A solid is the state of matter in which constituent particles are held in fixed positions by strong intermolecular or interionic forces, giving it a definite shape, volume and high density. Solids are broadly classified into two types based on how their particles are arranged.
Crystalline solids have a long-range, regular and repeating arrangement of particles. They are anisotropic (physical properties such as refractive index and electrical conductivity differ with direction), have sharp melting points, definite geometry, and are true solids. Examples: NaCl, diamond, quartz, ice, metals. Amorphous solids (Greek amorphos = no form) have only short-range order, are isotropic, soften over a range of temperature, lack a sharp melting point, and are regarded as supercooled liquids or pseudo-solids. Examples: glass, rubber, plastics.
Crystalline solids are further classified by the nature of the binding force and the particles occupying the lattice points:
- Ionic solids — ions held by electrostatic force; hard, brittle, high melting, conduct only when molten/aqueous (NaCl, ZnS).
- Covalent (network) solids — atoms in a continuous covalent network; very hard, very high melting, insulators except graphite (diamond, $\text{SiO}_2$).
- Molecular solids — molecules held by van der Waals, dipole or hydrogen bonds; soft, low melting, non-conducting ($\text{I}_2$, dry ice $\text{CO}_2$, ice).
- Metallic solids — kernels in a sea of delocalised electrons; malleable, ductile, lustrous, good conductors (Cu, Fe, Mg).
The orderly three-dimensional arrangement of points representing particle positions is the crystal lattice (space lattice); each point is a lattice point. The smallest repeating portion that, on translation in three dimensions, generates the whole lattice is the unit cell. A unit cell is described by three edge lengths $a,b,c$ and three angles $\alpha,\beta,\gamma$ between them. There are 7 crystal systems and 14 Bravais lattices.
Unit cells are either primitive (simple) — particles only at the eight corners — or centred — having additional particles. Centred cells include body-centred (bcc) (one extra particle at the centre of the body), face-centred (fcc/ccp) (one extra at the centre of each of the six faces) and end-centred (one extra at the centre of two opposite faces).
Each particle is shared between adjoining cells, so we count fractional contributions: a corner contributes $\tfrac{1}{8}$ (shared by 8 cells), a face $\tfrac{1}{2}$ (2 cells), an edge $\tfrac{1}{4}$ (4 cells), and a body-centre $1$ (one cell). Hence $z$ per unit cell is: simple cubic $z=8\times\tfrac{1}{8}=1$; bcc $z=8\times\tfrac{1}{8}+1=2$; fcc $z=8\times\tfrac{1}{8}+6\times\tfrac{1}{2}=4$.