Ring structure of selected two-dimensional procrystalline lattices

Breaking Rayleigh's Law with Spatially Correlated Disorder to Control Phonon Transport

Controlling thermal transport in insulators and semiconductors is crucial for many technological fields such as thermoelectrics and thermal insulation, for which a low thermal conductivity (κ) is desirable. A major obstacle for realizing low κ materials is Rayleigh's law, which implies that acoustic phonons, which carry most of the heat, are insensitive to scattering by point defects at low energy. We demonstrate, with large scale simulations on tens of millions of atoms, that isotropic long-range spatial correlations in the defect distribution can dramatically reduce phonon lifetimes of important low-frequency heat-carrying modes, leading to a large reduction of κ-potentially an order of magnitude at room temperature. We propose a general and quantitative framework for controlling thermal transport in complex functional materials through structural spatial correlations, and we establish the optimal functional form of spatial correlations that minimize κ. We end by briefly discussing experimental realizations of various correlated structures.

The network structure of the corneal endothelium

A generic network model is applied to study the structure of the mammalian corneal endothelium. The model has been shown to reproduce the network properties of a wide range of systems, from low-dimensional inorganic glasses to colloidal nanoparticles deposited on a surface. Available extensive experimental microscopy results are analyzed and combined to highlight the behavior of two key metrics, the fraction of hexagonal rings (p₆) and the coefficient of variation of the area. Their behavior is analyzed as a function of patient age, the onset of diabetes, and contact lens wearing status. Wearing contact lenses for ∼10 years is shown to change the endothelium structure by the equivalent of ∼30 years contact lens-free. Model network configurations are obtained using a Monte Carlo bond-switching algorithm, with the resulting topologies controlled by two potential model parameters (the bond and angular force constants) and the Monte Carlo temperature. The effect of systematically varying these parameters is investigated. In addition, the effect of constraining the ring size distribution is investigated. The networks generated with relatively weak bond force constants are shown to correlate best with the experimental information. The importance of extracting the full ring size distribution (rather than simply the fraction of hexagons) is discussed.

Truchet-tile structure of a topologically aperiodic metal-organic framework

When tiles decorated to lower their symmetry are joined together, they can form aperiodic and labyrinthine patterns. Such Truchet tilings offer an efficient mechanism of visual data storage related to that used in barcodes and QR codes. We show that the crystalline metal-organic framework [OZn₄][1,3-benzenedicarboxylate]₃ (TRUMOF-1) is an atomic-scale realization of a complex three-dimensional Truchet tiling. Its crystal structure consists of a periodically arranged assembly of identical zinc-containing clusters connected uniformly in a well-defined but disordered fashion to give a topologically aperiodic microporous network. We suggest that this unusual structure emerges as a consequence of geometric frustration in the chemical building units from which it is assembled.

Mesoscopic Structures and Coexisting Phases in Silica Films

Silica films represent a unique two-dimensional film system, exhibiting both crystalline and vitreous forms. While much scientific work has focused on the atomic-scale features of this film system, mesoscale structures can play an important role for understanding confined space reactions and other applications of silica films. Here, we report on mesoscale structures in silica films grown under ultrahigh vacuum and examined with scanning tunneling microscopy (STM). Silica films can exhibit coexisting phases of monolayer, zigzag, and bilayer structures. Both holes in the film structure and atomic-scale substrate steps are observed to influence these coexisting phases. In particular, film regions bordering holes in silica bilayer films exhibit vitreous character, even in regions where the majority film structure is crystalline. At high coverages mixed zigzag and bilayer phases are observed at step edges, while at lower coverages silica phases with lower silicon densities are observed more prevalently near step edges. The STM images reveal that silica films exhibit rich structural diversity at the mesoscale.

Persistent homology in two-dimensional atomic networks

The topology of two-dimensional network materials is investigated by persistent homology analysis. The constraint of two dimensions allows for a direct comparison of key persistent homology metrics (persistence diagrams, cycles, and Betti numbers) with more traditional metrics such as the ring-size distributions. Two different types of networks are employed in which the topology is manipulated systematically. In the first, comparatively rigid networks are generated for a triangle-raft model, which are representative of materials such as silica bilayers. In the second, more flexible networks are generated using a bond-switching algorithm, which are representative of materials such as graphene. Bands are identified in the persistence diagrams by reference to the length scales associated with distorted polygons. The triangle-raft models with the largest ordering allow specific bands B_n (n = 1, 2, 3, …) to be allocated to configurations of atoms separated by n bonds. The persistence diagrams for the more disordered network models also display bands albeit less pronounced. The persistent homology method thereby provides information on n-body correlations that is not accessible from structure factors or radial distribution functions. An analysis of the persistent cycles gives the primitive ring statistics, provided the level of disorder is not too large. The method also gives information on the regularity of rings that is unavailable from a ring-statistics analysis. The utility of the persistent homology method is demonstrated by its application to experimentally-obtained configurations of silica bilayers and graphene.