## Densest ternary sphere packings

In the recent research, we have exhaustively explored the densest ternary sphere packings (DTSPs) under periodic boundary conditions at 45 kinds of radius ratios and 237 kinds of compositions. Since any composition ratio can be achieved by the combination of the densest FCC structures and/or the DBSPs, it is not apparent whether there is at least one DTSP in the densest phase separation at any radius and composition ratio. However, we have successfully constructed the ternary phase diagrams with discovering of 37 putative DTSPs. Furthermore, we have discussed the semi-DTSPs (SDTSPs) that are denser than any phase separation consisting of only the FCC structures and/or the other ternary packings: It means that we exclude the DBSPs when we identified the densest phase separations. As a result, we have discovered 65 SDTSPs, and found that some of SDTSPs are highly well-ordered, characterized by a space group of high symmetry. We expect that discovering not only DTSPs and but also SDTSPs with high symmetries may lead to discovering of novel crystal structures. You can download this paper here.
In this page, we present the phase diagrams for the ternary systems, and describe the discovered 37 putative DTSPs. You can download the structural data of the DTSPs. Note that the names of small, medium, and large spheres are H, Na, Sc, respectively. The radius of Sc is set to be 1.0. You can also download the structural data of the SDTSPs.

Phase diagram and the DTSPs