Sub-Nanometer-Range Structural Effects From Mg2+ Incorporation in Na-Based Borosilicate Glasses Revealed by Heteronuclear NMR and MD Simulations

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.


INTRODUCTION
Incorporating highly charged and/or small electropositive cations in oxide glasses, in particular rare-earth (RE 3+ ) ions, often improves their thermal and mechanical properties. 1−8 However, the high cost and toxicity of RE 3+ species make Mg 2+ an inexpensive and environmental-friendly alternative for glasses in a sustainable future society, as the cation field strength (CFS) of the small Mg 2+ cation is only marginally lower than that of La 3+ .(The CFS scales as the charge divided by the square of the cation radius). 9−23 It also remains unclear as to whether the physical-property boosts observed for Mg 2+ -bearing AS glasses (relative to those with lower-CFS alkali/alkaline earth metal ions) also apply to the BS glass context.Results from MO−Na 2 O−B 2 O 3 −SiO 2 glasses merely suggest that the larger Sr 2+ and Ba 2+ cations offer higher hardness and better elastic properties than their Mg 2+ counterpart. 22hese differences may be traced to the distinct effects from high-CFS Mg 2+ and RE 3+ incorporation in AS versus BS structures.While the physical glass properties are enhanced slightly from stronger Mg 2+ /RE 3+ −O bonds relative to those of lower-CFS M + /M 2+ glass-network modifiers, all M−O bonds remain markedly weaker than their F−O counterparts, where F denotes a network forming species, F = {Si, Al, B}.Rather, the structure-strengthening effects and accompanying improved thermal/mechanical properties upon high-CFS M z+ inclusion in AS glasses stem from the effects on the Al speciation, where the dominant AlO 4 groups partially convert into higher-coordination yet network-forming AlO 5 and AlO 6 polyhedra, 24,25 whose higher network cross-linking enhances the physical glass properties. 5,7,25,26Including high-CFS M z+ cations in BS glasses, on the other hand, strongly alters their B speciations.−31 However, high-CFS cations tend to promote B [3] formation at the expense of B [4] , 19,22,32−37 which lowers the overall glass-network connectivity and may thereby degrade physical properties.Yet, little is known about the precise structure− property relationships of high-CFS M z+ -bearing BS glasses, which are strongly dependent on the precise glass stoichiometry and likely also on the M z+ size (alone); 22 for example, incorporating Mg 2+ into a few Na 2 O−B 2 O 3 −SiO 2 glass compositions reduced their hardness and elastic properties, whereas these properties improved when instead introducing the larger high-CFS La 3+ cation. 22y utilizing atomistic molecular dynamics (MD) simulations and magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, we report here on the structural alterations from Mg 2+ -for-Na + substitutions in four Na 2 O− B 2 O 3 −SiO 2 base-glass compositions.Besides the {B [p] } and {O [q] } speciations, we examine the local Na and Mg coordination environments and their distinctly different propensities for coordinating the bridging oxygen (BO; O [2] coordinations) and nonbridging oxygen (NBO; O [1] ) species.We particularly aim to understand the dependence of the local glass structure on the M z+ CFS, which besides Na + and Mg 2+ also involves results from Ca 2+ -bearing BS glass models along with previously published data from RE 3+ cations in AS glasses.
We then move the spotlight from the first F [p] and M [p] coordination shells onto the F−O−F′ glass-network linkages, where the silicate and borate group intermixing was probed by computational modeling and heteronuclear double-resonance 11 B/ 29 Si MAS NMR experiments.Current B/Si interconnectivity insights partially stem from 17 O triple-quantum MAS (3QMAS) 38 experimentation. 24,36,37,39,40Although widely applied, it may not unambiguously discriminate between the B [3] and B [4] coordination numbers of the B−O−Si and B−O−B linkages (let alone quantify them, although such claims have been made 36,37,40 ).The heteronuclear magnetic 11 B− 29 Si dipolar interaction, which is mediated directly through space and scales as the inverse cube of the 11 B− 29 Si distance, 24,25,41,42 offers a more direct probing of the 11 B [p] / 29 Si intermixing in BS glasses.However, its application is relatively sparse, 43−49 mainly stemming from the requirement of dedicated glass syntheses from costly 29 Si-enriched silica to enable high-quality experimental data for quantitative analyses, which is otherwise severely hampered or even precluded by the low natural abundance (4.7%) of the NMR-active 29 Si isotope.The impact of Mg 2+ incorporation on the relative degrees of B [3] −O−Si and B [4] −O−Si bonding in the Mg/Na-bearing BS glass networks is discussed in relation to current literature, as well as the implications for existing simplified BS-glass structure descriptions/models.

Borosilicate Glasses.
Our study involved the eight BS glass compositions listed in Table 1, encompassing four ternary RNa 2 O−B 2 O 3 −KSiO 2 glasses and four quaternary R[0.5MgO− 0.5Na 2 O]−B 2 O 3 −KSiO 2 analogs.They constitute a subset of a large BS glass ensemble examined previously. 22,50,51We adopt the glass nomenclature of ref 50, where each Na-and Mg/Nabased glass is denoted by NaK−R and MgNaK−R, respectively, with the {K, R} parameters defined by 52,53 (1) (2) Each nominal glass composition in Table 1 is expressed in terms of its oxide equivalents and the atomic fraction of each element E in the (Mg)−Na−B−Si−O glass, ) (3) where n E is the corresponding stoichiometric amount.MD simulations were performed for all glass compositions in Table 1.The need for dedicated glasses synthesized from costly 29 SiO 2 to enable the heteronuclear 11 B/ 29 Si NMR experiments, however, limited them to three specimens: Na4.0−0.75,MgNa4.0−0.75, and MgNa4.0−2.1.
The CFS of an M z+ cation is defined according to 9 x B 4 values listed to the left are reproduced from Lv et al., 22 while those to the right (in bold) are results from the present 29 Si-enriched glasses; the latter data are employed throughout the experimental analyses of those glass specimens.c NBO fraction, x NBO , out of all BO and NBO species, as either obtained by MD simulations (uncertainty ±0.001) or calculated from eq 9 (±0.01) by using the NMR-derived { [ ] x B 4 } data.The experimental x NBO values listed to the left and right (in bold) correspond to the results presented by Lv et al. 22 and those of the present 29 Si-enriched glasses, respectively; the latter data are assumed throughout this work.d Prepared with 29 Si isotopic enrichment (section 2.2).

The Journal of Physical Chemistry B
where r M is the cation radius and r O = 1.36 Å.Table S1 lists the CFS values of the F = {Si, B [3] , B [4] } network formers and the M z+ = {Na + , Mg 2+ } network modifiers primarily targeted here, along with a few other M z+ cations discussed in section 3.For consistency, we employed r M values for sixfold-coordinated M z+ species (M [6] ) throughout.The coordination number is not indicated for exclusively tetrahedrally coordinated Si ≡ Si [4] atoms.
2.2.Glass Preparation.The 29 Si-enriched Na4.0−0.75,MgNa4.0−0.75, and MgNa4.0−2.1 glasses were prepared in 250 mg batches from analytical grade 29 SiO 2 (99.8% 29 Si), H 3 BO 3 , Na 2 CO 3 , and MgO precursors.After removing potential OH/ H 2 O contaminations by preheating the 29 SiO 2 powder at 950 °C for 24 h, the precursors were mixed thoroughly in a mortar, transferred to a Pt crucible, and decarbonated at 950 °C for 2 h before being heated to final melt temperatures of 1000, 1100, and 1200 °C for the MgNa4.0−2.1,Na4.0−0.75, and MgNa4.0−0.75 batches, respectively.Those temperatures were deduced from multiple preparations using regular (nonenriched) SiO 2 so as to ensure complete melting but minimal evaporation losses and close fictive temperatures to previous BS glass specimens of identical nominal compositions but prepared in larger batches (6 g) at ≈200 °C higher melting temperatures. 22The melt was held for 20 min and then quenched by immersing the crucible bottom in cold water.
All glass specimens were free of crystalline impurities.Their compositions are expected to be close to their batched/nominal counterparts listed in Table 1, as corroborated by the minute evaporation losses during heating of 1.0 wt % and 1.6 wt % for MgNa4.0−2.1 and MgNa4.0−0.75, respectively.Although the Na4.0−0.75 glass revealed a markedly higher loss (5.6% wt %) than the 1−2 wt % we normally observe, 22,34 it mainly reflects accidental melt-loss prior to quenching.Indeed, relative to the batched B 2 O 3 contents, the B 2 O 3 masses determined from 11 B MAS NMR experiments calibrated to H 3 BO 3 as the standard (see refs 22 amd 34) revealed marginal relative deviations from 0.6% for Na4.0−0.75 to 1.7% for MgNa4.0−0.75.

