Introduction

We are all too familiar with the ideas of packing, whether we go on a trip or when we move from one house to another. Nature too uses the principles of efficiency and economy in its myriad forms of close packed structures. We will illustrate these principles with spherical objects for simplicity. For non spherical objects too, packing is governed by the "sizes" of objects and the intermolecular forces.

Close packed Structures

Consider a single horizontal line of touching hard spheres. When we want to place the next layer below it, the second layer has to be shifted by one radius so that it can closely fit into the "gaps" provided between every two adjacent spheres of the first layer. The next lower layer, i.e., the third layer is now parallel to the first layer and uses the gaps below the second layer. This is the closed packed arrangement in a plane. (If all the three layers were exactly parallel to one another without a lateral shift, the packing would have been short of closest packing, and this would correspond to a simple cubic lattice).

To get three dimensional structures, we need to place a plane of spheres (similar to the original plane) such that each sphere rests on the cavities formed in the first plane of spheres (this is to ensure closest packing; you may convince yourself of this by using marbles or ping pong balls). Let us label the second layer as the b layer and the first as the a layer. The third layer of atoms can now be exactly on top of the first layer giving an arrangement like ababab-----or it can be placed at cavities labeled c, giving an arrangement abcabcabc...... the first arrangement (abab...) is the hexagonal closest packed (HCP) structure and the second arrangement is the cubic closest packed structure (CCP) which is identical to a face centered cubic (FCC) Lattice. This is illustrated in the picture below (figures 17.1and 17.2).

Figure 17.1 Packing arrangements in a plane.