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Mechanically stable sphere packings are generated in three-dimensional spaceusing the discrete element method, which span a wide range in structural order,ranging from fully amorphous to quasi-ordered structures, as characterized bythe bond orientational order parameter. As the packing pressure, $p$, variesfrom the marginally rigid limit at the jamming transition ($p \approx 0$) tothat of more robust systems ($p \gg 0$), the coordination number, $z$, followsa familiar scaling relation with pressure, namely, $\Delta z = z - z_c \simp^{1/2}$, where $z_c = 2d = 6$ ($d=3$ is the spatial dimension). While it haspreviously been noted that $\Delta z$ does indeed remain the control parameterfor determining the packing properties, here we show how the packing structureplays an influential role on the mechanical properties of the packings.Specifically, we find that the elastic (bulk $K$ and shear $G$) moduli,generically referred to as $M$, become functions of both $\Delta z$ and thestructure, to the extent that $M-M_c \sim \Delta z$. Here, $M_c$ are values ofthe elastic moduli at the jamming transition, which depend on the structure ofthe packings. In particular, the zero shear modulus, $G_c=0$, is a specialfeature of fully amorphous packings, whereas more ordered packings take larger,positive values, $G_c > 0$.

Structural and mechanical characteristics of sphere packings near the jamming transition: From fully amorphous to quasi-ordered structures