Molecular Dynamics Simulations.
Atomistic MD simulations mimicking a melt-quench process were utilized to produce BS glass models with the stoichiometries from Table 1.The computations utilized the DLPOLY4.09program, 54 where NVT ensembles in a cubic box with periodic boundary conditions were simulated using a box size and number of atoms (6600−11600) to match the nominal chemical glass composition and the experimental density (Table S2).Each melt-quench protocol started from randomly positioned atoms, which were equilibrated for 100 ps at 3500 K, followed by a stepwise temperature reduction (5 K/ps) to 300 K.The equations of motion were integrated in steps of 0.2 fs by using the velocity Verlet integrator, while the temperature was controlled by a gentle stochastic thermostat with a 1.0 ps time constant and a 1.0 ps −1 Langevin friction constant.The structural data were sampled and averaged over the last 150 ps of a final 200 ps equilibration stage.The average value and uncertainty of each reported structural parameter were obtained by performing the melt-quench protocol four times.−60 Every cation carries its full formal charge, 58 but the O 2− species are represented by core (O C ) and shell (O S ) portions with masses m C = 15.7994u and m S = 0.2000 u, respectively, and corresponding charges z C = +0.8482eand z S = −2.8482e(obeying z C + z S = −2), where "u" is the atomic mass unit and e is the elementary charge.Each core−shell unit is connected by a harmonic potential with a force constant of 74.92 eV/Å 2 . 58The interaction energy of two atom/ion species α and β separated by a distance r αβ was modeled by a modified Buckingham potential that accounted for all short-range O S −O S and cation−O S pair interactions.It was evaluated out to r αβ = 0.8 nm.9 Si MAS NMR spectra were acquired at a magnetic field (B 0 ) of 9.4 T (79.47 MHz 29 Si Larmor frequency) using 4 mm zirconia rotors undergoing MAS at ν r = 14.00 kHz and radio frequency (rf) pulses with a ≈70°flip angle (ν Si = 84 kHz nutation frequency), relaxation delays of 3600 s, and 16 accumulated NMR signal transients.The 11 B (spin-3/2) NMR spectra were recorded at B 0 = 14.1 T (−192.5 MHz 11 B Larmor frequency) and ν r = 24.00kHz using full 3.2 mm zirconia rotors and strong/ short rf pulses (0.33 μs, 13°flip angle, ν B = 105 kHz).The {B [3] , B [4] } populations of each glass were determined from the integrated central-transition (CT) NMR-signal intensities, 22,50 which were corrected for the satellite-transition centerband peak that overlaps with the main CT 11 B [4] signal by using standard procedures. 61Every 11 B NMR spectrum was corrected for probehead "background" signals by subtracting the result from the empty rotor recorded under otherwise identical experimental conditions. 29Si (δ Si ) and 11 B (δ B ) shifts were referenced relative to neat tetramethylsilane (TMS) and BF 3 •OEt 2 , respectively.
The Van Vleck dipolar second moment 62 is proportional to the sum over the inverse sixth power of the interatomic distance of each heteronuclear S j −I k spin-pair in a structure: Here, μ 0 is the permeability of vacuum, γ I (γ S ) is the magnetogyric ratio of spin species I (S), and N I and N S are the respective total numbers of I and S nuclei in the glass obtained from its stoichiometry with , where N A is Avogadro's number and E the natural isotopic abundance.I denotes the spin quantum number of the nuclide I, i.e., I = 1/2 ( 29 Si) and I = 3/2 ( 11 B) for the respective M 2 (B [p] −Si) and M 2 (Si−B [p] ) entities.We stress the unit of s −2 in eq 6, which is consistent with our previous work 57,63,64 but differs from the original M 2 definition with units of rad 2 /s 2 , 62   42).The two dipolar second-moment definitions are related by 4π 2 M 2 [s −2 ] = M 2 [rad 2 /s 2 ].Units aside, we comment that incorrect M 2 (S−I) expressions are stated in two recent review articles, 24,25 which should appear as in ref 64 and eq 6.
The M 2 (B [p] −Si) value of a given BS glass may be estimated from a 11 B{ 29 Si} REDOR NMR experiment 65 that restores/ "recouples" the MAS-averaged 11 B [p] − 29 Si dipolar-interaction effects during a recoupling period (τ rec ) by a series of rotorsynchronized 180°rf pulses applied to 29 Si, during which the 11 B [p] NMR signal [S(τ rec )] becomes attenuated ("dephased") relative to that obtained by a spin−echo experiment [S 0 (τ rec )] 65 obtained by CT-selective 11 B rf pulses.
All double-resonance 11 B{ 29 Si} REDOR NMR experiments were performed at B 0 = 14.1 T and ν r = 9.00 kHz with each glass powder centered to the 1/3 volume of a 4 mm zirconia rotor to reduce the impact from rf inhomogeneity. 41,66,67All experiments were started by a saturation-recovery rf-pulse comb followed by a 1.5 s relaxation delay.The 180°dipolar recoupling pulses operated at ν Si = 46 kHz with the XY8 phase-cycling scheme to minimize rf-pulse errors. 68The 11 B 90°and 180°spin−echo rf pulses were 17.0 μs and 34.0 μs, respectively.The dipolar recoupling period was sampled out to several ms at even integer multiples n of the rotor period, and M 2 (B [4] −Si) value was extracted from the respective integrated 11 B [3] and 11 B [4] NMR intensities of the S 0 (τ rec ) and S(τ rec ) spectra, whereupon the resulting {τ rec , ΔS/ S 0 } data (restricted to ΔS/S 0 ⩽ 0.2 24,41,42 ) were fitted to the expression 41,42,63 2−4 independent NMR-data blocks with 256−512 accumulated signal transients per block were acquired for each glass specimen.The average value of each M 2 (B [p] −Si) estimate and its uncertainty were extracted from these independent {M 2 (B [p] −Si)} best-fit results.

