Curved ZnO nanowires were deliberately prepared on a Si substrate and the strain effect on their near band edge (NBE) emission was investigated by spatially resolved cathodoluminescence (CL). By moving the electron beam step-by-step across individual curved nanowires and acquiring the CL spectra simultaneously, we found that the NBE emissions from the inner region of the curved nanowires with compressive strain show blueshift, while those from the outer region with tensile strain show redshift. Both the strains have been estimated from the local curvature by a geometrical model and have been further examined by high-resolution transmission electron microscopy. A nearly linear relation between the strain and the peak energy shift in NBE emission was obtained. The result indicates that the optical band gap of ZnO nanowire is quite sensitive to and can be readily modulated by the induced strain via simply curving the nanowire, which has potential applications for designing new optical-electromechanical (OEM) and flexible optoelectronic nanodevices.
Batteries with lithium metal anodes
are promising because of lithium’s
high energy density. However, the growth of Li dendrites on the surface
of the Li electrode in a liquid electrolyte during cycling reduces
the safety and cycle performance of batteries, hindering their commercial
application. In this work, we observe for the first time a smooth
and dendrite-free Li deposition with a vertically grown, self-aligned,
and highly compact columnar structure formed during cycling in a mixed
carbonate–ether electrolyte. The stable microsized (∼10
μm in diameter and ∼20 μm in length) Li deposits
are aligned in arrays on the surface of the Li electrode. The columnar
Li deposits still exhibit a dendrite-free morphology and a compact
structure after 200 cycles at a current density of 1 mA/cm2 and a 1.5 mAh/cm2 cycling capacity in a mixed carbonate–ether
electrolyte. This work shows an optimiztic outlook for Li batteries
with liquid electrolytes.
Let k be an odd natural number ≥ 5, and let G be a (6k − 7)-edge-connected graph of bipartite index at least k − 1. Then, for each mapping f : V (G) → N, G has a subgraph H such that each vertex v has H-degree f (v) modulo k. We apply this to prove that, if c : V (G) → Z k is a proper vertex-coloring of a graph G of chromatic number k ≥ 5 or k − 1 ≥ 6, then each edge of G can be assigned a weight 1 or 2 such that each weighted vertex-degree of G is congruent to c modulo k. Consequently, each nonbipartite (6k − 7)-edge-connected graph of chromatic number at most k (where k is any odd natural number ≥ 3) has an edge-weighting with weights 1, 2 such that neighboring vertices have distinct weighted degrees (even after reducing these weighted degrees modulo k). We characterize completely the bipartite graph having an edge-weighting with weights 1, 2 such that neighboring vertices have distinct weighted degrees. In particular, that problem belongs to P while it is NP-complete for nonbipartite graphs. The characterization also implies that every 3-edge-connected bipartite graph with at least 3 vertices has such an edge-labelling, and so does every simple bipartite graph of minimum degree at least 3.
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