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Sodium chloride and caesium chloride have the same kind of formula, contain one alkali-metal cation and one chloride ion per formula unit, and are both colourless, water-soluble salts. Yet their crystals are built quite differently. In NaCl each ion has six oppositely charged neighbours; in CsCl each has eight. Zinc sulfide, with the same 1 : 1 ratio, gets by with only four.
The reason is geometry. An ionic lattice is a compromise between two urges: pack as many oppositely charged ions around each ion as possible (more attraction), while keeping ions of the same charge from getting too close (less repulsion). How that compromise plays out depends mostly on the relative sizes of the ions and on the formula. This list groups the classic structures that nearly every chemistry course meets, with a reason for each one, plus two close relatives worth knowing. For the general idea of a lattice, start with ionic lattice structure; for how to count ions in a cell, see unit cells.
A tool for predicting the structure: the radius ratio
Divide the cation radius by the anion radius (anions are usually the larger ions):
radius ratio = r₊ ÷ r₋
The smaller the cation relative to the anion, the fewer anions can fit around it while still touching it. Simple hard-sphere geometry gives rough ranges:
| Radius ratio r₊/r₋ | Preferred cation coordination | Shape around cation |
|---|---|---|
| 0.225 – 0.414 | 4 | Tetrahedral |
| 0.414 – 0.732 | 6 | Octahedral |
| above 0.732 | 8 | Cubic |
Treat these as guidelines. Real ions are not hard spheres, and bonding with some covalent character favours lower coordination than the ratio predicts. The rule works nicely for many alkali halides and fails for plenty of others, which is itself a clue about the bonding. Ionic sizes are discussed in more depth in ionic radius explained.
Group 1: 1 : 1 salts with high coordination
1. Rock salt (NaCl) structure: 6 : 6
What it looks like. Picture the chloride ions arranged face-centred cubic: at every corner and every face centre of a cube. The sodium ions fill every octahedral hole, which in this cell means the midpoint of each edge and the centre of the cube. The result is two interpenetrating FCC lattices, one of each ion, offset by half a cell edge. If you look along any axis, Na⁺ and Cl⁻ simply alternate, like the squares on a chessboard extended into three dimensions.
Coordination. Each Na⁺ has 6 Cl⁻ neighbours arranged octahedrally, and each Cl⁻ has 6 Na⁺. It’s written 6 : 6.
Contents of the cell. 4 Na⁺ and 4 Cl⁻, so 4 formula units. Along an edge the ions touch, so a = 2(r₊ + r₋). With a ≈ 564 pm, the sum of the radii is about 282 pm.
Who adopts it. A long list: most alkali halides (NaCl, KCl, LiF, NaBr), many oxides of divalent metals (MgO, CaO, NiO) and silver chloride.
Why. Na⁺ is roughly half the size of Cl⁻, so the ratio sits comfortably in the octahedral range. Six neighbours is the most anions that fit around a cation of this size without the anions pushing into each other. Rock salt is the default structure for 1 : 1 ionic solids with moderately sized cations, which is why it is the best-known ionic lattice of all.
2. Caesium chloride (CsCl) structure: 8 : 8
What it looks like. Chloride ions sit at the eight corners of a cube and a single Cs⁺ ion sits in the centre (or the other way round; the two views are equivalent).
Coordination. Each Cs⁺ is surrounded by 8 Cl⁻ at the corners of a cube, and each Cl⁻ by 8 Cs⁺. It’s 8 : 8.
Contents of the cell. 8 × ⅛ = 1 Cl⁻ and 1 Cs⁺, so 1 formula unit. The ions touch along the body diagonal: a√3 = 2(r₊ + r₋).
Who adopts it. CsCl, CsBr and CsI, plus some intermetallic compounds such as β-brass (CuZn).
Why. Caesium is one of the largest monatomic cations, so the radius ratio climbs into the cubic range. A large cation can hold eight anions around it without the anions touching each other, and eight neighbours means more attraction per ion than six.
The trap. CsCl is often mistaken for body-centred cubic. It isn’t: in a true BCC lattice the corner and centre sites must be identical, and here they hold different ions. CsCl is a simple cubic lattice with a two-ion basis.
Group 2: 1 : 1 salts with low coordination
3. Zinc blende (sphalerite, ZnS) structure: 4 : 4
What it looks like. Start again with FCC anions, this time sulfide ions. There are 8 tetrahedral holes inside the cell; the Zn²⁺ ions fill half of them, in an alternating pattern. If every atom were carbon, you’d have the diamond structure, which explains why zinc blende often appears alongside diamond and silicon in materials science courses (see giant covalent structures).
Coordination. Each Zn²⁺ is at the centre of a tetrahedron of 4 S²⁻, and each S²⁻ is surrounded tetrahedrally by 4 Zn²⁺: 4 : 4.
