Fig. 4: \({{v}}_{\mathrm{a}} \propto {{q}}_1^{ - {{d}}}\) in the 3D systems.

\({{v}}_{\mathrm{a}} \propto {{q}}_1^{ - {{d}}}\) (a, b) \(v_{\mathrm{a}}\sim q_1^{ - d}\) with d ≃ 3.0 in 3DHH and 3DWCA glasses with (η, λ) = (0.5, 1.3). c \(v_{\mathrm{a}}\sim q_1^{ - d}\) holds in the crystal regime with d = 2.95 ≃ D (red line) and in the glass regime with d = 2.48 (blue line). Most of the crossover regime can be fitted by \(v_{\mathrm{a}} \propto q_1^{ - 4.03}\) (green line). The abrupt jump of q₁ at ϕ = 0.5 reflects a first-order-like transition in 3D. d Compression-induced crystal-glass transition in the 3DSH system with (η, λ) = (0.4,1.25). Orange, yellow and white spheres denote face-centered cubic, hexagonal close-packed and disordered particles, respectively. They are identified from the weighted bond-orientational order parameters (see Methods)^42,44. The ordered structure becomes completely disordered in a small density range, 0.48 < ϕ < 0.52, reflecting a sharp transition at ϕ = 0.5.