Section 9.2.1.1.1. Close-packed layer

In a close-packed layer of spheres, each sphere is in contact with six other spheres as shown in Fig. 9.2.1.1 . This is the highest number of nearest neighbours for a layer of identical spheres and therefore yields the highest packing density. A single close-packed layer of spheres has two-, three- and sixfold axes of rotation normal to its plane. This is depicted in Fig. 9.2.1.2(a), where the size of the spheres is reduced for clarity. There are three symmetry planes with indices , , and (11.0) defined with respect to the smallest two-dimensional hexagonal unit cell shown in Fig. 9.2.1.2(b). The point-group symmetry of this layer is 6mm and it has a hexagonal lattice. As such, a layer with such an arrangement of spheres is often called a hexagonal close-packed layer. We shall designate the positions of spheres in the layer shown in Fig. 9.2.1.1 by the letter `A'. This A layer has two types of triangular interstices, one with the apex angle up and the other with the apex angle down . All interstices of one kind are related by the same hexagonal lattice as that for the A layer. Let the positions of layers with centres of spheres above the centres of the and interstices be designated as `B' and `C', respectively. In the cell of the A layer shown in Fig. 9.2.1.1 (a = b = diameter of the sphere and γ = 120°), the three positions A, B, and C on projection have coordinates (0, 0), , and , respectively.

Figure 9.2.1.1| top | pdf | The close packing of equal spheres in a plane.

Figure 9.2.1.2| top | pdf | (a) Symmetry axes of a single close-packed layer of spheres and (b) the minimum symmetry of a three-dimensional close packing of spheres.