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

Non-perturbative embedding of local defects in crystalline materials

We present a new variational model for computing the electronic first-order density matrix of a crystalline material in presence of a local defect. A natural way to obtain variational discretizations of this model is to expand the difference Q between the density matrix of the defective crystal and the density matrix of the perfect crystal, in a basis of precomputed maximally localized Wannier functions of the reference perfect crystal. This approach can be used within any semi-empirical or Density Functional Theory framework.Comment: 13 pages, 4 figure

Use of Local Materials In The Preservation of Garcinia Kola (Bitter Kola) Seeds

Storage of Bitter kola (Garcinia kola) was carried out using different local materials to evaluate the most appropriate storage material relative to the extension of its shelf life. The materials were kept moist by wetting them throughout the period of study (8 weeks). The local materials used were sandy soil, jute bag, clay pot and Plantain leaves. Three different parameters were used to assess the effectiveness of these local materials. The parameters were weight loss, colour change and shrinkage.Colour and shrinkage were evaluated visually. For weight loss, storage materials were significantly different (

Local origins of volume fraction fluctuations in dense granular materials

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and inter-particle friction $\mu$ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Vorono\"i tessellation, we find the variance of the local volume fraction $\phi$ monotonically decreases as the system becomes more dense, independent of boundary condition and $\mu$. We examine the universality and origins of this trend using experiments and the recent granocentric model \cite{Clusel-2009-GMR,Corwin-2010-MRP}, modified to draw particle locations from an arbitrary distribution ${\cal P}(s)$ of neighbor distances $s$. The mean and variance of the observed ${\cal P}(s)$ are described by a single length scale controlled by $\bar \phi$. Through the granocentric model, we observe that diverse functional forms of ${\cal P}(s)$ all produce the trend of decreasing fluctuations, but only the experimentally-observed ${\cal P}(s)$ provides quantitative agreement with the measured $\phi$ fluctuations. Thus, we find that both ${\cal P}(s)$ and ${\cal P}(\phi)$ encode similar information about the ensemble of observed packings, and are connected to each other by the local granocentric model

Thermodynamics of non-local materials: extra fluxes and internal powers

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic

More ferroelectrics discovered by switching spectroscopy piezoresponse force microscopy?

The local hysteresis loop obtained by switching spectroscopy piezoresponse force microscopy (SS-PFM) is usually regarded as a typical signature of ferroelectric switching. However, such hysteresis loops were also observed in a broad variety of non-ferroelectric materials in the past several years, which casts doubts on the viewpoint that the local hysteresis loops in SS-PFM originate from ferroelectricity. Therefore, it is crucial to explore the mechanism of local hysteresis loops obtained in SS-PFM testing. Here we proposed that non-ferroelectric materials can also exhibit amplitude butterfly loops and phase hysteresis loops in SS-PFM testing due to the Maxwell force as long as the material can show macroscopic D-E hysteresis loops under cyclic electric field loading, no matter what the inherent physical mechanism is. To verify our viewpoint, both the macroscopic D-E and microscopic SS-PFM testing are conducted on a soda-lime glass and a non-ferroelectric dielectric material Ba0.4Sr0.6TiO3. Results show that both materials can exhibit D-E hysteresis loops and SS-PFM phase hysteresis loops, which can well support our viewpoint.Comment: 12 pages,4 figure

JUXTAPOSING L 1 CULTURE AND L 2 CULTURE IN ELT MATERIALS

It is generally agreed that learning language means learning culture since language is a part of culture. In English Language Teaching (ELT) context, the process of teaching and learning will basically involve two cultures: L1 culture referring to the learner’s culture (local culture) and L2 culture to the target culture. From this perspective, ELT materials can roughly be divided into two kinds: the ones orientated to local culture and the ones to Anglo or American culture. In order to make ELT materials more balanced, an English teacher may juxtapose or combine the L1 and L2 cultures in his/ her materials. One of the benefits is the learners will get broader cultural perspectives so that they will be more prepared to be a global citizen. This paper aims to propose practical teaching ideas in which an English teacher may include L1 and L2 cultures in his/her teaching materials