Crystalline solids

MDCAT Chemistry · Chemistry · Solids. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

In a crystalline solid the particles are packed in a regular pattern that repeats in three dimensions, the crystal lattice. The smallest repeating block is the unit cell. Such solids melt sharply, split along cleavage planes and are anisotropic: some properties differ with direction. An amorphous solid, such as glass, has no long-range order. It softens over a range of temperature and is isotropic.

The properties of a crystal depend on its particles and on the forces between them. This gives four types: ionic, covalent, molecular and metallic.

Lattice energy is the energy released when one mole of an ionic crystal forms from its gaseous ions. It measures the strength of the ionic bonding.

Rules to remember

Unit cell: 6 parameters (edges a, b, c and angles α, β, γ); 7 crystal systems, e.g. cubic a = b = c, α = β = γ = 90°
Ionic (NaCl): hard, brittle, high melting point, conducts only when molten or dissolved; in NaCl each ion has 6 nearest neighbours of the other kind
Covalent network (diamond, SiO₂): very hard, very high melting point. Molecular (ice, I₂, dry ice): soft, low melting point, non-conductor
Metallic: positive ions in a sea of free electrons; conducts as a solid, malleable and ductile
Lattice energy is larger for smaller ions and for ions of higher charge
Isomorphism: different substances, same crystal form (NaF and MgO, both cubic). Polymorphism: one compound, more than one crystal form. Allotropy: the same for an element (diamond and graphite)
Radius ratio r⁺/r⁻: 0.225 to 0.414 gives coordination number 4; 0.414 to 0.732 gives 6; 0.732 to 1.0 gives 8

Common mistake

Students say ionic solids conduct electricity because they contain ions. In the solid the ions are fixed in the lattice; they carry current only when the solid is molten or dissolved.

Worked example

Sodium fluoride, NaF, and magnesium oxide, MgO, have the same crystal structure, and their ions are of similar size. Which has the larger lattice energy and the higher melting point?

Lattice energy depends on the charges of the ions and the distance between them.
The distances are similar, so compare the charges: Na⁺ and F⁻ are 1+ and 1−; Mg²⁺ and O²⁻ are 2+ and 2−.
Doubling both charges makes the attraction about 2 × 2 = 4 times as strong.
Stronger attraction means more energy released on forming the lattice and more heat needed to melt it.

Answer: MgO has the larger lattice energy and the higher melting point

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