Refining glass structure in two dimensions

Abstract

Recently determined atomistic scale structures of near-two dimensional bilayers of vitreous silica (using scanning probe and electron microscopy) allow us to refine the experimentally determined coordinates to incorporate the known local chemistry more precisely. Further refinement is achieved by using classical potentials of varying complexity; one using harmonic potentials and the second employing an electrostatic description incorporating polarization effects. These are benchmarked against density functional calculations. Our main findings are that (a) there is a symmetry plane between the two disordered layers; a nice example of an emergent phenomenon, (b) the layers are slightly tilted so that the Si-O-Si angle between the two layers is not $180^{\circ}$ as originally thought but rather $175 \pm 2 ^{\circ}$ and (c) while interior areas that are not completely imagined can be reliably reconstructed, surface areas are more problematical. It is shown that small crystallites that appear are just as expected statistically in a continuous random network. This provides a good example of the value that can be added to disordered structures imaged at the atomic level by implementing computer refinement.Comment: 5 pages, 4 figure

Ring correlations in random networks

“…These new results on 2D glasses have opened up numerous opportunities to study the structure of glasses using actual atomic coordinates. Recent work on 2D glasses includes modeling of silica bilayers [13,14], ring distribution [15], medium-range order [16], suitable boundary conditions to recover missing constraints in the surface [17] and the refinement of experimental samples [18]. Rigidity theory has also uncovered a connection between 2D glasses and jammed disk packings [19,20].…”

Realizations of Isostatic Material Frameworks

“…Recently, silica bilayers have been synthesized [19,20] which are effectively a 2D network of corner-sharing triangle. [25] These triangles are formed with oxygens at their corners. The network has rings of many sizes, but the mean ring size is six.…”

“…An example of the former is SiO 2 or GeO 2 and of the latter is a silica bilayer which, although, is 3D dimensional, but it can be seen as two mirroring layers of 1 atom thick of oxygens connected through bridging atoms to complete the chemical bonds. [25] In 2D glasses, every atom/vertex is fourfold coordinated (four shared constraints), but as each vertex has two degrees of freedom (translational degrees of freedom), 2D glasses are locally isostatic. [27] However, boundary conditions determine the global rigidity of the framework.…”

“…An example of the former is SiO 2 or GeO 2 and of the latter is a silica bilayer which, although, is 3D dimensional, but it can be seen as two mirroring layers of 1 atom thick of oxygens connected through bridging atoms to complete the chemical bonds. [ 25 ]…”

Anchored boundary conditions for locally isostatic networks

“…The red Si atoms at the centers of the triangles in Figure 1 have also been removed for clarity. The boundary is formed as a smooth analytic curve by using a Fourier series with 16 sine and 16 cosines terms to match the number of surface vertices, where the center for the radius r(θ) is placed at the centroid of the 32 boundary vertices [12]. Note that sliding boundary conditions do not require an even number of boundary sites.…”