Close packed structures

The three-dimensional close packed structure is best understood by building it up in stages: first a single row of spheres, then a layer, then a stack of layers.

a. Close packing in one dimension : A row of spheres touching one another edge to edge is the only way to close-pack spheres in one dimension. Each sphere is in contact with two neighbours, so its coordination number is 2.

b. Close packing in two dimensions : A two-dimensional close packed layer is obtained by stacking close packed rows one against another, and there are two distinct ways of doing it:

i. Square close packing : Successive rows are placed so that their spheres align both horizontally and vertically -- every row a repeat of the first, giving an AAAA... type arrangement. Each sphere touches 4 neighbouring spheres, so the 2-D coordination number is 4, and joining the centres of those four neighbours traces a square -- hence the name square close packing.

ii. Hexagonal close packing : Successive rows are staggered, each sphere nestling into the depression between two spheres of the row below. Alternate rows repeat, giving an ABAB... type arrangement. Each sphere touches 6 neighbouring spheres, so the 2-D coordination number is 6, and joining their centres traces a regular hexagon. Hexagonal packing leaves less empty space than square packing -- it is the more efficient of the two two-dimensional packings.

c. Close packing in three dimensions : Three-dimensional structures arise by stacking the two-dimensional layers on top of one another, and what results depends on which kind of layer is stacked, and how.

i. Stacking of square close packed layers: Placing square close packed layers exactly one above the other -- every sphere directly over a sphere of the layer below -- repeats the same layer throughout, an AAAA... pattern. The structure generated is the simple cubic structure, whose unit cell is the primitive (simple) cubic cell. Polonium is the only metal that crystallises in this structure.

ii. Stacking of two hexagonal close packed layers : A closer-packed three-dimensional structure starts from hexagonal close packed layers. The spheres of the second layer are placed in the depressions of the first layer; calling the first layer A, the differently placed second layer is called B. Only half of the triangular depressions of the A layer can hold spheres of the B layer -- the sphere resting in a depression touches the three spheres around it, blocking the neighbouring depressions.

The depressions of the A layer that ARE covered by B-layer spheres become tetrahedral voids: each is surrounded by four spheres whose centres, when joined, form a tetrahedron (Fig. 1.6). The depressions that remain uncovered combine with the triangular depressions of the B layer above them to form octahedral voids: each is surrounded by six spheres whose centres, when joined, form an octahedron (Fig. 1.7).

iii. Placing third hexagonal close packed layer : There are two distinct ways of placing a third hexagonal close packed layer on the two-layer AB stack: …