Order metrics and order maps of octahedron packings.

We apply the ideal octahedron model and the relaxation algorithm in generating octahedron packings. The cubatic order parameter [ P 4 ] 1 , bond-orientational order metric Q 6 , and local cubatic order parameter P 4 l o c a l of the packings are calculated and their correlations with the packing density are investigated in the order maps. The border curve of packing density separates the geometrically feasible and infeasible regions in the order maps. Observing the transition phenomenon on the border curve, we propose the concept of the maximally dense random packing (MDRP) as the densest packing in the random state in which the particle positions and orientations are randomly distributed and there is no nontrivial spatial correlations among particles. The MDRP characterizes the onset of nontrivial spatial correlations among particles. A special packing with a density about 0.7 is found in the order maps and considered to be the MDRP of octahedra. The P 4 l o c a l is proposed as a new order parameter for octahedron packings, which measures the average order degree in the neighborhoods of particles. The [ P 4 ] 1 , Q 6 and P 4 l o c a l evaluate the order degree of orientation, bond orientation and local structures, respectively and are applied simultaneously to measure the order degree of the octahedron packings. Their thresholds in the random state are determined by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]