Probing Metal-Bridging Oxygen and Configurational Disorder in

Dec 5, 2014 - Probing Metal-Bridging Oxygen and Configurational Disorder in Amorphous Lead Silicates: Insights from 17O Solid-State Nuclear Magnetic ...
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Probing Metal-Bridging Oxygen and Configurational Disorder in Amorphous Lead Silicates: Insights from 17O Solid-State Nuclear Magnetic Resonance Sung Keun Lee* and Eun Jeong Kim Laboratory of Physics and Chemistry of Earth Materials, School of Earth and Environmental Sciences, Seoul National University, Seoul, 151-742, Korea ABSTRACT: The detailed degree of mixing between framework Si and metal cations and the nature of oxygen that only links metal cations (metal-bridging oxygen) in archetypal metal oxide glasses have been among the unsolved problems in physical chemistry. Binary lead silicate (PbO-SiO2) glass is an ideal model system for exploring the extent of cation disorder and metal-bridging oxygen because of its peculiar glass-forming ability at high PbO concentration. Here we report the first high-resolution 17O solid-state NMR spectra for binary lead silicate glasses with varying composition (near that of orthosilicate, i.e., Pb/Si = 2), where peaks due to metal-bridging oxygen (Pb-O-Pb), as well as Pb-O-Si and Si-O-Si are clearly resolved. The spectra also reveals that the metal-bridging oxygen possesses a greater topological disorder due to structural complexity in Pb coordination environments. Together with a statistical thermodynamic model of oxygen speciation proposed to describe mixing behavior in oxide glasses with any oxygen coordination number, the current 17O NMR results allow direct quantification of the degree of Pb/Si disorder and estimation of relative energy difference among the oxygen clusters [Pb-O-Pb + Si-O-Si = 2(Pb-O-Si)] of ∼−6 kJ/mol. This corresponds to a degree of mixing (Q) between Pb and network Si of ∼0.9, which implies that it deviates from random distribution (Q = 0) but shows a tendency toward Pb/Si order (Q = 1) that favors the formation of the Pb-O-Si cluster. The calculated configurational enthalpy of lead silicate glasses based on 17O NMR data showed a negative deviation and is consistent with those estimated from experimental solution calorimetry, unveiling atomistic origins of bulk macroscopic properties in the amorphous oxide. The results and methods shed light on a unique opportunity to explore the nature of intermixing and topological disorder in diverse complex amorphous oxides with varying cation types and oxygen coordination numbers by estimating the exact proportion of metal-bridging oxygen.

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INTRODUCTION Binary metal silicate glasses are among the archetypal glassforming systems, providing insights into complex multicomponent amorphous oxides with diverse technological applications and fundamental implications in physical chemistry of amorphous matters.1 Particularly, binary lead silicate (PbOSiO2) glasses have served as model systems for other metal silicate glasses with high metal concentration because of their prominent glass-forming ability even near orthosilicate (i.e., Pb/Si = 2) composition. Multicomponent lead silicate glasses have been used since ∼1400 B.C.2 and Pb, though minor, can play an important role in magmatic processes.3 They could also yield rare access to the otherwise difficult path to study geologically relevant peridotite melts with high Mg content [e.g., forsterite (Mg2SiO4) composition]. Furthermore, amorphous lead silicates can be potentially useful host materials for oxide nanoclusters4−6 and lead chalcogenide quantum dots (e.g., see refs 7−11 and references therein). Structural information on how Pb incorporates into amorphous silica network is of prime importance as it controls most of the macroscopic properties (e.g., configurational enthalpy and © 2014 American Chemical Society

activity coefficient of PbO) and transport properties (viscosity and diffusivity), as well as the topology of nanoclusters in a glass matrix. Despite its importance, the degree of intermixing among cations in metal oxide glasses remains among the difficult problems in physical chemistry and glass sciences. The intermixing between a metal cation and silicon in amorphous oxide networks can be estimated by exploring the atomic environments around oxygen (e.g., see refs 12−15 and references therein). In a fully polymerized amorphous SiO2, [4] Si’s are linked by corner-sharing bridging oxygen (BO, [4]SiO-[4]Si). With increasing metal oxide (MO) content in binary metal silicate glasses, the fraction of oxygen linking [4]Si and a metal cation (M-O-[4]Si) increases at the expense of BO. If the metal cation is the network modifier, M-O-[4]Si forms a nonbridging oxygen (NBO), where the M-O bond has an ionic nature.1 With a further increase in MO content, near orthosilicate and further toward suborthosilicate composition Received: September 27, 2014 Revised: December 4, 2014 Published: December 5, 2014 748

