Lead silicate glass structure: New insights from diffraction and modeling of probable lone pair locations

Structures of binary PbO-SiO 2 glasses have been studied in detail over the compositional range 35 to 80 mol% PbO using high-resolution neutron diffraction, high-energy X-ray diffraction, static 207 Pb NMR, and structural modeling. The changes in the local environment of Pb(II) are subtle; it has a low coordination to oxygen ( ∼ 3 to 4) plus a stereochemically active electron lone pair and, thus, behaves as a glass network forming (or intermediate) cation over the entire composition range. This conclusion contradicts previous reports that Pb(II) is a network modifier at low concentrations, and is supported by an analysis of lead and alkaline earth silicate glass molar volumes. The Pb-O peak bond length short-ens by 0.04 Å with increasing PbO content, indicating stronger, more covalent bonding, and consistent with an increase in the number of short ( ≤ 2.70 Å) Pb-O bonds, from 3.3 to 3.6. This is accompanied by increased axial symmetry of the Pb(II) sites, and is interpreted as a gradual transition toward square pyramidal [PbO 4 ] sites such as those found in crystalline PbO polymorphs. An attendant decrease in the periodicity associated with the first sharp diffraction peak (FSDP) toward that of β -PbO, accompanied by increases in the correlation lengths associated with the plumbite network (FSDP) and silicate anions (neutron prepeak), provides evidence of increased intermediate-range order and has implications for the glass forming limit imposed by crystallization. Pb(II) electron lone pairs occupy the natural voids within the silicate network at low PbO contents, while at high PbO contents they aggregate to create voids that form part of the plumbite network, analogous to the open channels in Pb 11 Si 3 O 17 and the layered structures of α - and β -PbO. Si-O and Pb-O bond lengths have been correlated with 29 Si and 207 Pb NMR chemical shifts, respectively. This is the first time that such correlations have been demonstrated for glasses and attests to the accuracy with which pulsed neutron total scattering can measure average bond lengths.

We present results from high-energy X-ray diffraction and also from neutron diffraction, where we have obtained the highest real-space resolution to date. 207 Pb NMR spectroscopy is used to reveal details of the subtle changes to the Pb(II) environment that occur between 35 and 80 mol% PbO, as implied by previous publications covering the evolution of the 207 Pb NMR lineshape between 31 and 73 mol% PbO. 15,21 Previously, we have demonstrated 2 that the sterically active Pb(II) electron LPs in 80PbO.20SiO 2 glass organize to create voids, analogous to the channels within crystalline Pb 11 Si 3 O 17 43 and the interlayer spaces in the PbO polymorphs. 44,45 This was achieved by empirical potential structure refinement (EPSR) of neutron and X-ray diffraction data with an imposed, fixed polarization on the Pb 2+ cations, and we here apply this technique to a low lead, 35PbO.65SiO 2 , glass to reveal the probable locations of the LPs within the network, and to determine if a model consistent with Pb acting only as a network former can be derived.
We take pains to emphasize that we consider Pb(II) sites with sterically active LPs and concomitant low coordination numbers to oxygen as "network forming," consistent with the fact that oxide glasses can be obtained to very high mole fractions of PbO (Figure 1), at which, models have shown plumbite network formation, 2 indicating its role as a conditional (requiring other oxide additions) glass former. Pb(II) sites without sterically active LPs are expected to have higher coordination numbers and act like typical alkaline-earth network modifiers, with Pb(II) having a similar ionic radius to Sr(II) (see Figure 1 inset). Examples of such Pb(II) sites, with a high degree of modifier character, are found in PbTiO 3 perovskite, TA B L E 1 Measured molar compositions, mass and number densities, molar volumes, and glass transition temperatures for six lead silicate glasses and a silica reference  47,48 and lead vanadates and phosphates. 5 Furthermore, it should be noted that plumbite networks are quite distinct from canonical glass networks, such as silica, and do not follow Zachariasen's rules, owing to the low formal valence of Pb(II), and hence, relatively high oxygen-cation coordination numbers, in excess of two.

