content_image/332886.jpg content_image/332884.jpg
then the correlation length is given by 

where n$_{s}$ is the number of clusters of size s in the packing. 

<img src='content_image/332886.jpg'>

<img src='content_image/332884.jpg'>

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. 

## E. Radial distribution function 

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. 