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see ref 21). Thus, it would be desirable to extend these previous efforts to account for mixing in these glasses for any given oxygen coordination number. Additionally, 17O is a quadrupolar nuclide [with a nuclear spin (I) of 5/2] that possesses nonspherical nuclear charge distribution, leading to a quadrupole interaction between nuclear electric quadrupole moment and electric field gradient. The interaction thus depends on local symmetry and structures. The magnitude of this interaction is parametrized with the quadrupolar coupling constant (Cq). These 17O NMR parameters, including the isotropic chemical shift (δiso) and Cq of oxygen clusters, are thus sensitive to variations in local topology and atomic configurations around oxygen in oxide glasses.12,53−56,59,62−65 While these detailed NMR parameters are essential in providing the electronic origins of the differences in structure of lead and other metal silicate glasses, no 17O NMR data have been reported for oxygen-linking Pb in the glasses. Herein, we report the first high-resolution 17O solid-state NMR spectra for binary lead silicate glasses. On the basis of a modified oxygen cluster population model for oxide glasses, we report the extent of PbSi intermixing in lead silicate glasses near orthosilicate composition. Detailed 17O NMR parameters for the newly resolved oxygen sites are also provided. These oxygen cluster populations from 17O NMR results are used to constrain macroscopic configurational enthalpy, yielding quantitative insights into the atomistic origins of configurational disorder and macroscopic properties in metal oxide glasses.

(i.e., MO/SiO2 > 2), oxygens linking two metal cations (metalbridging oxygen, MBO, M-O-M) can be formed. The MBO fraction may depend on the type of metal cation (e.g., Na+, Ca2+, Mg2+, and Pb2+) as well as MO/SiO2 ratio (e.g., see refs 16−19 and references therein). The unambiguous estimation of the fractions of these oxygen clusters, particularly of MBO, has not been trivial as most binary alkali and alkaline earth silicate glasses do not have glass-forming ability near the orthosilicate composition.18,20 In contrast, previous experimental studies of lead silicate glasses, together with earlier 207Pb NMR studies of glasses near orthosilicate composition, suggested that the bonding of Pb with oxygen possesses a greater degree of covalency and Pb partly acts as a network-former at high Pb content.16,21−36 The glasses thus have excellent glass-forming ability beyond a PbO content >80%; unlike other binary silicate glasses that require levitation facilities and rapid quenching for synthesis, lead silicate glasses near orthosilicate composition can be synthesized via conventional melt-quenching, allowing direct access to the oxygen configuration including MBO for a wide range of composition near MO/SiO = 2. While pioneering experimental efforts with oxygen 1s X-ray photoelectron spectroscopy (XPS) provided initial and important insights into oxygen configurations in lead silicate glasses (e.g., see refs 16 and 17 and references therein), the considerable overlap between NBO with MBO peaks poses a challenge in unambiguously estimating MBO fractions in metal silicate glasses (see refs 16−18 and 20 and references therein). Together with the limited usefulness of conventional scattering and spectroscopic techniques in estimating the degree of disorder in glasses, a full understanding of how Pb and Si are linked and the nature of the metal-bridging Pb-O-Pb cluster thus remain unsolved. As evidenced by the relatively smaller configurational enthalpy (from solution calorimetry) in binary lead silicate glasses,37,38 the degree of Pb-Si intermixing in lead silicate glasses is expected to be quite different from that of other binary metal oxide glasses which show significant negative deviation in configurational enthalpy.37 Spectroscopic evidence to account for the observed macroscopic configurational properties has been anticipated. The degree of configurational disorder among cations in oxide glasses has often been studied with double-resonance nuclear magnetic resonance (NMR) spectroscopy exploring through-space (dipolar coupling) and through-bond (Jcoupling) interactions involving metal cations (e.g., see refs 39−46 and references therein). Alternatively, 17O NMR [particularly high-resolution 17O triple quantum magic angle spinning (3QMAS) NMR] has been successful in directly resolving various BO and NBO sites in the glasses with varying composition, temperature, and pressure (e.g., see refs 13, 18, and 47−59 and references therein). These studies yield unprecedented insight into the extent of mixing among network formers connected by a corner-sharing oxygen (i.e., oxygen coordination number of 2) and NBO. Recent studies also showed evidence of MBO species in Ca-Mg silicate glasses toward suborthosilicate composition.18,20 On the basis of the previous 17O NMR studies of simple oxide glasses, order parameters were proposed to quantify the degree of intermixing of cations [spanning from chemical order (Q = 1) to complete phase separation (Q = −1)].13,60,61 These previous statistical thermodynamic models with order parameters have only been useful in describing mixing between framework cations with an oxygen coordination number of 2, whereas oxygen coordination numbers in lead and other metal silicates is higher than 2 (e.g.,

