Abstract: Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.

Abstract: The continuous miniaturization of nanodevices, such as transistors, solar cells, and optical fibers, requires the controlled synthesis of (ultra)thin gate oxides (<10 nm), including Si gate-oxide (SiO2) with high quality at the atomic scale. Traditional thermal growth of SiO2 on planar Si surfaces, however, does not allow one to obtain such ultrathin oxide due to either the high oxygen diffusivity at high temperature or the very low sticking ability of incident oxygen at low temperature. Two recent techniques, both operative at low (room) temperature, have been put forward to overcome these obstacles: (i) hyperthermal oxidation of planar Si surfaces and (ii) thermal or plasma-assisted oxidation of nonplanar Si surfaces, including Si nanowires (SiNWs). These nanooxidation processes are, however, often difficult to study experimentally, due to the key intermediate processes taking place on the nanosecond time scale.
In this Account, these Si nano-oxidation techniques are discussed from a computational point of view and compared to both hyperthermal and thermal oxidation experiments, as well as to well-known models of thermal oxidation, including the Deal−Grove, Cabrera−Mott, and Kao models and several alternative mechanisms. In our studies, we use reactive molecular dynamics (MD) and hybrid MD/Monte Carlo simulation techniques, applying the Reax force field. The incident energy of oxygen species is chosen in the range of 1−5 eV in hyperthermal oxidation of planar Si surfaces in order to prevent energy-induced damage. It turns out that hyperthermal growth allows for two growth modes, where the ultrathin oxide thickness depends on either (1) only the kinetic energy of the incident oxygen species at a growth temperature below Ttrans = 600 K, or (2) both the incident energy and the growth temperature at a growth temperature above Ttrans. These modes are specific to such ultrathin oxides, and are not observed in traditional thermal oxidation, nor theoretically considered by already existing models. In the case of thermal or plasma-assisted oxidation of small Si nanowires, on the other hand, the thickness of the ultrathin oxide is a function of the growth temperature and the nanowire diameter. Below Ttrans, which varies with the nanowire diameter, partially oxidized SiNW are formed, whereas complete oxidation to a SiO2 nanowire occurs only above Ttrans. In both nano-oxidation processes at lower temperature (T < Ttrans), final sandwich c-Si|SiOx|a-SiO2 structures are obtained due to a competition between overcoming the energy barrier to penetrate into Si subsurface layers and the compressive stress (∼2−3 GPa) at the Si crystal/oxide interface. The overall atomic-simulation results strongly indicate that the thickness of the intermediate SiOx (x < 2) region is very limited (∼0.5 nm) and constant irrespective of oxidation parameters. Thus, control over the ultrathin SiO2 thickness with good quality is indeed possible by accurately tuning the oxidant energy, oxidation temperature and surface curvature.
In general, we discuss and put in perspective these two oxidation mechanisms for obtaining controllable ultrathin gate-oxide films, offering a new route toward the fabrication of nanodevices via selective nano-oxidation.

Abstract: Colloidal CsPbX3 (X = Br, Cl, and I) perovskite nanocrystals (NCs) have emerged as promising phosphors and solar cell materials due to their remarkable optoelectronic properties. These properties can be tailored by not only controlling the size and shape of the NCs but also postsynthetic composition tuning through topotactic
anion exchange. In contrast, property control by cation exchange is still underdeveloped for colloidal CsPbX3 NCs. Here, we present a method that allows partial cation exchange in colloidal CsPbBr3 NCs, whereby Pb2+ is exchanged for several isovalent cations, resulting in doped CsPb1−xMxBr3 NCs (M= Sn2+, Cd2+, and Zn2+; 0 < x ≤ 0.1), with preservation of the original NC shape. The size of the parent NCs is also preserved in the product NCs, apart from a small (few
%) contraction of the unit cells upon incorporation of the guest cations. The partial Pb2+ for M2+ exchange leads to a blue-shift of the optical spectra, while maintaining the high photoluminescence quantum yields (>50%), sharp absorption features, and narrow emission of the parent CsPbBr3 NCs. The blue-shift in the optical spectra is attributed to the lattice contraction that accompanies the Pb2+ for M2+ cation exchange and is observed to scale linearly with the lattice contraction. This work opens up new possibilities to engineer the properties of halide perovskite NCs, which to date are demonstrated to be the only known
system where cation and anion exchange reactions can be sequentially combined while preserving the original NC shape, resulting in compositionally diverse perovskite NCs.

