Crystal structure Created 2026-10-14 Updated 2026-10-18
A crystal structure specifies the chemical species and spatial arrangement of the chemical atoms or ions in a crystal. For an ideal periodic structure, separate two ingredients: a Bravais lattice specifies the translations that repeat the arrangement, and an atomic basis of a crystal specifies the chemical motif repeated at every lattice point. The outward shape, or crystal habit, is a different description: the internal arrangement is what this article describes.
For a concrete two-dimensional model, choose primitive lattice translation vectors and in arbitrary length units. At every lattice point , with integers , place species A at and a different species B at . Translating by or preserves both the positions and their chemical labels. Translating by sends one A position to a B position, so it is not a translation symmetry of the labeled structure. A picture of dots with the labels erased can therefore conceal essential chemical information.
Figure 1.
A translation lattice decorated with a two-site chemical motif
. Original two-dimensional model: the same two-site atomic basis of a crystal is repeated at every lattice point. Each shaded primitive unit cell has area and contains one A site and one B site; shifting the cell boundary avoids shared boundary sites. Dots are positions, not atomic radii, and the two-site motif need not be a molecule. Details.
A primitive unit cell contains one lattice point, but may contain several chemical atoms. A conventional unit cell can contain several lattice points to display the symmetry more clearly. Thus the conventional cube of a face-centered cubic lattice contains four lattice points, whereas a body-centered cubic lattice has two. Neither lattice name alone specifies which chemical species occupies the repeated motif. The NaCl conventional cell and coordination example makes the distinction explicit.
This separation is useful experimentally: interplanar spacings constrain the repeating geometry, while relative wave intensities also depend on the atomic basis of a crystal through the crystal basis structure factor. The Bragg crystal reflection experiment of 1913 describes the X-ray spectrometer, angular scans and detector checks in detail. Its conversion from angle to length is developed under Bragg's law; a geometrically possible reflection can still have zero wave intensity.
William Lawrence Bragg's 1913 structure determination supplied a complementary test. He directed X-rays through sodium chloride sections cut parallel to a cube face and recorded spots on photographic plates. Comparing section thicknesses tested how transmission altered the pattern: the relative spot strengths changed. Comparing related salts led him to two interpenetrating face-centered cubic lattices, one for each kind of constituent. He explicitly distinguished evidence for that arrangement from the still-needed identification of a single chemical atom with each scattering center. The photographs were evidence for a structural model, not direct pictures of labeled ions.[ref]