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EXPERIMENTAL SECTION

Sample Preparation. Binary lead silicate glasses with varying PbO/SiO2 ratios [2.5:1 (nominal PbO2/SiO2 ratio), 2:1 (Pb2SiO4 orthosilicate composition), and 1.5:1] were synthesized from mixtures of PbO (Sigma-Aldrich) and 40% 17O enriched SiO2 (ref 49). Enrichment was achieved by hydrolyzing SiCl4 with 40% 17O-enriched H2O. The mixtures in a Pt crucible were fused at 1100 °C in an Ar environment for 1 h and subsequently quenched into glasses. As partitioning of Pb into the Pt crucible may be feasible, the crucible was presaturated with Pb2SiO4 liquids at 1100 °C prior to the synthesis of the 17O enriched glasses studied here. While metallic Pb was observed under stereoscope, the fraction is negligible and thus its presence does not affect overall results of the study. Negligible weight loss was observed, indicating that the chemical compositions of the glasses were close to the nominal composition. NMR Spectroscopy. The 17O NMR spectra for the glasses were collected using a Varian 400 MHz spectrometer at 9.4 T with a Larmor frequency of 54.23 MHz. A 3.2 mm Varian double-resonance probe with a spinning speed of 19.5 kHz was used. The 17O magic angle spinning (MAS) NMR spectra were collected with an rf pulse length of 0.3 μs (∼15° tip angle for solids). The 17O 3QMAS NMR spectra for the glasses were collected using fast-amplitude-modulation-based shifted-echo pulse sequences comprising hard pulses with durations of 3.3 and 0.7 μs (refs 66−70 and references therein). An echo delay of ∼0.5 ms and soft echo pulse of ∼12 μs were used. A phase table with 96 cycles was used to select a full echo. A recycle delay of 1 s was used for both 1D and 2D NMR spectra. The 17 O NMR spectra were measured with external tap water as reference. 749

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RESULTS AND DISCUSSION Oxygen Environments in Lead Silicate Glasses near Orthosilicate Composition: Insights from 17O NMR. Figure 1 shows the 17O MAS NMR spectra for binary lead

