# Mapping the structural trends in zinc aluminosilicate glasses

Rita Mendes da Silva, Anita Zeidler, Hesameddin Mohammadi, Lawrence V. D. Gammond, Esther Girón Lange, Randall E. Youngman, Bruce G. Aitken, Alex C. Hannon, Chris J. Benmore, Gavin B. M. Vaughan, et al.

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Rita Mendes da Silva, Anita Zeidler, Hesameddin Mohammadi, Lawrence V. D. Gammond, Esther Girón Lange, et al.. Mapping the structural trends in zinc aluminosilicate glasses. The Journal of Chemical Physics, 2023, 159 (6), pp.064501. 10.1063/5.0157790. hal-05087967

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# Mapping the structural trends in zinc aluminosilicate glasses

Rita Mendes Da Silva ·; Anita Zeidler ·; Hesameddin Mohammadi ·; Lawrence V. D. Gammond ·;

Esther Girón Lange ·; Randall E. Youngman ·; Bruce G. Aitken ·; Alex C. Hannon ·; Chris J. Benmore ·;

Gavin B. M. Vaughan ·; Philip S. Salmon ·

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J. Chem. Phys. 159, 064501 (2023)

https://doi.org/10.1063/5.0157790

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# Mapping the structural trends in zinc aluminosilicate glasses

Cite as: J. Chem. Phys. 159, 064501 (2023); doi: 10.1063/5.0157790

Submitted: 11 May 2023 • Accepted: 20 July 2023 •

Published Online: 8 August 2023

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Rita Mendes Da Silva,<fnref n="1" /> ID
Anita Zeidler,<fnref n="1" /> ID
Hesameddin Mohammadi,<fnref n="1" /> ID
Lawrence V. D. Gammond,<fnref n="1" /> ID
Esther Girón Lange,<fnref n="1" />,<fnref n="2" /> ID
Randall E. Youngman,<fnref n="3" /> ID
Bruce G. Aitken,<fnref n="3" /> ID
Alex C. Hannon,<fnref n="4" /> ID
Chris J. Benmore,<fnref n="5" /> ID
Gavin B. M. Vaughan,<fnref n="6" /> ID
and Philip S. Salmon<fnref n="1" />,⁸

## AFFILIATIONS

## ABSTRACT

The structure of zinc aluminosilicate glasses with the composition $(ZnO)_x(Al_2O_3)_y(SiO_2)_{1-x-y}$, where $0 \le x < 1$, $0 \le y < 1$, and $x + y < 1$, was investigated over a wide composition range by combining neutron and high-energy x-ray diffraction with $^{27}$Al magic angle spinning nuclear magnetic resonance spectroscopy. The results were interpreted using an analytical model for the composition-dependent structure in which the zinc ions do not act as network formers. Four-coordinated aluminum atoms were found to be in the majority for all the investigated glasses, with five-coordinated aluminum atoms as the main minority species. Mean Al–O bond distances of 1.764(5) and 1.855(5) Å were obtained for the four- and five-coordinated aluminum atoms, respectively. The coordination environment of zinc was not observed to be invariant. Instead, it is dependent on whether zinc plays a predominantly network-modifying or charge-compensating role and, therefore, varies systematically with the glass composition. The Zn–O coordination number and bond distance were found to be 4.36(9) and 2.00(1) Å, respectively, for the network-modifying role vs 5.96(10) and 2.08(1) Å, respectively, for the charge-compensating role. The more open coordination environment of the charge-compensator is related to an enhanced probability of zinc finding bridging oxygen atoms as nearest-neighbors, reflecting a change in the connectivity of the glass network comprising four-coordinated silicon and aluminum atoms as the alumina content is increased.

© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0157790

## I. INTRODUCTION

Zinc is an important additive in many commercial glasses where it is used to improve the chemical resistance and mechanical properties of the material.<fnref n="1" /> A case example is provided by zinc aluminosilicate $ZnO–Al_2O_3–SiO_2$ (ZnAS) glasses, which have a high glass transition temperature, low coefficient of thermal expansion, and high chemical durability and can act as the host for luminescent ions.<fnref n="2" />,<fnref n="3" /> Here, a low coefficient of thermal expansion is a

prerequisite for high thermal-shock resistance, making the glasses favorable for high-power laser applications.<fnref n="4" /> Doped zinc silicates are widely used as display phosphors<fnref n="5" />,<fnref n="6" /> and can be prepared via a glass-ceramic route, where doped willemite ($Zn_2SiO_4$) is the desired product.⁷ In addition, Zn is an important ingredient in bioactive glass, playing a vital role in bone formation, resorption, and tissue engineering.⁸

The structural role played by zinc is largely unknown, partly because of the flexible coordination geometry of the $Zn^{2+}$ ion, which

<footnote n="1">¹Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom</footnote>

<footnote n="2">²Institut Laue Langevin, 71 Avenue des Martyrs, 38042 Grenoble Cedex 9, France</footnote>

<footnote n="3">³Science and Technology Division, Corning Incorporated, Corning, New York 14831, USA</footnote>

<footnote n="4">⁴ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom</footnote>

<footnote n="5">⁵X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, USA</footnote>

<footnote n="6">⁶ESRF–The European Synchrotron, 71 Avenue des Martyrs, 38000 Grenoble, France</footnote>

<footnote>a) Author to whom correspondence should be addressed: p.s.salmon@bath.ac.uk</footnote>
can be four-, five-, or six-coordinated.⁹ Zinc is commonly classified as an “intermediate” in glass science, sitting in the ambiguous space between traditional network-forming elements, such as silicon, which form strong bonds with oxygen and have a large cation field strength, and traditional network-modifying/charge-compensating elements, such as calcium, which form weak bonds with oxygen and have a small cation field strength.¹⁰,¹¹ A small Zn–O coordination number of four is frequently regarded as the indicator of a network-forming role for zinc, but this taxonomy can be erroneous (Sec. VI G). Often, the Zn²⁺ ion is spectroscopically silent. For example, from the perspective of solid-state nuclear magnetic resonance (NMR) spectroscopy,⁶⁷Zn is the only stable NMR-active isotope of zinc, but it is difficult to extract structural information because of its unfavorable NMR properties:⁶⁷Zn has a small gyromagnetic ratio, low natural isotopic abundance (4.1%), and significant quadrupole moment (nuclear spin *I* = 5/2).¹² The Zn²⁺ ion is also diamagnetic with a d¹⁰ electronic configuration and is not, therefore, amenable to investigation by methods such as electron spin resonance or UV–Vis spectroscopy. The coordination environment can be probed using extended x-ray absorption fine structure (EXAFS) spectroscopy,¹³,¹⁴ but these experiments can deliver erroneous results if the Zn²⁺ ions occupy sites with a broad asymmetric distribution of nearest-neighbors.¹⁵

In this paper, we explore the structure of the ZnAS glasses (ZnO)ₐ(Al₂O₃)b(SiO₂)₁⁻ₓ⁻ᵧ, where 0 ≤ x < 1, 0 ≤ y < 1, and x + y < 1, by combining neutron diffraction (ND) and high-energy x-ray diffraction (XRD) with ²⁷Al magic angle spinning (MAS) NMR spectroscopy. A wide range of compositions was investigated along tie-lines in the system where (i) the silica content was kept constant at 50, 60, or 70 mol. % or (ii) the ratio *R* = *x*/*y* was kept at a constant value of unity. The latter corresponds to the tech- tosilicate tie-line where the charge on Zn²⁺ can be balanced by forming two [AlØ₄/₂]⁻ units, where Ø denotes a bridging oxygen (BO) atom. This balance facilitates the possibility of a glass network in which all the silicon atoms are in SiØ₄/₂ units such that the number of non-bridging oxygen (NBO) atoms per tetrahedron *N*<sub>NBO</sub>/N<sub>T</sub> = 0. The results are interpreted with the aid of the GYZAS analytical model for the composition-dependent structure of aluminosilicate glasses, named after the first letters of the surnames of its authors.¹⁶

This paper is organized as follows. The essential theory for the ND and XRD experiments is given in Sec. II. The sample preparation is described in Sec. III along with the ²⁷Al MAS NMR and diffraction experiments. The results are summarized in Sec. IV. The basic tenets of the GYZAS model are described in Sec. V, and the results are discussed by reference to this model in Sec. VI. Conclusions are drawn in Sec. VII.

