# Research

My research interests focus on the use of magnetic resonance to probe dynamics and structure in disordered and heterogeneous materials. Motivated by the challenges of such difficult-to-characterize materials, we have developed numerous magnetic resonance methodologies, theories, and analyses over the years. Below is a short summary of our efforts and results. References numbers correspond to articles on our Publications page.

# NMR instrumentation and methodology

Our group develops NMR methodologies for material science and chemistry. Examples of our NMR methodology work include
• Switched-angle spinning probes, designed and built in our lab for performing dynamic-angle spinning and magic-angle flipping measurements. [13,15,17-19,22-25,29-31,48,63,68,74,75,78]
• MQ-MAS. Initially developed by Lucio Frydman to obtain high-resolution spectra of half-integer quadrupolar nuclei, our lab published one of the first and still popular implementations[26], as well as other refinements for improving MQ-MAS sensitivity[34,37], including the FASTER method[39] which enhances sensitivity by well over an order of magnitude.
• RAPT (Rotor Assisted Population Transfer) and multi-RAPT are methods for enhancing the sensitivity of the central transition spectrum of half-integer spin quadrupolar nuclei ranging from a factor of two for spin 3/2 nuclei to nearly an order of magnitude for spin 9/2 nuclei[38,40,46,62]. In addition to the sensitivity enhancement, we have also shown that RAPT can be used to measure quadrupolar coupling constants [43,54], and perform selective excitation or suppression of an NMR site based on the size of its quadrupolar coupling constant[45,56].
• TOP[54], TOP-PASS[67], and PASS-PIETA[71] are improvements to multi-dimensional NMR methods for measuring chemical or paramagnetic shift anisotropies from spinning sideband patterns.
• COASTER[60] and the Shifting d-Echo experiment[72,79], for separating and correlating the anisotropies of the chemical/paramagnetic shift and quadrupolar interactions.
• MAF-CPMG (Magic-Angle Flipping with CPMG acquisition). This approach combined paramagnetic relaxation enhancement strategies to obtain high throughput studies of glasses using natural abundance $^{29}$Si NMR[74,78] and was critical in our discovery of the modifier cation percolation threshold in cesium silicate glasses.
• PIETA (Phase Incremented Echo Train Acquisition) [69], eliminates a number of artifacts in the Carr-Purcell-Meiboom-Gill (CPMG) experiment and provides more accurate measures of $T_2$ and the ability to measure $J$ couplings in single-shot experiments. More recently, we have developed SE-PIETA (Shifted-Echo PIETA) [80] for improved single-shot'' measurement of 2D $J$-resolved spectra.
• dOp NMR (derivative Operando NMR) [77], improves the resolution of operando NMR spectra of batteries by removing time-independent signals, such as electrolyte and SEI, and further distinguishes between time-dependent signals associated with the formation and removal of species. This approach not only provides better resolution but also more clearly reveals correlations between resonances and the chemical transformations occurring at a specific potential.
• soft-CPMG [82] is a simple approach for obtaining up to a 1000-fold NMR sensitivity enhancement for half-integer quadrupolar nuclei in solids. This approach enables the acquisition of natural abundance O-17 NMR spectra in 1 hour of signal averaging instead of a century. It requires no additional hardware or added expense, can be implemented on any NMR spectrometer, and is utilized for sensitivity gain in combination with a number of popular NMR pulse sequences for quadrupolar nuclei. This new approach enables access to atomic-level structural details in a greater range of samples by eliminating the need for expensive isotopic enrichments.
• a new formalism for describing multi-pulse NMR experiments that we call the "Symmetry Pathways" approach[65,71,79]. This formalism not only provides a powerful tool for designing new NMR experiments but can be a useful pedagogical tool for NMR, allowing students to quickly grasp a number of modern NMR experiments without the need to enter into a full density (or product) operator description of each experiment.

# Software Development

Our group develops also develops software for machine learning in NMR spectroscopy. Some examples include:
• csdmpy: Open-source Python package and documentation for supporting the core scientific dataset (CSD) model file exchange format. Documentation available at csdmpy.readthedocs.io.
• mrsimulator: Open-source Python package for fast simulation and analysis of multi-dimensional solid-state NMR spectra of crystalline and non-crystalline materials. Documentation available at mrsimulator.readthedocs.io.
• mrinversion: Open-source Python package based on the statistical learning technique for determining the distribution of the NMR tensor parameters from two-dimensional spectra correlating the isotropic to anisotropic frequencies. Documentation available at mrinversion.readthedocs.io.
• PhySyCalc: a scientific and engineering calculator app for iOS, and Mac OS
• RMN: a scientific multi-dimensional signal processing app for Mac OS.

