Close-Packing Model for the Alum Crystal

Problem The explanation for the symmetric octahedral shape of the crystal lies in its chemical structure which can be described as a cubic packing of hydrated potassium ions whose octahedral and tetrahedral gaps are filled with hydrated aluminum ions and sulfate ions, respectively. If one assumes the simple particle model of alum particles and chooses the spherical model for one alum particle, then one can explain the simple structure as a cubic close packing of many similar spheres. It is possible to reconstruct such a sphere packing in an octahedral form and it can be recognized as a structural model when compared with the original crystal. 

Material 100 spheres (cellulose or styrofoam, white, 30 mm diameter), glue. 

Procedure Glue together a layer of 5 x 5 spheres in a square shape, in addition glue together further layers with 4x4 spheres, with 3x3 and with 2x2 spheres. Place these layers upon each other as demonstrated (see Fig. 4.3). Finish the arrangement placing one single sphere on top, and another sphere at the bottom. 

Observation Octahedral shapes of alum crystals and close-packing models are identical. 

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