## II. THEORY

In a diffraction experiment on ZnAS glass, the total structure factor¹⁸

$$S(k) = 1 + \frac{1}{(\langle w(k) \rangle)^2} \sum_{\alpha} \sum_{\beta} c_{\alpha} c_{\beta} w_{\alpha}(k) w_{\beta}(k) [S_{\alpha\beta}(k) - 1] \quad (1)$$

is measured as a function of the magnitude of the scattering vector *k*. The structural information is contained in the Faber–Ziman

partial structure factors *S*<sub>αβ</sub>(*k*) for the chemical species α and β, which are weighted by terms that depend on the atomic fraction *c*<sub>α</sub> and the scattering amplitude *w*<sub>α</sub>(*k*) of chemical species α. In an XRD or ND experiment, *w*<sub>α</sub>(*k*) represents either the *k*-dependent atomic form-factor *f*<sub>α</sub>(*k*) or the *k*-independent coherent neutron scattering length *b*<sub>α</sub>, respectively. Its mean value is given by ⟨*w*(*k*)⟩ = Σ<sub>α</sub> *c*<sub>α</sub>*w*<sub>α</sub>(*k*).

The real-space information is contained in the total pair-distribution function,

$$\begin{aligned} D'(r) &= \frac{2}{\pi} \int_{0}^{\infty} dk k [S(k) - 1] M(k) \sin(kr) \\ &= D(r) \otimes M(r), \end{aligned} \quad (2)$$

where *r* is a real-space distance and ⊗ is the one-dimensional convolution operator. The window function *M*(*k*) is given by *M*(*k*) = 1 for *k* ≤ *k*<sub>max</sub> and *M*(*k*) = 0 for *k* > *k*<sub>max</sub>, where *k*<sub>max</sub> is the maximum accessible *k*-value, and *M*(*r*) is the real-space manifestation of *M*(*k*). If *k*<sub>max</sub> is sufficiently large that *M*(*k*) does not truncate the oscillations in *S*(*k*), Eq. (2) delivers the unmodified total pair-distribution function *D*(*r*). In the following, the functions measured by XRD and ND will be denoted by subscripts “X” and “N,” respectively.

In the ND experiments, the unmodified total pair-distribution function is given by

$$D_N(r) = \frac{4\pi\rho r}{\langle b \rangle^2} \sum_{\alpha} \sum_{\beta} c_{\alpha} c_{\beta} b_{\alpha} b_{\beta} [g_{\alpha\beta}(r) - 1], \quad (3)$$

where *ρ* is the atomic number density, ⟨*b*⟩ is the mean neutron coherent scattering length, and *g*<sub>αβ</sub>(*r*) is the partial pair-distribution function for the chemical species α and β. Each peak *i* in *rg*<sub>αβ</sub>(*r*) can be represented by the Gaussian function,

$$p_{\alpha\beta}^{i}(r) = \frac{1}{4\pi\rho} \frac{\tilde{n}_{\alpha}^{\beta}(i)}{c_{\beta}^{i} r_{\alpha\beta}^{i}} \frac{1}{\sqrt{2\pi}\sigma_{\alpha\beta}^{i}} \exp\left[-\frac{(r - r_{\alpha\beta}^{i})^{2}}{2(\sigma_{\alpha\beta}^{i})^{2}}\right], \quad (4)$$

with position *r*<sub>αβ</sub><sup>*i*</sup> and standard deviation *σ*<sub>αβ</sub><sup>*i*</sup>. *ñ*<sub>α</sub><sup>*β*</sup>(*i*) gives the coordination number of chemical species β around α. To allow for the effect of the window function, the measured *D*'<sub>N</sub>(*r*) function was fitted to a sum of Gaussian functions, convoluted with *M*(*r*), using the procedure described in Ref. 19. The goodness-of-fit was assessed by the parameter *R*<sub>*Y*</sub>.²⁰

In the XRD experiments, the contribution of each Gaussian peak *p*<sub>αβ</sub><sup>*i*</sup>(*r*) to [S<sub>*X*</sub>(*k*) − 1] was calculated and Fourier transformed to real-space using the same *M*(*k*) function as used for the experimental data.¹⁹ An appropriate sum of these Fourier transforms was then fitted to *T*'<sub>*X*</sub>(*r*) = *T*<sub>*X*</sub>(*r*) ⊗ *M*(*r*) using a least-squares procedure in the program PXFIT,²¹ where *T*<sub>*X*</sub>(*r*) ≡ *D*<sub>*X*</sub>(*r*) + *T*<sub>*X*</sub><sup>0</sup>(*r*) and *T*<sub>*X*</sub><sup>0</sup>(*r*) = 4π*ρr*. The fitted functions are presented in the form *D*'<sub>*X*</sub>(*r*) = [*T*<sub>*X*</sub>(*r*) − *T*<sub>*X*</sub><sup>0</sup>(*r*)] ⊗ *M*(*r*) = *T*'<sub>*X*</sub>(*r*) − 4π*ρr* to facilitate comparison with the ND results.

## III. EXPERIMENT

### A. Sample preparation and characterization

The compositions of the investigated ZnAS glasses are shown in Fig. 1. The glasses are designated by ZnAS<sub>*x*</sub>(100 − *x* − *y*), with
<figure><img src="image_13.png" /><figcaption>FIG. 1. Ternary composition diagram showing the make-up of the investigated ZnAS glasses. Series I–III correspond to tie-lines with 50, 60, and 70 mol. % silica, respectively, and series IV corresponds to the tectosilicate tie-line.</figcaption></figure>

$x$ and $y$ expressed in mol. %. The glass compositions and densities are summarized in Table I, where the density was measured using a helium pycnometer.

The first set of glasses was made by melting 900 g batches of powder in covered Pt crucibles at 1650 °C and pouring the melt onto a steel table.¹⁶ The glasses were annealed at a temperature of 650 or 690 °C, and the aluminum speciation is reported elsewhere.¹⁶

A second set of glasses was prepared from high purity ZnO (Aldrich, ≥99.999%), Al₂O₃ (Sigma, 99.998%), and SiO₂ (Alfa Aesar, 99.9%) powders that had been dried at 1000 °C for 1–2 h. For each sample, a batch of powder of mass ~4 g was melted at 1600 °C (ZnAS_24_60) or 1650 °C (ZnAS_43_50, ZnAS_33_50, ZnAS_17.5_65) in a covered Pt/10%Rh crucible for 2 h, and the melt was quenched by placing the bottom of the crucible into a water bath (ZnAS_17.5_65) or onto a liquid nitrogen cooled copper block (all other samples). For the ZnAS_43_50 composition, the sample was ground and the melt and quench procedure was repeated to ensure glass homogeneity. The overall mass loss during processing was ~1%, which is probably related to the loss of water re-adsorbed after the initial drying procedure. The composition of each glass was, therefore, taken from the batch composition. We were unable to prepare homogeneous alumina-free zinc silicate glasses by conventional melt quenching or by aerodynamic levitation with laser heating, in accordance with the findings from Ref. 9. The phase diagram for the ZnO–Al₂O₃–SiO₂ system is reported in Ref. 22.

The crystalline Zn₂SiO₄ phase I or willemite sample was prepared using a procedure adapted from Ref. 23. ZnO (Aldrich, ≥99.999%) and SiO₂ (Alfa Aesar, 99.9%) powders were dried at 1000 °C for 2 h, mixed to give the correct stoichiometry, and ~3 g of material was pelletized under a pressure of ~0.74 GPa for 5 min. The pellets were sintered at 1000 °C for 18 h and were finely ground

using an agate pestle and mortar. The resultant powder was pelleted and sintered at 1250 °C for 24 h in a covered Pt/10%Rh crucible. The previous grinding, pelletizing, and sintering cycle was then repeated. The willemite crystal structure was confirmed by powder x-ray diffraction.²⁴

## B. Solid-state NMR experiments

The ²⁷Al MAS NMR experiments were performed at 16.4 T using an Agilent DD2 spectrometer, a triple-resonance 3.2 mm MAS NMR probe, and a shielded narrow-bore super-conducting magnet. The powdered glasses were loaded into low-Al content zirconia rotors with an outer diameter of 3.2 mm. These rotors gave a weak background signal around 0 ppm, which was treated in the protocol used to fit the measured spectra. Single pulse experiments were performed with a 0.6 µs pulse width (π/12 tip angle), a 4 s recycle delay between scans, and a signal averaging of 1000 scans. The sample spinning frequency was computer controlled to 22.0 kHz using compressed nitrogen gas. The signal processing was performed without line broadening using commercial software (Agilent VnmrJ). The spectra were fitted in DMFit²⁵ using Czjzek line shapes to represent the second-order quadrupolar broadened peaks for aluminum in different coordination environments. The chemical shift was referenced to an external aqueous solution of aluminum nitrate at 0.0 ppm.

