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## C. Local orientational disorder 

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We have established that crystalline structures appear in the coexistence region and solid-like branch. The remaining question is what kind of lattice structure dominates in the crystallized packings. Since the differences of the orientational order parameters, especially Q$_{6}$ , are not significant between different perfect lattice clusters (such as the icosahedral, FCC, HCP, BCC, and SC clusters, see [19], Fig. 2) we apply another measure, the local orientational disorder, to identify the crystalline nuclei as defined in M. Bargiel and E. M. Tory, Adv. Powder Technol. 12 , 533 (2001). 

For a given sphere i , let θ$_{ijk}$ be the angle between the j th and k th neighbors. Furthermore let θ fcc jk , θ hcp jk , θ icos jk be similarly calculated angles for the perfect 13-sphere fragments of FCC, HCP and icosahedral packings, θ bcc jk be the angles for the 8-sphere fragment of a perfect BCC packing, and θ sc jk be the angles for the 6-sphere fragment of a perfect SC packing. The local disorders are defined as following: 

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