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Finite Fields
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
This splitting field is an extension of Fp in which the polynomial f has p zeros, i.e., f has as many zeros as possible because the degree of f is p. For p = 22 = 4, it can be checked step by step by using the above multiplication table that all four elements of F4 satisfy the equation x4 = x, so they are zeros of f. However in F2, f has only two zeros (namely 0 and 1), so f does not split into linear factors in this smaller field. Elaborating further on basic field-theoretic notions, it can be shown that two finite fields with the same order are isomorphic. It is thus customary to speak of the finite field with p elements, denoted by Fp or GF(p) (Bussey, 1910).
Nanoscale hetero-interfaces for electrocatalytic and photocatalytic water splitting
Published in Science and Technology of Advanced Materials, 2022
Baopeng Yang, Dingzhong Luo, Shimiao Wu, Ning Zhang, Jinhua Ye
In electrocatalytic water splitting field, the defects that exist on hetero-interfaces have a significant impact on the chemical properties and electronic structures of the materials, and they have the potential to significantly boost the electrocatalytic efficacy of the materials when used to split water. For example, Fan et al. fabricated a FeF2/Fe2O3 hetero-interface by anodization/fluorination process [92]. The HRTEM images (Figure 16a1) show that the high-electrical-conductivity FeF2/Fe2O3 hetero-interface includes embedded disorder phases in the crystalline lattices, and it also features various distributed defects, such as interphase boundaries, stacking faults, oxygen vacancies, and dislocations on the surfaces and contact. This FeF2/Fe2O3 hetero-interface presents a remarkable electrocatalytic water splitting activity (Figure 16a2). Both empirical research and theoretical computations point to the fact that the surface and edge defects play a substantial role in the high performance of FeF2/Fe2O3 hetero-interface.
Catalytic applications of phosphorene: Computational design and experimental performance assessment
Published in Critical Reviews in Environmental Science and Technology, 2023
Monika Nehra, Neeraj Dilbaghi, Rajesh Kumar, Sunita Srivastava, K. Tankeshwar, Ki-Hyun Kim, Sandeep Kumar
The moderate deformation of phosphorene can cause a transition from a semiconductor to a semimetal or even a metal (Swaroop et al., 2017). As compared to chemical functionalization and doping, strain engineering has been reported as an effective tool for tuning the optoelectronic and thermal properties of phosphorene (Kaur et al., 2018). For instance, the phosphorene lattice showed better stability under tensile strain in comparison to compression strain, as confirmed by lattice dynamic calculations (Sa et al., 2014). Further, Zhang and Hao (2018) examined the optoelectronic responses of armchair- and zigzag-edge quasi 1D phosphorene nanoribbons to an external field and strain on the basis of tight-binding calculations. Accordingly, the two types of phosphorene nanoribbons have (i) insulating properties due to the large direct band gap (by applying inter-plane strain) and (ii) the metallic ground state (by applying global strain) in the case armchair-and zigzag-edge structures, respectively. Moreover, band gap responses to the electric field also showed strong dependence on direction; that is, monotonic and non-monotonic increases were observed in the bandgap due to the inter-plane electric field and the electric field along the width direction. Li et al. (2019) confirmed the linear dichroism as well as the optical conductivity of few-layer phosphorene in a perpendicular electric field. In phosphorene, the anisotropic interband transitions can be tuned at finite temperature to offer new possibilities in optoelectronics. Using ab initio molecular dynamics along with nonadiabatic quantum dynamics simulations, Guo et al. (2021) demonstrated robust modulation of carrier mobility, carrier lifetime, and band gap through excitation of out-of-plane acoustic phonons (ZA). In case of phosphorene, these electronic properties can be tuned simply by changing the amplitude of ZA mode excitation through tensile strain, Figure 2. The absorption as well as scattering phenomena in phosphorene were also studied on the basis of Zeeman spin-splitting field strength and also optical energy parameters (Phuong et al., 2020). By applying the tight-binding Hamiltonian model, both spin-down and spin-up bands can be separated to investigate their respective behavior for determination of new phases (i.e. electronic) of the system. In this study, three different regimes of the system were identified including: (i) two same gapped phases in the Zeeman field absence, (ii) gapped and gapless phases for stronger fields, and (iii) the emergence of band inversion and Dirac-like cone phase due to spin-up bands for stronger Zeeman fields.