Glass preparation
The 35-80 mol% PbO compositional range accessed in this study was limited at the lower end by the rapidly rising liquidus, 49 and at the higher end by crystallization, even under conditions of rapid twin-roller quenching. Powders of PbO (Aldrich, 99.9+%) and SiO 2 (Aldrich, 99.6%) were mixed in quantities to yield 10 g batches of glass with nominal compositions given in Table 1. The mixtures, in pure platinum crucibles, were placed into an electric furnace for 20 min. The hold temperature of the furnace was 1000 o C for the three highest lead compositions, 1300 o C for the lowest lead composition, and 1200 o C for the two intermediate compositions of 50 and 60 mol% PbO. After this 20-min period, the crucibles were removed, the mass loss was recorded, and then replaced into the furnace for an additional 10 min. The glass compositions, calculated assuming mass loss due solely to volatilization of PbO, are given in Table 1. The liquids, after the second period in the furnace, were vitrified using rapid twin-roller quenching which involved pouring into a 40 μm gap between two counter-rotating steel cylinders, giving an estimated cooling rate of approximately 10 5 o C/s. 50 The resultant flakes of glass have a yellowgold color, which is weak at low lead concentrations, but becomes very strong at 80 mol% PbO. A number of such batches were produced to obtain sufficient volume for neutron diffraction experiments. This has the disadvantage of potentially introducing small variations in glass composition and thermal history between batches, but does have the advantage of reducing the spread in glass fictive temperature which occurs as a result of the difference in thermal histories between the liquid which first contacts the roller quencher, and that which contacts last.

Density measurement
The volumes of samples of known mass were measured by helium pycnometry in a Quantachrome Micropycnometer, and used to calculate the mass densities, ρ m . The ρ m obtained were used to derive molar volumes, V M , and atomic number densities, ρ 0 (Table 1), which are plotted in Figure 1.

Energy-dispersive X-ray spectroscopy
Glass composition was measured by using energydispersive X-ray spectroscopy (EDX) in a Zeiss SUPRA 55-VP field-emission gun scanning electron microscope operating at an accelerating voltage of 20 kV. Samples were mounted on aluminum stubs using an organic silver paste, and carbon coated using a vacuum evaporator to provide conduction pathways and avoid surface charging of the glass. EDX spectra were collected over 100 s exposure times at various points on the surface of a number of different glass pieces. Quantification of the glass composition was based on the integrated intensities of the Pb L and Si K lines of the spectra after background subtraction and correction for atomic number (Z) dependent electron backscatter and stopping power, absorption and fluorescence, collectively known as ZAF correction, using the EDAX Genesis software, which employs internal standards.

Differential thermal analysis
Glass transition temperatures, T g , were measured using a Perkin-Elmer DSC-7, and a heating rate of 40 o C/min. Table 1 lists the average values extracted and most of  these agree, within experimental uncertainties, with those  reported by Feller et al., 22 which were measured using the same heating rate. An exception is the 50 mol% PbO glass, for which the value in Table 1 is 41 o C higher than that measured previously. 22

Nuclear magnetic resonance
207 Pb static NMR spectra were acquired using a field-step method (described previously 51 ) to irradiate, with equal efficiency, the entire broad spectral envelope for Pb(II) with LP. A primary field of 7.05 T and operating frequencies of 62.36 to 62.43 MHz were used in pulse-echo (π/2 → τ→ π) experiments with π/2 and π pulse widths of 3 and 6 μs, respectively, and τ = 100 μs, 2 to 8 s pulse delays, and 500 kHz spectral width at each step. A total of 960 to 1296 acquisitions were made at each of 28 or 31 steps of 22.72 kHz, resulting in total spectral widths in excess of 1.1 MHz. Spectra are referenced to tetramethyl lead at 0 ppm, using polycrystalline β-PbO as a secondary reference (δ iso = 1515 ppm 52 ).

Neutron diffraction
Time-of-flight neutron diffraction measurements were made using the GEM 53 diffractometer at the ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, UK. The glasses, in the form of small (few mm 2 ) flakes, were loaded into cylindrical, thin-walled (25 μm) vanadium containers of internal diameter 8.3 mm. Data were collected with sufficient statistics to justify the use of a maximum momentum transfer Q max = 40.0 Å -1 for Fourier transformation. Measurements were also performed on an empty vanadium container, the empty instrument, and an 8.34 mm diameter vanadium rod for normalization purposes and to allow for the subtraction of background signals. A vitreous silica rod was also measured. 2