The ²⁹Si MAS NMR experiment was performed at 4.7 T using an Agilent DD2 spectrometer, a double resonance 5 mm probe, and a wide-bore (89 mm) super-conducting magnet. The powdered sample was packed into a zirconia rotor with an outer diameter of 5 mm, which was spun at a frequency of 7 kHz. Single pulse experiments were performed with $π/2$ pulses of width 5.4 µs, a relaxation delay of 900 s, and a signal averaging of 86 scans. The data were processed using Agilent VnmrJ without any extra line broadening. The chemical shift was referenced to an external tetramethylsilane (TMS) standard at 0.0 ppm. ²⁹Si MAS NMR experiments were not performed on the ZnAS glasses because of the difficulty in providing an unambiguous interpretation of the measured spectra.¹⁶

## C. Diffraction experiments

The ND experiments on the glassy samples were performed using the instrument GEM at the ISIS pulsed neutron source.²⁶ The samples were coarsely ground and held in a cylindrical vanadium container of wall thickness 0.04 mm and an inner diameter of either 8.30 or 10.30 mm. Diffraction patterns were measured at room temperature (≈298 K) for each of the samples in its container, an empty container of each size, the empty instrument, and a cylindrical rod of the null-scattering alloy V₀.⁹⁴⁸⁶Nb₀.⁵⁰¹⁴ (diameter 7.95 mm) for normalization purposes. The datasets were processed using the Gudrun analysis program²⁷ with inelasticity corrections calculated according to Ref. 28. ND experiments were also performed on finely powdered willemite using both GEM and the instrument D4c at the Institut Laue–Langevin.²⁹ For the latter, the incident wavelength was 0.4978(1) Å and the sample was held in a cylindrical vanadium container of wall thickness 0.1 mm and inner diameter 4.8 mm. Diffraction patterns were measured at room temperature for the sample in its container, the empty container, the empty instrument,
<table><caption>**TABLE I.** ZnAS crystal and glass compositions and characterization. The number density $\rho$ is given with an error of $\pm 0.0001$ Å$^{-3}$. The samples were investigated using both ND and XRD. For the $^{27}$Al MAS NMR experiments, the aluminum speciation is given (with an error of $\pm 2\%$) along with the mean Al–O coordination number $\bar{n}_{Al}^O$. The latter was calculated using the full precision of the result found from the NMR analysis.</caption><thead><tr><th>Glass</th><th>x</th><th>y</th><th>1-x-y</th><th>R</th><th>ρ (Å<sup>-3</sup>)</th><th>Diffraction method</th><th>Al(IV) (%)</th><th>Al(V) (%)</th><th>Al(VI) (%)</th><th>n&#773;<sup>O</sup><sub>Al</sub></th><th><sup>27</sup>Al or <sup>29</sup>Si NMR Reference</th></tr></thead><tbody><tr><td>c-Zn<sub>2</sub>SiO<sub>4</sub></td><td>0.6667</td><td>...</td><td>0.3333</td><td>...</td><td>0.0799</td><td>ND<sup>a</sup>, XRD<sup>b</sup></td><td>...</td><td>...</td><td>...</td><td>...</td><td>This work</td></tr><tr><td>ZnAS_43_50</td><td>0.4250</td><td>0.0750</td><td>0.5000</td><td>5.667</td><td>0.0773</td><td>ND, XRD<sup>b</sup></td><td>94</td><td>4</td><td>2</td><td>4.08(8)</td><td>This work</td></tr><tr><td>ZnAS_40_50</td><td>0.4000</td><td>0.1000</td><td>0.5000</td><td>4.000</td><td>0.0781</td><td>ND, XRD</td><td>94</td><td>5</td><td>1</td><td>4.07(8)</td><td>16</td></tr><tr><td>ZnAS_38_50</td><td>0.3750</td><td>0.1250</td><td>0.5000</td><td>3.000</td><td>0.0781</td><td>ND, XRD</td><td>95</td><td>4</td><td>1</td><td>4.06(8)</td><td>16</td></tr><tr><td>ZnAS_33_50</td><td>0.3264</td><td>0.1736</td><td>0.5000</td><td>1.880</td><td>0.0776</td><td>ND, XRD<sup>b</sup></td><td>93</td><td>5</td><td>2</td><td>4.09(7)</td><td>This work</td></tr><tr><td>ZnAS_28_50</td><td>0.2778</td><td>0.2222</td><td>0.5000</td><td>1.250</td><td>0.0781</td><td>ND, XRD</td><td>91</td><td>7</td><td>2</td><td>4.12(7)</td><td>16</td></tr><tr><td>ZnAS_25_50</td><td>0.2500</td><td>0.2500</td><td>0.5000</td><td>1.000</td><td>0.0782</td><td>ND, XRD</td><td>86</td><td>11</td><td>3</td><td>4.17(7)</td><td>16</td></tr><tr><td>ZnAS_22_50</td><td>0.2222</td><td>0.2778</td><td>0.5000</td><td>0.800</td><td>0.0784</td><td>ND, XRD</td><td>82</td><td>15</td><td>3</td><td>4.22(7)</td><td>16</td></tr><tr><td>ZnAS_27_60</td><td>0.2667</td><td>0.1333</td><td>0.6000</td><td>2.000</td><td>0.0751</td><td>ND, XRD</td><td>88</td><td>11</td><td>1</td><td>4.13(7)</td><td>16</td></tr><tr><td>ZnAS_24_60</td><td>0.2445</td><td>0.1555</td><td>0.6000</td><td>1.572</td><td>0.0752</td><td>ND, XRD<sup>b</sup></td><td>86</td><td>11</td><td>3</td><td>4.17(7)</td><td>This work</td></tr><tr><td>ZnAS_22_60</td><td>0.2222</td><td>0.1778</td><td>0.6000</td><td>1.250</td><td>0.0753</td><td>ND, XRD</td><td>92</td><td>7</td><td>1</td><td>4.09(7)</td><td>16</td></tr><tr><td>ZnAS_20_60</td><td>0.2000</td><td>0.2000</td><td>0.6000</td><td>1.000</td><td>0.0755</td><td>ND, XRD</td><td>87</td><td>11</td><td>2</td><td>4.14(7)</td><td>16</td></tr><tr><td>ZnAS_18_60</td><td>0.1778</td><td>0.2222</td><td>0.6000</td><td>0.800</td><td>0.0757</td><td>ND, XRD</td><td>86</td><td>12</td><td>2</td><td>4.15(7)</td><td>16</td></tr><tr><td>ZnAS_17.5_65</td><td>0.1750</td><td>0.1750</td><td>0.6500</td><td>1.000</td><td>0.0734</td><td>ND, XRD<sup>b</sup></td><td>85</td><td>12</td><td>3</td><td>4.18(7)</td><td>This work</td></tr><tr><td>ZnAS_17_70</td><td>0.1667</td><td>0.1333</td><td>0.7000</td><td>1.251</td><td>0.0727</td><td>ND, XRD</td><td>90</td><td>9</td><td>1</td><td>4.12(7)</td><td>16</td></tr><tr><td>ZnAS_15_70</td><td>0.1500</td><td>0.1500</td><td>0.7000</td><td>1.000</td><td>0.0729</td><td>ND, XRD</td><td>88</td><td>10</td><td>2</td><td>4.13(7)</td><td>16</td></tr><tr><td>ZnAS_13_70</td><td>0.1333</td><td>0.1667</td><td>0.7000</td><td>0.800</td><td>0.0733</td><td>ND, XRD</td><td>82</td><td>16</td><td>2</td><td>4.20(7)</td><td>16</td></tr><tr><td>ZnAS_0_100</td><td>0.0000</td><td>0.0000</td><td>1.0000</td><td>...</td><td>0.0662</td><td>ND<sup>c</sup></td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

and a cylindrical vanadium rod of 6.08 mm diameter for normalization purposes. The datasets were processed using the procedure described elsewhere.³⁰ The scattering lengths $b_{Zn} = 5.680(5)$ fm, $b_{Al} = 3.449(5)$ fm, $b_{Si} = 4.1491(10)$ fm, and $b_{O} = 5.803(4)$ fm³¹ were used in the data analysis.