RESULTS AND DISCUSSION
3.1.Boron and Oxygen Speciations.All BS glasses considered herein comprise networks of interconnected SiO 4 , BO 3 and [BO 4 ] − groups, where [ ] x B 3 and [ ] x B 4 denote the respective fractional populations of B [3] and B [4] .Table 1

lists each [ ] x
B 4 value obtained from either the 11 B MAS NMR spectrum or MD simulations, whereas the corresponding BO 3 fraction is given from the following normalization: The experimental { [ ] x B 4 } data were reproduced from ref 22 except for the three 29 Si-enriched Na4.0−0.75,MgNa4.0−0.75, and MgNa4.0−2.1 specimens that were prepared specifically for the present study.Their borate speciations match very well those of glasses prepared from regular (non- 29 Si-enriched) SiO 2 , 22 suggesting very close stoichiometries and fictive temperatures for both specimens of each Na4.0−0.75,MgNa4.0−0.75, and MgNa4.0−2.1 stoichiometry (see Table 1 and Figure 1).The MD simulations revealed O speciations solely comprising NBO and BO sites, whereas "free O 2− anions" (O [0] ) are absent throughout and the "O tricluster" (O [3] ) populations remain <0.02% out of each {O [q] } ensemble.Hence, the fractional populations of NBO (x NBO ) and BO (x BO ) species obey x NBO + x BO = 1.
The Na + /Mg 2+ cations compensate the negative charges of the [BO 4 ] − and NBO (O − ) moieties, implying that the fractional populations of B [4] and NBO anions are coupled according to

O NBO Na
Mg .Hence, x NBO is readily deduced from the glass stoichiometry and the 11 B NMRderived [ ] x B 4 value as follows: Equation 9 reflects the well-known dual "network modifier" and "charge compensator" structural properties of the M z+ cations in borate-based glasses, 24,27,52,53,69,70 which result in 4] conversions.The borate speciation of a BS-based glass depends strongly on both its stoichiometry and CFS M . 19,22,32−37 As expected from the higher CFS Mg = 0.46 Å −2 than CFS Na = 0.18 Å −2 , 19,22,32,33 introducing Mg 2+ to a NaK−R glass boosts the NBO content for fixed {K, R} parameters, while the B [4] population is markedly reduced (Table 1).This effect is particularly drastic for the NaK−0.75 and Na4.0−2.1 glasses with : when half of the Na + ensemble is replaced by Mg 2+ , a significant B [4] → B [3] conversion occurs, rendering BO 3 groups most abundant in all MgNaK−R specimens.
For a clear-cut discrimination between the M z+ and F species, we employ the ancient "network modifier" terminology when referring to the M + /M 2+ cations, although the categorical "modifier" and "charge-compensator" classification is oversimplified. 56,57For instance, both MD simulations and NMR experiments reveal that a significant/major portion of the {Na + } ensemble associates with the formally charge-neutral Si(O [2] ) 4 and B(O [2] ) 3 moieties via Na + •••O−Si/B [3] fragments (rather than with the negatively charged [BO 4 ] − and F−NBO  29 SiO 2 (black traces) or from SiO 2 with 29 Si at natural abundance (red traces; reproduced from Lv et al. 22 ).The glasses were prepared under similar conditions and reveal very similar 11 B NMR spectra and borate speciations (Table 1).
The Journal of Physical Chemistry B moieties), rendering Na−BO contacts prevalent for all but very NBO-rich glasses. 56,57 long-standing problem of classical MD simulations of Bbearing glasses is their (in −81 The modeled BO 4 and NBO populations listed in Table 1  , they grow progressively for increasing values of [ ] x B 4 (Table 1).The underestimated (overestimated) modeled BO 4 (BO 3 ) populations are reasons for concern regarding reliable predictions of some medium-range (0.3−1 nm) glass-structure features.Gratifying, however, is the typically (very) good agreement observed consistently relative to experimental data on several interatomic-distance-related structural parameters, such as the relative B [3] /B [4] •••Na + and P−O−B [p] contacts in boro(phospho)silicate glasses, 55,57 as well as their B [p] −O− B [q] linkage statistics, 34,50,55 which constitute the most sensitive medium-range structural parameters on the precise } fractions; notwithstanding that the NMR/MD-derived B [p] − O−B [q] populations do differ, all experimental findings were reproduced qualitatively/semiquantitatively by the glass models. 34,50,55Moreover, the relative B [3] /B [4] −O−Si contacts predicted by the glass models in section 3.5 agree very well with our experiments, encompassing the Na4.0−0.75 glass.Indeed, out of the plethora of B−O force fields proposed to date (e.g., refs 74−81), solely the herein utilized option 55,56 has been assessed extensively against experimental interatomic-distancerelated parameters directly reflecting the medium-range glass organization.

MD-Derived Average F−O and M−O Distances.
Here and in sections 3.3 and 3.4, we examine the MD-derived first coordination shells of the network formers and modifiers, paying particular attention to the structural bearings from Mg 2+ , thereby complementing our previous structural reports on large sets of Na + and Na + /Ca 2+ bearing borate and boro(phospho)silicate glasses with variable B, Si, and NBO contents. 56,57or each {Si, B [3] , B [4] } network former, Table 2 compiles the average F [p] −O [q] interatomic distance, r (F [p] −O [q] ), for each of O [1] and O [2] , along with the corresponding {r (F [p] −O)} result that represents the weighted average of the F [p] −O [1] /O [2] distances over all {FO p } polyhedra.We stress that each F [p] − O/O [q] and M [p] −O/O [q] interatomic distance ("bond-length") discussed herein constitutes the arithmetic average across the Table 2 −O [q] and M−O [q]  distances between the NBO (O [1] coordination) and BO (O [2] ) species for } and M = {Na, Mg}, where the latter involve the entire {Na [p] } and {Mg The Journal of Physical Chemistry B entire F−O [q] (M−O [q] ) bond ensemble in the structure.
was not extracted from the respective pairdistribution maximum, which constitutes the most probable F− O distance but is frequently reported as r (F−O) (e.g., see refs 60, 76, and 83−86).Because the various Si/B [p] −BO/NBO distances are governed by the high-CFS Si 4+ and B 3+ cations (Table S1), they remain similar for all BS glasses regardless of the precise network modifier species.All F [p] −O [q] distances in Table 2 conform well with those discussed by Stevensson et al. 56 for Na−(Ca)−B−Si−O glasses, which agreed well with the sparsely available experimental data.The direct dependence of each F−O distance on the NBO content of the glass is evident when contrasting the r (Si−O) and r (B [3] −O) data from each NaK−R glass with its MgNaK−R analog (in contrast with r (B [4] −O); vide infra): the distances in the Mg-bearing glass are marginally but consistently shorter by ≈0.3 pm due to the slightly higher NBO contents in those glasses coupled with the shorter F−NBO distances relative to F−BO (Table 2).
We next consider the F−O [1] and F−O [2] bond-length variations.The large CFS of the very small B 3+ cation manifests as tightly confined B [3] −O [1] and B [4] −O [1] bond lengths (134− 135 pm throughout), which are markedly shorter than those of Si−O [1] (161−162 pm; see Table 2).5][76][77]84 Table 2 confirms the anticipated feature of nearly constant r (F [p] −O [1] ) values regardless of the n Si /n B molar ratio of the glass (related to K) or its NBO content (related to R). 56 In contrast, all {r (F−O [2] )} values increase slightly for increasing x NBO . For istance, contrast the bond lengths from each NaK−0.75 and MgNaK− 0.75 structure with those of its NBO-richer NaK−2.1 and MgNaK−2.1 counterpart: r (F [p] −O [2] ) is increased by 1−2 pm for Si and slightly more for the two B [3] and B [4] coordinations (2−3 pm; Table 2).However, for the Mg 2+ /NBO-richer MgNaK−2.1 glasses, for which any bond-length effect from Mg 2+ is expected to be most pronounced, it is notable that r (B [3] −O [2] ) is shorter by ≈1 pm than that for their NaK−2.1 analogs, whereas the reverse trend of a ≈1 pm longer r (B [4] − O [2] ) bond length is observed.
We onward focus on the average M−O [1] , M−O [2] , and M−O distances listed in Table 2 for the Na + and Mg 2+ species, which are averages over all M [p] coordinations in the structure.As expected, the Na/Mg−O [1] bond lengths are significantly shorter than their Na/Mg−O [2] counterparts.Marginal variations of the average Mg−O [1] and Mg−O [2] distances are observed throughout, regardless of the precise B, Si, or NBO content of the glass (Table 2).The mean Na−{O, O [1] , O [2] } bond lengths predicted from the NaK−R glass models conform well to those discussed for Na-and Na/Ca-bearing borate/BS glasses in ref 56.Notwithstanding that r (Na−O [2] ) only varies marginally among the eight glass structures (Table 2), the Na− O [1] distances are markedly longer (by 5−8 pm) in each MgNaK−R glass relative to its NaK−R counterpart (Table 2).This is attributed primarily to the sharing of many NBO sites in the MgNaK−R structure between Na + and Mg 2+ , coupled with the tighter control of Mg 2+ to maintain a short Mg−O [1] bond (≈203 pm; Table 2), which lengthens r (Na−O [1] ) by 5−8 pm relative to the bond length of ≈240 pm of the Mg-free glasses.
3.3.MD-Derived {NaO p } and {MgO p } Speciations.Figure 2 plots the distributions of {Na [p] } and {Mg [p] } coordinations observed from the glass models.As expected, the larger Na + cation exhibits higher coordination numbers than Mg 2+ , which is mirrored in average coordination numbers Z ( ) M ranging over Z 5. 8  6.4 Na and Z 5.2 5.5 Mg and corresponding distributions peaking at Na [6] and Mg [5] .Along previous findings from (boro)phosphosilicate glasses, 56,64,87 substantial Na [5] and Na [7] populations are also present throughout all BS glass models (Figure 2).In contrast, the The Journal of Physical Chemistry B {Mg [p] } ensemble is more strongly peaked at p = 5, although significant contributions from MgO 4 and MgO 6 polyhedra are encountered in all structures, with the NaMg2.0−2.1 glass revealing nearly equal Mg [5] and Mg [6] populations.The herein modeled Z Mg values accord well with those observed by Pedone and co-workers from NBO-rich phosphosilicate 86 and aluminoborosilicate 83 glasses, all of which are higher than those reported in ref 85.Potential relationships between Z Na /Z Mg and the glass compositions are discussed in section S1.The less dispersed distribution of {Mg [p] } populations relative to {Na [p] } stems from the larger CFS Mg and the higher capacity of Mg 2+ to control its coordination shell, as also mirrored in the respective standard deviation  3).

