Closest Sphere Packings as Models for Metal Crystals

2 Closest Sphere Packings as Models for Metal Crystals 

Problem The structure of many metal crystals can best be described by using closest sphere packing models. Because there are two possibilities of systematically sphere packings, these should be introduced first (see also Figs. 5.3 and 5.4). Both packings can be differentiated by the layering sequence ABAB and ABCA - with respect to the densely packed triangular layers. 

Procedure and Observation (a) First, build triangles made of 3 spheres and hexagonal layers made of 7 spheres (see picture). Layer them on top of each other in two different layering sequences ABAB relates to the hexagonal closest packing, ABCA relates to the cubic closest packing (see Fig. 5.3). Determine the coordination number for each one sphere is touched in each case by 12 other 

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