The XRD experiments were performed using either beamline 6-ID-D at the Advanced Photon Source or beamline ID15A at the European Synchrotron Radiation Facility.³² The 6-ID-D experiments used an incident photon energy of 100.233 keV and a Varex 4343CT amorphous silicon flat panel detector, with the sample to detector distance set at 311 mm as found from the diffraction pattern measured for crystalline CeO₂. The ID15A experiment used an incident photon energy of 87.5 keV and a DECTRIS Pilatus3 X CdTe 2M detector, with the sample to detector distance set at 186.3 mm as found from the diffraction pattern measured for crystalline Cr₂O₃. The powdered glass samples were held in cylindrical Kapton polyimide tubes of internal diameter 1.80(1) mm (6-ID-D) or 1.00(1) mm (ID15A) and wall thickness 0.051(6) mm. Diffraction patterns were measured at room temperature for each of the samples in its container, an empty container, and the empty instrument. The data were converted to one-dimensional diffraction patterns using FIT2D³³ (6-ID-D) or an in-house modified version of pyFAI³⁴,³⁵ that also performed the beam polarization correction (ID15A). PDFgetX²⁶ was used to perform the corrections for background scattering, beam attenuation, and Compton scattering. In the case of the 6-ID-D data, it was also used to perform the beam

polarization correction. Neutral atom form-factors were used in the data analysis.³⁷

## IV. RESULTS

### A. Structure of crystalline Zn₂SiO₄

Figures 2 and 3 show the measured total structure factors and the corresponding total pair-distribution functions for crystalline willeminite, respectively. The crystal structure is based on corner-sharing tetrahedral SiO₄ and ZnO₄ units where each of the four NBO atoms in a Si-centered tetrahedron is connected to two ZnO₄ units and is, therefore, threefold coordinated.⁶,²⁴ In consequence, the measured ²⁹Si MAS NMR spectrum of Fig. 4 shows a single sharp peak with a chemical shift $\delta_{iso}^{(29)Si} = -70.9(1)$ ppm corresponding to Q" species with $n = 0$, where $n$ is the number of Si–BO bonds per SiO₄ tetrahedron, as found in previous work.²³ Accordingly, the first three peaks in $D'_{N}(r)$ and $D'_{X}(r)$ were attributed to the Si–O, Zn–O, and O–O correlations, respectively, and were fitted with the Si–O, Zn–O, and O–O coordination numbers set at 4, 4, and 3, respectively. The O–O peak makes a comparatively small contribution toward $D'_{X}(r)$. The next peak at around 3.2 Å has contributions from multiple pair-correlation functions and was fitted accordingly after constraining the coordination numbers to the values found from crystallography.⁶ In $D'_{X}(r)$, the Zn–Zn and Zn–Si correlations are prominent, with peak shapes that extend to lower-$r$ values. The fitted para-

<footnote><sup>a</sup>ND experiments used both GEM and D4c.</footnote>

<footnote><sup>b</sup>XRD experiment used beamline ID15A.</footnote>

<footnote><sup>c</sup>ND data taken from Ref. 17.</footnote>
<figure><img src="image_14.png" /><figcaption>FIG. 2. The $S_N(k)$ and $S_X(k)$ functions for crystalline $Zn_2SiO_4$ measured using ND-GEM, ND-D4c, or XRD.</figcaption></figure>

meters are listed in Table S1. For the $D'_N(r)$ function measured using GEM, there is an excursion in the residual for the region around 2.25 Å that is absent for both $D'_X(r)$ and the $D'_N(r)$ function measured using D4c and is likely to originate from Fourier transform artifacts.

<figure><img src="image_15.png" /><figcaption>FIG. 3. The fitted $D'_N(r)$ and $D'_X(r)$ functions for crystalline $Zn_2SiO_4$ obtained by Fourier transforming the $S_N(k)$ and $S_X(k)$ functions shown in Fig. 2 with $ρ = 0.0799 Å^{-3}$ and a $k_{max}$ value of 31.95 Å$^{-1}$ (ND-GEM), 23.50 Å$^{-1}$ (ND-D4c), or 26.31 Å$^{-1}$ (XRD). In each panel, the black solid circles show the measured function, the black solid curve gives the fitted function, and the other curves show the contributions from the Si-O (blue broken curves), Zn-O (magenta curves), O-O (green broken curves), Zn-Si (cyan curves), and Zn-Zn (red solid curves) correlations. The displaced green solid curve shows the residual for the fitted range of 1.30–3.80 Å with $R_χ = 4.97\%$ (ND-GEM) or $R_χ = 4.71\%$ (XRD) or for the fitted range of 1.01–3.80 Å with $R_χ = 2.43\%$ (ND-D4c).</figcaption></figure>

## B. Aluminum speciation

The fitted $^{27}$Al MAS NMR spectra are shown in Fig. 5, and the fitted parameters are listed in Table S2. The aluminum speciation is summarized in Table I. The results indicate that the majority of aluminum forms four-coordinated species Al(IV). Five-coordinated aluminum Al(V) is also present at every glass composition, along with a small fraction of six-coordinated aluminum Al(VI). The proportion of higher-coordinated species increases with the alumina content along the 50 and 70 mol. % silica tie-lines but changes little along the 60 mol. % silica tie-line.

<figure><img src="image_16.png" /><figcaption>FIG. 4. The measured $^{29}$Si MAS NMR spectrum for crystalline $Zn_2SiO_4$.</figcaption></figure>

## C. Diffraction results

Figures 6 and 7 show the measured $S_N(k)$ and $S_X(k)$ functions for the glasses along the 50 mol. % silica tie-line. For a given composition, there is contrast between the measured functions that originates from the different weighting factors given to the partial structure factors in neutron vs x-ray diffraction experiments [Eq. (1)]. For example, there is a principal peak at $k_2 \approx 2.7$ Å$^{-1}$ in $S_N(k)$ that is absent in $S_X(k)$. The measured $S_N(k)$ functions for the tectosilicate tie-line are shown in Fig. 8, and the total structure factors for the other compositions are shown in Figs. S1–S4. Systematic changes are observed as the glass composition is varied, e.g., the so-called first sharp diffraction peak at $k_1 \approx 1.5$ Å$^{-1}$ and the third peak

at $k_3 \approx 5.2$ Å$^{-1}$ both sharpen with increasing silica content along the tectosilicate tie-line (Fig. 8).

Figures 9–12 show the measured $D'_N(r)$ and $D'_X(r)$ functions for the glasses along the 50 mol. % silica tie-line. The large $k_{max}$ values accessible in the ND work (Table S3) lead to excellent resolution of the features in $D'_N(r)$, although the statistical error associated with the data points at larger $k$-values does contribute some noise. The first peak at $\tilde{r}_{SiO} \approx 1.62$ Å originates from the Si-O bonds in tetrahedral $SiO_4$ units. The peak has a shoulder on its high-$r$ side that is associated with the Al-O bonds in Al-centered polyhedral units. It grows in prominence with the alumina content of
<figure><img src="image_17.png" /><figcaption>FIG. 5. The measured $^{27}$Al MAS NMR spectra (black curves) for several of the ZnAS glasses. In each panel, the orange curve gives the background measured for the empty rotor, and the Czjzek fit to the spectral components is given by the blue curve for Al(IV), the green curve for Al(V), and the magenta curve for Al(VI). The sum of the fitted functions is given by the red curve, which overlays the black curve at most values of $\delta_{MAS}$.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>FIG. 7. The measured $S_X(k)$ functions for the ZnAS glasses with 50 mol. % silica. For clarity of presentation, several of the curves are displaced vertically and the datasets are shown to 25 Å$^{-1}$.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>FIG. 6. The measured $S_N(k)$ functions for the ZnAS glasses with 50 mol. % silica. The vertical error bars are smaller than the curve thickness at most $k$ values. For clarity of presentation, several of the curves are displaced vertically and the datasets are shown to 30 Å$^{-1}$.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>FIG. 8. The measured $S_N(k)$ functions for the ZnAS glasses along the tectosilicate tie-line. The vertical error bars are smaller than the curve thickness at most $k$ values. For clarity of presentation, several of the curves are displaced vertically and most of the datasets are shown to 30 Å$^{-1}$.</figcaption></figure>

