Condensed Matter Theory

Abstract:

Theoretical modeling is presented for a freestanding vitreous silica bilayer which has recently been synthesized and characterized experimentally in landmark work. While such two-dimensional continuous random covalent networks should likely occur on energetic grounds, no synthetic pathway had been discovered previously. Here the bilayer is modeled using a computer assembly procedure initiated from a single layer of a model of amorphous graphene, generated using a bond-switching algorithm from an initially crystalline graphene structure. Each bond is decorated with an oxygen atom and the carbon atoms are relabeled as silicon, generating a two-dimensional network of corner-sharing triangles. Each triangle is transformed into a tetrahedron, by raising the silicon atom above each triangular base and adding an additional singly coordinated oxygen atom at the apex. The final step in this construction is to mirror-reflect this layer to form a second layer and attach the two layers to form the bilayer. We show that this vitreous silica bilayer has the additional macroscopic degrees of freedom to form easily a network of identical corner-sharing tetrahedra if there is a symmetry plane through the center of the bilayer going through the layer of oxygen ions that join the upper and lower monolayers. This has the consequence that the upper rings lie exactly above the lower rings, which are tilted in general. The assumption of a network of perfect corner- sharing tetrahedra leads to a range of possible densities that we characterize as a flexibility window, with some similarity to flexibility windows in three dimensional zeolites. Finally, using a realistic potential, we have relaxed the bilayer to determine the density and other structural characteristics such as the Si-Si pair distribution functions and the Si-O-Si bond angle distribution, which are compared with experimental results obtained by direct imaging.

Abstract:

This is a first undergraduate textbook in Solid State Physics or Condensed Matter Physics. While most textbooks on the subject are extremely dry, this book is written to be much more exciting, inspiring, and entertaining.