Philip J. Grandinetti

A simplified theoretical description of multiple-quantum excitation and mixing for nuclear magnetic resonance of half-integer quadrupolar nuclei is presented. The approach recasts the multiple-quantum nutation behavior in terms of reduced excitation and mixing curves through a scaling of the first-order offset frequency by the quadrupolar coupling constant. The two-dimensional correlation of the static first-order anisotropic line shape to the second-order anisotropic magic-angle-spinning (MAS) line shape is utilized to transform the three-dimensional integral over the three Euler angles into a single integral over the dimensionless first-order offset parameter. These transformations lead to a highly efficient algorithm for simulating the multiple-quantum (MQ)-MAS spectrum for arbitrary excitation and mixing radio frequency (RF) field strengths, pulse durations, and MAS rates within the static limit approximation, which is defined in terms of the rotation period, pulse duration, RF field strength, and quadrupolar coupling parameters. This algorithm enables a more accurate determination of the relative site populations and quadrupolar coupling parameters in a least-squares analysis of MQ-MAS spectra. Furthermore, this article examines practical considerations for eliminating experimental artifacts and employing affine transformations to improve least-squares analyses of MQ-MAS spectra. The optimum ratio of RF field strength to the quadrupolar coupling constant and the corresponding pulse durations that maximize sensitivity within experimental constraints are also examined.

The open-source Python package, MRSimulator, is presented as a simple-to-use, fast, versatile, and extendable package capable of simulating one- and higher-dimensional Nuclear Magnetic Resonance (NMR) spectra under static, magic-angle, and variable-angle conditions. High benchmarks in spectral simulations are achieved by assuming that there are no degeneracies in the energy eigenstates, i.e., all dipolar couplings are in the weak limit and that there are no rotational resonances during evolution periods. Under these assumptions, the symmetry pathway formalism is exploited to reduce an NMR method applied to a spin system into a sum of individual transition pathways, whose signals are more efficiently calculated individually than as part of a full-density matrix simulation. To increase numerical efficiencies further, our approach restricts coherence transfer among transitions to pure rotations about an axis in the x–y plane of the rotating frame or through an artificial total mixing operation between selected transitions of adjacent free evolution periods. The assumptions used in this approach are valid for most commonly used solid-state NMR methods. Details of the implementation, along with example code usage, are given, including a least-squares spectral analysis.

A modified shifted-echo PIETA pulse sequence is developed to acquire natural abundance ²⁹Si 2D J-resolved spectra in crystalline silicates.

An approach is presented for simulating multipulse nuclear magnetic resonance (NMR) spectra of polycrystalline solids directly in the frequency domain. The approach integrates the symmetry pathway concept for multipulse NMR with efficient algorithms for calculating spinning sideband amplitudes and performing interpolated finite-element numerical integration over all crystallite orientations in a polycrystalline sample. The numerical efficiency is achieved through a set of assumptions used to approximate the evolution of a sparse density matrix through a pulse sequence as a set of individual transition pathway signals. The utility of this approach for simulating the spectra of complex materials, such as glasses and other structurally disordered materials, is demonstrated.

A new algorithm has been developed to simulate two-dimensional (2D) spectra with correlated anisotropic frequencies faster and more accurately than previous methods. The technique uses finite-element numerical integration on the sphere and an interpolation scheme based on the Alderman–Solum–Grant algorithm. This method is particularly useful for numerical calculations of joint probability distribution functions involving quantities with a parametric orientation dependence. The technique’s efficiency also allows for practical least-squares fitting of experimental 2D solid-state nuclear magnetic resonance (NMR) datasets. The simulation method is illustrated for select 2D NMR methods, and a least-squares analysis is demonstrated in the extraction of paramagnetic shift and quadrupolar coupling tensors and their relative orientation from the experimental shifting-d echo 2H NMR spectrum of a NiCl2 · 2D2O salt.