The herein observed [ ] p
Na values from a rather modest Na− (Mg)−B−Si−O glass ensemble agree well with those of previous MD-derived results gathered from large sets of Nabearing borate, boro(phospho)silicate, and phosphosilicate glasses. 56,64Notably, the Ca 2+ cation with an intermediate CFS between Na + and Mg 2+ (Table S1) reveals Z Ca values close to and only marginally lower than those of Na + .However, the
−92 Yet, discriminating between those two distinct structural scenarios is not straightforward even from glass models because precise and reliable criteria are difficult to formulate given that all electropositive M z+ cations coordinate a significant number of BO sites at the SiO 4 and BO p moieties (section 3.4).Table 3 reveals that Mg [4] accounts for 12−22% of the Mg speciations of the present BS glasses.Even if {Mg [4] } would assume a partial network-forming role, it is likely to be only minor.Indeed, eq 9 rests on the assumption that all Na + /Mg 2+ cations act as modifiers, where the excellent agreement between the MDderived NBO populations and those obtained experimentally via eq 9 (Table 1) suggests that a vast majority of the Mg 2+ cations (if not all) assume the expected network-modifying role.To widen the perspective, non-negligible Na [4] populations are also predicted in MD-derived oxide-glass models (see Table 3 and  refs 56 and 87), but a potential network-forming capacity of the archetypal Na + modifier has to our knowledge not yet been suggested.

CFS-Dependent Preferences for M−BO/NBO
Bonding.We now examine the MD-derived BO/NBO partitioning in the first coordination shells of the Na + and Mg 2+ cations in each BS glass structure, i.e., the distribution of the O [2] /O [1] coordinations of the respective {NaO p } and {MgO p } ensembles presented in x p Mg denote the corresponding fractional populations of the Na [p] and Mg [p] coordination species and  56,93 For nonpreferential M−BO/NBO bond formation, P(M− NBO) = P(M−BO) = 1 and the fractions of M−NBO and M− BO contacts match the respective x NBO and x BO values of the glass.The cases P(M−O [q] ) > 1 and P(M−O [q] ) < 1 mark the preference and reluctance of M−O [q] formation, respectively, with the deviation from unity of P(M−O [q] ) conveying the degree of preference/reluctance.
The data of Table 4 confirm the well-documented propensities of Na + and Ca 2+ cations to coordinate NBO rather than BO species 56,60,64,83,87,94−97 and that P(M−NBO) increases concurrently with the M z+ CFS as follows: 56,64,86,87 P(Na−NBO) < P(Ca−NBO) < P(Mg−NBO).The precise P(M−NBO) value depends not only on the M z+ identity but also on the {R, K} parameters of the BS glass: all Na + , Ca 2+ , and Mg 2+ cations strongly prefer NBO coordination, which accentuates for (i) increasing n Si /n B ratio (i.e., increasing K) and, in particular, (ii) decreasing x NBO (i.e., decreasing R).Consequently, all three network-modifier species manifest the overall strongest preference for M−NBO bond formation in the {K, R} = {4.0,0.75} structures (Table 4).
Trend (ii) is unsurprising, i.e., that the strongest preference for M−NBO bonding occurs in NBO-poor BS glasses.It conforms to the frequently encountered feature of oxide glasses in which their propensity for forming a given structural moiety deviates the most from that predicted by an unrestricted random/statistical distribution whenever its abundance is for low P contents (x P ≲ 0.015), which manifest a minor P−P aggregation. 102,103(III) The preference for each of the two prevalent P−O−B [4] and P−O−Si linkages in borophosphosilicate glasses is strongest in Si-rich and B-rich glass structures, respectively, i.e., when the accompanying fractions of P−O−Si and P−O−B [4] linkages dominate. 55Exceptions to this crude "rule of thumb" do indeed exist, such as that the spatial distribution of Na + cations in Na 2 O−(CaO)−B 2 O 3 −SiO 2 glasses, which is most uniform in Na-poor compositions but randomizes in modifier-richer glasses. 57he stronger preference for NBO coordination of the higher-CFS Ca 2+ and Mg 2+ ions compared to that of Na + (refs 56, 64, 83, 86, 87, and 96) is also mirrored in the reduced P(Na−NBO) value in each MgNaK−R glass relative to that its ternary NaK−R analog, notwithstanding that some of the mixed-cation glasses manifest slightly larger x(Na−NBO) f ractions than their NaK− R counterparts due to their higher NBO contents accompanying Mg 2+ introduction (Table 4).Yet, except for the overall NBOrichest {K, R}={2.0,2.1} glasses (x NBO ≈ 0.36), the low-CFS Na + ion consistently features more BO than NBO contacts throughout all R = 0.75 glasses, for which NBO species accounts only for 11−17% of all Na−O bonds in each {NaO p } ensemble.That contrasts sharply with the {MgO p } speciation of the MgNa4.0−0.75 glass, for which NBO anions constitute 62% of all Mg−O [q] bonds despite the low NBO abundance (x NBO = 0.077), which is readily rationalized by the 2−3 times stronger Mg−NBO than Na−NBO affinity (Table 4).
The P(M−BO) < 1 values observed in Table 4 throughout all BS glass models and all three network modifier species mirror the as-expected reluctance of M−BO bond formation, which is accentuated for increasing M z+ CFS values as follows: P(Na− BO) > P(Ca−BO) > P(Mg−BO).Although the much stronger propensity for M−NBO over M−BO contacts in oxide glasses is both intuitive and well documented by computational modeling, 56,60,64,83,86,87,94,95 it is challenging to quantif y the Table 4. MD-Derived Fractional Populations and Preferences for {Na, Ca, Mg}−{BO, NBO} Bonding a x(M−O [1] ) P(M−O [1] ) x(M−O [2] ) Fractional x(M−O [1] ) and x(M−O [2] ) populations out of the entire O speciation for M = {Na, Ca, Mg}, along with the corresponding preferences for M−O [p] bonding defined by NBO .b The data uncertainties are ±1σ with σ given for each entity.

