Packing concave molecules in crystals and amorphous solids: on the connection between shape and local structure

Abstract

The structure of the densest crystal packings is determined for a variety of concave shapes in 2D constructed by the overlap of two or three discs. The maximum contact number per particle pair is defined and proposed as a useful means of categorizing particle shape. We demonstrate that the densest packed crystal exhibits a maximum in the number of contacts per particle but does not necessarily include particle pairs with the maximum contact number. In contrast, amorphous structures, generated by energy minimisation of high temperature liquids, typically do include maximum contact pairs. The amorphous structures exhibit a large number of contacts per particle corresponding to over-constrained structures. Possible consequences of this over-constraint are discussed.

Keywords:

• dense packing
• molecular crystal
• amorphous structure

Acknowledgements

The authors would like to acknowledge the important contributions of Jean-Pierre Hansen to the theory of simple liquids, the statistical mechanics of freezing and the study of supercooled liquids, contributions for which the authors are indebted. The authors also acknowledge the support of the Australian Research Council through the Discovery Project programme.

Disclosure statement

No potential conflict of interest was reported by the authors.