Oxygen sites coordinating three network-forming cations in aluminosilicate (AS) glasses—i.e., O^[3] coordination species referred to as “oxygen triclusters”—was proposed 60 years ago and has since then been heavily debated because irrefutable experimental proof for their existence is still lacking. We introduce a protocol for predicting the O^[3] population from the average coordination number of Al () and the fraction of non-bridging O (NBO) species, which are available from routine ²⁷Al and ¹⁷O NMR experiments, respectively. Although O^[3] species were proposed for balancing the negatively charged [AlO_4/2]^- groups that typically dominate the Al speciation in AS glasses, recent computational modeling reveals a stronger propensity for the higher-coordination Al^[5] (AlO₅) and Al^[6] (AlO₆) species to coordinate O triclusters for charge-compensation. We discuss the structural roles of the O^[3] and Al^[5]/Al^[6] entities, all of which remain unclear despite extensive previous research. For a large set of AS glasses involving various  M⁺, M²⁺, and M³⁺ cations, the fractional O^[3] population () increases concurrently with the net number of Al^[5] and Al^[6] sites in the glass, but decreases for increasing M^z+ cation potential. Both O^[3] and Al^[5]/Al^[6] species have been suggested to enhance the glass hardness and crack resistance. For AS glasses involving various trivalent rare-earth cations, the microhardness correlated better with the average coordination number of Al () than with , as did the crack resistance of a limited set of Ca AS glasses. Nevertheless, contributions from O^[3] sites cannot be excluded for the latter glasses and further studies are needed for firm conclusions.

By using density functional theory (DFT) calculations, we refined the H atom positions in the structures of β-caffeine (C), α-oxalic acid (OA; (COOH)₂), α-(COOH)₂·2H₂O, β-malonic acid (MA), β-glutaric acid (GA), and I-maleic acid (ME), along with their corresponding cocrystals of 2 : 1 (2C–OA, 2C–MA) or 1 : 1 (C–GA, C–ME) stoichiometry. The corresponding ¹³C/¹H chemical shifts obtained by gauge including projector augmented wave (GIPAW) calculations agreed overall very well with results from magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy experiments. Chemical-shift/structure trends of the precursors and cocrystals were examined, where good linear correlations resulted for all COO¹H sites against the H⋯O and/or H⋯N H-bond distance, whereas a general correlation was neither found for the aliphatic/caffeine-stemming ¹H sites nor any ¹³C chemical shift against either the intermolecular hydrogen- or tetrel-bond distance, except for the ¹³COOH sites of the 2C–OA, 2C–MA, and C–GA cocrystals, which are involved in a strong COOH⋯N bond with caffeine that is responsible for the main supramolecular stabilization of the cocrystal. We provide the first complete ¹³C NMR spectral assignment of the structurally disordered anhydrous β-caffeine polymorph. The results are discussed in relation to previous literature on the disordered α-caffeine polymorph and the ordered hydrated counterpart, along with recommendations for NMR experimentation that will secure sufficient ¹³C signal-resolution for reliable resonance/site assignments.

We discuss the prospects for accurate ¹¹B magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectral deconvolutions for reaching beyond the readily extracted borate speciations offered by the integrated resonances of the coexisting B^[3] and B^[4] species of the respective BO₃ and BO₄ network groups in borosilicate (BS) glasses. We critically review hitherto proposed ¹¹B^[3] and ¹¹B^[4] NMR-peak assignments relating to their neighboring Si, B^[3] and B^[4] species, as quantified by MAS NMR spectral deconvolution. Guidance to these resonance assignments was offered from double-quantum–single-quantum (2Q–1Q) ¹¹B MAS NMR experiments that inform about the B^[p]–O–B^[q] network linkages. The NMR spectral deconvolutions from two BS glass series with low nonbridging oxygen (NBO) contents and fixed molar ratios n_Si/n_B = {1.0, 2.0} but variable network-modifying cations of alkali metals and Mg²⁺ revealed a dominance of B^[4]–O–Si linkages, yet with a significant dependence on the BO₃ population of the glass, which was rationalized by the different propensities for B^[4]–O–{Si, B^[3], B^[4]} linkage formation. For BS glasses with comparable B and Si contents, we recommend three-peak deconvolutions of the ¹¹B^[4] spectral region, whose ¹¹B^[4](mSi) sites differ in their (average) numbers of m B^[4]–O–Si and 4 – m B^[4]–O–B^[p] bonds, where B^[p] may assume B^[3] or B^[4]. We also discuss the structural origin of the two rather arbitrarily classified “ring” and “non-ring” B^[3] entities, where 2Q–1Q ¹¹B NMR suggests the former to primarily constitute BO₃ groups that coexist with BO₄ moieties in (superstructural) ring units largely devoid of bonds to Si, whereas the “non-ring” B^[3] sites involve linkages to all of B^[3], B^[4], and Si, with B^[3]–O–Si linkages prevailing. The limitations of ¹¹B NMR spectral deconvolutions are discussed, including the remaining challenges in analyzing NBO-rich BS glasses.

Magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations were employed to investigate Na2O-B2O3-SiO2 and MgO-Na2O-B2O3-SiO2 glass structures up to ≈0.3 nm. This encompassed the {Na[p]}, {Mg[p]}, and {B[3], B[4]} speciations and the {Si, B[p], M[p]}-BO and {Si, B[p], M[p]}-NBO interatomic distances to the bridging oxygen (BO) and nonbridging oxygen (NBO) species, where the superscript indicates the coordination number. The MD simulations revealed the dominance of Mg[5] coordinations, as mirrored in average Mg2+ coordination numbers in the 5.2-5.5 range, which are slightly lower than those of the larger Na+ cation but with a narrower coordination distribution stemming from the higher cation field strength (CFS) of the smaller divalent Mg2+ ion. We particularly aimed to elucidate such Na+/Mg2+ CFS effects, which primarily govern the short-range structure but also the borosilicate (BS) glass network order, where both MD simulations and heteronuclear double-resonance 11B/29Si NMR experiments revealed a reduction of B[4]-O-Si linkages relative to B[3]-O-Si upon Mg2+-for-Na+ substitution. These effects were quantified and discussed in relation to previous literature on BS glasses, encompassing the implications for simplified structural models and descriptions thereof.

We examine the borate group intermixing in a series of 25 borosilicate (BS) glasses from the [0.5M₍₂₎O–0.5Na₂O]–B₂O₃–SiO₂ systems with M = {Li, K, Rb, Mg, Ca} along with ternary K₂O–B₂O₃–SiO₂ and Na₂O–B₂O₃–SiO₂ glasses by double-quantum–single-quantum (2Q–1Q) ¹¹B correlation nuclear magnetic resonance (NMR) experiments. The alterations of the fractional populations of B^[3]–O–B^[3], B^[3]–O–B^[4], and B^[4]–O–B^[4] linkages in the glass networks were monitored for variable n_Si/n_B molar ratios, nonbridging O contents of the glass, and the (average) cation field strength (CFS) of the M^z+/Na⁺ network modifiers. A significant B^[4]–O–B^[4] bonding is observed in all glasses, thereby conclusively demonstrating that the normally assumed “BO₄–BO₄ avoidance” is far from strict in BS glasses, regardless of the M^z+ field strength. We show that the degree of B^[4]–O–B^[4] bonding depends foremost on its underlying BO₄ population and to a lesser degree on the NBO content of the glass; we also provide a straightforward prediction of the B^[4]–O–B^[4] population in an arbitrary BS glass from parameters readily obtained by routine ¹¹B NMR. The propensity for forming B^[4]–O–B^[4] linkages increases concurrently with either the CFS or the amount of glass network modifiers, roughly scaling as the square root of the “effective CFS” that encompasses both parameters. Although BO₃–BO₃ and BO₃–BO₄ pairs remain favored throughout all examined BS glass networks, the borate group intermixing randomizes significantly for increasing effective CFS, out of which the amount and charge of the glass-network modifier cations dominate over their size. Our results are discussed in relation to the two prevailing but formally mutually exclusive “random network” and “superstructural unit” models of borate and BS glasses.

We examine the impact of the glass network-modifier cation field strength (CFS) on ion irradiation-induced mechanical property changes in borosilicate (BS) glasses for the ternary M2O-B2O3-SiO2 systems with M = {Na, K, Rb} and the quaternary [0.5M((2))O-0.5Na(2)O]-B2O3-SiO2 systems with M = {Li, Na, K, Rb Mg, Ca, Sr, Ba}. B-11 nuclear magnetic resonance (NMR) experiments on the as-prepared BS glasses yielded the fractional population of four-coordinated B species (B-[4]) out of all {B-[3], B-[4]} groups in the glass network, along with the fraction of B-[4]-O-Si linkages out of all B-[4]-O-Si/B bonds. Both parameters correlated linearly with the (average) CFS of the M+ and/or {M(2)+, Na+} cations. Both the nanoindentation-derived hardness and Young's modulus values of the glasses reduced upon their irradiation by Si2+ ions, with the property deterioration decreasing linearly with increasing Mz+ CFS, that is, for higher Mz+center dot center dot center dot O interaction strength. The irradiation damage of the glass network also increased linearly with the fraction of B-[4]-O-Si linkages, which are the second weakest in the structure after the Mz+center dot center dot center dot O bonds. Our results underscore the advantages of employing BS glasses with high-CFS cations for enhancing the radiation resistance for nuclear waste storage.

