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Two-Dimensional Photocatalytic Heterojunction Hybrid Nanomaterials for Environmental Applications
Published in A. Pandikumar, K. Jothivenkatachalam, S. Moscow, Heterojunction Photocatalytic Materials, 2022
R. Baby Suneetha, Suguna Perumal, P. Karpagavinayagam, C. Vedhi
These are the techniques that use X-ray sources to illuminate the sample and then draw the inference from the interaction of X-ray with sample. The most popular use of X-ray for characterization is in the form of XRD. Following Bragg’s law, it is well known that a periodic lattice acts as a diffraction grating for X-ray beam that produces a reciprocal lattice, from which the crystal structure and a plethora of information can be determined. This is also applied to 2DMs, but only if they have a large size. XRD is not a surface-specific method. There is another important X-ray based technique, namely, X-ray photoelectron spectroscopy (XPS), that can provide surface information like spatial distribution of different components of heterostructures. The principle involves recording photoelectron emission spectra (with characteristic peaks corresponding to particular atoms or states) after the sample is irradiated with X-ray, and thus it can provide information about elemental composition, chemical state, and so on. For 2DMs, XPS is particularly useful to probe chemical bonds and study interfaces.
Crystalline Structure of Different Semiconductors
Published in Jyoti Prasad Banerjee, Suranjana Banerjee, Physics of Semiconductors and Nanostructures, 2019
Jyoti Prasad Banerjee, Suranjana Banerjee
Just as a perfect single crystal is a three-dimensional repetition of identical building blocks, the reciprocal lattice in Fourier space (reciprocal space) is a three-dimensional array of points separated by distances inversely proportional to the interplanar spacing of planes in direct lattice. The vectors in the reciprocal space have the dimension of [L]−1. This may be compared with the dimension of wave vector associated with photon, lattice vibration, or a free electron. The reciprocal space is converted into momentum space when each coordinate of wave vector is multiplied by ℏ or h2π, where ℏ is the reduced Planck’s constant.
Introductory Concepts
Published in Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck, Computational Electronics, 2017
Dragica Vasileska, Stephen M. Goodnick, Gerhard Klimeck
The Brillouin zone [7] is a primitive unit cell of the reciprocal lattice. In mathematics and solid-state physics, the first Brillouin zone is a uniquely defined primitive cell of the reciprocal lattice in the frequency domain. It is found by the same method as for the Wigner–Seitz cell in the Bravais lattice. The importance of the Brillouin zone stems from the Bloch wave description of waves in a periodic medium, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. Taking the surfaces at the same distance from one element of the lattice and its neighbors, the volume included is the first Brillouin zone shown in Figure 2.9. Another definition is as the set of points in k-space that can be reached from the origin without crossing any Bragg plane. There are also second, third, etc. Brillouin zones, corresponding to a sequence of disjoint regions (all with the same volume) at increasing distances from the origin, but these are used more rarely. As a result, the first Brillouin zone is often called simply the Brillouin zone. (In general, the nth Brillouin zone consists of the set of points that can be reached from the origin by crossing n − 1 Bragg planes.)
Green synthesis, characterization and antimicrobial activity of zinc oxide nanoparticles using Artemisia pallens plant extract
Published in Inorganic and Nano-Metal Chemistry, 2021
The Lorentz-polarization factor is another most important experimental quantity that control X-ray intensity with respect to diffraction angle. When each lattice point on the reciprocal lattice intersects the diffractometer circle, a diffraction related to the plane represented will occur. The diffractometer typically moves at a constant 2θ rate, the amount of time spent at each point in the diffracting condition will be a function of the diffraction angle. If the angle is increased, the intersection approach tangent to the circle. If the angle is high time taken is more in the diffracting condition. This may be corrected by Lorentz factor and Lorentz polarization factor. Thus, Lorentz factor and Lorentz polarization factor needs to be considered while calculating the intensity. Lorentz factor and Lorentz Polarization factor were calculated using equations given in Appendix 2 and the values thus obtained are given in Table 3. It was observed that as the 2θ value increases, Lorentz factor value and Lorentz polarization factor value decreases.
Low-frequency property and vibration reduction design of chiral star-shaped compositive mechanical metamaterials
Published in Mechanics of Advanced Materials and Structures, 2023
Ying Zhang, Liang Wang, Qian Ding, Hongge Han, Jinxin Xu, Hao Yan, Yongtao Sun, Qun Yan, Haoqiang Gao
Since the reciprocal lattice is also periodic, the wave vector in the reciprocal lattice is defined as the Brillouin region. In order to improve the computational efficiency, the wave vector is confined to the edge of the first Brillouin region to study the bandgap variation. Select any lattice point in the reciprocal lattice as the center point. Make it connected to each adjacent point, the perpendicular bisector intersection area of these lines is the first Brillouin zone. The black region in Figure 1(d) is the first Brillouin region of quadrilateral lattice, and the wave vector is scanned along the direction shown.
Possible nucleus of the Bergman cluster in the Zn–Mg–Y alloy system
Published in Philosophical Magazine, 2018
Kei Nakayama, Masaya Nakagawa, Yasumasa Koyama
As mentioned above, the Zn23Y6 state was present as minor regions in the sample. We also determined the orientation relation between the IQ and the Zn23Y6 structure by using their coexistence areas. Figure 3 shows electron diffraction patterns and a corresponding bright-field image, which were taken from one of the coexistence areas including a quasicrystal/Zn23Y6 boundary. We first look at the image of the coexistence area in the inset, which was used for the analysis. It is seen that there are bright- and dark-contrast regions separated by a curved boundary, which are referred to as Regions A and B. To identify these regions, we took their electron diffraction patterns with various electron beam incidences at room temperature. The pattern in Figure 3(a) was taken from Region A, while two patterns from Region B are shown in Figure 3(b) and (b′). The pattern of Region A exhibits an arrangement of reflections with five-fold symmetry with respect to the origin 0 0 0. From an analysis of electron diffraction patterns with various beam incidences, including the pattern in Figure 3(a), the state in Region A was identified as the F-type IQ, just as in the case of the above-mentioned (quasicrystal + H) coexistence area. On the other hand, the patterns of Region B show a simple regular arrangement of reflections, as seen in Figure 3(b) and (b′). To determine the crystal structure in Region B, we constructed its reciprocal lattice by using electron diffraction patterns obtained experimentally. The constructed reciprocal lattice for Region B is schematically depicted in the inset in Figure 3(b′). Based on the determined reciprocal lattice, it was found that the state in Region B was entirely consistent with the Zn23Y6 state with cubic-Fmm symmetry.