the glass and is most apparent in the higher-resolution $D'_N(r)$ functions. The next peak at ≈1.97 Å is asymmetric, having a shoulder on its high-$r$ side, and is attributed to Zn–O correlations. It corresponds to typical Zn–O bond lengths (Table II), and in accordance

with the larger weighting of the Zn–O correlations in the XRD work, it is, for a given glass composition, more prominent in $D'_X(r)$ than in $D'_N(r)$. The peak at ≈2.65 Å will have a contribution from the O–O correlations associated with the tetrahedral $SiO_4$ units, which
<figure><img src="image_21.png" /><figcaption>FIG. 9. The fitted $D'_N(r)$ functions for the lower alumina content ZnAS glasses with 50 mol. % silica. In each panel, the black solid circles show the measured function, the black solid curve gives the fitted function, and the other curves show the contributions from the Si-O (blue broken curve), Al-O (red solid curve), Zn-O (magenta solid curves), and O-O (green broken curve) correlations. The displaced green solid curve shows the residual. The O-O correlations were introduced to constrain the peaks fitted at smaller r-values.</figcaption></figure>

are expected at a distance $\bar{r}_{OO} \approx \sqrt{8/3}\bar{r}_{SiO} \approx 2.65$ Å. It is a well-defined feature in $D'_N(r)$ for all the glass compositions and grows in prominence in $D'_X(r)$ as the silica content of the glass increases. In $D'_X(r)$, there is overlap with a large peak at around 3.2 Å that will have contributions from *inter alia* Zn–Si and Zn–Zn correlations (Sec. IV A).

The real-space functions were fitted with the Si–O coordination number fixed at four and the Al–O coordination number fixed at the value measured in the 27 Al MAS NMR experiments. The asymmetry of the Zn–O peak required its representation by two Gaussian functions. The fitted $D'_N(r)$ and $D'_X(r)$ functions are shown in Figs. 9–12 and S5–S8. The fitted Si–O, Al–O, and Zn–O peak parameters are listed in Tables S4–S7.

It is notable that the position of the first Zn–O peak at 1.97–2.00 Å is typical of four-coordinated zinc (Table II). The high-$r$ shoulder to the first peak in $g_{ZnO}(r)$ leads, however, to an overall Zn–O coordination number that is significantly larger than four, taking a value in the range 4.62–6.10 that is dependent on the glass composition. In an EXAFS experiment on a ZnAS glass at the Zn K-edge, an omission of the high-$r$ shoulder from the data analysis will, therefore, lead to an erroneous interpretation of the results,¹⁵ and the delivery of a Zn–O bond distance typical of tetrahedral $ZnO_4$ units does not necessarily mean that zinc is predominantly four-coordinated.¹³ In the case of ZnAS_25_50 glass, a distribution of $Zn^{2+}$ ions in four, five,

and six coordinated sites has been reported from a recent molecular dynamics simulation, giving $\bar{n}_{Zn}^O = 4.66$ for a cut-off distance of 2.5 Å.⁹

<figure><img src="image_22.png" /><figcaption>FIG. 10. The fitted $D'_N(r)$ functions for the higher alumina content ZnAS glasses with 50 mol. % silica. In each panel, the black solid circles show the measured function, the black solid curve gives the fitted function, and the other curves show the contributions from the Si–O (blue broken curve), Al–O (red solid curve), Zn–O (magenta solid curves), and O–O (green broken curve) correlations. The displaced green solid curve shows the residual. The O–O correlations were introduced to constrain the peaks fitted at smaller r-values.</figcaption></figure>

V. STRUCTURAL MODEL

In the GYZAS model for vitreous materials with the composition $(M_2O)_x(Al_2O_3)_y(SiO_2)_{1-x-y}$ or $(MO)_x(Al_2O_3)_y(SiO_2)_{1-x-y}$, where $0 \le x < 1$, $0 \le y < 1$, and $x + y < 1$, the starting point is a glass network formed by the four-coordinated Si and Al(IV) atoms and all the oxygen atoms.¹⁶ The latter can adopt either a BO or NBO role with O–A coordination numbers of two and one, respectively, where A denotes either a four-coordinated Si or Al(IV) atom. The connectivity of the network, therefore, depends on the relative fractions of these oxygen species. The model considers a simple set of reactions (see Sec. VI) that enable a wide variety of structural parameters to be calculated from knowledge of the glass composition and the value of a single empirical parameter $p$ ($0 \le p \le 1$).¹⁶,⁴⁴ Significantly, this parameter allows for the creation of Al(V) and/or Al(VI) atoms within the $M_2O$ or MO rich regime where $R = x/y \ge 1$. Within the GYZAS model, the monovalent $M^+$ or divalent $M^{2+}$ cations and the higher coordinated Al(V) and Al(VI) species do not contribute toward the glass network. Instead, they bind to the available oxygen atoms within the network structure to adopt a network-modifying and/or charge-compensating role.

For a given system, $p$ is found from the aluminum specification measured in 27 Al MAS NMR experiments for the composition regime where $R \ge 1$. Specifically, $p = 2\langle f_{Al(IV)} \rangle - 1$, where $\langle f_{Al(IV)} \rangle$ is the mean fraction of four-coordinated aluminum atoms found
<figure><img src="image_23.png" /><figcaption>FIG. 11. The fitted $D'_χ(r)$ functions for the lower alumina content ZnAS glasses with 50 mol. % silica. In each panel, the black solid circles show the measured function, the black solid curve gives the fitted function, and the other curves show the contributions from the Si-O (blue broken curve), Al-O (red solid curve), Zn-O (magenta solid curves), O-O (green broken curve), and higher-r (cyan curve) correlations. The displaced green solid curve shows the residual. The O-O and higher-r correlations were introduced to constrain the peaks fitted at smaller r-values.</figcaption></figure>

from experiment. The results show that $\langle f_{Al(IV)} \rangle$ and p decrease linearly with increasing cation field strength $F_M = Z_M/r_M^2$, where $Z_M$ is the formal charge on the M⁺ or M²⁺ ion and $r_M$ is the cation radius (Fig. 13). From other work, the degree of aluminum avoidance Q is also found to decrease linearly as $F_M$ increases, where Q takes a maximum value of unity in the absence of Al-O-Al bonds and a minimum value of zero for a random distribution of Al/Si-O-Al/Si bonds.⁴⁵ Thus, as $F_M$ increases, there are less Al(IV) atoms to contribute toward the glass network and Al-O-Al bonds become more prevalent in a progressive breakdown of Loewenstein's aluminum avoidance rule.⁴⁶ The predictions of the GYZAS model for the composition-dependent fraction of NBO atoms for $R \ge 1$ are in accord with the results found from solid-state NMR experiments.¹⁶

## VI. DISCUSSION

The Si-O bond length shows little dependence on the glass composition across the investigated range of R values [Fig. 14(a)]. Its average $\langle \tilde{r}_{SiO} \rangle = 1.620(4)$ Å is consistent with four-coordinated silicon atoms. In comparison, there is an indication from Figs. 14(b) and 15(a) that the Al-O bond length increases with the Al-O coordination number as the peraluminous regime ($R < 1$) is accessed.

