Structural and electrochemical properties of LiNi1/3Co1/3Mn1/3O2 material prepared by a two-step synthesis via oxalate precursor

LiNi_1/3Co_1/3Mn_1/3O₂ (LNMCO) powders were formed by a two-step synthesis including preparation of an oxalate precursor by ??chimie douce?? followed by a solid-state reaction with lithium hydroxide. The product was characterized by TG-DTA, X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), Fourier transform infrared (FTIR), Raman spectroscopy, electron spin resonance (ESR), and SQUID magnetometry. XRD data revealed well-crystallized layered LNMCO with ??-NaFeO₂-type structure (R-3?m space group). Morphology studied by SEM and TEM shows submicronic particles of 400?C800?nm with a tendency to agglomerate. The local structure investigated by vibrational spectroscopy (FTIR, Raman), ESR, and SQUID measurements confirms the well-crystallized lattice with a cation disorder of 2.6% Ni²⁺ ions in Li(3b) sites. Electrochemical tests were carried out in the potential range 2.5?C4.5?V vs. lithium metal on samples heated at 900?°C for 12?h. Initial discharge capacity is 154 mAh/g at C/5, while a capacity of 82 mAh/g is still delivered at 10 C by the two-step synthesized LiNi_1/3Co_1/3Mn_1/3O₂ as cathode material.     

Practical choice of ¹H-¹H decoupling schemes in through-bond ¹H-{X} HMQC experiments at ultra-fast MAS

Three (1)H-(1)H homonuclear dipolar decoupling schemes for (1)H indirect detection measurements at very fast MAS are compared. The sequences require the following conditions: (i) being operable at very fast MAS, (ii) a long T(2)(') value, (iii) a large scaling factor, (iv) a small number of adjustable parameters, (v) an acquisition window, (vi) a low rf-power requirement, and (vii) a z-rotation feature. To satisfy these conditions a modified sequence named TIlted Magic-Echo Sandwich with zero degree sandwich pulse (TIMES(0)) is introduced. The basic elements of TIMES(0) consist of one sampling window and two phase-ramped irradiations, which realize alternating positive and negative 360° rotations of (1)H magnetization around an effective field tilted with an angle θ from the B(0) axis. The TIMES(0) sequence benefits from very large chemical shift scaling factors at ultra-fast MAS that reach κ(cs)=0.90 for θ=25° at ν(r)=80kHz MAS and only four adjustable parameters, resulting in easy setup. Long κ(cs)T(2)(') values, where T(2)(') is a irreversible proton transverse relaxation time, greatly enhance the sensitivity in (1)H-{(13)C} through-bond J-HMQC (Heteronuclear Multiple-Quantum Coherence) measurements with (1)H-(1)H decoupling during magnetization transfer periods. Although similar sensitivity can be obtained with through-space D-HMQC sequences, in which (13)C-(1)H dipolar interactions are recoupled, J-HMQC experiments incorporating (1)H-(1)H decoupling benefit from lower t(1)-noise, more uniform excitation of both CH, CH(2) and CH(3) moieties, and easier identification of through-bond connectivities.     

Nearby motives and motivic nearby cycles

We prove that the construction of motivic nearby cycles, introduced by Jan Denef and François Loeser, is compatible with the formalism of nearby motives, developed by Joseph Ayoub. Let $k$ be an arbitrary field of characteristic zero, and let $X$ be a smooth quasi-projective $k$ -scheme. Precisely, we show that, in the Grothendieck group of constructible étale motives, the image of the nearby motive associated with a flat morphism of $k$ -schemes $f:X\rightarrow \mathbb A ^1_k$ , in the sense of Ayoub’s theory, can be identified with the image of Denef and Loeser’s motivic nearby cycles associated with $f$ . In particular, it provides a realization of the motivic Milnor fiber of $f$ in the “non-virtual” motivic world.     

Random pinning model with finite range correlations: Disorder relevant regime

The purpose of this paper is to show how one can extend some results on disorder relevance obtained for the random pinning model with i.i.d disorder to the model with finite range correlated disorder. In a previous work, the annealed critical curve of the latter model was computed, and equality of quenched and annealed critical points, as well as exponents, was proved under some conditions on the return exponent of the interarrival times. Here we complete this work by looking at the disorder relevant regime, where annealed and quenched critical points differ. All these results show that the Harris criterion, which was proved to be correct in the i.i.d case, remains valid in our setup. We strongly use Markov renewal constructions that were introduced in the solving of the annealed model.     

