Structural characterization of soft-core and hard-core glasses by Delaunay tessellation

Abstract

Methods of the Delaunay and Voronoi tessellation are applied to investigate significant structures and structural differences among liquids, glasses, and crystals of the soft-core (inverse 12th power potential) and hard-core models for which molecular dynamics (MD) techniques are used. With particle configurations obtained by MD simulations the Delaunay tessellation for the three dimensional systems defines uniquely a network of tetrahedra. Density dependent properties of the irregularity distribution which measures the magnitude of distortion of each Delaunay tetrahedron (DT) from regular shape (equal edge lengths) and of the length of edges of DT are examined in detail for both models. Clear differences between the hard-core and soft-core systems are observed. Short range correlation of DT is calculated on the pair distribution function of center-to-center distances of the circumspheres of DT, which turns out to be useful to distinguish the short range order of glasses from that of crystals or liquids. It is also shown that there are no clear differences in the distribution of various types of Voronoi polyhedron (VP) between liquids and glasses. However, among various types of polygons (i-edged faces) of VP, the contribution from i=5 increases rather rapidly with increasing density around the glass transition point.

Random close packing of spheres in a round cell

“…We rationalize this by noting that in these early models there were many Ôcollineations', and clusters with many 12 contact points, giving local order which allows for densification, thus releasing free space and destabilising the structure. Also found in more recent simulations were regular tetrahedra that can be joined into a ring of five (R5) with minimum distortion, which is considered important in characterisation of glasses [14]. In simulated sodium glasses, the presence of approximately 3% of icosahedra was found [19].…”

“…There are other measures of orientational order, for example, (i) spherical harmonics [8], (ii) standard deviation of areas of spherical triangles formed by contact points [13], or (iii) distortion of Delauny tetragonal edges [14]. Ziman noted that a disordered system cannot be adequately described analytically unless we go up the hierarchy of distribution functions, to higher order [15].…”

Structural anomalies of fluids: Origins in second and higher coordination shells

“…5,6,7,8,9,10,11,12,13,14,15 Although the second shell of the RDF has received comparatively less attention, there is evidence that it also contains structural information relevant for understanding nontrivial behaviors of liquids. One notable feature is the shoulder 16 that it develops near the freezing transition, which in turn becomes a pronounced split peak 17,18,19,20,21,22,23,24,25,26 in supercooled liquid and glassy states. Analysis of the configurations that give rise to this structural motif indicate that it reflects frustration of icosahedral 23 and emerging crystalline 16,26 order in the fluid.…”

Role of local structure on motions on the potential energy landscape for a model supercooled polymer

“…In these simulations, particles have been classified into liquid-or solid-like categories on the basis of free volume, and various measures of shape 14 and distortion 15 of the Voronoi polyhedra and Delaunay simplices. 16,17 Structural signatures in the form of percolation thresholds 14,18,19 of Delaunay networks and increase in icosahedral ordering [20][21][22] have been observed near T g . Further, a higher degree of icosahedral order has been observed when the cooling rate is reduced.…”