AB, AB₂ & Complex Crystal Structures

In an AB type ionic solid, equal numbers of cations (A) and anions (B) pack together. Which structure forms depends mainly on the radius ratio r⁺/r⁻ — bigger cations need bigger coordination numbers. Three structures you must know are given below.

1. Rock Salt Structure — Sodium Chloride (NaCl)

• Arrangement: Cl⁻ ions form a face-centred cubic (fcc) lattice; Na⁺ ions occupy all the octahedral voids.
• Coordination number: 6 : 6 — each Na⁺ is surrounded by 6 Cl⁻ and each Cl⁻ by 6 Na⁺.
• Formula units per unit cell (Z): 4 (4 Na⁺ + 4 Cl⁻).
• Radius ratio: r(Na⁺)/r(Cl⁻) ≈ 0.52 — fits the octahedral range 0.414–0.732.
• Other examples: KCl, MgO, CaO, AgCl, LiF, MnO.

2. Caesium Chloride Structure (CsCl)

• Arrangement: Cl⁻ ions form a simple cubic lattice; one Cs⁺ ion sits at the body centre of the cube.
• Coordination number: 8 : 8 — each Cs⁺ touches 8 Cl⁻ and vice versa.
• Formula units per unit cell (Z): 1 (1 Cs⁺ + 1 Cl⁻).
• Radius ratio: r(Cs⁺)/r(Cl⁻) ≈ 0.93 — above 0.732, so cubic (8-fold) coordination is stable.
• Other examples: CsBr, CsI, TlCl, TlBr.

3. Zinc Blende vs Wurtzite (both ZnS)

Both are 4 : 4 coordinated structures of zinc sulphide. They differ only in the stacking of the sulphide ions. This comparison is a favourite 5-mark question.

Here there are twice as many anions as cations. The cation usually has a higher coordination number than the anion.

1. Fluorite Structure — Calcium Fluoride (CaF₂)

• Arrangement: Ca²⁺ ions form a ccp (fcc) lattice; F⁻ ions occupy all the tetrahedral voids.
• Coordination number: 8 : 4 — each Ca²⁺ is surrounded by 8 F⁻, each F⁻ by 4 Ca²⁺.
• Formula units per unit cell: 4 (4 Ca²⁺ + 8 F⁻).
• Other examples: SrF₂, BaF₂, CdF₂, UO₂, ThO₂.

2. Antifluorite Structure — Sodium Oxide (Na₂O)

• Arrangement: Exactly the reverse of fluorite — O²⁻ ions form the ccp lattice and Na⁺ ions occupy all the tetrahedral voids.
• Coordination number: 4 : 8 — each Na⁺ is surrounded by 4 O²⁻ and each O²⁻ by 8 Na⁺.
• Other examples: K₂O, Li₂O, Na₂S.

3. Rutile Structure — Titanium Dioxide (TiO₂)

• Arrangement: O²⁻ ions are approximately hexagonal close packed; Ti⁴⁺ ions occupy half of the octahedral voids.
• Coordination number: 6 : 3 — each Ti⁴⁺ by 6 O²⁻, each O²⁻ by 3 Ti⁴⁺.
• Other examples: MnO₂, SnO₂, PbO₂, GeO₂, MgF₂.

4. Cadmium Iodide (CdI₂) — Layer Structure

• Arrangement: I⁻ ions are hexagonal close packed; Cd²⁺ ions fill the octahedral voids of alternate layers only.
• The result is a layered (sandwich) structure: I–Cd–I sheets held to each other only by weak van der Waals forces, so the crystals are soft and cleave easily.
• Coordination number: 6 : 3. Other examples: CdBr₂, FeCl₂, Mg(OH)₂.

The mineral perovskite is CaTiO₃. The general formula is ABX₃, where A is a large cation, B a smaller cation and X usually oxygen (oxide perovskites) or a halide.

Ideal cubic structure

• A²⁺ (Ca²⁺) — at the corners of the cube (coordination number 12).
• B⁴⁺ (Ti⁴⁺) — at the body centre (coordination number 6, octahedral).
• X²⁻ (O²⁻) — at the face centres (each B is surrounded by an octahedron of 6 X ions).
• So the structure can be seen as a network of corner-sharing BX₆ octahedra with the large A cation sitting in the 12-coordinate cavity between them.