Tin, silicon and other intermetallic forming electrodes have large volumetric lithium capacities—nearly 10 times that of graphite. Such a high capacity combined with their low cost make intermetallics promising materials for the next generation of rechargeable batteries. Unfortunately, severe capacity fade remains the greatest obstacle in their commercial use. For example, in 2005 Sony introduced their NEXELION battery technology using nanostructured SnCo electrodes but eventually had to pull these batteries from the market due to substantial capacity loss with cycling. While a major reason for capacity fade in these electrodes is thought to be cracking from large volume changes during transitions between intermetallic phases, little evidence for cracking in nanostructured electrodes has been found; and the mechanism for capacity fade in nanostructured intermetallic electrodes has remained a mystery. Using derivative operando (dOp) ⁷Li NMR we have discovered a mechanism for capacity fade in Li_xSn nanoparticle electrodes that may solve this mystery. In short, the capacity fade in nanoparticle electrodes is the result of nanoparticles losing contact with the carbon/PVDF binder. Yet, it occurs in a peculiar way which causes the cell to reach full capacity at the end of every cycle on lithiation. In other words, capacity fade only occurs during delithiation. We present clear NMR evidence showing that particle disconnection occurs during the delithiation (volume contraction of the electrode particles) process. During lithiation (volume expansion of the electrode particles) our NMR data further reveals that connected particles are surprisingly pushed back into contact with the disconnected particles which then rejoin the circuit and allow the cell to reach full capacity on lithiation. Our dOp ⁷Li NMR spectra also reveal the structural transformation pathways between Li-Sn intermetallics during lithiation and delithiation of Sn nanoparticles. The disconnecting particles are associated with Li_xSn phases undergoing large decreases in diameters on delithiation, i.e., Sn, Li₂Sn₅, LiSn, and Li₇Sn₃. The Li–Sn phases observed are somewhat consistent with the structural evolution expected from the equilibrium binary phase diagram, but there are some notable exceptions with the observation of a metastable phase Li₂Sn₃, and two vacancy rich metastable phases, Li_7−ζSn₃, and Li_13−δSn₅ during delithiation. Although this new capacity fade mechanism is simple, we know no in-situ microscopy method capable of detecting and following such a disconnection-connection mechanism. Our approach clearly show the power of operando NMR spectroscopy for revealing such fundamental processes. These results point the way for future efforts in both industrial and academic research labs to reduce capacity fade in a wider range of nano-structured intermetallic electrodes, involving Si, Ge and Sb. Figure 1

The ratio of Si-29 nuclear magnetic resonance coherence lifetimes for Q ⁴ and Q ³ sites under magic-angle spinning and a π-pulse train in silicate glasses can detect phase separation, even at small scales where the glass appears optically homogenous.

Many linear inversion problems involving Fredholm integrals of the first kind are frequently encountered in the field of magnetic resonance. One important application is the direct inversion of a solid-state nuclear magnetic resonance (NMR) spectrum containing multiple overlapping anisotropic subspectra to obtain a distribution of the tensor parameters. Because of the ill-conditioned nature of this inverse problem, we investigate the use of the truncated singular value decomposition and the smooth least absolute shrinkage and selection operator based regularization methods, which (a) stabilize the solution and (b) promote sparsity and smoothness in the solution. We also propose an unambiguous representation for the anisotropy parameters using a piecewise polar coordinate system to minimize rank deficiency in the inversion kernel. To obtain the optimum tensor parameter distribution, we implement the k-fold cross-validation, a statistical learning method, to determine the hyperparameters of the regularized inverse problem. In this article, we provide the details of the linear-inversion method along with numerous illustrative applications on purely anisotropic NMR spectra, both synthetic and experimental two-dimensional spectra correlating the isotropic and anisotropic frequencies.

The Core Scientific Dataset (CSD) model with JavaScript Object Notation (JSON) serialization is presented as a lightweight, portable, and versatile standard for intra- and interdisciplinary scientific data exchange. This model supports datasets with a p-component dependent variable, {U₀, …, U_q, …, U_p−1}, discretely sampled at M unique points in a d-dimensional independent variable (X₀, …, X_k, …, X_d−1) space. Moreover, this sampling is over an orthogonal grid, regular or rectilinear, where the principal coordinate axes of the grid are the independent variables. It can also hold correlated datasets assuming the different physical quantities (dependent variables) are sampled on the same orthogonal grid of independent variables. The model encapsulates the dependent variables’ sampled data values and the minimum metadata needed to accurately represent this data in an appropriate coordinate system of independent variables. The CSD model can serve as a re-usable building block in the development of more sophisticated portable scientific dataset file standards.