<figure><img src="image_24.png" /><figcaption>FIG. 12. The fitted $D'_χ(r)$ functions for the higher alumina content ZnAS glasses with 50 mol. % silica. In each panel, the black solid circles show the measured function, the black solid curve gives the fitted function, and the other curves show the contributions from the Si-O (blue broken curve), Al-O (red solid curve), Zn-O (magenta solid curves), O-O (green broken curve), and higher-r (cyan curve) correlations. The displaced green solid curve shows the residual. The O-O and higher-r correlations were introduced to constrain the peaks fitted at smaller r-values.</figcaption></figure>

The first peak for the Zn-O nearest-neighbors is broad and asymmetric, which required its representation by two Gaussian functions (Figs. 9–12). For this reason, the weighted mean bond distance

$$ \tilde{r}_{ZnO} = \frac{\int_{r_1}^{r_2} dr \, rg_{ZnO}(r)}{\int_{r_1}^{r_2} dr \, g_{ZnO}(r)} \quad (5) $$

is represented in Fig. 14(c), where $g_{ZnO}(r)$ was obtained by summing the contributions from each of the fitted Gaussian functions and $r_1 \le r \le r_2$ defines the overall extent of these functions. For each glass composition, the $\tilde{r}_{ZnO}$ value found from XRD is on average 1.5% larger than the distance found from ND, which may reflect the increased overlap between the Zn-O and higher-r correlations in XRD (Figs. 11 and 12) as compared to ND (Figs. 9 and 10). In comparison to ND, the oxygen form factor in XRD leads to an O-O peak shape with a broad tail in $D'_χ(r)$, leading to an increased overlap with the Zn-O correlations. In XRD, the increased overlap also originates from the zinc correlations that make a relatively large contribution toward the peak at around 3.15 Å in $D'_χ(r)$ (cf. Fig. 3). All the diffraction results show that $\tilde{r}_{ZnO}$ increases with the Zn-O coordination number as $R \to 1$ from high-R compositions.

According to the GYZAS model, in the $R \to \infty$ limit when the alumina content of the glass is reduced to zero, the Zn²⁺ ions play a solely network-modifying role in which they create Si-NBO connections through a reaction scheme, such as

$$ \mathrm{ZnO} + \mathrm{SiO}_2 \rightarrow \mathrm{Zn}^{2+} + [\mathrm{Si}\Theta_{2/2}\mathrm{O}_2]^{2-}, \quad (6) $$
<table><caption>TABLE II. The Si–O, Al–O, and Zn–O coordination numbers and bond distances for several Zn-containing crystalline systems. The aluminosilicates form zeolite structures.</caption><thead><tr><th>Crystal</th><th>x</th><th>y</th><th>1-x-y</th><th>R</th><th>Polyhedron</th><th>Atom pair</th><th>Distance (Å)</th><th>References</th></tr></thead><tbody><tr><td>ZnO</td><td>1.0000</td><td>0.0000</td><td>0.0000</td><td>...</td><td>ZnO<sub>4</sub></td><td>Zn–O</td><td>1.978(9)</td><td>38</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>SiO<sub>4</sub></td><td>Si–O</td><td>1.62(1)</td><td></td></tr><tr><td>ZnSiO<sub>3</sub></td><td>0.5000</td><td>0.0000</td><td>0.5000</td><td>...</td><td>ZnO<sub>4</sub></td><td>Zn–O</td><td>1.98(6)</td><td>39</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>ZnO<sub>6</sub></td><td>Zn–O</td><td>2.14(15)</td><td></td></tr><tr><td>Zn<sub>2</sub>SiO<sub>4</sub>–I</td><td>0.6667</td><td>0.0000</td><td>0.3333</td><td>...</td><td>SiO<sub>4</sub></td><td>Si–O</td><td>1.588–1.643</td><td>6 and 24</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>ZnO<sub>4</sub></td><td>Zn–O</td><td>1.936–1.993</td><td></td></tr><tr><td>Zn<sub>2</sub>SiO<sub>4</sub>–II</td><td>0.6667</td><td>0.0000</td><td>0.3333</td><td>...</td><td>SiO<sub>4</sub></td><td>Si–O</td><td>1.615</td><td>40</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>ZnO<sub>4</sub></td><td>Zn–O</td><td>1.979(3)</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>SiO<sub>4</sub></td><td>Si–O</td><td>1.65(6)</td><td></td></tr><tr><td>Zn<sub>27.23</sub>Al<sub>55</sub>Si<sub>137</sub>O<sub>384</sub></td><td>0.1420</td><td>0.1434</td><td>0.7145</td><td>0.99</td><td>AlO<sub>4</sub></td><td>Al–O</td><td>1.65(6)</td><td>41</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>ZnO<sub>3</sub></td><td>Zn–O</td><td>2.183–2.227</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>SiO<sub>4</sub></td><td>Si–O</td><td>1.64(6)</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>AlO<sub>4</sub></td><td>Al–O</td><td>1.64(6)</td><td></td></tr><tr><td>Zn<sub>35.5</sub>Al<sub>71</sub>Si<sub>121</sub>O<sub>384</sub></td><td>0.1849</td><td>0.1849</td><td>0.6302</td><td>1</td><td>ZnO<sub>3</sub></td><td>Zn–O</td><td>2.096–2.228</td><td>42</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>ZnO<sub>6</sub></td><td>Zn–O</td><td>2.137–2.771</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>AlO<sub>4</sub></td><td>Al–O</td><td>1.945</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>AlO<sub>6</sub></td><td>Al–O</td><td>1.914</td><td></td></tr><tr><td>ZnAl<sub>2</sub>O<sub>4</sub></td><td>0.5000</td><td>0.5000</td><td>0.0000</td><td>1</td><td>ZnO<sub>4</sub></td><td>Zn–O</td><td>1.945</td><td>43</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>ZnO<sub>6</sub></td><td>Zn–O</td><td>1.914</td><td></td></tr></tbody></table>

<figure><img src="image_25.png" /><figcaption>FIG. 13. Dependence of the parameters ($f_{Al(IV)}$, $p$, and $Q$ on the cation field strength $F_M$ of the $M^+$ or $M^{2+}$ ions in aluminosilicate glasses. For $F_M \ge 0.53 \text{ Å}^{-2}$, the linear dependence is given by ($f_{Al(IV)}$) = -0.032(2)$F_M$ + 1.017(5), $p$ = -0.064(4)$F_M$ + 1.034(9), or $Q$ = -0.104(10)$F_M$ + 1.058(23). The figure is adapted from the works of L. V. D. Gammond, R. E. Youngman, A. Zeidler, B. G. Aitken, and P. S. Salmon, J. Chem. Phys. 156, 064503 (2022). Copyright 2022 Author(s), licensed under a Creative Commons Attribution 4.0 License.¹⁶</figcaption></figure>

where the open symbol on the right-hand side denotes an NBO atom. When alumina is added, ZnO can also react with Al₂O₃ according to a scheme such as

$$ \mathrm{ZnO} + \mathrm{Al}_{2}\mathrm{O}_{3} \rightarrow \mathrm{Zn}^{2+} + 2[\mathrm{Al}\Phi_{4/2}]^{-}, \quad (7) $$

where the negative charge on the network-forming $[Al\Phi_{4/2}]^-$ units is compensated by the positive charge on the $Zn^{2+}$ ions. The observed increase in the Zn–O coordination number and bond distance as $R \to 1$ is, therefore, accompanied by a change in the role of the $Zn^{2+}$ ions from predominantly network-modifying to predominantly charge-compensating.

### A. R dependence of the aluminum coordination environment

In the standard model for aluminosilicate glasses, there is no reaction between alumina and silica on the ZnO-rich side of the phase diagram where all the aluminum is in $[Al\Phi_{4/2}]^-$ units, and the fraction of oxygen atoms that are non-bridging is given by $f_{NBO} = 0$ at $R = 1$.⁴⁷ The ²⁷Al MAS NMR results for ZnAS glasses show, however, that Al(V) and Al(VI) atoms do exist in the composition regime where $R \ge 1$ (Table I). In the GYZAS model for aluminosilicates,¹⁶ these higher coordinated species are generated through a reaction scheme, such as

$$ \mathrm{Al}_{2}\mathrm{O}_{3} + \mathrm{SiO}_{2} \rightarrow [\mathrm{Al}\Phi_{4/2}]^{-} + \mathrm{Al}^{3+} + [\mathrm{Si}\Phi_{2/2}\mathrm{O}_{2}]^{2-}, \quad (8) $$