Tolerance factor and structural distortion

Whether the ideal cubic structure actually forms depends on the relative sizes of A, B and X. This is measured by the Goldschmidt tolerance factor:

• t ≈ 0.9 – 1.0 → ideal cubic perovskite (e.g. SrTiO₃).
• t < 0.9 → A cation too small; the BX₆ octahedra tilt and the structure distorts to orthorhombic or rhombohedral symmetry (e.g. CaTiO₃ itself is orthorhombic at room temperature).
• t > 1.0 → A cation too large; distortion towards hexagonal structures.

Ilmenite structure (FeTiO₃)

• Ilmenite is related to the corundum (α-Al₂O₃) structure: O²⁻ ions are approximately hcp and the cations fill two-thirds of the octahedral voids.
• The difference from corundum is ordering: Fe²⁺ and Ti⁴⁺ occupy alternate layers of octahedral sites in an ordered fashion. It can be viewed as an ordered derivative of the corundum structure.

Applications

The mineral spinel is MgAl₂O₄. General formula AB₂O₄: O²⁻ ions form a ccp lattice; the A²⁺ and B³⁺ cations distribute themselves between the tetrahedral and octahedral voids. How they distribute gives two types:

Degree of inversion: Real spinels often lie between the two extremes. The fraction of A²⁺ ions present in octahedral sites is called the inversion parameter — 0 for a perfect normal spinel and 1 for a perfect inverse spinel. Crystal field stabilisation energy (CFSE) decides the preference: ions with high octahedral CFSE (like Ni²⁺, Cr³⁺) prefer octahedral sites.

Cation distribution and magnetic implications

• In magnetite, Fe₃O₄ (inverse spinel, Fe³⁺[Fe²⁺Fe³⁺]O₄), the magnetic moments of Fe³⁺ ions in tetrahedral sites align antiparallel to those in octahedral sites, so they cancel each other.
• The net magnetic moment comes only from the Fe²⁺ ions in octahedral sites (4 unpaired electrons → 4 Bohr magnetons per formula unit).
• This antiparallel-but-unequal arrangement is called ferrimagnetism — the reason magnetite is a natural magnet (lodestone).

• Arrangement: Carbon atoms form a ccp lattice, and additional carbon atoms occupy half of the tetrahedral voids.
• Coordination number: 4 — every carbon is tetrahedrally bonded to 4 others by strong covalent bonds.
• Atoms per unit cell: 8 (4 from the ccp lattice + 4 from the filled tetrahedral voids).
• Examples: Diamond (C), silicon (Si), germanium (Ge) — the basis of the semiconductor industry.
• The strong directional covalent bonding in 3D gives diamond its extreme hardness and high melting point.

Diamond vs Zinc Blende vs Wurtzite — quick comparison

The basic building block of every silicate is the SiO₄ tetrahedron — one silicon atom at the centre, tetrahedrally bonded to four oxygen atoms. Silicates are classified by how many oxygens each tetrahedron shares with its neighbours. More sharing = more polymerised = higher Si : O ratio.

Sheet silicates in daily life

Isomorphous substitution and ion exchange

• Isomorphous substitution means one ion replaces another of similar size in the crystal without changing the structure — e.g. Al³⁺ replaces Si⁴⁺ in the SiO₄ tetrahedra of sheet and framework silicates.
• Since Al³⁺ has one less positive charge than Si⁴⁺, the framework gains a net negative charge.
• This charge is balanced by loosely held cations (Na⁺, K⁺, Ca²⁺) sitting in the interlayer spaces or cavities.
• These cations are not fixed — they can be exchanged for other cations from solution. This is the ion-exchange property of clays and zeolites.

Zeolites — industrial applications

• Water softening (permutit process): sodium zeolite exchanges its Na⁺ for Ca²⁺ and Mg²⁺ in hard water: Na₂-zeolite + Ca²⁺ → Ca-zeolite + 2Na⁺.
• Molecular sieves: uniform cage/channel sizes trap only molecules small enough to enter — used for drying gases and separating mixtures.
• Catalysis: zeolites like ZSM-5 are solid-acid catalysts in petroleum cracking and petrochemical manufacture.
• Detergents: zeolite A replaces phosphates as a builder, softening wash water.