X-ray diffraction
Wiggler beamline BW5 54,55 on the synchrotron radiation source DORIS III, HASYLAB at DESY, was used for Xray diffraction measurements of the powdered glasses, which were held inside 1.5 mm diameter silica glass capillaries (10 μm wall thickness). Measurements of an empty capillary and the empty instrument were made to allow the removal of background scattering. The X-ray energy of 84.768 keV (wavelength λ = 0.14626 Å) was optimised so as to minimize the photoelectric absorption cross-section while avoiding fluorescence associated with the Pb K-edge at 88.0045 keV, 56 and this wavelength makes accessible a large maximum momentum transfer, Q max = 4πsin(θ max )/λ = 23.62 Å -1 , at the maximum scattering angle of 2θ max = 32.0 o . Data were collected in three angular ranges using different attenuators between sample and detector, owing to the form factor dependence of the X-ray signal, and to ensure that the count rate in the Ge detector did not greatly exceed 5 × 10 4 counts per second. All sets of data were combined after omission of bad points, dead-time correction, normalization to the incident beam monitor counts, correction for the geometrical arrangement of the detector and sample, and scaling as required for datasets for which different levels of in-beam attenuation were used. A vitreous silica sample was also measured. 2

Total scattering formalism
Herein the same definitions of the real-and reciprocalspace scattering functions are used as in our previous work. 2 The real-space total correlation function is defined by where R = N or X denotes the radiation type; i N (Q) is the measured distinct 57 neutron scattering, whereas is the measured distinct X-ray scattering after division by a sharpening 58 function used to approximately eliminate the X-ray form factor, f i (Q), Q-dependence of the scattering. 59 Subscripts i denote elements of the periodic table and c i are atomic fractions. In Equation (1), M(Q) is a modification function which can be chosen to reduce the effects of the finite limits (0 ≲ Q ≲ Q max ) of the integral which are used in practice. In this study, the M(Q) due to Lorch 60 is chosen. The T R,0 (r) represent average scattering density terms and are given by: where bound coherent neutron scattering lengths 61 are denoted̄. The i R (Q) may be written as sums of Faber-Ziman 62 partial structure factors, S ij (Q), and the T R (r) as sums of partial pair correlation functions, t ij (r) = 4πrc j ρ 0 g ij (r), with g ij (r) the standard pair distribution functions. 57,63

Structure refinement
The application of EPSR to the modeling of a high lead content silicate glass has been described in detail elsewhere. 2 Lead ions were modelled in two different ways, in one of which the LP of electrons was simulated by treating Pb(II) as a dipole, Pb'-LP, with separation of 1.0 Å, 64,65 which was held constant by using a large value for the intramolecular potential energy and setting the Pb' and LP masses to be equal. This is referred to as the LP model while the model without this fixed polarization applied to the Pb 2+ ions is referred to as the Ionic model. The models for 35PbO.65SiO 2 glass consisted of a cubic box, edge length 39.95 Å, and with the same reference potential parameters as used previously, 2 other than the σ Pb = 2.19 Å and σ Si = 0.70 Å (Table 2), which were adjusted slightly according to the measured average bond lengths. It should be noted that the parameters for Pb have to be modified in the presence of the LP, giving Pb'.

Diffraction
Data reduction procedures were conducted as described previously, 2 and the resultant interference functions, Qi R (Q), are displayed in Figure 2 (numerical data available as Supplementary Material), where, particularly in the neutron diffraction case, the importance of collecting data to high Q, with good statistics, is illustrated by the presence of oscillations extending over the full Q range. These oscillations are progressively damped as PbO replaces SiO 2 . In the X-ray case, the Pb-Pb term is dominant and a clear first F I G U R E 2 X-ray (upper) and neutron (lower) interference functions for lead silicate glasses, as compared to those measured for vitreous silica, shown to emphasize the high Q region. The mol% compositions are indicated on the plots and vertical offsets have been used for clarity sharp diffraction peak (FSDP) at approximately 2.0 Å −1 dominates the diffraction patterns. Figure 3 shows selected regions of the distinct scattering, i R (Q), to emphasize the low-Q features. In particular, the data for the 35PbO.65SiO 2 glass show small-angle X-ray scattering (SAXS) intensity peaking at approximately 0.7 Å −1 . When more PbO is added to the glass composition, a prepeak, at approximately 1.2 Å −1 , becomes resolved in the neutron i N (Q) at 60 mol% PbO, and is also visible in i X (Q) for the two highest PbO content glasses. The positions and widths of the FSDPs and prepeaks are recorded in Table 3, along with their corresponding real-space periodicities and correlation lengths which are plotted in Figure 4. The realspace correlation functions obtained using Q max = 40.00 Å −1 (neutron) and 23.62 Å −1 (X-ray) and Lorch 60 modification are shown in Figure 5. Compared to previous neutron diffraction studies, 3,4,6,8 the benefit of using a high Q max and suitable modification function can be seen in the lower part of Figure   [SiO 4 ] tetrahedra at approximately 2.65 Å, while truncation oscillations to either side of the peaks are practically negligible. Sequential peak fitting to the T N (r), with appropriately broadened Gaussian bond-length distributions, was conducted as described elsewhere, 2 and is illustrated in Figure 6. The resulting parameters are recorded in Table 4 and selected average bond lengths, distribution widths, and coordination numbers are plotted in Figures 7 and 8.

