Extended Data Fig. 7: Atomic-scale mechanism of structural relaxation for a locally favoured structure in fragile liquids (liquid I and PHD).

a-c, Liquid I. a, Depiction of an LFS motif comprised of 8 red particles exhibiting a pentagonal shape (marked by orange lines). Each particle is labelled with numbers 1-8 to monitor their movements. b, Illustration of the LFS transformation into an intermediate disordered state by two T1 processes (yellow triangles). Each T1 process involves four particles breaking old bonds and creating new ones. c, Formation of a new LFS (orange pentagon) through two successive T1 processes (yellow triangles). The centre of the new LFS retains 6 old neighbours and gains a new neighbour, resulting in the transformation from the initial loose pentagon-shaped arrangement to a new, tight-packed LFS. Therefore, the old LFS shown in panel a undergoes a rotation to transform into the new LFS through this particle rearrangement process. B particles are shown in blue and large, while A particles are depicted in green for better visualisation. d-f, PHD. d, Depiction of an LFS motif with hexatic ordering. Each particle is labelled with numbers 1–9 to track their movements. e, Occurrence of a T1 process among atoms 1–2–3–7 from panel d, creating an intermediate disordered state. f, Another T1 process among atoms 1–4–8–9 from panel e. The central atom (red) escapes from its initial cage formed by atoms 2–3–4–5–6–7 (see panel d) while maintaining the order of 4–5–7–3–8–9 during sequential T1 events. In this polydisperse system, atoms are represented as equal-sized for simplicity in visualisation.