Extended Data Fig. 7: The structure and hyperuniformity of weakly polydisperse crystals.
From: Ideal non-crystals as a distinct form of ordered states without symmetry breaking
We characterise crystals with extremely weak polydispersities to demonstrate their similarity to ideal non-crystals. a, Visualisation of a typical crystalline configuration with a polydispersity Δ = 0.231% and steric order Θ = 1.58 × 10−3 (approximately the same as ideal non-crystals). The packing fraction is set to ϕ = 0.92 and particles are coloured according to their steric order Θ. b, The bare configuration corresponding to a without colour coding, which is visually indistinguishable from a perfect hexagonal crystal. This plot gives some intuitive sense of how ordered the obtained ideal non-crystals are compared to the underlying perfect state (Θ=0). c, Spectral density χV(k) for weakly polydisperse crystals with different degree of steric order Θ. The corresponding polydispersities are Δ = 1.155%, 0.577%, 0.231%, 0.115%, and 0.058% for decreasing Θ. d, The plateau value of spectral density when approaching the low-k limit χV(k → 0) as a function of steric order Θ. The dashed line is a power-law extrapolation fitting of the data χV(k → 0) ~ Θ2.