NMR
207 Pb static NMR spectra for selected glasses are shown in Figure 9. The chemical shift tensor components, δ 11 ,

F I G U R E 4 Periodicities (left) and correlation lengths (right) of the FSDP (upper), in neutron and X-ray diffraction patterns, arising from
Pb-Pb separations, and of the prepeak (lower) in neutron diffraction patterns of lead silicate glasses, assigned to intersilicate anion separations. The periodicities for α-PbO (011, d = 3.121 Å) 45 and β-PbO (111, d = 3.068 Å) 44 are also shown, while, in the ideal crystalline state, the correlation lengths would be effectively infinite. Lines in the upper panels are linear fits to the data. The dashed line in the lower panel represents the average Si-Si separation, r SiSi = (c Si ρ 0 ) −1/3 , based on the partial number density ρ Si = c Si ρ 0 . In color online δ 22 , and δ 33 , were obtained by fitting the NMR peaks with static chemical shift anisotropy (CSA) lineshapes. 66 The peaks are then characterized by the derived CSA parameters: isotropic shift, δ iso = (δ 11 + δ 22 + δ 33 )/3; span, Ω = δ 11 -δ 33 ; and skew, κ = 3(δ 22 -δ iso )/Ω ; for axial symmetry δ 11 = δ 22 ≠ δ 33 and κ = ± 1. Isotropic chemical shifts were also determined independently from any fitting by integration and determination of the first moment (center of gravity) of the spectral lineshape. In agreement with previous measurements, 15,21,23 the spectra for 35 and 50 mol% PbO silicate glasses are near identical, with only an approximately +56 ppm difference in isotropic chemical shift, compared to spans in excess of 4000 ppm ( Table 5). The distribution of Pb environments in a glass means that the lineshape used in fitting should be simulated using distributions of the CSA parameters (or chemical shift tensors). Fitting with single-valued parameters, as performed herein, leads to significant uncertainties since the distributions cannot be accommodated by the broadening function which is applied to achieve a fit. This is particularly obvious for the 35 and 50 mol% PbO samples, where the lineshapes cannot adequately be approximated by any single, broadened line. Table 5 gives the parameters which have been extracted. The values of κ for the 35 and 50 mol% samples are effectively zero, indicating a range of asymmetric sites. The 207 Pb static NMR spectrum for 80PbO.20SiO 2 glass ( Figure 9) has not previously been reported. The lineshape has a value of skew (κ = 0.69) which is approaching that of axial symmetry and strongly indicative of sites such as the square pyramidal units of α-PbO (κ = 1) and the distorted pyramidal units of β-PbO (κ = 0.81) as previously determined by Fayon et al. 52 Their values are used to simulate the lineshapes for α-PbO and β-PbO in Figure 9 for comparison.
Statistical uncertainties in parentheses. and X-ray scattering. However, when the PbO content is low enough, as for the 35PbO.65SiO 2 glass, quantitative agreement between Q n species distributions from the model and 29 Si NMR is found. 68 Therefore, we focus here on the modeling of the 35 mol% PbO silicate glass, such that the gross structural differences, and similarities, with previously published 2 models of an 80 mol% PbO silicate glass can be enumerated and discussed. Table 6 lists some ensemble (>6.8 × 10 3 configurations) average values derived from EPSR models of 35PbO.65SiO 2 glass, both with (LP) and without (Ionic) the fixed polarization applied to the Pb 2+ ions. A snapshot of the LP model is illustrated in Figure 10, while the model interference functions, Qi R (Q), are compared to those measured by neutron and X-ray diffraction in Figure 11. Also shown ( Figure 11) are the weighted partial pair interference functions which show clearly the dominant contributions to the experimental neutron (O-O, Si-O) and X-ray (Pb-X) diffraction patterns. It is evident that the two models, Ionic and LP, are substantially the same at this composition, as far as the goodness-of-fit and partial structure factors are concerned. Real-space pair correlation functions, g ij (r), are plotted in Figure 12, where it is clear that the Pb-O peak has a shoulder to the high r side, and g PbO (r) does not fall to zero after its first maximum. As such, Table 7, which records various coordination number distributions (CNDs), shows those for two characteristic Pb-O cut-off radii of r 2 = 2.70 or 3.27 Å. Figure 13 compares the g LPLP (r) of 35 and 80 mol% PbO 2 silicate glasses. Selected bond angle distributions (BADs) are displayed in Figure 14 and Table 6 records some of their mean values and standard deviations.