where the $Al^{3+}$ ion serves the dual purpose of modifying the $SiO_2$ network by the creation of NBO atoms and compensating the charge on the $[Al\Phi_{4/2}]^-$ unit. This modifying/charge-compensating aluminum species represents an Al(V) or Al(VI) atom, is denoted by $Al_{mcc}$, and is not treated as a network former. In the GYZAS model, the relative importance of the reaction schemes represented in Eqs. (6)–(8) is controlled by the parameter $p$ (Sec. V). On the ZnO-rich side of the phase diagram where $R \ge 1$, the fraction of aluminum that forms Al(IV) species is given by $f_{Al(IV)} = (1 + p)/2$. The standard model corresponds to $p = 1$, and $Al_{mcc}$ species are generated when $p < 1$. The value of $p$ is obtained from the mean value of $f_{Al(IV)}$ found from ²⁷Al MAS NMR experiments in the regime where $R \ge 1$ and takes the value $p = 0.82(7)$ for ZnAS glasses¹⁶ (Sec. V). On the peraluminous side of the phase diagram where $R \le 1$, the GYZAS model gives $f_{Al(IV)} = (y + px)/2y$. For this regime, if $p = 1$, there is no reaction between ZnO and $SiO_2$, and all the $Zn^{2+}$ ions play a charge-compensating role.
<figure><img src="image_26.png" /><figcaption>FIG. 14. Dependence of the (a) Si–O, (b) Al–O, and (c) Zn–O bond distances on the ratio *R* for glassy ZnAS. The datasets were obtained from the ND or XRD experiments of the present work. The Zn–O values were calculated using Eq. (5). The vertical lines show representative error bars. The red solid curves show (a) the average Si–O bond distance $\langle r_{SiO} \rangle = 1.620(4)$ Å or (b) and (c) the predictions of the GYZAS model.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>FIG. 15. Dependence of the (a) Al–O and (b) Zn–O coordination numbers on the ratio *R* for glassy ZnAS. The datasets in (a) were obtained from the ²⁷Al MAS NMR experiments listed in Table I or reported in Ref. 9, and those in (b) were obtained from the ND and XRD experiments. The vertical lines show representative error bars. The red solid curves show the predictions of the GYZAS model.</figcaption></figure>

The GYZAS model can be used to interpret the measured com-
position dependence of the aluminum coordination environment.
The mean Al–O coordination number is given by

$$
\tilde{n}_{\text{Al}}^{\text{O}} = f_{\text{Al(IV)}} \tilde{n}_{\text{Al(IV)}}^{\text{O}} + f_{\text{Al(V+)}} \tilde{n}_{\text{Al(V+)}}^{\text{O}}, \quad (9)
$$

where the fraction of aluminum atoms with an Al–O coordination
number of five or greater is given by $f_{\text{Al(V+)}} = 1 - f_{\text{Al(IV)}}$, $\tilde{n}_{\text{Al(IV)}}^{\text{O}} = 4$,

<table><caption>TABLE III. The Al–O and M–O (M = Zn or Mg) coordination numbers and bond dis-
tances for ZnAS vs MgAS⁴⁴ glasses. The ratio of the longest to shortest Al–O or M–O
bond distances is also given.</caption>
  <thead>
    <tr>
      <th rowspan="2">Atom pair α-β</th>
      <th colspan="3">ZnAS</th>
      <th colspan="3">MgAS</th>
    </tr>
    <tr>
      <th>ñ&#773;<sup>β</sup><sub>α</sub></th>
      <th>r&#773;<sub>αβ</sub> (Å)</th>
      <th>Ratio</th>
      <th>ñ&#773;<sup>β</sup><sub>α</sub></th>
      <th>r&#773;<sub>αβ</sub> (Å)</th>
      <th>Ratio</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Al(IV)-O</td>
      <td>4<sup>a</sup></td>
      <td>1.764(5)</td>
      <td>...</td>
      <td>4<sup>a</sup></td>
      <td>1.760(5)</td>
      <td>...</td>
    </tr>
    <tr>
      <td>Al(V)-O</td>
      <td>5<sup>a</sup></td>
      <td>1.855(5)</td>
      <td>1.05</td>
      <td>5<sup>a</sup></td>
      <td>1.827(5)</td>
      <td>1.04</td>
    </tr>
    <tr>
      <td>M<sub>m</sub>-O</td>
      <td>4.36(9)</td>
      <td>2.003(10)</td>
      <td>...</td>
      <td>4.46(9)</td>
      <td>2.024(10)</td>
      <td>...</td>
    </tr>
    <tr>
      <td>M<sub>cc</sub>-O</td>
      <td>5.96(10)</td>
      <td>2.078(10)</td>
      <td>1.04</td>
      <td>5.39(10)</td>
      <td>2.120(10)</td>
      <td>1.05</td>
    </tr>
  </tbody>
</table>

<sup>a</sup>Fixed parameter.

and $5 \le \tilde{n}_{Al(V+)}^O \le 6$. The weighted mean Al–O bond distance is given by

$$
\tilde{r}_{\text{AlO}} = \frac{f_{\text{Al(IV)}} \tilde{n}_{\text{Al(IV)}}^{\text{O}} \tilde{r}_{\text{Al(IV)O}} + f_{\text{Al(V+)}} \tilde{n}_{\text{Al(V+)}}^{\text{O}} \tilde{r}_{\text{Al(V+)O}}}{f_{\text{Al(IV)}} \tilde{n}_{\text{Al(IV)}}^{\text{O}} + f_{\text{Al(V+)}} \tilde{n}_{\text{Al(V+)}}^{\text{O}}}. \quad (10)
$$

The Al(IV)–O bond distance $\tilde{r}_{\text{Al(IV)O}}$ and the Al(V+)-O bond dis-
tance $\tilde{r}_{\text{Al(V+)O}}$ can be estimated from a least squares fit of Eq. (10) to
the measured values shown in Fig. 14(b) for the regime where $R < 1$, subject to the conditions that (i) the same value $p = 0.82$ applies across the entire composition range, (ii) all the higher coordinated aluminum is Al(V) such that $\tilde{n}_{\text{Al(V+)}}^{\text{O}} = \tilde{n}_{\text{Al(V)}}^{\text{O}} = 5$, (iii) the bond dis-
tances are constrained such that Eq. (10) gives the mean value $\langle \tilde{r}_{\text{AlO}} \rangle = 1.774(8)$ Å found from the diffraction experiments for the regime where $R \ge 1$, and (iv) $f_{\text{Al(IV)}}$ is given by the GYZAS model in both composition regimes.

The fitted function is shown in Fig. 14(b), and the fitted
distances are compared to those found for magnesium aluminosil-
icate (MgAS) glasses in Table III. The distances are commensu-
rate with those found from experiment⁴⁸ or bond-valence the-
ory,⁴⁹ which give $\tilde{r}_{\text{Al(IV)O}} = 1.74-1.76$ Å vs $\tilde{r}_{\text{Al(V)O}} = 1.81-1.84$ Å.
Figure 15(a) shows the *R* dependence of $\tilde{n}_{\text{Al}}^{\text{O}}$, calculated from
Eq. (9) using the GYZAS model predictions for $f_{\text{Al(IV)}}$ with $\tilde{n}_{\text{Al(V+)}}^{\text{O}} = \tilde{n}_{\text{Al(V)}}^{\text{O}} = 5$.

B. *R* dependence of the zinc coordination
environment

The GYZAS model can also be used to interpret the measured
composition dependence of the zinc coordination environment. The
mean Zn–O coordination number is given by

$$
\tilde{n}_{Zn}^{O} = f_{Zn_{m}} \tilde{n}_{Zn_{m}}^{O} + f_{Zn_{cc}} \tilde{n}_{Zn_{cc}}^{O}, \quad (11)
$$

where subscripts m and cc denote the network-modifying and
charge-compensating species, respectively. On the ZnO-rich side of
the phase diagram, the fraction of Zn atoms that play a network-
modifying role is given by $f_{Zn_m} = 1 - (p/R)$ and the fraction that
plays a charge-compensating role is given by $f_{Zn_{cc}} = p/R$. In compar-
ison, on the peraluminous side of the phase diagram, $f_{Zn_m} = 1 - p$
and $f_{Zn_{cc}} = p$. In consequence, $\tilde{n}_{Zn}^O$ should be invariant within the
$R \le 1$ regime. The individual Zn–O coordination numbers can be
estimated from a least squares fit of Eq. (11) to the measured values shown in Fig. 15(b) for the regime where $R \ge 1$, subject to the conditions that (i) the same value $p = 0.82$ applies across the entire composition range and (ii) the coordination numbers are constrained such that Eq. (11) gives the mean value $\langle \tilde{n}_{Zn}^O \rangle = 5.67(29)$ found from experiment for the regime where $R \le 1$. The fitted function is shown in Fig. 15(b), and the fitted coordination numbers are listed in Table III.