Contents of the cell. 4 S²⁻ (FCC) and 4 Zn²⁺ inside, so 4 formula units.
Who adopts it. ZnS (the mineral sphalerite), copper(I) chloride and the semiconductor gallium arsenide, GaAs.
Why. The Zn²⁺ ion is small compared with S²⁻, and the Zn–S bond has substantial covalent character. Tetrahedral coordination suits directional, partly covalent bonding using sp³-like orbitals, so low coordination wins even where a pure radius-ratio argument might be borderline.
4. Wurtzite (ZnS) structure: 4 : 4 (bonus relative)
Zinc sulfide has a second crystal form, wurtzite. The coordination is the same, 4 : 4 tetrahedral, but the sulfide ions are hexagonally close-packed (ABAB stacking) instead of cubic close-packed (ABC). It’s the ionic counterpart of the FCC/HCP pair among metals (see metal crystal structures). Zinc oxide, ZnO, crystallises in this form.
Why include it? Because it shows that the coordination number is set by the ion sizes and bonding, while the stacking sequence is a separate, finer choice. Two compounds can have identical local environments and different long-range patterns.
Group 3: salts with unequal numbers of ions
When the formula is not 1 : 1, the two ions can’t have the same coordination number. The ratio of coordination numbers must match the inverse of the ratio of ions: in MX₂ there are twice as many X as M, so each M must have twice as many neighbours as each X.
5. Fluorite (CaF₂) structure: 8 : 4
What it looks like. The Ca²⁺ ions form an FCC array. The F⁻ ions fill all 8 tetrahedral holes in the cell, forming a small cube of fluoride ions inside the larger cube of calcium ions.
Coordination. Each Ca²⁺ sits at the centre of a cube of 8 F⁻, and each F⁻ sits in a tetrahedron of 4 Ca²⁺: 8 : 4. The 2 : 1 ratio of coordination numbers matches the 1 : 2 formula exactly.
Contents of the cell. 4 Ca²⁺ and 8 F⁻, giving 4 CaF₂ formula units.
Who adopts it. CaF₂ (the mineral fluorite), SrF₂, BaF₂ and uranium dioxide, UO₂, the ceramic used in many nuclear fuel pellets.
Why. The cation is large enough relative to fluoride to hold eight neighbours, and the formula then forces each anion to have four.
6. Antifluorite structure: 4 : 8 (bonus relative)
Swap the roles of the ions and you get the antifluorite structure: anions in the FCC positions, cations in all the tetrahedral holes. It suits M₂X compounds such as Li₂O, Na₂O and K₂O. Each metal ion has 4 oxide neighbours; each oxide has 8 metal ions. Recognising antifluorite as “fluorite inside out” saves you learning a new structure.
The four core structures at a glance
| Structure | Example | Coordination (cation : anion) | Anion arrangement | Cation sites | Formula units per cell |
|---|---|---|---|---|---|
| Rock salt | NaCl | 6 : 6 | FCC | All octahedral holes | 4 |
| Caesium chloride | CsCl | 8 : 8 | Simple cubic | Cube centre | 1 |
| Zinc blende | ZnS | 4 : 4 | FCC | Half the tetrahedral holes | 4 |
| Fluorite | CaF₂ | 8 : 4 | Simple cube of F⁻ inside a Ca²⁺ FCC array | Ca²⁺ on FCC sites; F⁻ fill all tetrahedral holes | 4 |
Why these structures matter
Structure is not a curiosity. It shapes properties you can measure:
- Lattice energy depends on how many opposite charges surround each ion and at what distance. Madelung constants, which sum these interactions over the whole lattice, differ from one structure to another, so the same ions in a different arrangement would have a different lattice energy.
- Cleavage follows planes in the structure. Rock salt splits into neat cubes because cutting parallel to a cube face separates layers that each contain equal numbers of both ions.
- Electronic behaviour in zinc blende semiconductors such as GaAs depends on its tetrahedral framework, the same one that silicon and diamond use. Every atom forms four directional bonds, which is exactly the bonding pattern that gives these materials their band gaps.
Key takeaways
- Ionic structures balance maximum attraction against minimum like-charge repulsion; ion size ratio and formula decide the winner.
- Rock salt (NaCl) is 6 : 6 with 4 formula units per cell; CsCl is 8 : 8 with 1; zinc blende (ZnS) is 4 : 4 with 4; fluorite (CaF₂) is 8 : 4 with 4.
- The radius ratio rule (0.225, 0.414, 0.732) is a useful guide, not a law; covalent character pushes structures towards lower coordination.
- CsCl is simple cubic with a two-ion basis, not BCC.
- Wurtzite and antifluorite are relatives: same local coordination with different stacking, or the same framework with the ions swapped.
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