coordination numbers of Pb and O, respectively. n = 3, 4 and m = 3, 4, while a minor fraction of the cluster with m = 2 is also possible). Similarly, the Pb-O-Si peak is also due to various oxygen environments linking one [4]Si and more than one [3,4] Pb depending on composition and, thus, represents [n] Pb-[m]O-[4]Si (n = 3, 4, while m can vary from 2 to 4). The 17 O NMR results at a significant fraction of [n]Pb-[m]O-[4]Si provide an intriguing evidence for the extensive mixing of [n]Pb and [4]Si. Furthermore, the presence of noticeable and seemingly similar fractions of both [n]Pb-[m]O-[n]Pb and [4] [2] Si- O-[4]Si in the orthosilicate composition demonstrates unambiguously that the Pb/Si distribution in the glass network certainly deviates from Pb-Pb avoidance, where no [n] Pb-[m]O-[n]Pb and [4]Si-[2]O-[4]Si would be expected. While the current peak assignment using MAS NMR spectra is straightforward, double-resonance correlation NMR techniques utilizing through-space and through-bond connectivity between 207 Pb and 17O in the Pb-silicate glasses would certainly be useful to confirm the current assignment. Figure 2 shows the 17O 3QMAS NMR spectra for binary lead silicate glasses with varying PbO/SiO2 ratio. The spectra show well-resolved oxygen clusters as labeled. The [n]Pb-[m]O-[n]Pb peak intensity apparently increases with an increase in PbO content at the expense of the [4]Si-[2]O-[4]Si peak as also shown in the 1D MAS NMR spectra. The peak position (δ3QMAS, δMAS) of each oxygen cluster in the 2D NMR spectra does not change significantly within the studied composition range, suggesting that the 17O δiso and Cq of each oxygen cluster may not change significantly with varying Pb/Si near the orthosilicate composition. Nevertheless, slight changes in their peak positions provide insight into the effect of composition on local topology (T-O-T bond angle and T-O bond length) and, consequently, the structurally relevant NMR parameters. The 17O δiso and quadrupolar coupling product (Pq) of each oxygen cluster was obtained from the center of gravity of the peak. Subsequently, Cq was estimated as Cq = Pq /(1 + η2/3)1/2, where Cq and η are the quadrupolar coupling constant and quadrupolar asymmetry parameter (0 ≤ η ≤ 1), respectively (Table 1). In the present case, η is assumed to be 0.5. There is relatively minor difference in Cq upon varying η from 0.3 to 0.7. The 17O Cq for the [4]Si-[2]O-[4]Si peak is similar to those reported for previous studies of other silicate glasses (approximately 4.3 MHz)18,48,49,59 and slightly decreases with increasing Pb content. Taking into consideration previous correlations between 17O Cq and the [4]Si-[2]O-[4]Si bond angle,64,65 the trend indicates that the Si-O-Si angle increases with Pb content. The 17O δiso of the [4]Si-[2]O-[4]Si peak in the suborthosilicate glass (with Pb/Si = 2.5:1) is slightly larger than that in the glass with Pb/Si = 1.5:1. This may be attributed to a slight decrease in Si-O bond length with Pb content.53 The estimated 17O Cq of [n]Pb-[m]O-[4]Si and [n]Pb-[m]O-[n]Pb peaks in the glasses is ∼2.9 and ∼3.0 MHz, respectively, and does not vary with PbO content. Note that these Cq values for [n] Pb-[m]O-[n]Pb are largely different from that of corner-sharing oxygen in BaPbO373 or edge-sharing oxygen in PbO,74 indicating that the oxygen topology in the glasses is different from those of crystals. Taking into consideration the oxygen coordination number in the lead silicate glasses near orthosilicate composition, the topology would be similar to oxygen triclusters (triply coordinated oxygen) observed in the silicate glasses at high pressure. 76 The 17 O δ iso of [n] Pb-[m]O-[n]Pb slightly deceases with increasing PbO content.

Figure 1. 17O MAS NMR spectra for binary lead silicate (PbO-SiO2) glasses with varying PbO/SiO2 ratio as labeled. * refers to spinning side band.

silicate glasses with varying PbO/SiO2 ratio where three fully resolved peaks at ∼40, ∼ 130, and ∼260 ppm were observed. While the fraction of the 130 ppm peak does not change significantly with varying SiO2 content, the intensity of the 260 ppm peak increases and that of the 30 ppm peak decreases with decreasing SiO2 (and thus increasing PbO) content. Based on the variation of the peak intensity with PbO/SiO2 ratio, together with previous 17O NMR studies of other metal silicate and aluminosilicate glasses consisting of Si-O-Si (e.g., see refs 12, 13, 18, 47−50, 52, 55, 56, 58−60, 64, 65, 71, and 72), these peaks can be assigned to Pb-O-Pb (∼260 ppm), Pb-O-Si (∼130 ppm), and Si-O-Si (∼40 ppm). While the peak at ∼40 ppm unambiguously corresponds to Si-O-Si, there is no previous report on the oxygen NMR characteristics of both Pb-O-Pb and Pb-O-Si in the glasses. There are, however, a few earlier 17O NMR studies for Pb-bearing crystals, which showed that corner-sharing oxygen linking two [6] Pb’s in BaPbO 3 ([6]Pb-[2]O-[6]Pb) has an isotropic chemical shift (17O δiso) of ∼300−350 ppm and quadrupolar coupling constant (Cq) of ∼7 MHz (ref 73). The 17O δiso of oxygen sites in PbO (litharge) is ∼294 ppm with Cq of ∼0.9 MHz (ref 74). Additionally, tricoordinated oxygen (with three Pb’s) in Pb4O(OtBu)6 shows a sharp peak at 200−230 ppm (ref 75). These previous results suggest that the ∼260 ppm peak (with 17O δiso of ∼280 ppm, see below) likely corresponds to Pb-O-Pb and, thus, the most abundant peak at the orthosilicate composition to Pb-O-Si. We note that the Pb-O-Pb peak can be due to diverse oxygen environments with a varying number of Pb around oxygen: because the average Pb coordination number is ∼3−4 in the lead silicate glasses near orthosilicate composition,(e.g.,21) the average oxygen coordination number for the Pb-O-Pb cluster should also be higher than 3 (see below for further discussion). Thus, the Pb-O-Pb peak in the 17O NMR spectrum represents oxygen environments coordinated with varying number of [3,4] Pb (i.e., [n]Pb-[m]O-[n] Pb, where m and n are the 750

