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Chemistry · Ch 1 — Solid State

Crystal, lattice and basis

1.4.1

Crystal, lattice and basis

A lattice is a geometrical arrangement of points in a three-dimensional periodic array -- purely a mathematical scaffold of positions, with no physical particle yet attached to it. A crystal structure is obtained by attaching a constituent particle (an atom, an ion or a molecule) to each and every one of these lattice points; the constituent particles attached in this way are together called the basis of the crystal lattice. The relationship is summarised as:

Lattice+Basis=Crystal\text{Lattice} + \text{Basis} = \text{Crystal}

Figure lattice-basisPictorial equation Lattice + Basis = Crystal: a grid of bare lattice points, plus a two-atom basis motif, gives the full crystal in which the same motif decorates every lattice point.
Fig. lattice-basis — Pictorial equation Lattice + Basis = Crystal: a grid of bare lattice points, plus a two-atom basis motif, gives the full crystal in which the same motif decorates every lattice point.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. A pictorial equation in three parts. Left: a regular grid of small dots -- the bare lattice points. Centre: a single basis motif (one large filled circle with a small open circle attached). Right: the crystal -- the same grid, but with a copy of the two-circle basis motif sitting on every lattice point …

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