Space filling of crystal structures A contribution to the graphical presentation of geometrical relationships in simple crystal structures

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Abstract
The well-known but little used concept of space filling proves to be an excellent method for presenting geometrical relationships of different simple crystal structures. By introducing the radius ratio into the equation for space filling it is possible to express space filling in a way which is independent of the particular size of the atoms involved, but is instead characteristic for each structure type. The shape of the space-filling curves allows one to distinguish homeotect structure types, structure types with commutative partial structures and structure types with identical partial structures. The features of space-filling curves can be related to the values in L aves ' construction formula. The space-filling concept can be used to find geometrical correlations which have heretofore been obscured by the differing methods used to describe various structures. By comparing space-filling values one can predict the possible pressure structures of compounds. Finally the space-filling diagram offers a convenient way to present geometrical structure arguments. This is demonstrated for the known relations applicable to valence compounds and Hägg compounds. This discussion is complemented by a further demonstration of the use of space-filling diagrams in respect to certain new relations found to be valid for monosilicides and borides.

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