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intermediate (∼151 ppm) between those of [n]Pb-[m]O-[n]Pb and [4]Si-[2]O-[4]Si, indicating that chemical shielding of oxygen cluster decreases with increasing Pb around oxygen. Figure 3 presents the total isotropic projection of the 17O 3QMAS NMR spectra for binary lead silicate glasses, which

Figure 3. Total isotropic projection of 17O 3QMAS NMR spectra for binary lead silicate (PbO-SiO2) glasses with varying PbO/SiO2 ratio.

demonstrates the effect of PbO on the oxygen cluster populations and their peak widths. The [4]Si-[2]O-[4]Si peak intensity decreases with increasing PbO, while the relative intensity of the [n]Pb-[m]O-[4]Si peak is apparently constant. In contrast to 1D MAS NMR spectra showing similar peak widths for the three oxygen clusters (the peak width in the MAS spectra is controlled by both the chemical shift dispersion and Cq), isotropic projection of the 2D NMR spectra clearly shows different peak widths in the isotropic dimension (free from quadrupolar broadening) for the oxygen clusters. The peak width of [4]Si-[2]O-[4]Si in the isotropic dimension (with a fwhm of ∼12 ppm) is much narrower than that of [n]Pb-[m]O-[4]Si (with a fwhm of ∼20 ppm). Furthermore, the [n]Pb-[m]O-[n]Pb peak (with a fwhm of ∼35 ppm) is much broader than that of [n] Pb-[m]O-[4]Si. As the peak width in the isotropic dimension is primarily affected by chemical disorder (and, consequently, the degree of structural variations), the trend indicates a greater structural disorder for [n]Pb-[m]O-[n]Pb and [n]Pb-[m]O-[4]Si than for [4]Si-[2]O-[4]Si. This is primarily due to structural diversity in the Pb coordination environment and, thus, the resulting complexity in the oxygen coordination environments in [n] Pb-[m]O-[n]Pb. This also leads to a relatively low S/N ratio of the [n]Pb-[m]O-[n]Pb peak in the MQMAS NMR spectrum for the glasses with low PbO content (i.e., PbO/SiO2 = 1.5:1 glass

Figure 2. 17O 3QMAS NMR spectra for binary lead silicate (PbOSiO2) glasses with varying PbO/SiO2 ratios, as labeled. Contour lines are drawn from 3 to 93% of the relative intensity at a 5% increment and an additional line at 5%.

The [n]Pb-[m]O-[n]Pb peak in the glasses studied here lies within a slope (3QMAS/MAS) of approximately −31/17. The trend indicates that the dispersion in the spectrum is mostly due to isotropic chemical shift at a nearly constant Cq.50,66 While the correlation between 17O NMR parameters and topology of [n] Pb-[m]O-[n]Pb remains to be established, these variations in 17 O δiso suggest non-negligible changes in Pb-O bond lengths and the associated configuration disorder in Pb environments with varying Pb/Si ratio. The 17O δiso of [n]Pb-[m]O-[4]Si is

Table 1. 17O NMR Parameters (Isotropic Chemical Shift δiso and Quadrupolar Coupling Constant Cq) for Oxygen Clusters in Binary Lead Silicate Glasses at Different PbO Contents (XPbO) 17

a

O δiso (ppm)

17

O Cqa (MHz)

