/4 = 3) and one sits wholly inside at the body centre (counts as a full 1). Total sodiums = 3 + 1 = 4.
- Read off the formula and Z. Four Cl- with four Na+ gives the ratio 1:1, confirming the formula NaCl, and four formula units per cell, so Z = 4. Check it against the structure: filling all the octahedral holes (one per anion) must give one cation per anion — and it does.
Beyond 1:1: fluorite, rutile and perovskite
Not every compound is 1:1. For an MX2 compound like calcium fluoride the [[fluorite-structure|fluorite structure]] is the canonical answer. The calcium ions form a cubic close-packed array, and the fluorides fill all of the tetrahedral holes — and recall there are twice as many tetrahedral holes as spheres, which is exactly the 1:2 ratio you need. So each Ca2+ ends up eight-coordinate (inside a cube of fluorides) while each F- is only four-coordinate, making fluorite 8:4 coordinate with Z = 4. Swap the roles — anions close-packed, small cations filling all the tetrahedral holes — and you get the antifluorite structure (4:8 coordinate) of the alkali oxides and sulfides like Na2O and Li2S. The roomy fluorite anion sublattice is why stabilized zirconia conducts oxide ions, the heart of fuel cells and oxygen sensors.
When the cation in an MX2 compound is too small to hold eight neighbours, it settles for six, giving the [[rutile-structure|rutile structure]] of titanium dioxide — the white pigment in paint and sunscreen. Each Ti4+ sits at the centre of an octahedron of six oxides, and each oxide is shared by three titaniums in a flat trigonal arrangement: 6:3 coordinate, which is again exactly the 1:2 stoichiometry. The cell is tetragonal — a stretched box, not a cube — with Z = 2, a useful contrast to all the cubic types. The size logic is clean: large Zr4+ gives fluorite ZrO2, smaller Ti4+ gives rutile TiO2. (Beware: TiO2 also crystallizes as anatase and brookite — same formula, different structures, called polymorphs — a reminder that one composition can pack several ways.)
The crown of the family is the [[perovskite-structure|perovskite structure]], the ABO3 blueprint behind superconductors, piezoelectric ceramics and the newest solar cells. Picture small, highly charged B cations (such as Ti4+) each at the centre of an oxide octahedron; these BO6 octahedra link by sharing every corner into an open three-dimensional framework. The large A cation (such as Ca2+) rattles in the big cavity at the centre of eight octahedra, surrounded by twelve oxides — so A is 12-coordinate while B is 6-coordinate, a 12:6 compound with Z = 1. A common slip is to give A and B the same coordination; they are very different. Perovskite earns its fame because tiny distortions of that framework unlock dramatic behaviour: shift Ti4+ slightly off-centre in BaTiO3 and each cell gains a permanent dipole, making it ferroelectric and piezoelectric — squeeze it and it makes a voltage.
Which structure? The radius-ratio rule — and why it only guesses
Why does NaCl take six neighbours while the larger CsCl takes eight and the smaller ZnS takes four? The [[radius-ratio-rules|radius-ratio rules]] give a beautifully simple first answer: it comes down to how big the cation is relative to the anion. The bigger the cation, the more anions can crowd around it before they bump into one another. The reasoning is pure geometry — imagine the cation just touching the anions packed around it, and work out the smallest ratio that keeps the anions from overlapping. That gives clean thresholds for the ratio (cation radius divided by anion radius).
r(cation) / r(anion) predicted coordination example structure
------------------- ------------------------- -----------------
< 0.225 3 (trigonal planar)
0.225 to 0.414 4 (tetrahedral) zinc blende ZnS
0.414 to 0.732 6 (octahedral) rock salt NaCl
> 0.732 8 (cubic) cesium chloride CsCl
NaCl: 102 pm / 181 pm = 0.56 -> 6-coordinate (correct: rock salt)
CsCl: 167 pm / 181 pm = 0.93 -> 8-coordinate (correct: CsCl)Now the honest part, and it matters. The radius-ratio rule is a useful guide and a lovely teaching tool, but it fails surprisingly often — right perhaps two times in three, not a law. It assumes hard, perfectly spherical ions and purely ionic bonding, and neither is strictly true: real ions are squishy, bonds carry covalent character, and small highly-charged cations distort their neighbours through polarization. Worse, the ionic radius itself depends on coordination number, so the prediction is faintly circular. Lithium iodide is the classic embarrassment — the numbers call for four-coordination, yet it crystallizes as rock salt. When the rule fails, it is because covalency, polarization, or the energetics of the whole lattice have simply outvoted the geometry.