Properties of the Voronoi tessellations arising from the random 2D distribution points are reported. We applied the procedure of dividing the sides of Voronoi cells into equal or random parts to Voronoi diagrams generated by a set of randomly placed on the plane points. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude, that by applying even a simple set of rules to a random set of seeds we introduce order into an initially disordered system. At the same time, the Voronoi entropy showed a tendency to values typical for completely random patterns and did not distinguish the short-range ordering. The Voronoi entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase of the number of the iteration steps. Voronoi entropy grew, with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Voronoi entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Voronoi entropy.

Many studies of hypervelocity impact craters have described the characteristics of quartz grains shock-metamorphosed at high pressures of > 10 GPa. In contrast, few studies have investigated shock metamorphism at lower shock pressures. In this study, we test the hypothesis that low-pressure shock metamorphism occurs in near-surface nuclear airbursts and that this process shares essential characteristics with crater-forming impact events. To investigate low-grade shock microstructures, we compared quartz grains from Meteor Crater, a 1.2-km-wide impact crater, to those from near-surface nuclear airbursts at the Alamogordo Bombing Range, New Mexico in 1945 and Kazakhstan in 1949/1953. This investigation utilized a comprehensive analytical suite of high-resolution techniques, including transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD). Meteor Crater and the nuclear test sites all exhibit quartz grains with closely-spaced, sub-micron-wide fractures that appear to have formed at low shock pressures. Significantly, these micro-fractures are closely associated with Dauphiné twins and are filled with amorphous silica (glass), widely considered a classic indicator of shock metamorphism. Thus, this study confirms that glass-filled shock fractures in quartz form during near-surface nuclear airbursts, as well as crater-forming impact events, and by extension, it suggests that they may form in any near-surface cosmic airbursts in which the shockwave is coupled to Earth’s surface. The robust characterization of such events is crucial because of their potential catastrophic effects on the Earth’s environmental and biotic systems.

Many studies of hypervelocity impact craters have described the characteristics of quartz grains shock-metamorphosed at high pressures of >10 GPa, but in contrast, few studies have investigated shock metamorphism at lower shock pressures. In this study, we test the hypothesis that low-pressure shock metamorphism occurs in near-surface nuclear airbursts and that this process shares important characteristics with impact-cratering events. To investigate low-grade shock microstructures, we compared quartz grains from Meteor Crater, a 1.2-km-wide impact crater, to those from near-surface nuclear airbursts at the Alamogordo Bombing Range, New Mexico in 1945 and Kazakhstan in 1949/1953. This investigation utilized a comprehensive analytical suite of high-resolution techniques, including transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD). Meteor Crater and the nuclear test sites all exhibit metamorphosed quartz grains with closely-spaced, sub-micron-wide fractures that appear to have formed at low shock pressures. Importantly, these micro-fractures are closely associated with Dauphiné twins and are filled with amorphous silica (glass), widely considered to be a classic indicator of shock metamorphism. Thus, this study confirms that glass-filled shock fractures in quartz form during near-surface nuclear airbursts, as well as crater-forming impact events, and by extension, it suggests they also may form in near-surface cosmic airbursts.