The Journal of Physical Chemistry B
x(M−NBO) and x(M−BO) fractions using experiments.Yet, this was recently accomplished by exploiting double-resonance 17 O{ 23 Na} and 17 O{ 27 Al} NMR applied to an AS glass of composition 10.8Na 2 O−32.3CaO−13.0Al 2 O 3 −44.0SiO 2 . 96hat yielded estimated x(M−BO)/x(M−NBO) ratios of 1.4 and 0.37 for Na + and Ca 2+ , respectively, 96 incidentally very close to those of 1.3 (Na + ) and 0.40 (Ca 2+ ) predicted herein for the M−BO/NBO partitioning of the NaCa2.0−2.1 glass (Table 4).However, given the by definition very local structural information encoded by the Na−O [q] contacts of the NaO p polyhedra�and M−O [q ̅ ] bonds in general�coupled with the direct scaling of the x(Na−NBO) and x(Na−BO) fractions with the NBO content of the glass (e.g., see Table 4 and ref 56), we discourage attempts to draw even qualitative conclusions about medium-range glassstructure features from {x(M−O [p] )} data alone, encompassing inferences about the spatial Na + distribution and its possible implications for the (sub)nanometer-scale glass organization. 96,97.5.B [p] /Si Intermixing Probed by 11 B{ 29 Si} REDOR NMR and MD Simulations.3.5.1.Relative Degrees of B [3] − O−Si and B [4] −O−Si Bonding.The relative extents of B [3] −O− Si and B [4] −O−Si bonding in the Na4.0−0.75,MgNa4.0−0.75, and MgNa4.0−2.1 structures were assessed by 11 B{ 29 Si} REDOR NMR experiments.Figure 3 displays the "dephasing" responses observed from the 11 BO 3 and 11 BO 4 resonances for increasing "dipolar recoupling" periods (τ rec ) of 11 B [p] − 29 Si through-space interactions that are responsible for the NMRsignal dephasing. 65,104While the 11 B [p] -resonance dephasing is unaffected by any B [p] −O−B [q] or Si−O−Si linkage of the structure, its rate increases concurrently with the number of 11 B [p] −O− 29 Si linkages, thereby accelerating the progress toward the ΔS/S 0 = 1 limit of "complete dephasing" 24,25,41,42 (Figure 3a−c).As expected from the higher-coordination B [4] sites and previous 11 B{ 29 Si} REDOR NMR reports from other BS glasses, 44,46 their resonances reach the complete limit of complete dephasing well before their 11 B [3] counterparts (Figure 3a−c), except for the MgNa4.0−0.75 glass (vide infra).
Numerical fitting of the initial 11 B [p] NMR-signal dephasing regime with "short" τ rec values (Figure 3d−f) to eq 7 yields an estimate of the dipolar second moment M 2 (B [p] −Si), which reflects the "aggregate" 11 B [p] − 29 Si contact in the structure 24,41,42 and grows concomitantly with the net number of direct B [p] −O−Si bridges, N(B [p] −O−Si), i.e., the average number of Si atoms in the second coordination shell of the {B [p] } sites: M 2 (B [p] −Si) ≈ N(B [p] −O−Si).As highlighted by previous reports utilizing M 2 /dipolar-interaction-based NMR analyses to make inferences about bonding statistics/preferences, 34,42,64 however, this relationship is only approximate because M 2 (B [p] − Si) involves a sum over all r(B [p] −O−Si) distances in the structure (eq 6).Although the analysis of section S2 reveals that M 2 (B [p] −Si) approximates well the targeted information about the (average) number of direct B [p] −O−Si linkages, other factors degrade quantitative assessments of B [4] −O−Si bonding relative to B [3] −O−Si, which becomes underestimated by ≈25%.
Table 5 compiles the experimental M 2 (B [p] −Si) data together with those extracted from the glass models via eq 6.The consistently lower experimental M 2 (B [p] −Si) values compared to their MD-derived counterparts (by 40−55%) stem primarily from experimental imperfections, in particular rf inhomogeneity. 66,67Consequently, we focus our comparisons on the relative M 2 (B [p] −Si) trends among the B [3] /B [4] coordinations encoded by each NMR-and MD-derived dipolar second-moment ratio (section S2): Calculated from eq 11 by using the {M ).For a statistical/nonpreferential F−O−F′ linkage-formation among {F, F′}={Si, B [3] , B [4] } in a BS structure devoid of NBO species, M 2 rel (B) is given by M 2 rel (stat) ≈ 1.18 (section S2).The MD derived M 2 rel (B) data, and notably the experimental counterparts, are markedly larger than M 2 rel (stat) for all glasses but MgNa4.0−0.75, in particular for the NBO-rich R = 2.1 members (Table 5).Two structural factors account for these observations: (i) The NBO partitioning among Si, B [3] , and B [4] species in BS glasses was discussed previously, 34,50,56 suggesting a substantially stronger propensity for B [3] −NBO bonding relative to B [4] −NBO.Except for very NBO-rich glasses, 105 the latter is even considered "forbidden" by most scientists in the field 27,69,106−108 but remains frequently observed to minor extents in numerous MDderived glass models. 34,55,56,75,77,82Consequently, a progressively growing NBO accommodation at the BO 3 groups for increasing x NBO reduces the possibility of any B [3] −O−F linkage type, thereby boosting the M 2 rel (B) values of all NBO-rich glasses (Table 5), while the relative dipolar second moment (eq 10) is independent of the degree of Si−NBO bonding.Although the bonding preferences depend slightly on the glass composition, the trends of Table 5 conform well to those discussed previously for Na/Ca-bearing boro-(phospho)silicate glasses, 34,50,55,56 revealing the strongest preference (reluctance) for BO 3 −BO 4 (BO 4 −BO 4 ) pairs.While B [3] −O−B [3] linkages are also disfavored, all remaining Si−O−{Si, B [3] , B [4] } linkages form nearly statistically, i.e., each fractional population is given roughly by the product of the respective {x Si , 4 } molar fractions in the glass structure.Nonetheless, along previous findings from boro(phospho)silicate glasses, 34,50,55,56 [4] Environments with Variable Numbers of Si and B Neighbors. Figure 4a, c, and e shows the REDOR "reference" 11 B NMR spectrum, S 0 (τ rec ), of each Na4.0−0.75,MgNa4.0−0.75, and MgNa4.0−2.1 glass recorded at the shortest τ rec = 0.22 ms value, along with two REDOR spectra [S(τ rec )] observed for long dephasing periods of τ rec ={1.78, 2.67} ms.As expected from the ΔS/S 0 dephasing data of Figure 3, the latter spectra manifest progressively diminished 11 B [3] and (particularly) 11 B [4] resonance intensities for increasing τ rec , except for the MgNa4.0−0.75 specimen, which reveals comparable NMRsignal decays.

