FIG. 8: Correlation length ξ of crystalline clusters. To calculate the correlation length, we first introduce the radius of gyration, R$_{g}$ ( s ), of a cluster consisting of s particles. The correlation length of a perfect FCC lattice with periodic boundary condition is L/ 2, where L is the system size, so the correlation length is scaled by L/ 2 in the figure. The crystalline clusters start to percolate at φ$_{j}$ = 0 . 68 as ξ/ ( L/ 2) reaches a plateau with value 1. The results also show that the percolation at φ$_{melt}$ does not depend on the system size. then the correlation length is given by where n$_{s}$ is the number of clusters of size s in the packing. The correlation length ξ of the crystalline clusters is measured near the melting point. Figure 8 confirms the linear increase of the size of crystals along the coexistence region from the freezing point where ξ = 0 to the melting point. When the system melts at φ$_{melt}$ , ξ reaches a plateau consistent with the system size. The radial distribution function g ( r ) of the packing with volume fraction 0.72 in Fig. 9 shows all the peaks in FCC and HCP packings, which are indications of long range spatial order. On the other hand, the radial distribution functions of random packings only have two or three peaks (the second peak splits at φ$_{j}$ = 0 . 64), corresponding to short range order. E. Radial distribution function ξ 2 = 2 ∑ s R 2 g ( s ) s $^{2}$n$_{s}$ s s $^{2}$n$_{s}$ , (19) 26 0.56 0.60 0.64 0.68 0.72 0.0 0.2 0.4 0.6 0.8 1.0 GLYPH<a241> GLYPH<a242> GLYPH<a243> GLYPH<a244> GLYPH<a245> GLYPH<a246> GLYPH<a247> GLYPH<a248> GLYPH<a249> GLYPH<a250> GLYPH<a251> GLYPH<a252> /( L /2) j