XPbO

Si-O-Si

Pb-O-Si

Pb-O-Pb

Si-O-Si

Pb-O-Si

Pb-O-Pb

0.6 0.67 0.71

74.6 ± 2.0 79.0 ± 2.0 80.2 ± 2.0

150.7 ± 2.0 151.6 ± 2.0 151.7 ± 2.0

287.5 ± 4.0 285.7 ± 2.0 282.6 ± 2.0

4.4 ± 0.2 4.3 ± 0.2 4.1 ± 0.2

2.9 ± 0.2 2.9 ± 0.2 2.9 ± 0.2

3.1 ± 0.2 3.0 ± 0.2 3.0 ± 0.2

Asymmetry parameter (η) of 0.5 was used to calculate Cq from the quadrupolar coupling product Pq. 751

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The Journal of Physical Chemistry C where the expected [n]Pb-[m]O-[n]Pb peak intensity is ∼6% (see below for further discussion). We note that this information, together with structural relevant NMR parameters of oxygen clusters, cannot be obtained from the 1D MAS NMR data alone, demonstrating that 17O 3QMAS NMR spectra for the glasses provide additional insight into the structures of oxide glasses. Quantification of the Degree of Si and Pb Mixing in Amorphous Lead Silicates/Atomistic Origins of Configurational Enthalpy of Network Glasses. The detailed nature of oxygen clusters revealed from 17O NMR above, combined with the statistical thermodynamic model of effect of the degree of disorder on oxygen speciation, allows direct quantification of the degree of Pb/Si disorder in the amorphous networks. The following model is based on our previous analytical model of cation mixing developed to quantify mixing between two framework cations linked by a corner-sharing oxygen (i.e., oxygen coordinated to only two cations, as in [4] Si-[2]O-[4]Si and [4]Ge-[2]O-[3]B).60 Because the oxygen coordination number (m) in a [n]Pb-[m]O-[n]Pb cluster should also be larger than 3, as is often the case for other metal silicate glasses, the previous model has been modified to incorporate an oxygen cluster with any oxygen coordination number. In a MaOb-SiO2 binary amorphous oxide with a cation to anion ratio (M/O) of a/b for the metal oxide, the average coordination number of cation M (Zm) and oxygen coordination number (ZO) satisfies the following relation: Zm × a = ZO × b. The following quasi-chemical reaction among oxygen clusters can then be used to describe the mixing behavior of cation M and [4] Si in binary metal silicate glasses: [Zm]

M‐[ZO]O‐[Zm]M +

β=

where XSi′ = 4XSi/(4XSi + ZmXm) and XM * = 2ZmXm/[ZO(4XSi + ZmXm)]. XSi and Xm are the mole fractions of Si and the metal cation, respectively [i.e., Xm = M/(M + Si)]. Note again the above oxygen cluster population model is fully general in that it can be applied to any oxide glasses, regardless of types of cations (network modifier, network former) and coordination numbers of oxygens (ZO). Figure 4 shows the variation in oxygen cluster populations with PbO content in binary lead silicate glasses. As the 3QMAS

Figure 4. Fraction of oxygen clusters in the binary lead silicate (PbOSiO2) glasses with varying PbO/SiO2 ratio. Thin, moderately thick, and thick lines refer to the calculated fractions of oxygen clusters with varying Q from 0 (random), 0.9, to 1 (chemical order), respectively.

Si‐[2]O‐[4]Si = 2([Zm]M‐[ZO′]O‐[4]Si)

[4]

(1)

where [Zm]M-[ZO]O-[Zm]M refers to MBO and [Zm]M-[ZO′]O-[4]Si is the oxygen species linking [4]Si and M with an average coordination number Zm and oxygen coordination number ZO′. The degree of M/Si mixing can be modeled with the degree of framework disorder (Q) that depends on the oxygen cluster energy difference in eq 1 {2W = 2E[[Zm]M-[ZO′]O-[4]Si] E[[Zm]M-[ZO]O-[Zm]M + [4]Si-[2]O-[4]Si]}. The relationship between 2W and Q was previously defined as follows:60

