Figure 4

Topological order and long-range density fluctuations.

(a–d) The ring size statistics for the very first recorded TEM image (density deficit of 0.3%), at the transition point between crystalline and disordered states (3.8%), at a density deficit of 7.1% and at the end of the experiment (19.7%), respectively. (e) Log-normal probability distribution of the ring statistics for the same structures and three literature results (from Refs. 7,8,24). (e) Crystallinity, as calculated from ring statistics as a function of the density deficit. The color bar indicates the transition from the ordered (gray) via nano-crystallite (blue) to a random network (red). (g) Structure of the disordered carbon glass corresponding to a density deficit of ca. 19.7%, with selected sampling areas (avoiding larger holes and edges) for the analysis of density variations. The largest and second largest sampling sizes are shown; smaller ones are obtained by dividing these areas. (h) Density fluctuations at different scales. The plot shows the atom number density (ρ) standard deviation among the boxes versus the box width (w). The 1/w dependence, as shown by the dotted line, indicates the behaviour that would be expected for a completely random structure or white noise. The inset shows the sampling areas corresponding to the data points at the same scale as panel (g).