We demonstrate a tunable bandgap from 2.32 eV to 2.09 eV in phase-pure BiFeO3 by controlling the particle size from 65 nm to 5 nm. Defect states due to oxygen and microstrain show a strong dependence on BiFeO3 particle size and have a significant effect on the shape of absorbance curves. Oxygen-defect induced microstrain and undercoordinated oxygen on the surface of BiFeO3 nanoparticles are demonstrated via HRTEM and XPS studies. Microstrain in the lattice leads to the reduction in rhombohedral distortion of BiFeO3 for particle sizes below 30 nm. The decrease in band gap with decreasing particle size is attributed to the competing effects of microstrain, oxygen defects, and Coulombic interactions.
The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simplicial complexes. In this paper, we show how to optimally compress the Simplex Tree while retaining its functionalities. In addition, we propose two new data structures called the Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List under various settings.
Given a set of n points in R d , the (monochromatic) Closest Pair problem asks to find a pair of distinct points in the set that are closest in the p -metric. Closest Pair is a fundamental problem in Computational Geometry and understanding its fine-grained complexity in the Euclidean metric when d = ω(log n) was raised as an open question in recent works (Abboud-Rubinstein-Williams [FOCS'17], Williams [SODA'18], ).In this paper, we show that for every p ∈ R ≥1 ∪ {0}, under the Strong Exponential Time Hypothesis (SETH), for every ε > 0, the following holds:No algorithm running in time O(n 2−ε ) can solve the Closest Pair problem in d = (log n) Ωε(1) dimensions in the p -metric.ThereIn particular, our first result is shown by establishing the computational equivalence of the bichromatic Closest Pair problem and the (monochromatic) Closest Pair problem (up to n ε factor in the running time) for d = (log n) Ωε(1) dimensions.Additionally, under SETH, we rule out nearly-polynomial factor approximation algorithms running in subquadratic time for the (monochromatic) Maximum Inner Product problem where we are given a set of n points in n o(1) -dimensional Euclidean space and are required to find a pair of distinct points in the set that maximize the inner product.At the heart of all our proofs is the construction of a dense bipartite graph with low contact dimension, i.e., we construct a balanced bipartite graph on n vertices with n 2−ε edges whose vertices can be realized as points in a (log n) Ωε(1) -dimensional Euclidean space such that every pair of vertices which have an edge in the graph are at distance exactly 1 and every other pair of vertices are at distance greater than 1. This graph construction is inspired by the construction of locally dense codes introduced by Dumer-Miccancio-Sudan [IEEE Trans. Inf. Theory'03].
Many promising attributes of ZnO nanoparticles (nZnO) have led to their utilization in numerous electronic devices and biomedical technologies. nZnO fabrication methods can create a variety of intrinsic defects that modulate the properties of nZnO, which can be exploited for various purposes. Here we developed a new synthesis procedure that controls certain defects in pure nZnO that are theorized to contribute to the n-type conductivity of the material. Interestingly, this procedure created defects that reduced the nanoparticle band gap to ~3.1 eV and generated strong emissions in the violet to blue region while minimizing the defects responsible for the more commonly observed broad green emissions. Several characterization techniques including TGA, FT-IR, XPS, TEM, Raman, photoluminescence and ICP-MS were employed to verify the sample purity, assess how modifications in the synthesis procedure affect the various defects states and understand how these alterations impact the physical properties. Since the band gap significantly decreased and a relatively narrow visible emissions band were created by these defects, we investigated utilizing these new nZnO for bio-imaging applications using traditional fluorescent *
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