Voronoi Tessellation in Model Glass Systems

摘要

Numerical Voronoie tessellation is usedto investigate the mechanisms of frustration in some model glass systems. First, random packings of 8192 hard spheres of increasing volume fraction c are built in the flat three dimensional space using an efficient computer algorithm. Their Voronoie statistics evolves with c as if the system would like to reach a pure icosahedral order when extrapolating the volume fration above the Bernal limit c_b approx = 0.645. Secon, this stydy is extended in curved space, he sphere S_3. When decurving the space by increasing the number N of spheres, the most compact packings converge to the Bernal packing. For particular N values, the volume frations exhibit maxima corresponding to narrower histograms for the number of edges of Voronoie polyhedra faces. Third, super-cooled liquid and glass sampels of 1000 atoms are generated at different temepratures T after a quench from the liquid state, using classical micro-canonical molecular dynamics with a simple soft-sphere potential. when decreasing T, the ideal icosahedral order appears again as an extrapolated situation which cannot be realized due to geometrical frustration.