Physical Chemistry Third Edition

1156 28 The Structure of Solids, Liquids, and Polymers

Cubic,P Cubic,I

Orthorhombic,P

Monoclinic,PMonoclinic,C Triclinic Trigonal Hexagonal

Orthorhombic,C Orthorhombic,I Orthorhombic,F

Tetragonal,P Tetragonal,I

Cubic,F

Figure 28.2 The Unit Cells of the Fourteen Bravais Lattices.

Some of the crystal systems have more than one kind of lattice. Aprimitive latticeor

simple lattice(denoted byP) is one in which lattice points occur only at the corners of

the unit cell. A unit cell of a primitive lattice contains one basis (one-eighth of the basis

at each corner). Abody-centeredlattice (denoted byI, for Germaninnenzentriert)is

one in which there is a lattice point at the center of the unit cell as well as at the corners.

Aface-centeredlattice (denoted byF) is one in which there is a lattice point at the

center of each face of the unit cell as well as at the corners. The sodium chloride lattice

is a face-centered cubic lattice. Abase-centeredlattice orend-centeredlattice (denoted

byC) is one in which there is a lattice point at the center of one pair of opposite faces as

well as at the corners. Table 28.1 and Figure 28.2 show the 14 possible lattices, which

are calledBravais lattices.

Exercise 28.1

For each of the 14 Bravais lattices, give the number of basis units in the unit cell.

A number of monatomic substances, including the inert gases and most metals,

crystallize inclose-packed lattices. If a collection of spheres of equal size is packed

as closely as possible, each sphere is in contact with 12 other spheres. We say that