Local environment of Pb(II)
A key conclusion of the present study is that the first coordination sphere, and hence structural role, in Si-O coordination has been observed, nor is expected (at ambient pressure) at lower PbO contents (≲ 35 mol% PbO), and therefore, NBOs must be present, to which strong, short, and more covalent Pb-O bonds can form.
The following discussion covers those aspects of the Pb(II) environment which do change over the 35 to 80 mol% PbO range. Most striking is the change in 207 Pb NMR lineshape (Figure 9), and values of skew indicating an increase in axial symmetry of the Pb 2+ site with increasing PbO content. Indeed there is great similarity between the measured spectra for 80PbO.20SiO 2 glass and β-PbO, although the glass spectrum has an isotropic shift (δ iso ) approximately 400 ppm less positive than that of the crystal. Changes in the 207 Pb NMR spectra as PbO content increases are accompanied by small, but significant, changes in the Pb-O pair correlations measured by diffraction. These include: (i) a reduction in the peak Pb-O bond length ( Figure 6), (ii) a reduction in width of the first fitted Pb-O peak (Figure 6), (iii) changes in the shape of g PbO (r) (Figure 12), (iv) changes in O-Pb-O BAD (Figure 14).
The Pb-O environment is difficult to characterize unambiguously due to the asymmetry (shoulder to high r) of the Pb-O bond length distributions (Figures 4, 5, 11) and the overlap between first and second shell Pb-O distances, giving rise to a nonzero minimum in g PbO (r) at distances greater than the first peak maximum (Figure 12). In cal-culating the Pb-O coordination numbers, and their distributions, from EPSR models (Table 7) we have, therefore, chosen two different radial cut-offs, r 2 , of 2.70 and 3.27 Å, to include only "short" and "short" plus "long" Pb-O bonds, respectively. Comparing the values obtained for 35PbO.65SiO 2 glass (Table 7) with our previously published results for 80PbO.20SiO 2 glass, 2 it is evident that there is a small increase, of approximately 0.2, in the average number of short Pb-O bonds from 3.33 at 35 mol% PbO, to 3.55 at 80 mol% PbO. This is consistent with a transition toward a more axially symmetric, square pyramidal environment, at higher PbO content, as implied by the 207 Pb NMR results. There is much greater experimental uncertainty regarding the number of longer Pb-O bonds, however, modeling indicates there are approximately 1.3 longer Pb-O bonds at 35 mol% PbO and 1.1 to 1.5 at 80 mol% PbO, dependent upon model specifics. 2 Note that the above values are not directly comparable with those from peak fitting ( Table 4, Figures 6  and 7), where the effective cut-off radius tended to decrease as PbO content increased, due to decreasing peak positions and widths.
The O-Pb-O BAD ( Figure 14) shows an increase in local order at high PbO contents, and this is also consistent with 207 Pb NMR results, and the small increase, of approximately 0.2, in the average number of short Pb-O bonds. As discussed previously, 2 the O-Pb-O BADs derived by EPSR F I G U R E 5 Total X-ray (upper) and neutron (lower) correlation functions from lead silicate glasses, as compared to that measured for vitreous silica. A Lorch 60 modification function and Q max = 23.62 Å −1 (X-ray) or 40.00 Å −1 (neutron) were used. Vertical offsets have been used for clarity also show greater local order than those derived by RMC methods, 3 and this is true over the full range of glass compositions. Indeed, at 80 mol% PbO, the EPSR -derived O-Pb-O BAD approaches that of crystalline Pb 11 Si 3 O 17 , 43 as well as those of the PbO polymorphs, demonstrating that it generates a more realistic picture than the broader, RMCderived BADs.
The decrease of r PbO and the narrowing of the first Pb-O peak fitted to T N (r), with increasing PbO content (Figure 7), are evidence for strengthening and an increased covalency of these bonds. This is consistent with the measured change in position of the 207 Pb NMR spectrum with glass composition. Figure 15 shows the chemical shift of the 207 Pb NMR lineshape (center of gravity) as a function of the peak bond length measured by diffraction. Results for some lead germanate glasses 71 have been included to increase the significance of the linear correlation, where a  present results reveal that a correlation between δ iso ( 207 Pb) and r PbO also holds for the more covalent materials, this, combined with the published observations for crystals, would imply significant dependence on the second oxide component. Indeed, Figure 15 indicates that improved correlations would be obtained by fitting the data for silicate and germanate glasses separately, although the number of data points in each case is too low to do so with confidence. We are not aware of previous reports of any set of Si-O bond lengths with such high precision for any binary silicate glass series. We therefore take the opportunity to discuss some of the structural implications of the observed trend. It has been demonstrated 77,78 that the Si-O-Si bond angle and Si-O bond length are correlated, with the latter increasing as the former decreases, and the oxygen porbital character increases. Thus, one might naively interpret the trend in Figure 7 as indicating that an increase in PbO leads to a reduction in Si-O-Si angle. However, it also results in depolymerization of the silicate network resulting in Si-O-Pb linkages. There are then two additional effects to consider: (i) the number of Pb coordinating F I G U R E 1 0 Slices, ∼5 Å thick, through single configurations of EPSR models of 35PbO.65SiO 2 Figure 14) as PbO is added to the glass composition. This latter contribution is not entirely independent, and is thought to be due to the steric repulsion between Pb pairs due to the increasing average NBO-Pb coordination number. Following the linear increase of r SiO with PbO content, there is a plateau in r SiO between approximately 67 and 80 mol% PbO (Figure 7). This is likely indicative of the growing dominance of monomeric, Q 0 , and dimeric, Q 1 , species, as measured by 29 Si MAS NMR, 22 where the large Si-O-Si bond angles typical of the Q 1 dimers are associated with a contraction of the average Si-BO bond.
Both the Si-O bond length and the Si-O-Si bond angle have previously been correlated with the isotropic 29 Si NMR chemical shift, δ iso , for various silicate minerals and zeolites, as reviewed by Mackenzie and Smith. 79 Here, for the first time, we are able to demonstrate a correlation between measured average Si-O bond length, and average (first moment) 29 Si MAS NMR chemical shift 22 in a series of glasses. This is illustrated in Figure 15, where the linear fit, given by (in ppm and Å) is close, over the region studied, to the composite trend given by MacKenzie and Smith 79 as δ = 999 r SiO -1709. Also shown in Figure 7 are the widths, < u SiO 2 > 1/2 , which pass through a maximum at approximately 67 mol% PbO, which reflects the Q n species distribution, whose standard deviation itself passes through a maximum at approximately 50 mol% PbO. The difference in location of these two maxima indicates additional broadening mech-anisms of the Si-O bond length distribution, which are the distribution of different O-Pb coordination numbers and the local structural disorder about the Pb atoms. In other words, the reduction in < u SiO 2 > 1/2 with PbO content above approximately 67 mol% PbO is attributed to a narrowing of the oxygen site distribution, due to both the Q n species and Pb site distributions also narrowing.

