M.C. Rechtsman
Department of Physics, Princeton University, Princeton, New Jersey, 08544, USA

F. H. Stillinger
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

S. Torquato
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA; Program in Applied and Computational Mathematics and PRISM, Princeton, New Jersey, 08544, USA; Princeton Center for Theoretical Physics, Princeton, New Jersey, 08544, USA

Phys. Rev. E 75, 031403 (2007).

(Received 23 September 2006; revised 11 January 2007; published 26 March 2007)

Abstract

Using inverse statistical-mechanical optimization techniques, we have discovered isotropic pair interaction potentials with strongly repulsive cores that cause the tetrahedrally coordinated diamond and wurtzite lattices to stabilize, as evidenced by lattice sums, phonon spectra, positive-energy defects, and self-assembly in classical molecular dynamics simulations. These results challenge conventional thinking that such open lattices can only be created via directional covalent interactions observed in nature. Thus, our discovery adds to fundamental understanding of the nature of the solid state by showing that isotropic interactions enable the self-assembly of open crystal structures with a broader range of coordination number than previously thought. Our work is important technologically because of its direct relevance generally to the science of self-assembly and specifically to photonic crystal fabrication.