Figure 5

(Color online) The estimated jamming packing fraction ${\tilde{\varphi }}_j$ as a function of packing fraction $\varphi$ for $d=3$. Shown are systems of 4096 spheres with various expansion rates and systems of 10 976 spheres placed in an fcc lattice with negative expansion rates $\gamma =-{10}^{-4}$, $-{10}^{-5}$, and $-{10}^{-6}$ (last three curves). Also plotted are approximations to the equilibrium EOS for the fluid phase, the coexistence region, and the crystal phase [47], as well as the Percus-Yevick (PY) EOS for the fluid phase. Compare this figure to the curves shown in Figs. 3 and 4. For the curves showing no partial crystallization (i.e., $\gamma =32⨰{10}^{-6}$, $64⨰{10}^{-6}$, and $128⨰{10}^{-6}$), curves with smaller expansion rates have larger peak heights. For the curves that show partial crystallization (i.e., $\gamma ={10}^{-6}$, $4⨰{10}^{-6}$, and $16⨰{10}^{-6}$), curves with smaller expansion rates lie farther to the left. For the melting curves (i.e., $\gamma =-{10}^{-4}$, $-{10}^{-5}$, and $-{10}^{-6}$), curves with smaller compression rates lie farther to the right.Reuse & Permissions