B
We now focus on the 11 B [4] NMR-signal dephasing, which is more pronounced for the low-δ B spectral region <−1 ppm, as is most transparent from the normalized NMR spectra presented in Figure 4b, d, and f.Along the 11 B NMR spectral deconvolution results of the Na4.0−0.75 and NaMg4.0−0.75 glasses presented by Lv et al., 51 the two peak components at ≈ −1.8 ppm and ≈ −0.3 ppm are attributed to B [4] (OSi) 4 and B [4] (OSi) 3 (OB) moieties, respectively, [35][36][37]40,72 which are abbreviated as B [4] (4Si) and B [4] (3Si).Owing to its larger number of Si neighbors, the resonance decay of 11 B [4] (4Si) is stronger than that of its 11 B [4] (3Si) counterpart. To adequtely deconvolute the 11 B [4] NMR signal region of the two Na4.0− 0.75 and MgNa4.0−0.75 glasses, however, it was necessary to also include a minor peak at ≈1.2 ppm from 11 B [4] (2Si) environments (accounting for 9% and 17% out of all B [4] (mSi) groups, respectively).51 These NMR signals are not clearly discernible in the REDOR spectra, but they are expected to decay even slower than the 11 B [4] (3Si) resonance, as is also hinted in Figure 4.  5).These effects are evident from the nearly coincident 11 B [p] {Si} REDOR NMR dephasing curve observed for MgNa4.0−0.75 (Figure 3b,e), in sharp contrast to those of the other two glasses for which the 11 B [4] NMR-signal dephasing rate consistently exceeds that of 11 B [3] .
We stress that although a lower total number of B [4] −O−Si linkages upon Mg 2+ incorporation is indeed anticipated from the drastic decrease of the BO 4 population alone (Table 5), that effect is inconsequential for M 2 (B [4] −Si) because its value is 4 } (eq 6), in contrast to 2 (Si−B [4] ); see section 3.7.Notably, the MD-generated preference factors of Table 5 rationalize these quantitative trends of dipolar second moments and the number of B [p] −O−Si bonds as originating from the more fundamental feature of a decrease in P(B [4] −O− Si) upon the introduction of the high-CFS Mg 2+ cation, which for all NBO-poor (Mg)NaK−0.75glasses is moreover emphasized by a concomitant increase of P(B [3] −O−Si) (see section S2).
The weakened B [4] /Si contacts upon Mg 2+ -for-Na + substitution reflect a general trend of a linearly decreasing fraction of B [4] −O−Si linkages (out of all B [4] −O−Si/B bridges) for increasing CFS M , as deduced from 11 B [4] MAS NMR spectra deconvolutions. 51These CFS effects are also mirrored in the 29 Si MAS NMR spectra of the Na4.0−0.75,−113 Hence, the 29 Si MAS NMR information content is very limited, at best offering qualitative inferences. 113,114Even for the (almost) NBO-free Na4.0−0.75 and MgNa4.0−0.75 glasses, the net 29 Si NMR peak s t e m s f r o m a p l e t h o r a o f u n r e s o l v e d 29 Si(OB [3] ) p (OB [4] ) q (OSi) 4−p−q resonances.
The 29 Si chemical-shift dispersion and the precise value of the most probable shift ( ) −113 Hence, the markedly reduced number of Si−O−B [4] bonds in the MgNa4.0−0.75 structure and the concurrently increased number of Si−O−B [3] and Si−O−Si linkages rationalize its net 29 Si resonance-displacement toward lower shifts relative to Na4.0−0.75, while the evident high-ppm "tail" of the NMR stems from the few(er) remaining 29 Si−O− B [4] sites (Figure 5).The structural complexity is accentuated further in the NBO-rich(er) MgNa4.0−2.1 glass, which additionally exhibits variable numbers of Si−NBO bonds among the SiO 4 groups.−119 A glass-in-glass separation occurs upon cooling, typically identified as (or often merely assumed to involve) one Si-dominated phase coexisting with a B-rich borate/BS counterpart 37,115−118 and manifested by 29   Si MAS NMR peak displacement toward more negative chemical shifts 117 near ≈ −110 ppm observed for vitreous SiO 2 . 113Incidentally, that is also observed for the MgNa4.0−0.75 glass (Figure 5) but is readily attributed to the significantly fewer Si−O−B [4] bonds in the MgNa4.0−0.75 structure relative to Na4.0−0.75 (note that both 29 Si−O−Si/B [3] environments resonate at near-equal shifts 113 ).Notably, previous heteronuclear 11 B/ 29 Si NMR studies on the bearings from thermal annealing of BS glasses, which may induce structural inhomogeneities and/or phase separation, also reveal that the number of Si−O−B [3] bonds increases relative to Si−O− B [4] , 45−48 thereby mirroring the herein observed 29 Si shielding accompanying Mg 2+ incorporation into a Na 2 O−B 2 O 3 −SiO 2 glass.However, backscatter scanning electron microscopy (SEM) images (not shown) did not indicate phase separation.Yet nanometer-scale inhomogeneities cannot be excluded, as they would remain undetected both over the ≳1 μm and <0.5 nm length scales probed by our SEM and NMR experimentation, respectively.
Remarkably, despite numerous reports on phase-separated BS glasses, the precise chemical compositions of the two (assumed) coexisting phases remain surprisingly poorly defined.Interestingly, all of the few studies using techniques that directly inform on the Si/B [p] intermixing (i.e., heteronuclear NMR) of annealed/phase-separated BS glasses do not point toward a categorical separation into Si-rich and B-rich phases, but merely to a significant reduction of the number of Si−O−B [4] linkages, while the number of Si−O−B [3] bonds remains invariant, or even increases, 45−48 within one, or several, borosilicate phase(s).A recently reported elemental analysis of a phase-separated Na BS glass did reveal two such phases with distinct Si and B contents; however, both contents were substantial in each phase. 119This issue should be investigated further to better define what phases coexist in BS glasses attributed to exhibit nanometer-range structural inhomogeneities.

Relative Degrees of Si−O−B [3]
/B [4] Bonding.This section discusses the dipolar second moments {M 2 (Si−B [p] )} listed in Table 5.They are accessible from the {M 2 (B [p]  for 11 B, whereas 29 Si constitutes ≈100% of all Si sites in the isotopically enriched glasses = ( 1)