We explore the formation and composition–structure–property correlations of transparent Ca–Al–Si–O–N glasses, which were prepared by a standard melt-quenching technique using AlN as the nitrogen source and incorporating up to 8 at.% of N. Their measured physical properties of density, molar volume, compactness, refractive index, and hardness—along with the Young, shear, and bulk elastic moduli—depended roughly linearly on the N content. These effects are attributed primarily to the improved glass-network cross-linking from N compared to O, rather than the formation of higher-coordination AlO₅ and AlO₆ groups, where ²⁷Al magic-angle-spinning nuclear magnetic resonance experimentation revealed that aluminum is predominately present in tetrahedral coordination as AlO₄ units. Yet, several physical properties, such as the refractive index along with the bulk, shear, and Young's elastic moduli, increase concomitantly with the Al content of the glass. We discuss the incompletely understood mechanical–property boosting role of Al as observed both herein and in previous reports on oxynitride glasses, moreover suggesting glass-composition domains that are likely to offer optimal mechanical properties. 

In molecular dynamics simulations utilizing enhanced-sampling techniques, reweighting is a central component for recovering the targeted ensemble averages of the unbiased system by calculating and applying a bias-correction function c(t). We present enhanced reweighting protocols for variationally enhanced sampling (VES) simulations by exploiting a recent reweighting method, originally introduced in the metadynamics framework [Giberti et al. J. Chem. Theory Comput., 2020, 16, 100-107], which was modified and extended to multiple-walker simulations: these may be implemented either as independent walkers (associated with one unique correction function per walker) or cooperative ones that all share one correction function, which is the hitherto only explored option. When each case is combined with the two possibilities of determining c(t) by time integration up to either t or over the entire simulation period , altogether four reweighting options result. Their relative merits were assessed by well-tempered VES simulations of two model problems: locating the free-energy difference between two metastable molecular conformations of the N-acetyl-l-alanine methylamide dipeptide, and the recovery of an a priori known distribution when one water molecule in the liquid phase is perturbed by a periodic free-energy function. The most rapid convergence occurred for large cooperative walkers, regardless of the upper integration limit, but integrating up to t proved advantageous for small walker ensembles. That novel reweighting method compared favorably to the standard VES reweighting, as well as to current state-of-the-art reweighting options introduced for metadynamics simulations that estimate c(t) by integration over the collective variables. For further gains in computational speed and accuracy, we also introduce analytical solutions for c(t), as well as offering further insight into its features by approximative analytical expressions in the high-temperature regime.

This Primer critically reviews the possibilities and limitations of probing the short-range structure of an oxide-based glass by routine magic-angle spinning (MAS) or triple-quantum MAS (3QMAS) nuclear magnetic resonance (NMR) experiments. We briefly outline the structural features of oxide-based glasses and the basics of solid-state NMR. Besides suggesting guidelines for selecting favorable experimental conditions and important considerations for recording high-quality MAS NMR spectra amenable for subsequent analysis, we review options for extracting NMR observables and their distributions from spins-1/2 as well as half-integer spin quadrupolar nuclei. Considering that the isotropic chemical shift remains the primary probe of local structure by MAS NMR, we thoroughly review its dependence on the short-range oxide-based glass parameters from the viewpoint of a very simple and intuitive but qualitative model. The utility of deconvolutions of notably 29Si and 31P MAS NMR spectra are discussed critically. We also suggest alternative yet qualitative analysis options that are available whenever MAS NMR spectral deconvolutions are not warranted without additional information, which incidentally applies to a majority of modern multicomponent glasses.

Solid-state nuclear magnetic resonance (NMR) spectroscopy is the arguably most powerful technique for structural characterizations of amorphous inorganic materials, such as oxide-based glasses that are the focus of this review. We describe the most widely employed routine magic-angle-spinning (MAS) NMR experimentation that primarily informs about the short-range (≲0.3 nm) glass structure, as well as advanced MAS NMR techniques capable of probing the medium-range glass organization across a 0.3-0.7nm scale, which due to the fragility of most glasses to electron irradiation is exceedingly difficult to assess accurately by other means than solid-state NMR. We also discuss the advantages and limitations of the various MAS NMR protocols relative to other options. With a coverage of the literature from the pioneering reports in the early 1980s to the most recent cutting-edge NMR applications as of around year 2020, we aim at offering a critical review that combines depth and breadth, so as to appeal to practitioners in the area of NMR on glasses, to those working in the field of glasses but not having a deep understanding of their structures and how they may be probed, as well as to those new to both topics of glass structure and NMR. Hence, no prior knowledge of either topic is assumed, both of which are introduced in the first few sections of the article.