FIG. 7: (A) Distributions of local disorder θ fcc i defined in Eq. (13) for packings with different φ$_{j}$ as indicated. The distribution functions below φ$_{j}$ = 0 . 64 are Gaussian, the center of the peak moves to θ fcc i = 0 . 2 as the volume fraction φ$_{j}$ approaches 0.64. This disordered peak decreases above φ$_{j}$ = 0 . 64 and seems to disappear above φ$_{j}$ = 0 . 68. Two ordered peaks appear after RCP, the one at θ fcc i = 0 corresponds to FCC structure, while the other one at θ fcc i = 0 . 16 corresponds to HCP. The peak at zero eventually evolves to a delta function as the packing structure approaches a perfect FCC. We use the median of the FCC peak and the disordered peak at φ$_{j}$ = 0 . 64 as a cutoff to identify local FCC structure, ie., particles with θ fcc i < θ fcc c are defined as FCC crystalline nuclei, where θ fcc c = 0 . 1. (B) Distributions of local disorder θ hcp i defined in Eq. (14) for packings with different φ$_{j}$ as indicated. The distribution functions have similar behavior as those of θ fcc i . The cutoff θ hcp c = 0 . 075 is used to identify HCP crystalline nuclei. Note that to calculate the values properly, we first need to sort the angles θ$_{ijk}$ , θ fcc $_{jk}$, θ hcp jk , θ icos jk , θ bcc jk and θ sc $_{jk}$, and then compare them one by one. Also note that the BCC and SC clusters have fewer neighbors than FCC, HCP and icosahedral clusters. 24 θ icos i = √ 1 66 11 ∑ j =1 12 ∑ k = j +1 ( θ$_{ijk}$ − θ icos jk ) $^{2}$, (15) θ bcc i = √ 1 28 7 ∑ j =1 8 ∑ k = j +1 ( θ$_{ijk}$ − θ bcc jk ) $^{2}$, (16) θ sc i = √ 1 15 5 ∑ j =1 6 ∑ k = j +1 ( θ$_{ijk}$ − θ sc jk ) $^{2}$. (17) (B) 0.00 0.05 0.10 0.15 0.20 0 20 40 60 GLYPH<a209> GLYPH<a210> GLYPH<a211> P ( GLYPH<a212> GLYPH<a213> GLYPH<a214> ) GLYPH<a215> GLYPH<a216> GLYPH<a217> GLYPH<a218> GLYPH<a219> GLYPH<a220> GLYPH<a221> GLYPH<a222> GLYPH<a223> GLYPH<a224> GLYPH<a225> GLYPH<a226> GLYPH<a227> GLYPH<a228> GLYPH<a229> GLYPH<a230> GLYPH<a231> GLYPH<a232> GLYPH<a233> GLYPH<a234> GLYPH<a235> GLYPH<a236> GLYPH<a237> GLYPH<a238> GLYPH<a239> GLYPH<a240> (A) 0.00 0.05 0.10 0.15 0.20 0.25 0 20 40 120 ➧ ➨ ➩ P ( ➫ ➭ ➯ ) ➲ ➳ ➵ ➸ ➺ ➻ ➼ ➽ ➾ ➚ ➪ ➶ ➹ ➘ ➴ ➷ ➬ ➮ ➱ ✃ ❐ ❒ ❮ ❰ GLYPH<a207> GLYPH<a208>