Hypersurfaces of Spinc Manifolds and Lawson Type Correspondence

Simply connected three-dimensional homogeneous manifolds ${\mathbb{E}(\kappa, \tau)}$ , with four-dimensional isometry group, have a canonical Spin^c structure carrying parallel or Killing spinors. The restriction to any hypersurface of these parallel or Killing spinors allows to characterize isometric immersions of surfaces into ${\mathbb{E}(\kappa, \tau)}$ . As application, we get an elementary proof of a Lawson type correspondence for constant mean curvature surfaces in ${\mathbb{E}(\kappa, \tau)}$ . Real hypersurfaces of the complex projective space and the complex hyperbolic space are also characterized via Spin^c spinors.     

Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals

We demonstrate a mesoscopic self-collimation effect in photonic crystal superlattices consisting of a periodic set of all-positive index 2D photonic crystal and homogeneous layers. We develop an electromagnetic theory showing that diffraction-free beams are observed when the curvature of the optical dispersion relation is properly compensated for. This approach allows us to combine slow-light regime together with self-collimation in photonic crystal superlattices presenting an extremely low filling ratio in air.     

Helmholtz equation in periodic media with a line defect

We consider the Helmholtz equation in an unbounded periodic media perturbed by an unbounded defect whose structure is compatible with the periodicity of the underlying media. We exhibit a method coupling Dirichlet-to-Neumann maps with the Lippmann–Schwinger equation approach to solve this problem, where the Floquet–Bloch transform in the direction of the defect plays a central role. We establish full convergence estimates that makes the link between the rate of decay of a function and the good behavior of a quadrature rule to approximate the inverse Floquet–Bloch transform. Finally we exhibit a few numerical results to illustrate the efficiency of the method.     

The Lamb-shift experiment in Muonic helium

We propose to measure several transition frequencies between the 2S and the 2P states (Lamb shift) in muonic helium ions (μ ⁴He^?+? and μ ³He^?+?) by means of laser spectroscopy, in order to determine the alpha-particle and helion root-mean-square (rms) charge radius. In addition, the fine and hyperfine structure components will be revealed, and the magnetic moment distribution radius will be determined. The contribution of the finite size effect to the Lamb shift (2S???2P energy difference) in μHe^?+? is as high as 20 %. Therefore a measurement of the transition frequencies with a moderate (for laser spectroscopy) precision of 50 ppm (corresponding to 1/20 of the linewidth) will lead to a determination of the nuclear rms charge radii with a relative accuracy of 3 ×10^???4 (equivalent to 0.0005 fm). The limiting factor for the extraction of the radii from the Lamb shift measurements is given by the uncertainty of the nuclear polarizability contribution. Combined with an ongoing experiment at MPQ aiming to measure the 1S???2S transition frequency in the helium ion, the Lamb shift measurement in μHe^?+? will lead to a sensitive test of problematic and challenging bound-state QED terms. This measurement will also help to clarify the discrepancy found in our previous μ _p experiment. Additionally, a precise knowledge of the absolute nuclear radii of the He isotopes and the hyperfine splitting of μ ³He^?+? provide a relevant test of few-nucleon theories.     

The size of the proton

The root-mean-square (rms) charge radius r _p of the proton has so far been known only with a surprisingly low precision of about 1% from both electron scattering and precision spectroscopy of hydrogen. We have recently determined r _p by means of laser spectroscopy of the Lamb shift in the exotic “muonic hydrogen” atom. Here, the muon, which is the 200 times heavier cousin of the electron, orbits the proton with a 200 times smaller Bohr radius. This enhances the sensitivity to the proton’s finite size tremendously. Our new value r _p?=?0.84184 (67) fm is ten times more precise than the generally accepted CODATA-value, but it differs by 5 standard deviations from it. A lively discussion about possible solutions to the “proton size puzzle” has started. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, also yields improved values of the Rydberg constant, R _?∞??=?10,973,731.568160 (16) m^???1.