Diverse densest ternary sphere packings

Abstract The exploration of the densest structures multi-sized hard spheres under periodic boundary conditions is a fundamental problem in mathematics and wide variety sciences including materials science. We present our exhaustive computational ternary sphere packings (DTSPs) for 451 radius ratios 436 compositions on top previous study [Koshoji Ozaki, Phys. Rev. E 104, 024 101 (2021)]. unbiased by random structure searching method discovers diverse 22 putative DTSPs, thereby 60 DTSPs are identified total 38 discussed study. Some discovered well-ordered, example, medium (9-7-3) placed straight line with comprising unit cell, DTSP has Pm 3 ¯ m symmetry if structural distortion corrected. At considerable number ratios, highest packing fractions achieved phase separations consisting only FCC and/or binary (DBSPs) all compositions. trend becoming more evident as small getting larger, which suggests either actually or that dense have cells larger than those this On other hand, increase particle size gets small. diversity indicates many unknown may hide very narrow range ratio where smaller due to competition respect candidates. Finally, we discuss correspondence real crystals based space group. Our can be effectively used prototypes ternary, quaternary, quinary crystal structures.