sp3-Bonded silicon allotropes based on the Kelvin problem.

The Kelvin problem, how to partition three-dimensional space into cells of equal volume with minimal area, is a fascinating one. Aggregations of bubbles are naturally physical illustrations of the Kelvin problem. And the superconductor Na8Si46 as an inspiration leads to an amazing discovery of the Weaire-Phelan (WP) structure of foam - the optimal solution to the Kelvin problem to date. Here based on the structural similarity between sp(3)-bonded silicon allotropes and the solutions to the Kelvin problem, a series of new sp(3)-hybridization silicon allotropes, named "Kelvin Silicons", are presented. Furthermore, the structural stability and electronic properties of these new silicon allotropes are investigated using density-functional theory (DFT) calculations. The results show that Kelvin Silicons are structurally stable semiconductors with indirect bandgaps in the range of 0.17-1.40 eV, and their bulk moduli are about 75.9-88.5% that of the diamond phase. The simulated X-ray diffraction spectra of the new silicon crystalline structures would provide more information for possible experimental observations and synthesis.