Shapes of Delaunay Simplexes and Structural Analysis of Hard Sphere Packings

Delaunay Simplexes in Liquid Cyclohexane

“…The value of T close to zero indicates unambiguously that shape of a given simplex is close to the regular tetrahedron shape. As a boundary value of the measure to select a class of "tetrahedral" simplexes (close to shape of perfect tetrahedron) we used T=0.018, proposed in our previous papers, see references in [2,17]. Thus, we are interested in simplexes with T<0.018.…”

“…Delaunay decomposition was made by our programs for classical Voronoi-Delaunay tessellation [16]. For shape analysis of the Delaunay simplexes a "tetrahedricity" measure was used [2,17]:…”

“…Recently an extensive investigation of a large set of disordered packings of hard spheres with different packing fractions demonstrated that more dense packings contain more Delaunay simplexes (fours of the mutually closest spheres) with shape similar to perfect tetrahedron [1,2]. Increase in density of a packing is explained by appearance of additional tetrahedral configurations of spheres.…”

“…They spring up naturally in packings. Further to formation of the polytetrahedral clusters is more preferable then crystalline arrangement of tetrahedra [2,4]. In other words, tetrahedra and non-crystalline clusters of them arise easily, and prefer to keep their structure.…”

Microstructure and macroscopic properties of polydisperse systems of hard spheres

“…It therefore becomes highly significant to exploit some other methods of three-dimensional characterization of these structures. Many attempts have already been made to quantify local or long-range ordering, providing further characterization of disordered packings [69,70,[238][239][240][241][242][243][244][245][246].…”