Abstract: The polar corundum structure type offers a route to new room temperature multiferroic materials, as the partial LiNbO3-type cation ordering that breaks inversion symmetry may be combined with long-range magnetic ordering of high spin d(5) cations above room temperature in the AFeO(3) system. We report the synthesis of a polar corundum GaFeO3 by a high-pressure, high-temperature route and demonstrate that its polarity arises from partial LiNbO3 -type cation ordering by complementary use of neutron, X-ray, and electron diffraction methods. In situ neutron diffraction shows that the polar corundum forms directly from AlFeO3-type GaFeO3 under the synthesis conditions. The A(3+)/Fe3+ cations are shown to be more ordered in polar corundum GaFeO3 than in isostructural ScFeO3. This is explained by DFT calculations which indicate that the extent of ordering is dependent on the configurational entropy available to each system at the very different synthesis temperatures required to form their corundum structures. Polar corundum GaFeO3 exhibits weak ferromagnetism at room temperature that arises from its Fe2O3-like magnetic ordering, which persists to a temperature of 408 K. We demonstrate that the polarity and magnetization are coupled in this system with a measured linear magnetoelectric coupling coefficient of 0.057 ps/m. Such coupling is a prerequisite for potential applications of polar corundum materials in multiferroic/magnetoelectric devices.

Abstract: Synchrotron radiation phase-contrast computed nanotomography (nano-CT) and two-and three-dimensional (2D and 3D) nanoscopic X-ray fluorescence (nano-XRF) were used to investigate the internal distribution of engineered-cobalt nanoparticles (Co NPs) in exposed individuals of the nematode Caenorhabditis elegans. Whole-nematodes and selected tissues and organs were 3D-rendered: anatomical 3D renderings with 50 nm voxel size enabled the visualization of spherical nanoparticle aggregates. with size tip to 200 nm within intact C. elegans. A 20 X 37 nm(2) high-brilliance beam was employed to obtain XRF elemental distribution maps of entire nematodes or anatomical details such as embryos, which could be compared with the CT data, These maps showed Co NPs to be predominantly present within the intestine and the epithelium, and they were not colocalized with Zn granules found in the lysosonie-containing vesicles or Fe agglomerates in the intestine. Iterated XRF scanning of a specimen at 0 degrees and 90 degrees angles suggested that NP aggregates were translocated into tissues outside of the intestinal lumen. Virtual-slicing by means of 2D XRF tomography, combined with holotomography, indicated presumable presence of individual NP aggregates inside the uterus and within embryos.

Abstract: It was recently shown that the electronic band alignment in lateral two-dimensional heterostructures is strongly dependent on the system geometry, such as heterostructure width and layer thickness. This is so even in the absence of polar edge terminations because of the appearance of an interface dipole between the two different materials. In this study, this work is expanded to include two-dimensional materials that possess an electronic dipole over their surface, i.e., in the direction transverse to the crystal plane. To this end, a heterostucture consisting of polar hydrofluorinated graphene and non-polar graphane layers is studied with first-principles calculations. As for nonpolar heterostructures, a significant geometry dependence is observed with two different limits for the band offset. For infinitely wide heterostructures, the potential step in the vacuum is equally divided over the two sides of the heterostructure, resulting in a finite potential step in the heterostructure. For infinitely thick heterostructure slabs, on the other hand, the band offset is reduced, similar to the three-dimensional case.

Abstract: Straining graphene results in the appearance of a pseudo-magnetic field which alters its local electronic properties. Applying a pressure difference between the two sides of the membrane causes it to bend/bulge resulting in a resistance change. We find that the resistance changes linearly with pressure for bubbles of small radius while the response becomes non-linear for bubbles that stretch almost to the edges of the sample. This is explained as due to the strong interference of propagating electronic modes inside the bubble. Our calculations show that high gauge factors can be obtained in this way which makes graphene a good candidate for pressure sensing. Published by AIP Publishing.

Abstract: We study the excitation of spin waves in scaled magnetic waveguides using the magnetoelastic effect. In uniformly magnetized systems, normal strains parallel or perpendicular to the magnetization direction do not lead to spin wave excitation since the magnetoelastic torque is zero. Using micromagnetic simulations, we show that the nonuniformity of the magnetization in submicron waveguides due to the effect of the demagnetizing field leads to the excitation of spin waves for oscillating normal strains both parallel and perpendicular to the magnetization. The excitation by biaxial normal in-plane strain was found to be much more efficient than that by uniaxial normal out-of-plane strain. For narrow waveguides with a width of 200 nm, the excitation efficiency of biaxial normal in-plane strain was comparable to that of shear strain. Published by AIP Publishing.