We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and can describe elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures aroun...

In this paper, we verify the diameter of zero divisor graphs with respect to direct product. Keywords—Atomic lattice, complement of graph, diameter, direct product of lattices, 0-distributive lattice, girth, product of graphs, prime ideal, zero divisor graph.

Combinatorial test design (CTD) is an effective test design technique, considered to be a testing best practice. CTD provides automatic test plan generation, but it requires a manual definition of the test space in the form of a combinatorial model. As the system under test evolves, e.g., due to iterative development processes and bug fixing, so does the test space, and thus, in the context of ...

The structure of CeO2 films grown on (1102) sapphire and on YBCO thin films was investigated. The films reported on here were grown by pulsed excimer laser deposition and their surface structure was probed using atomic force microscopy. We found that CeO2 films grown on sapphire were epitaxial with a granular structure which is smooth on an atomic scale. We see evidence of a surface reconstruct...

Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra E that is not an orthomodular lattice there exists an (o)continuous state ω on E, which is subadditive. Moreover, we show properties of finite and compact elements of such lattice effect algebras.

The theory of Bloembergen and Pershan for the light waves at the boundary of nonlinear media is extended to a nonlinear two-dimensional (2D) atomic crystal, i.e., a single planar atomic lattice, placed between linear bulk media. The crystal is treated as a zero-thickness interface, a real 2D system. Harmonic waves emanate from it. Generalization of the laws of reflection and refraction give the...

Lattice strain is generated in crystal structures as a result of atomic size differences between host atom and solute elements during substitutional alloying. Extensive work has been performed to study lattice parameter variation with alloying elements, primarily using diffraction methods. The global information provided by reciprocal space analysis, however, limits access to local structural d...

Mapping atomic displacement at the nanoscale is crucial for developing and optimizing strain-engineered devices. In today’s transistors, a slight deformation of the silicon lattice in the source-drain regions enhances their performance. And in the future, strain-induced electro-optic effects may potentially form the basis of an all-silicon electronic and photonic device. Transmission electron m...

Flexible boundary condition methods couple an isolated defect to a harmonically responding medium through the bulk lattice Green’s function; in the case of an interface, interfacial lattice Green’s functions. We present a method to compute the lattice Green’s function for a planar interface with arbitrary atomic interactions suited for the study of line defect/interface interactions. The interf...