Oxygen environments
In contrast to the cationic environments, the anionic environments change drastically with lead silicate glass composition. This can be viewed as a continuous transition from the [OSi 2 ] BO environments, with less p character, in SiO 2 glass, toward the distorted sp 3 hybridized [OPb 4 ] plumbite oxygen environments common to the PbO polymorphs and lead silicate crystal structures. Our EPSR models which are in best agreement with the silicate Qspeciations derived from 29 Si MAS NMR indicate 2-3% plumbite (or "free") oxygen at 35 mol% PbO (Table 7) and 35% at 80 mol% PbO. 2 These amounts are in reasonably good agreement with the 2 and 40%, respectively, predicted based on the equilibrium constant of K ≈ 12 for the reaction 2(Pb-O-Si) → Pb-O-Pb + Si-O-Si, as derived from O 1s X-ray photoelectron spectroscopy measurements. 30 The oxygen speciations in our models also compare favorably with a similar analysis based on 17

Pb lone pair distributions and intermediate-range order
The emergence of voids within high lead silicate glasses, owing to the organization of electron LPs, constitutes a key insight, made possible by the use of empirical structural modeling using polarized Pb 2+ ions. 2 Such voids in high lead (80 mol% PbO) silicate glass are analogous to the open channels in Pb 11 Si 3 O 17 and the layered structures of α-and β-PbO, and are characteristic of the plumbite glass network. At lower PbO contents, there is less tendency for LPs to cluster within voids, as is evident from Figures 10 and 13, and rather the Pb 2+ LP electron density occupies voids within the silicate network (see Figure 10), which are present as a result of the restricted Si-O-Si BAD and resultant topological constraints. The sharpening of the FSDP (attributed to Pb-Pb separations) with increasing PbO content (Figures 1 and 4) is considered to be a consequence of the ordering of LPs within voids, and resultant local layer-like structures, which form as the plumbite network regions increase in size, up to approximately 20 Å (Figure 4, Table 3). The concomitant reduction in periodicity associated with the FSDP position ( Figure 4) likely has consequences for the glass formation limit, as it, along with the local structure about the Pb atoms, becomes similar to that of β-PbO.
Edge-sharing of contiguous [PbO m ] polyhedra is another hallmark of plumbite glass networks and probably prevents glass-formation above 83 mol% PbO. 2,22 However, it is worth noting that the edge-sharing [Pb 2 O 4 ] pairs of trigonal pyramids proposed by Takaishi et al. 4 as the basic motif of the plumbite network over the entire compositional range is potentially misleading. The unit was proposed on the basis of the nearest neighbor Pb-Pb separation in T X (r) being independent of glass composition. However, within our structural models, F I G U R E 1 4 Selected bond angle distributions for EPSR models of 35PbO.65SiO 2 glass and the equivalent distributions for the depolymerized ("Q 0 ") LP model of 80PbO.20SiO 2 glass. 2 Only short (≤ 2.7 Å) Pb-O bonds have been included in most instances, and Si-O bonds ≤ 2.0 Å. The Si-O-Si distribution in the LP model of 80PbO.20SiO 2 glass is not necessarily accurate due to the low weight of the Si-Si partial in the diffraction measurements, and the crude distance-based constraint placed on Si-Si pairs, see Ref [2] for discussion and alternative models. In color online similar Pb-Pb distances are observed between both edge and corner-sharing [PbO m ] polyhedra.
