Cubic Close Sphere Packings as Models for a Silver Crystal

5 Cubic Close Sphere Packings as Models for a Silver Crystal 

Problem The Ag atoms in a silver crystal are arranged like spheres in the cubic closest packing. Students may pack spheres of the same diameter as densely as possible, thereby casually modeling the correct structure of the silver crystal. The structure is called the cubic close packing because a cubic packing of 14 spheres can be distinguished in the layered sphere structure - the basic cube can be regarded as a reflection of the entire structure. 

Procedure Glue together a triangle with central hole from 27 spheres (see picture below). Layer spheres as tightly as possible. Determine the coordination number. Construct the basic cube (see picture) using 14 spheres. Place the cube totally into the packing. 

Observation A regular tetrahedron is formed by the spheres, the coordination number is 12. It is possible to completely fit the basic cube into the tetrahedron packing with the use of the central hole for one corner of the cube. 

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