13.3.3: Exceptions to Closest Packing

Johannes Kepler first broached the idea of atoms as touching spheres in 1611. William Barlow described the systematics of closest-packed structures more than 250 years later in 1883. For a long time, all structures were thought to have simple repetitive closest packing. It was not long after the Braggs’s X-ray studies led to the first crystal structure determination that scientists found exceptions.

In closest-packed structures, the arrangement of anions means that only tetrahedral and octahedral sites are present (Figure 13.12). We can use closest packing to describe metals, sulfides, halides, some oxides, and other structures in which all cations are in tetrahedral or octahedral coordination. Sphalerite (ZnS), halite (NaCl), and native metals gold, silver, platinum, and copper are all examples of cubic closest-packed minerals. Wurtzite (ZnS), magnesium metal, and zinc metal are hexagonal closest packed. Other mineral structures are, however, not truly closest packed. In general, dense minerals with few large cations are most closely packed.

Today we know that some minerals have complicated structures, and that many minerals have polyhedral frameworks that are not closest packed at all. Minerals containing alkali or alkaline earth elements cannot be closest packed because alkalis and alkaline earths are too large to fit in tetrahedral or octahedral sites. The closest-packed model also fails for other minerals, such as fluorite, CaF₂, in which small anions are between large cations, and for metals that have a body-centered cubic structure in which each atom contacts eight others.