Mizuno et al. 80 placed the threshold for a percolating plumbite network at between 35 and 50 mol% PbO, based on the dissolution behavior of the glasses. It is interesting to note that in the 35 mol% PbO silicate glass model, based on the Pb-Pb CND, there are very few (∼11%) Pb atoms with only one (∼2%) or two (∼8%) Pb neighbors; the average n PbPb = 4.65 (r 2 = 4.75 Å) is indicative of a close to fully percolating network. The SAXS intensity, discussed at length by Golubkov et al., 81 rises sharply below 35 mol% PbO, implying inhomogeneous distributions of Pb atoms. Thus, the dramatic drop in diffusion coefficient, interpreted as a percolation threshold, appears as an observable feature in the SAXS. Figure 3 shows a peak in SAXS intensity from the 35PbO.65SiO 2 glass at approximately 0.7 Å −1 , and this is reproduced to some extent by the models, Figure 16, but shows oscillations due to the limited 39.95 Å box size. Nonetheless, lead-rich regions are visible in the model atom distributions such as that at the top left of Figure 10. A natural mechanism for clustering of Pb, or indeed any modifier, exists which is the requirement of NBOs to be shared by multiple modifier cations. In a simplified model in which Pb(II) is fourfold coordinated, then each NBO should bond to two Pb to provide charge balance, [OSiPb 2 ]. Such a mechanism is at the heart of the modified random network model proposed by Greaves,82 and it is interesting to speculate that, if the modifier-oxygen coordination number increases, so the NBO-modifier coordination must also increase, along with the size of the modifierrich clusters/channels. In this way, the morphology of the SAXS should be related to the local structure of the glass, in particular, the cation-oxygen coordination number. Our result shows that SAXS arises in 35PbO.65SiO 2 glass, despite Pb having low coordination number to oxygen, and hence, behaving more as a network-forming cation. We therefore refute the conclusion of Golubkov et al. 81 who state that the occurrence of SAXS in low lead silicate glasses is "...undoubtedly connected with the structural role of lead which acts here as a modifier of the silicon-oxygen network...," although it is possible that the peak in SAXS intensity at 25 mol% PbO may be associated with higher Pb-O coordination and a more modifying role of lead. Nonetheless, the structure of low lead silicate glasses remain unclear due to their high melting temperatures (i.e., difficult to produce) and predicted phase separability (liquid-liquid immiscibility). 49 An additional low Q feature (prepeak) is observed in the neutron scattering curves of high lead glasses, and has F I G U R E 1 5 Upper: First moments of the 207 Pb NMR lineshapes for three lead silicate and four lead germanate 71 glasses, as a function of peak Pb-O bond length measured by neutron diffraction. Molar compositions are indicated on the plot. The solid line is a least-squares fit to the data: δ( 207 Pb) = −13200 r PbO (peak) +30400, in ppm and Å (95% confidence bounds shaded), and the dashed line is given by Fayon et al., 52 δ( 207 Pb) = -8668.95 r PbO + 20854. The main reason for the offset between the two trend lines is attributed to the use of peak (modal) bond lengths herein, which are more easily determined from total scattering data than mean bond lengths, and hence, a more reliable indicator of the local environment. The Fayon et al., 52 correlation is based on mean bond lengths from crystal structures, not from total scattering. Lower: First moments of the 29 Si MAS NMR lineshapes for vitreous silica 88 and lead silicate glasses, 22 as a function of the average Si-O bond length measured by neutron diffraction. The solid line is a least-squares fit to the data: δ ( 29 Si) = 1250 r SiO -2130, in ppm and Å (95% confidence bounds shaded), and the dashed line the composite trend given by MacKenzie and Smith, 79 Figure 4 shows that the increase of the associated periodicity with increasing PbO content is consistent with the silicate anions becoming more dilute. The measured periodicities are greater than the average Si-Si distance calculated as r SiSi = ρ Si −1/3 , with ρ Si = c Si ρ 0 , which is indicative of residual polymerization, and the retention of some Q 1 species right up to 80 mol% PbO. The increasing correlation length associated with the prepeaks is consistent with that of the FSDPs and the overall increase of intermediaterange order at high PbO contents.

