Section 9.2.1.1.2. Close-packed structures

A three-dimensional close-packed structure results from stacking the hexagonal close-packed layers in the A, B, or C position with the restriction that no two successive layers are in identical positions. Thus, any sequence of the letters A, B, and C, with no two successive letters alike, represents a possible manner of stacking the hexagonal close-packed layers. There are thus infinite possibilities for close-packed layer stackings. The identity period n of these layer stackings is determined by the number of layers after which the stacking sequence starts repeating itself. Since there are two possible positions for a new layer on the top of the preceding layer, the total number of possible layer stackings with a repeat period of n is 2ⁿ⁻¹.

In all the close-packed layer stackings, each sphere is surrounded by 12 other spheres. However, it is touched by all 12 spheres only if the axial ratio h/a is , where h is the separation between two close-packed layers and a is the diameter of the spheres (Verma & Krishna, 1966). Deviations from the ideal value of the axial ratio are common, especially in hexagonal metals (Cottrell, 1967). The arrangement of spheres described above provides the highest packing density of 0.7405 in the ideal case for an infinite lattice (Azaroff, 1960). There are, however, other arrangements of a finite number of equal spheres that have a higher packing density (Boerdijk, 1952).