Evidence for Multiple M Sites in AMO₂ Compounds:  ⁵⁹Co Solid State NMR Studies on LiCoO₂

Abstract

The layered AMO 2 compounds (A ) alkali metal, M ) trivalent octahedral site cations) derived from the simple rock-salt structure have always been considered to have only one crystallographic site for the A and the M atoms. These structures are described in terms of close-packed oxygen layers with interstitial A and M atoms, especially when A ) Li. This gives a layer sequence (AO) -and (MO) + . The AMO 2 compounds are part of the compounds in the A-M-O systems such as A 2 MO 3 and A 5 MO 6 , which are derived from the rock-salt structure with alternating layers of pure (AO) -and mixed [(A,M)O] + layers with multiple interstitial octahedral sites in the (A,M)O layer for occupation by the different A and M cations. Evidence is presented from 59 Co NMR experiments on LiCoO 2 for the existence of at least two sites in the (CoO) + layer. Several NMR methodologies, such as the use of various pulse sequence, nutation experiments, and magic angle sample spinning (MASS) are employed. Magic-angle-sample-spinning experiments show only one isotropic peak.However, an analysis of spinning sidebands envelope at various spinning speeds clearly shows the presence of at least two sites. One of these has orthorhombic symmetry and another has axial symmetry, with closely related chemical shift anisotropy components that result in the observation of nearly identical isotropic chemical shifts. The possible importance of the absence or presence of holes on oxygen has been discussed in accounting for the two sites.

Exploring static and frequency-dependent third nonlinear polarizability of doped quantum dots driven by Gaussian white noise

“…Therefore H 0 is diagonalized in the direct product basis of harmonic oscillator eigenfunctions. Thus, the timeindependent Schrödinger equation has been solved using variational method expressing the trial wave function ψ(x, y) as a superposition of the product of harmonic oscillator eigenfunctions [47,48] φ n (px) and φ m (qy), respectively, as…”

“…where C n,m are the variational parameters and p = √ m * ω 0 / and q = √ m * Ω/ . The general expression for the matrix elements of H 0 and V imp (0) in the chosen basis have been derived [47,48], and in the linear variational calculation, an appreciably large number of basis functions have been exploited after making the required convergence test.…”

“…The noise comprises of random term (σ(t)) quite often assumed to be following a Gaussian distribution (produced by Box-Muller algorithm) having strength μ. It is characterized by the equations [47,48]:…”

“…Recently, we have explored the role of Gaussian white noise on the frequency-dependent linear [47] and first nonlinear polarizabilities [48] of doped QD. In the present manuscript, we explore the role of Gaussian white noise on the diagonal components of the static and the frequencydependent third (second-order) nonlinear polarizabilities (γ xxxx and γ yyyy ) of doped QD.…”

Synthesis and Structural Characterization of Lithiated and Delithiated LiCoO2 Using Different Chelating Agents

“…A lot of researches on physical and electrochemical properties of LiCoO 2 have been carried out for the applications of high-energy density electric vehicles (1)(2)(3)(4)(5) . LiCoO 2 is one of the most extensively used cathode material in rechargeable lithium ion batteries.…”