Si
. Although the M 2 (Si−B [p] ) and M 2 (B [p] −Si) values are directly related for a given glass specimen, they nonetheless convey complementary information: while M 2 (B [p] −Si) is proportional to the number of B [p] −O−Si linkages at the BO p ensemble, M 2 (Si−B [p] ) relates to the number of Si−O−B [p] bridges at {SiO 4 }.
From its definition (eq 6), it follows that M 2 (B x p B , while M (Si−B [p] ) scales linearly with the B [p] population of the glass but is independent of the Si content.That feature rationalizes the excellent agreement observed between the NMR/MD-derived M 2 rel (Si) ≡ M (Si−B [4] )/ M 2 (Si−B [3] ) data for the Mg-bearing glasses of Table 5 (whose sets accord very well), whereas the significantly underestimated MD-derived BO 4 population of Na4.0−0.75 (section 3.1) accounts for the lower modeled M 2 rel (Si) result.The direct M 2 (Si−B [p] ) dependence on [ ] x p B renders the M 2 rel (Si) ratio a very sensitive probe of the reduced Si−O− B [4] bonding in the glass structure upon Mg 2+ incorporation, as mirrored in the markedly lower {M 3 (eq 11).These parameter ratios are in Table S4, along with those of P rel (Si) ≡ P(Si−O−B [4] )/P(Si−O−B [3] ). Disregarding the MgNa4.0−0.75 glass with much weaker Si/B [4] contacts, P rel (Si) > 1 holds throughout.When taken together with N rel (stat) = 1.44 reflecting a nonpreferential/statistical Si−O−B [3] /B [4] bond formation (section S2), the product of the  S4), despite that the crude approximations made are only expected to capture the R = 0.75 glasses with low NBO contents (section S2).The good predictions also observed for the experimental M  5)�suggest BS glass networks with substantial The Journal of Physical Chemistry B {Si, B [3] , B [4] } intermixing.When combined with previous inferences of the coexistence of all three B [3] −O−B [3] , B [3] −O− B [4] and B [4] −O−B [4] , linkages, 34,50 the results portrays a network with all six F−O−F′ linkage-types among {Si, B [3] , B [4] } encountered in significant populations, each scaling with the molar fractions of its constituents but with higher-than-statistical numbers of the most preferred B [3] −O−B [4] and Si−O−B [4] bonds, while B [4] −O−B [4] linkages are present but disfavored (Table 5).
Bray and co-workers introduced a structural description,  27,70,120 ).Superstructural units are indeed known to build many crystalline borate/BS phases, 27 and numerous Raman studies support their existence for glasses as well. 28,110,120,121hile BS-based glass structures most likely do comprise some larger BO p /SiO 4 molecular aggregates, it is difficult to reconcile the main body of experimental reports with any dominating role thereof (except for limiting cases, such as vitreous B 2 O 3 27,122,123 ).Indeed, 11 B, 29 Si, and 17 O (3Q)MAS NMR reports suggest markedly more disordered BS networks than the (for a glass) exceptionally high medium-range order postulated by the YDBX model, notably its Si/B [3] /B [4] -intermixing predictions. 36,37,39,40,47,108,110,111We guide the reader to the thoughtful but critical remarks made by Moncke et al. 47 Notably, the YDBX model predicts that only Si−O−Si/B [4] and B [3] −O−B [3] /B [4] bonds occur in the present NaK−0.75glasses. 52,53Hence, Si−O−B [3] are absent, in sharp qualitative disagreement with the results for any glass of Table 5, encompassing direct experimental proof of significant Si−O− B [3] bonding in the Na4.0−0.75 glass, which is accentuated in the Mg-bearing glass structures.−49 The distinctly different Si/ B [p] intermixing predicted by the YDBX model and experimental/modeling herein and in refs 36, 37, 39, 40, and 46−48 stems from the YDBX-postulated but grossly underestimated degree of Si−O−B [3] bonding (i.e., P(Si−O− B [3] ) ≈ 0), whereas in fact P(Si−O−B [3] ) ≲ P(Si−O−B [4] ), yielding P(Si−O−B [4] )/P(Si−O−B [3] ) ≈ 1.2 (Table 5).Analogous contradictions with many experimental findings also plague the alternative branch of "random-network model" (RNM) descriptions 69,106,107,124 originating from Zachariasen and Warren, 125,126 which overestimate the structural disorder by largely ignoring F−O−F′ bonding preferences (see section 3.5 and comments in ref 50).
To reconcile the orthogonal implications for the structural order from the too categorical RNM 69,106,107,124 and "superstructural-unit" 27,70,120 borate/BS glass descriptions, we recently highlighted a "hybrid" model thereof. 50While we are unaware of previous explicit outlines or discussions of a BS glass network being built from some superstructural units along with near-randomly intermixed BO 3 /BO 4 /SiO 4 groups across a <1 nm scale, even the well established and noncontroversial structure of vitreous B 2 O 3 conforms to such a hybrid structural picture.Here, superstructural B 3 O 6 units (boroxol rings, which comprise ≈70% of all B [3] sites 27,123 ) coexist with ring-interlinking BO 3 groups. 27,122,123The introduction of network modifiers along with another network former (Si) naturally increases the structural disorder.This is, for instance, manifested by the strongly altered Si intermixing with both B [3] and B [4] accompanying the replacement of a low-CFS Na + cation by Mg 2+ (section 3.5) and also mirrored in B [3] −O−B [3] /B [4] and B [4] −O−B [4] populations somewhat closer to a statistical {B [p] − O−B [q] } intermixing in Mg-bearing BS glasses. 50Hence, all experimental/modeled results herein and in ref 50 as well as previous work 36,37,39,40,[47][48][49]110,111 are consistent with a hybrid random/superstructural-unit BS glass-network description, which nonetheless remains to be concretized from a quantitative standpoint.
whereas the propensity for B [3] −O−Si bridges either remain unaffected (for NBO-rich glasses; R = 2.1) or even increases (for NBO-poor glasses; R = 0.75).This results in P(B [4] −O−Si) ≈ P(B [3] −O−Si) for both MgNa2.0−0.75 and MgNa4.0−0.75 glasses, whereas B [4] −O−Si linkage formation remains (slightly) preferred for the R = 2.1 analogs.We stress that these bonding preferences are independent on the borate speciation.−113 We found no indications of phase separation of the MgNa4.0−0.75 glass specimen, which most likely constitutes a single amorphous borosilicate phase with emphasized B [3] /Si contacts as compared to its NBO-richer MgNa4.0−2.1 counterpart or any NaK−R glass structure.The findings herein of reduced B [4] /Si contacts in the Mg-bearing glasses echo those deduced from heteronuclear 11 B/ 29 Si NMR experimentation on heat-treated BS glasses 45−48 that are often taken to imply separation into Si and B dominated phases from face-value interpretations of routine infrared, Raman, or 29 Si NMR spectra.
More detailed information about the borate environments and the Si/B [p] intermixing require reliable 11 B MAS NMR spectral deconvolutions, which are far from straightforward concerning the 11 B [3] resonances 22,113 but could give more quantitative information about the M 2 (B [4] −Si) dipolar second moments for the B [4] (2Si), B [4] (3Si), and B [4] (4Si) environments that coexist in the glass and together yielding each average M 2 (B [4] −Si) value.This topic, along with the prospects for realistic 11 B NMR spectral deconvolutions, will be discussed in upcoming publications.
Discussion on the glass-composition dependence of Z̅ Na and the relationship between the dipolar second moment M 2 (F−F′) and the number of F−O−F′ linkages in the glass; tables with cation field strengths, MD simulation parameters, the dependence on M 2 on structural parameters, and MD-derived F−O−F′ bond lengths (PDF)
Nafor Na + but is consistently smaller for Mg 2+ ( [ ] 0.9 p Mg ) in the MgNaK− 0.75 glasses and yet lower in their NBO-rich MgNaK−2.1 counterparts: [ ] 0.8 p Mg (Table width.b The data uncertainties are ±1σ, with σ given for each entity.The Journal of Physical Chemistry B denoted by x(M−NBO) and x(M−BO), respectively.It was determined from the MD-derived glass model, whereupon the corresponding preferences for M−NBO and M−BO bonding were calculated by P(M−NBO) = x(M−NBO)/x NBO , and low.Some examples reported by us and others encompass the following: (I) the clustering of rare-earth cations in RE 2 O 3 − Al 2 O 3 −SiO 2 (refs 93 and 98) and Na 2 O−SiO 2 (refs 99 and 100) glasses (whereas if RE 2 O 3 oxides are added to molten SiO 2 , strong RE 3+ clustering occurs at any concentration 100,101 ); (II) the deviations from an otherwise essentially random spatial distribution of PO 4 3 anions in Ca−Na−P−Si−O glasses occur

Figure 3 .
Figure 3. 11 B{ 29 Si} REDOR NMR dephasing data (ΔS/S 0 ) plotted against the recoupling/dephasing interval (τ rec ) and recorded at 14.1 T and 9.00 kHz MAS from the (a, d) Na4.0−0.75, (b, e) MgNa4.0−0.75, and (c, f) MgNa4.0−2.1 glasses.The top panels (a−c) displays the entire 11 B [3] and 11B[3]  dephasing curves, whereas the bottom panels (d−f) show zoomed-in views of the initial dephasing regimes.Note that the lines in (a−c) only serve to guide the eye, while those of (d−f) are best-fit results to eq 7 for the data ΔS/S 0 ⩽ 0.20.All data uncertainties are within the symbol sizes.

c
Preference factor P(F−O−F′) =P(F′−O−F) for F− O−F′ linkage formation of {F, F′} = {B [3] , B [4] , Si}.P(F−O−F′) is defined as the ratio between the as-observed number of F−O−F′ linkages in the glass model relative and that predicted from nonpreferential (statistical) {F, F′} intermixing.d The uncertainties of the MD-derived data are ±1σ, with σ given for each entity.The Journal of Physical Chemistry B MgNa4.0−0.75 structure (16%) must be considered decent in view of the large number of potential error sources that could degrade the agreement, notably those of the MD-generated glass models.

