Bravais Lattice

a type of spatial crystal lattice first described by the French scientist A. Bravais in 1848. Bravais expressed the hypothesis that spatial crystal lattices are constructed of regularly spaced node-points (where the atoms are located) that can be obtained by repeating a given point by means of parallel transpositions (translations). (See Figure 1.) When straight lines and planes are constructed

Figure 1. Structural diagram of a spatial crystal lattice drawn by means of parallel translations

through these points, the spatial lattice becomes divided into equal parallelepipeds (cells). There are a total of 14 types of such lattices, by which the structure of any crystal can be described in the first approximation. Bravais lattices are divided into four types (Figure 2):

(1) primitive, in which the points occur only at the vertices of the parallelepiped;

(2) base-centered, having an additional point in each of the centers of two opposite faces;

(3) volume-centered, in which a point in the center of the cell is added to the primitive type;

(4) face-centered, having one point in the center of each face.

Figure 2. Bravais lattices. Crystal systems: cubic – a cube with sides a=b=c and angles between them α=β=γ=90°; tetragonal –a parallelepiped a=b≠c, α=β=γ0°; rhombic —a parallelepiped a≠b≠c, α≠β≠γ=90°; trigonal (rhombohedral) — a cube elongated along the spatial diagonal a=b=c, α=β=γ≠90° hexagonal – consists of three prisms with bases in the form of a rhombus a=b≠c, α=β=90°, γ=120°; monoclinic – a parallelepiped a≠b≠c, α=γ=90°, β≠90°; triclinic –an oblique-angled parallelepiped a≠b≠c, α≠β≠γ≠90°.

Bravais lattices are distributed among the crystal systems as follows: the triclinic system has one; the monoclinic, two; the tetragonal, two; the rhombic, four; the trigonal (rhombohedral), one; the hexagonal, one; and the cubic, three.