RESUMO
Carbonaceous materials are promising candidates as anode materials for non-lithium-ion batteries (NLIBs) due to their appealing properties such as good electrical conductivity, low cost, and high safety. However, graphene, a classic two-dimensional (2D) carbon material, is chemically inert to most metal atoms, hindering its application as an electrode material for metal-ion batteries. Inspired by the unique geometry of a four-penta unit, we explore a metallic 2D carbon allotrope C5-10-16 composed of 5-10-16 carbon rings. The C5-10-16 monolayer is free from any imaginary frequencies in the whole Brillouin zone. Due to the introduction of a non-sp2 hybridization state into C5-10-16, the extended conjugation of π-electrons is disrupted, leading to the enhanced surface activity toward metal ions. We investigate the performance of C5-10-16 as the anode for sodium/potassium-ion batteries by using first-principles calculations. The C5-10-16 sheet has high theoretical specific capacities of Na (850.84 mA h g-1) and K (743.87 mA h g-1). Besides, C5-10-16 exhibits a moderate migration barrier of 0.63 (0.32) eV for Na (K), ensuring rapid charging/discharging processes. The average open-circuit voltages of Na and K are 0.33 and 0.62 V, respectively, which are within the voltage acceptance range of anode materials. The fully sodiated (potassiated) C5-10-16 shows tiny lattice expansions of 1.4% (1.3%), suggesting the good reversibility. Moreover, bilayer C5-10-16 significantly affects both the adsorption strength and the mobility of Na or K. All these results show that C5-10-16 could be used as a promising anode material for NLIBs.
RESUMO
Computing the convolution between a 2D signal and a corresponding filter with variable orientations is a basic problem that arises in various tasks ranging from low level image processing (e.g. ridge/edge detection) to high level computer vision (e.g. pattern recognition). Through decades of research, there still lacks an efficient method for solving this problem. In this paper, we investigate this problem from the perspective of approximation by considering the following problem: what is the optimal basis for approximating all rotated versions of a given bivariate function? Surprisingly, solely minimising the L2-approximation-error leads to a rotation-covariant linear expansion, which we name Fourier-Argand representation. This representation presents two major advantages: 1) rotation-covariance of the basis, which implies a "strong steerability" - rotating by an angle α corresponds to multiplying each basis function by a complex scalar e-ikα; 2) optimality of the Fourier-Argand basis, which ensures a few number of basis functions suffice to accurately approximate complicated patterns and highly direction-selective filters. We show the relation between the Fourier-Argand representation and the Radon transform, leading to an efficient implementation of the decomposition for digital filters. We also show how to retrieve accurate orientation of local structures/patterns using a fast frequency estimation algorithm.