(
ii) The second effect underlying the increased NMR/MDderived M 2 rel (B) values in any BS glass is less influential but stems from a slightly higher preference for B[4]  −O−Si bridges than B [3] −O−Si linkages.Owing to the difficulties in quantifying the preference factor P(F−O−F′) for F−O− F′ bond formation by experiments, however, current quantitative insights stem dominantly from computational modeling; 55−57,64,109 see ref 50 for experimental attempts to estimate the {P(B [p] −O−B [q] )} subset.Table 5 lists the MD-derived {P(F−O−F′)} factors of the present BS glasses.Here, P(F−O−F′) = 1 denotes a strictly nonpreferential F/F′ intermixing, whereas P(F− O−F′) > 1 and P(F−O−F′) < 1 imply a preference and reluctance for F−O−F′ linkage formation, respectively.

3. 6 .
Effects from Mg 2+ on the B [p] /Si Intermixing.Although all herein discussed BS glasses but MgNa4.0−0.75 manifest a markedly larger number of B [4] −O−Si linkages than B [3] −O−Si bridges, the partial replacement of Na + by Mg 2+ leads to a non-negligible reduction of M 2 rel (B) throughout: contrasting the MD-derived M 2 (B [4] −Si) and M 2 (B [3] −Si) values of the NaK−R glass and its MgNaK−R counterpart in Table 5 reveals that the decrease of M 2 rel (B) stems from an increase of M 2 (B [3] −Si) at the expense of M 2 (B [4] −Si), altogether implying that Mg 2+ -for-Na + substitution is accompanied by an increase (decrease) in the number of B [3] −O−Si (B [4] −O−Si) linkages.The predictions of the Na4.0−0.75 and MgNa4.0−0.75 glass models are corroborated by the REDOR NMR experiments, which reveal a significant reduction in M 2 (B [4] −Si) for the MgNa4.0−0.75 glass (M 2 rel (B) = 1.05) relative to M 2 rel (B) = 1.44 for Na4.0−0.75 (yet the experimental M 2 (B [3] −Si) values of both glasses are nearly equal; Table

Figure 5 .
Figure5.29 Si MAS NMR spectra recorded at 9.4 T and 14.00 kHz MAS from the Na4.0−0.75,MgNa4.0−0.75, and MgNa4.0−2.1 glasses.The higher structural complexity of the NBO-rich MgNa4.0−2.1 structure is mirrored in its ≈5 ppm wider resonance relative to that of its MgNa4.0−0.75 counterpart with a low NBO content, along with a more deshielded chemical shift at the peak maximum (i.e., a higher value of δ Si ).
−Si)} set b y t h e g e n e r a l e x p r e s s i o n M 2 ( S − I ) spinpairs,63 which for S = 1/2 ( 29 Si) and I = 3/2 ( 11 B) evaluates to )} counterparts (Table5) and underscoring the time/effort-saving benefits of having both {M 2 (B [p] −Si)} and {M 2 (Si−B[p]  )} data available from one sole NMR experiment and eq 11 (seerefs 57, 63, and 64 for further examples.

6
and P rel (Si) parameters.Notably, although illustrated in the context of the M 2 (Si− B[p]  ) and M 2 rel (Si) entities, the various glass composition/ structure parameters discussed above are readily replaced by their analogs underpinning any M 2 (F−F′) entity reflecting the number of F−O−F′ linkages at FO p polyhedra that may interlink with two (or several) FO p , F′O p′ , and F″O p″ polyhedral types.3.8.Inferred Si/B [p]Intermixing Versus Current BS Glass-Structure Descriptions.The findings herein of an overall larger extent of B[4]  −O−Si than B[3]  −O−Si bonding� yet with both linkage-types being abundant throughout all glasses (Table −O−Si bonds in the quaternary MgNaK−R glasses.The former bridges dominate throughout all Na 2 O−B 2 O 3 −SiO 2 glasses, notably so for the NBO-rich members, where the stronger propensity for B [3] −NBO over B [4] −NBO bonding leads to glass networks with 1.7−2 times more B [4] −O−Si linkages compared with B [3] −O−Si, as estimated from dipolar second moments obtained from either 11 B{ 29 Si} REDOR NMR experiments or MD simulations.The diminished B [4] −O−Si bonding upon Mg 2+ incorporation is most evident for the MgNa4.0−0.75 glass network, which exhibits similar numbers of B [4] −O−Si and B [3] −O−Si linkages, whereas the Na4.0−0.75 analog features ≈1.4 times more B [4] −O−Si bridges than B [3] −O−Si.

. Solid-State NMR Experiments. All
NMR experiments were performed with Bruker Avance-III spectrometers.The

and The Journal of Physical Chemistry B
which is most frequently encountered in the literature (e.g., refs 19, 41, 34,55,56,82ed with the B−O interatomic potential parameters of refs 55 and 56, which have been validated for Naand Na/Ca-bearing borate and boro(phospho)silicate glasses over large composition domains.34,55,56,82Contrasting the modeled and experimental BO 4 populations of Table1, however, reveals a highly variable performance.The agreement is excellent for all MgNaK−R glasses (with relative deviations within 3%) but MgNa2.0−2.1, which along with all NaK−R models reveal markedly larger discrepancies to experiments, typically by ≈10% but with a substantial deviation of 17% for Na4.0−0.75.These errors stem from the distinctly different[ ]x B 4 ranges between the NaK−R and MgNaK−R glasses.As noted in refs 34, 55, and 56 but more clearly shown by Pedone and coworkers, 82,83 MD simulations with our B−O force field are prone to underestimating the BO 4 population: although the deviations are insignificant for glasses with [ ] x 0.5 B 4 A general tendency is that both[ ] 8888,89eases for increasing M z+ CFS values.For instance, all high-CFS La 3+ , Y 3+ , Lu3+, and Sc 3+ cations (TableS1) manifest narrow p-distributions in AS glasses.5,88,89Indeed,although the La 3+ ion is markedly larger than Mg2+�as is reflected in MD-derived average coordination numbers of 6.0−6.6 in La 2 O 3 −Al 2 O 3 −SiO 2 glasses88� CFS La = 0.52 Å −2 is slightly higher than CFS Mg = 0.46 Å −2 , yielding a coordination spread of [ ] 0.9 p La

Table 4 .
Because CFS Ca is intermediate between CFS Na and CFS Mg (Table S1) and the relative preferences for M [p] −BO/NBO bonding are strongly CFS-dependent, Table 4 also includes modeled data from R[0.5CaO−0.5Na 2 O]−B 2 O 3 −KSiO 2 glasses, denoted "CaNaK−R" and discussed in refs 22, 50, and 51.Each NBO and BO fraction in the first coordination shell of an M z+ cation is

Table 3 .
Distributions of Na[p]and Mg[p]Coordinations a

Table 5
reveals very good agreement between the experimental and modeled M 2 rel (B) values, whose deviations only amount to a few percent.Even the largest discrepancy observed for the Table 5 conveys the following subtle trend: P