NMR signal intensity depends on Cq77 and the oxygen clusters have different Cq values (Table 1), we used the oxygen cluster population obtained from the fitting of 17O MAS NMR spectra (without additional calibration of intensity that is needed for 3QMAS NMR data). Note again that oxygen cluster peaks are completely resolved in the 1D MAS NMR spectra and their peak intensities provide quantitative fractions of these oxygen clusters. The fraction of [n]Pb-[m]O-[4]Si (i.e., [Zm]M-[ZO′]O-[4]Si in eq 3) is rather invariant (∼7273%) within the studied composition range. The [n]Pb-[m]O-[n]Pb and [4]Si-[2]O-[4]Si fractions at the orthosilicate composition are identical (∼13.5%), as expected from the stoichiometry (Pb/Si = 2). The [n]Pb-[m]O-[n]Pb fraction increases from ∼6.7% (Pb/Si = 1.5) to 18.9% (Pb/Si = 2.5). Taking into consideration complete resolution along the oxygen clusters, the fractions should not be subject to any significant error. The experimental fractions are compared with oxygen site fractions calculated with Q values of 1 (chemical order), 0 (random), and −1 (phase separation) using eq 3. At the orthosilicate composition, the expected [n]Pb-[m]O-[4]Si fractions are 100% (Q = 1), 50% (Q = 0), and 0% (Q = −1). With [n]Pb-[m]O-[4]Si fraction of ∼73% at the orthosilicate composition, the estimated Q in binary lead silicate glasses is ∼0.9 at a constant fictive temperature (Tf) of 600 K. The estimated oxygen cluster energy difference (2W) is ∼−6 kJ/mol and the normalized energy difference (2W/RT) is ∼−1.2 J/K/mol, corresponding to a tendency toward chemical order that favors the formation of the [n]Pb-[m]O-[4]Si cluster. The current results can be

Q (2W , Tf ) =1 − exp(2W /RTf ), 2W ≤ 0, = exp[− (2W /RTf )] − 1, 2W ≥ 0

(2)

where R is the gas constant and Tf is the glass transition temperature (i.e., fictive temperature) below which the structure of supercooled liquids is kinetically frozen.1 With varying 2W value, Q ranges from 1 (chemical order, negative 2W) to −1 (clustering of metal cations, positive 2W), with Q = 0 indicating random distribution. The population of the oxygen cluster M-O-Si (e.g., [n]Pb-[m]O-[4]Si) can then be calculated from the following relationship with varying Q (and thus 2W)60 as well as coordination numbers of cations (Zm) and oxygen (ZO); ⎛ ⎞ *⎜ 1 ⎟ X [Zm]M −[ZO]O −[4]Si(Q , X m , ZO , Zm) = 4XSi′ XM ⎝ β + 1⎠ (3)

β=

* (Q /Q + 1) , 2W ≥ 0 1 − 4XSi′ XM

* Q , 2W ≤ 0 1 − 4XSi′ XM 752

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lead silicate glasses with varying metal content (Xm), with the negative deviation due to preferential proximity between Pb and Si in the glasses. Only the first term in eq 4 was used in the present case. Therefore, the Hconfig here refers to the enthalpy of mixing among oxygen clusters. The calculated Hconfig using 17O NMR showed a negative deviation. While the results are generally consistent with experimental solution calorimetry, they are slightly smaller than that of the experimental calorimetry data.37,38 The results indicate that there are evident contributions from topological changes beyond the short-range structure in the glasses.28 While the origin of the nanoscale structures is not yet clear, this could be the formation of local and medium-range topology associated with Pb: previous experimental study indicated that Pb bearing topology in the glass may possess similar structural ordering observed in the crystalline analogues.28 This could lead to a decrease in the configurational enthalpy. Nevertheless, the relatively small difference between the experimental data and calculated results shows that the 17O NMR method can provide an indirect way to predict thermodynamic properties. The calculated configurational enthalpies for other binary oxide glasses with two framework cations (B-Si and B-Ge) are also shown in Figure 5 for comparison. Taking into consideration the formation energy of the boroxol ring, the experimental Hconfig for binary borosilicate glasses obtained from solution calorimetry is well reproduced.60,61 While experimental configurational enthalpies of binary borogermanate glasses have not been reported, partly based on ab initio calculations, these glasses show a slight negative deviation from random distribution and a moderate prevalence of chemical mixing between B and Ge.60 In contrast, binary lead silicate glasses shows a slightly larger negative deviation than that shown by B-Ge, as expected from the larger Q values of the former. While the current study demonstrate that 2W (and Q) in eqs 1−3 can now be experimentally estimated using 17O NMR, and a qualitative trend can be established to account for the observed differences on the basis of the field strength of cation, we note that a quantitative model based on firstprinciples to predict Q from the chemical composition of melts and glasses is currently unavailable. Further experimental efforts with theoretical confirmation remain to be performed.