# Structure of disordered materials

The Nature of Glass remains anything but clear - Kenneth Chang

Another long-time focus of our lab is structural studies of non-crystalline materials. Glass structure is a difficult thing to characterize. Any structural model of glass is necessarily statistical in nature. Our lab has focused on increasing the information content of spectroscopic measurements through the use of more sophisticated multi-dimensional nuclear magnetic resonance (NMR) spectroscopy measurements and spectral analysis. In these efforts, our group has developed NMR hardware, pulse sequences, parameter/structure relationships, and software for data analyses for determining various statistical distributions of structures present in the glass. The primary application of this work has been oxide glasses, as 99% of 100 million commercial tonnages of glass produced annually consists of compositions that are oxides, and a significant fraction of that is silica-based. While it is understood that oxide glasses with predominantly covalent directed bonds have a high degree of short-range order, there remains considerable debate concerning the degree of structural order or disorder on the short- to medium-range length scales. Below is a short summary of this work. All citations refer to numbered references on our publications page.

• systematically determining, through quantum chemistry computations and experimental measurements, the relationships between the local structure around a Si-O-Si linkage and (1) O-17 electric field gradient [23,32,36,41,47,49] and (2) Si-29 geminal 2J coupling and Si-29 chemical shift[76,80]. These relationships have become essential tools in the NMR spectral analysis of crystalline and amorphous silicate frameworks.
• obtaining the two-dimensional correlated distribution of Si-O distances and Si-O-Si angles from a detailed analysis of the 2D O-17 NMR spectrum of silica glass[47,48]. This advance was quite significant because it revealed a strong positive correlation between Si-O-Si angle and Si-O distance, i.e., Si-O distance decreasing with decreasing Si-O-Si angle, which runs counter to conventional wisdom. This suggests that a commonly accepted notion–that SiO4 tetrahedra in silica glass are structurally identical to those in crystalline silica polymorphs–is fundamentally incorrect.
• obtaining the first O-17 NMR results to quantify positional order/disorder of network modifier cations around non-bridging oxygens in oxide glasses[14,29], and discovering correlations between modifier cation field strength and degree of substitutional disorder in glasses.
• using two-dimensional Si-29 magic-angle flipping (MAF) NMR experiments to quantify anionic species distributions in silicate glasses with over an order of magnitude higher precision than all prior studies and quantifying the influence of modifier cation field strength on silicate network depolymerization[30,31,63,68,74].
• discovering a linear relationship between Si-29 shift anisotropy of SiO4 tetrahedra and coordinating network modifier cation potential, providing a new specific probe into the variation of silicon--non-bridging oxygen bond lengths[74].
• discovering microscopic evidence for the modifier cation percolation threshold in cesium silicate glasses through a systematic study of the distribution of Q3 Si-29 chemical shift anisotropies in the glass. This spectroscopic result is unique in providing a rare glimpse into the intermediate range structure associated with modifier cation clustering in glasses[78].
• determining the bi-variate probability distribution correlating the central Si-O-Si angle of a Q4-Q4 linkage to its mean Si-O-Si angle (seven angles) from a Si-29 natural abundance 2D J-resolved NMR spectrum of silica glass [80]. Besides revealing the Si-O-Si angle probability distribution of the glass, the analysis of the 2D J-resolved NMR spectrum also showed no correlation between the four Si-O-Si angle distributions of a Q4 in the disordered tetrahedral network and, most interestingly, uncovered a positive correlation between Si-O-Si angle and Si-O distance in the glass, in full confirmation of our O-17 DAS results on silica glass. Taken together, these results provide new insights into the nature of the residual configurational entropy after the glass transition.

# Batteries

If batteries could do better they would have a tremendous impact on renewable energies, such as wind, wave, solar, and geothermal, which all require energy storage due to transient availabilities. Likewise, the impact on all-electric vehicles would be significant. Breakthroughs in finding battery materials with better performance have long been hampered by gaps in our fundamental understanding of processes occurring at the nano- and atomic scales during the real-time operation of a battery. Another focus of our research is the development of improved operando nuclear magnetic resonance methodologies and their application to the next generation of anode and cathode materials for rechargeable batteries.