62,084 research outputs found
Atom-Based Geometrical Fingerprinting of Conformal Two-Dimensional Materials
The shape of two-dimensional materials plays a significant role on their chemical and physical properties. Two-dimensional materials are basic meshes that are formed by mesh points (vertices) given by atomic positions, and connecting lines (edges) between points given by chemical bonds. Therefore the study of local shape and geometry of two-dimensional materials is a fundamental prerequisite to investigate physical and chemical properties. Hereby the use of discrete geometry to discuss the shape of two-dimensional materials is initiated.
The local geometry of a surface embodied in 3D space is determined using four invariant numbers from the metric and curvature tensors which indicates how much the surface is stretched and curved under a deformation as compared to a reference pre-deformed conformation.
Many different disciplines advance theories on conformal two-dimensional materials by relying on continuum mechanics and fitting continuum surfaces to the shape of conformal two-dimensional materials. However two-dimensional materials are inherently discrete. The continuum models are only applicable when the size of two-dimensional materials is significantly large and the deformation is less than a few percent. In this research, the knowledge of discrete differential geometry was used to tell the local shape of conformal two-dimensional materials. Three kind of two-dimensional materials are discussed: 1) one atom thickness structures such as graphene and hexagonal boron nitride; 2) high and low buckled 2D meshes like stanene, leadene, aluminum phosphate; and, 3) multi layer 2D materials such as Bi2Se3 and WSe2. The lattice structures of these materials were created by designing a mechanical model - the mechanical model was devised in the form of a Gaussian bump and density-functional theory was used to inform the local height; and, the local geometries are also discussed
Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations
We constructed physically stable sp2 negatively curved cubic carbon
structures which reticulate a Schwarz P-like surface. The method for
constructing such crystal structures is based on the notion of the standard
realization of abstract crystal lattices. In this paper, we expound on the
mathematical method to construct such crystal structures
Bending Frustration of Lipid-Water Mesophases Based on Cubic Minimal Surfaces
Inverse bicontinuous cubic phases are ubiquitous in lipid-water mixtures and
consist of a lipid bilayer forming a cubic minimal surface, thereby dividing
space into two cubic networks of water channels. For small hydrocarbon chain
lengths, the monolayers can be modeled as parallel surfaces to a minimal
midsurface. The bending energy of the cubic phases is determined by the
distribution of Gaussian curvature over the minimal midsurfaces which we
calculate for seven different structures (G, D, P, I-WP, C(P), S and F-RD). We
show that the free-energy densities of the structures G, D and P are
considerably lower than those of the other investigated structures due to their
narrow distribution of Gaussian curvature. The Bonnet transformation between G,
D, and P implies that these phases coexist along a triple line, which also
includes an excess water phase. Our model includes thermal membrane
undulations. Our qualitative predictions remain unchanged when higher order
terms in the curvature energy are included. Calculated phase diagrams agree
well with the experimental results for 2:1 lauric acid/dilauroyl
phosphatidylcholine and water.Comment: Revtex, 23 pages with 9 postscript figures included, to appear in
Langmui
Discrete model for laser driven etching and microstructuring of metallic surfaces
We present a unidimensional discrete solid-on-solid model evolving in time
using a kinetic Monte Carlo method to simulate micro-structuring of kerfs on
metallic surfaces by means of laser-induced jet-chemical etching. The precise
control of the passivation layer achieved by this technique is responsible for
the high resolution of the structures. However, within a certain range of
experimental parameters, the microstructuring of kerfs on stainless steel
surfaces with a solution of shows periodic ripples,
which are considered to originate from an intrinsic dynamics. The model mimics
a few of the various physical and chemical processes involved and within
certain parameter ranges reproduces some morphological aspects of the
structures, in particular ripple regimes. We analyze the range of values of
laser beam power for the appearance of ripples in both experimental and
simulated kerfs. The discrete model is an extension of one that has been used
previously in the context of ion sputtering and is related to a noisy version
of the Kuramoto-Sivashinsky equation used extensively in the field of pattern
formation.Comment: Revised version. Etching probability distribution and new simulations
adde
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