compared with the extent of cation disorder in other binary oxide glasses; for instance, while a moderate degree of phase separation between [3]B and [4]Si in binary borosilicate glasses has been estimated (Q ≈ −0.6), the extent of disorder in binary borogermanate tends toward chemical ordering between [3]B and [4]Ge with a Q of ∼0.4.60,61 The results confirm that the degree of framework disorder, which can be uniquely revealed by 17O NMR, is largely controlled by the types of cations in the metal silicate glasses. The difference in chemical order between lead silicate glasses and other binary silicate glasses is manifested in their configurational thermodynamic properties. The measured extent of disorder (positive Q) suggests that the configurational enthalpy (Hconfig) for binary lead silicate glasses is expected to show a negative deviation. In addition to the contribution from mixing among cations, structural topological rearrangement and/or changes in the medium-to-intermediate range structure (0.5−2 nm) may also affect the changes in melt properties. By considering both chemical mixing among framework cations with flexible oxygen coordination number in the glasses as well as composition-induced topological changes,60 the configurational enthalpy (Hconfig) can be expressed as follows: H config(X m , ZO , Zm , Q ) ⎛ [4XSi + 2(Zm/ZO)X m]2W ⎞ *⎜ * )⎟ = XSi′ XM + Ftopo(XM β+1 ⎝ ⎠ (4)

where the previous model of configurational enthalpy is modified to incorporate explicitly the generalized oxygen coordination number (ZO). The first term with 2W/(β + 1) accounts for the intermixing between M and Si in metal silicate glasses with varying ZO, while Ftopo(X*M) is an additional composition-dependent interaction parameter that accounts for the change in topology and/or medium-range structure with varying composition. Figure 5 shows the calculated Hconfig in

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CONCLUSION We quantified the extent of the intermixing between Pb and Si in binary lead silicate glasses using high-resolution 17O NMR, presenting the first unambiguous experimental evidence for the detailed nature of Pb/Si mixing in amorphous lead silicates. The metal-bridging oxygen ([n]Pb-[m]O-[n]Pb) is well resolved in both 1D and 2D 17O NMR spectra with varying Pb/Si nearorthosilicate composition, providing unique opportunity to explore the chemical disorder in binary metal silicate glasses. While the [n]Pb-[m]O-[n]Pb peak may not fully represent free oxide ion as in other metal silicate glasses, the current results with detailed 17O NMR parameters (isotropic chemical shift and quadrupolar coupling constant) for [n]Pb-[m]O-[n]Pb and [n] Pb-[m]O-[4]Si will potentially be useful in providing insights into the NMR characteristics of other MBO (e.g., Mg-O-Mg) in metal silicate glasses. The proposed statistical model in the current study explicitly takes into account varying oxygen coordination number, regardless of the type of cations (network-modifier or network-former). This shed lights on an opportunity to describe mixing behavior in diverse oxide glasses with varying cation and oxygen coordination numbers. While

Figure 5. Configurational enthalpy (Hconfig) for binary lead silicate glasses (gray curve) and those for binary borosilicate (red curves) and binary borogermanate glasses (blue curves) with varying fraction of cation (other than Si, Xm).15,60 Because the first term in eq 4 was used, the Hconfig here only accounts for the enthalpy of mixing among oxygen clusters (see text). Red and blue dotted lines represent the experimental values for borosilicate and lead silicate glasses, respectively, obtained by calorimetry37,38 (see text for discussion). 753

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The Journal of Physical Chemistry C

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the topological contribution to the total configurational enthalpy of mixing may not be neglected to fully account for the experimental Hconfig of binary lead silicate glasses, the calculated Hconfig obtained from 17O NMR with improved statistical thermodynamic modeling is consistent with the experimental data. The current progress on the estimation of degree of disorder with Q, together with 17O NMR studies, holds a strong promise to study and demonstrate the effect of pressure, temperature, and composition on the degree of intermixing among cations in the oxide glasses.14,78,79 The results with binary silicate glasses can be extended to quantify the extent of disorder in diverse amorphous oxides and quantum dot semiconductors with distinct oxobridges.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 822-880-6729. Fax: 822871-3269. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a research grant (2012-026-411) to S.K.L. from the National Research Foundation of Korea. The current manuscript is partly inspired by the earlier O 1s XPS studies of oxide glasses in the near orthosilicate composition. We deeply appreciate the helpful and constructive comments and suggestions by three anonymous reviewers.

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