Synthetic diamond and wurtzite structures self-assemble with isotropic pair interactions

2007/03/26 by Mikael C. Rechtsman, Frank H. Stillinger, Salvatore Torquato · 1 voice · 8 citations
Physics and Astronomy · #Photonic Crystals and Applications #Random lasers and scattering media #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.soft

paper · pdf · doi:10.1103/physreve.75.031403

published as Phys. Rev. E 75, 031403 (2007) · 16 pages, 10 figures

openalex publication_date 2007/03/26 · arxiv created 2007/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Designed interaction potentials via inverse methods for self-assembly

Cited by

• Computational self-assembly of a one-component icosahedral quasicrystal
• Novel ground-state crystals with controlled vacancy concentrations: From kagomé to honeycomb to stripes
• Self-Assembly of Monatomic Complex Crystals and Quasicrystals with a Double-Well Interaction Potential
• Negative Poisson’s Ratio Materials via Isotropic Interactions
• Probing the limitations of isotropic pair potentials to produce ground-state structural extremes via inverse statistical mechanics
• Inverse Design of Simple Pair Potentials for the Self-Assembly of Complex Structures
• Soft matter crystallography -- complex, diverse, and new crystal structures in condensed materials on the mesoscale
• Simulating complex crystal structures using the phase-field crystal model

Discussions

• In principle, there is no hard rule that says that isotropic pair potentials cannot give rise to low-coordinated crystal structures. In fact, there are several papers where the authors have carefully [stackexchange, 1 points]