CONCLUSIONS
Over the compositional range 35 to 80 mol% PbO, the local environment of Pb(II) in binary PbO-SiO 2 glasses changes only subtly. Pb(II) has a low coordination number to oxygen (∼3 to 4), plus a stereochemically active electron LP, and hence, behaves as an oxide glass network forming (or intermediate) cation. This conclusion contradicts conventional wisdom, as well as some of the literature 27,35 in which compositions are proposed at which the role of lead transforms from that of a network modifier to that of a network former. Although such a transformation at compositions with less than 35 mol% PbO is not ruled out, we argue that it is unlikely, especially given the higher molar volumes of lead versus strontium silicate glasses, but requires careful further study. Subtle changes in the local structure about Pb 2+ that do occur upon increasing from 35 to 80 mol% PbO include: 1. a shortening (of 0.04 Å) and strengthening of the average (short) Pb-O bond, with a concomitant shift of the 207 Pb NMR lineshape by +800-900 ppm. 2. an increase of approximately 0.22 in the number of short (≤ 2.70 Å) Pb-O bonds, from 3.3 to 3.6. 3. an increase in site axial symmetry, as evinced by 207 Pb NMR CSA lineshapes.
All of these points are consistent with a gradual transition toward axially symmetric square pyramidal [PbO 4 ] sites, such as those within the crystalline PbO polymorphs.
Even as the local structure about Pb(II) tends toward that in crystalline PbO, so the position of the FSDP increases with increasing PbO content, and the associated periodicity decreases toward that of the β-PbO polymorph. This occurs along with an attendant narrowing of the FSDP, and so an increase in correlation length (up to 19.7(6) Å) and intermediate-range ordering in the glass, which is also evident in the silicate anion ordering. All of these facts have implications for the glass-forming limit in the PbO-SiO 2 system, with crystallization becoming ever easier as the size of the plumbite network regions increase, and their structure becomes more and more similar to β-PbO.
Stereochemically active Pb(II) electron LPs occupy the natural voids within the silicate network at low PbO contents, while at high PbO contents they begin to aggregate within voids that form part of the plumbite network, in analogy to the open channels in Pb 11 Si 3 O 17 and the layered structures of α-and β-PbO.
Thus, the structural behavior of Pb(II) in lead silicate glasses differs markedly from typical M(II) modifiers in alkaline earth silicate glasses, evidence for which can be seen in the glass molar volumes (and atom number densities), by comparison with the ionic radii of the divalent cations, Figure 1.
As an additional point, we note that pulsed neutron total scattering is capable of measuring average bond lengths sufficiently accurately that correlations between Si-O or Pb-O bond lengths, with 29 Si or 207 Pb NMR chemical shifts respectively, could be measured. This is the first time that such correlations have been demonstrated for a series of glasses.
Our conclusions hold for the rapidly quenched glasses of the present study, and any effects of annealing, or otherwise varying the thermal history, remain an open area for further research.

A C K N O W L E D G M E N T S
This work is based on research presented in the doctoral thesis of Oliver L. G. Alderman. 68 This work was funded by the STFC Centre for Materials Physics and Chemistry under Grant CMPC09105 and the EPSRC. We thank the US National Science Foundation for supporting this work under Grant number NSF-DMR 1746230. Uwe Hoppe, Martin v. Zimmerman and Anke Watenphule are greatfully acknowledged for their assistance at beamline BW5, DORIS III, HASYLAB at DESY. O R C I D Oliver L. G. Alderman https://orcid.org/0000-0002-2342-811X Alex C. Hannon https://orcid.org/0000-0001-5914-1295