The weighted mean Zn–O distance is given by

$$ \tilde{r}_{ZnO} = \frac{f_{Zn_m} \tilde{n}_{Zn_m}^O \tilde{r}_{Zn_m O} + f_{Zn_{cc}} \tilde{n}_{Zn_{cc}}^O \tilde{r}_{Zn_{cc} O}}{f_{Zn_m} \tilde{n}_{Zn_m}^O + f_{Zn_{cc}} \tilde{n}_{Zn_{cc}}^O}. \quad (12) $$

The individual Zn–O bond distances can be estimated from a least squares fit of Eq. (12) to the measured values shown in Fig. 14(c) over the entire composition regime, with the coordination numbers $\tilde{n}_{Zn_m}^O$ and $\tilde{n}_{Zn_{cc}}^O$ set at the values found above. The fitted function is shown in Fig. 14(c), and the fitted values are given in Table III. In accordance with the larger $Zn_{cc}$–O coordination number, the $Zn_{cc}$–O bond distance is longer than its $Zn_m$–O counterpart. For comparison, the Zn–O bond distance predicted by bond valence theory⁴⁹ is 1.992(7) Å for $\tilde{n}_{Zn}^O = 4.36(9)$ vs 2.108(6) Å for $\tilde{n}_{Zn}^O = 5.96(10)$.

### C. 50 and 60 mol. % silica tie-lines

Figures 16 and 17 show the composition dependence of the Si–O, Al–O, and Zn–O bond distances along the tie-lines with 50 and 60 mol. % silica, respectively. The Si–O distance does not show a systematic change with the glass composition, and the values for a given tie-line are similar to the mean value $\langle \tilde{r}_{SiO} \rangle = 1.620(4)$ Å obtained for all glass compositions. The measured Al–O and Zn–O distances are in overall accord with those predicted by the GYZAS model.

<figure><img src="image_28.png" /><figcaption>FIG. 16. Dependence of the (a) Si–O, (b) Al–O, and (c) Zn–O bond distances on mol. % of alumina along the tie-line with 50 mol. % silica. The points with vertical error bars were obtained from the ND and XRD experiments. The red solid curves show (a) the mean Si–O bond distance for all glass compositions $\langle \tilde{r}_{SiO} \rangle = 1.620(4)$ Å or (b) and (c) the predictions of the GYZAS model.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>FIG. 17. Dependence of the (a) Si–O, (b) Al–O, and (c) Zn–O bond distances on mol. % of alumina along the tie-line with 60 mol. % silica. The points with vertical error bars were obtained from the ND and XRD experiments. The red solid curves show (a) the mean Si–O bond distance for all glass compositions $\langle \tilde{r}_{SiO} \rangle = 1.620(4)$ Å or (b) and (c) the predictions of the GYZAS model.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>FIG. 18. Dependence of the (a) Al–O and (b) Zn–O coordination numbers on mol. % of alumina along the tie-line with 50 mol. % silica. The datasets were obtained from (a) the $^{27}$Al MAS NMR experiments listed in Table I or reported in Ref. 9 and (b) the ND and XRD experiments. The vertical lines show representative error bars. The red solid curves show the predictions of the GYZAS model.</figcaption></figure>

The corresponding Al–O and Zn–O coordination numbers along the tie-lines with 50 and 60 mol. % silica are shown in Figs. 18 and 19, respectively. Again, the measured data points are in overall accord with the model, which predicts a change in behavior when $R = 1$. This composition corresponds to either 25 mol. % $Al_2O_3$ along the 50 mol. % silica tie-line or to 20 mol. % $Al_2O_3$ along the 60 mol. % silica tie-line. It would be beneficial to extend the results further into the peraluminous regime where glassy materials can be formed by using aerodynamic levitation with laser heating.⁹
<figure><img src="image_31.png" /><figcaption>FIG. 19. Dependence of the (a) Al-O and (b) Zn-O coordination numbers on mol. % of alumina along the tie-line with 60 mol. % silica. The datasets were obtained from (a) the 27Al MAS NMR experiments and (b) the ND and XRD experiments. The vertical lines show representative error bars. The red solid curves show the predictions of the GYZAS model.</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>FIG. 21. Dependence of the (a) Al-O and (b) Zn-O coordination numbers on mol. % of silica along the tectosilicate tie-line where R = 1. The datasets were obtained from (a) the 27Al MAS NMR experiments listed in Table I or reported in Ref. 9 and (b) the ND and XRD experiments. The vertical lines show representative error bars. The red solid curves show the predictions of the GYZAS model.</figcaption></figure>

### D. Tectosilicate tie-line

Figure 20 shows the composition dependence of the Si-O, Al-O, and Zn-O bond distances along the tectosilicate tie-line where R = 1. There is no discernible dependence on the composition, with the $\tilde{r}_{SiO}$ values spread around the mean value $\langle\tilde{r}_{SiO}\rangle = 1.620(4)$ Å for all glass compositions and the $\tilde{r}_{AlO}$ and $\tilde{r}_{ZnO}$ values spread around the predictions of the GYZAS model for the Al-O and Zn-O bond lengths. The composition dependence of the Al-O and Zn-O coordination numbers is shown in Fig. 21. The aluminum atoms are in a predominantly tetrahedral coordination environment across the entire composition range, which indicates that the majority of $Zn^{2+}$ ions are involved in a

charge-compensating role. The associated mean $\langle\tilde{n}_{Al}^{O}\rangle = 4.17(4)$ is above the expectation of $\tilde{n}_{Al}^{O} = 4.09$ from the GYZAS model. The Zn-O coordination number appears to increase with the silica content of the glass, changing from $\tilde{n}_{Zn}^{O} \approx 5.25$ at 50 mol. % silica to $\tilde{n}_{Zn}^{O} \approx 5.9$ at 70 mol. % silica. In comparison, an increase in the Mg-O coordination number with silica content along the tectosilicate tie-line is also indicated from diffraction experiments on MgAS glasses.⁴⁴

### E. Effect of Al speciation uncertainty

Figures 15(a), 18(a), and 21(a) indicate a spread in the Al-O coordination numbers found from different 27Al MAS NMR investigations. For instance, the $\tilde{n}_{Al}^{O}$ values found for a glass with the nominal composition ZnAS_25_50 are 4.17(7)¹⁶ vs 4.25(3)⁹ and the values found for a glass with the nominal composition ZnAS_20_60 are 4.14(7)¹⁶ vs 4.23(3)⁹ corresponding to a change in $\tilde{n}_{Al}^{O}$ of ~2%. Part of this discrepancy may originate from uncertainty in the glass composition and from variation in the procedure used to vitrify the materials. There may also be a contribution that originates from the magnetic field used to collect the NMR datasets and the sophistication of the data analysis procedure.

To assess the effect of a 2% change to $\tilde{n}_{Al}^{O}$ on the fitted Zn-O coordination environment, the $D'_{N}(r)$ function for the ZnAS_24_60 sample was re-analyzed by reducing $\tilde{n}_{Al}^{O}$ from 4.17 to 4.09. The results did not show a substantial change to the asymmetry of the Zn-O nearest-neighbor distribution of distances and led to an ~1% reduction in the overall Zn-O coordination number from 5.40 to 5.34. The spread in the Al-O coordination numbers shown in Figs. 15(a), 18(a), and 21(a) is not, therefore, anticipated to have a substantial effect on the composition-dependent structural role reported for the $Zn^{2+}$ ion.

<figure><img src="image_33.png" /><figcaption>FIG. 20. Dependence of the (a) Si-O, (b) Al-O, and (c) Zn-O bond distances on mol. % of silica along the tectosilicate tie-line where R = 1. The points with vertical error bars were obtained from the ND and XRD experiments. The red solid curves show (a) the mean Si-O bond distance for all glass compositions $\langle\tilde{r}_{SiO}\rangle = 1.620(4)$ Å or (b) and (c) the predictions of the GYZAS model.</figcaption></figure>

### F. Network connectivity: Effect of NBO atoms

The connectivity of the network formed from the four-coordinated Si and Al(IV) species will depend on whether the oxy-
<figure><img src="image_34.png" /><figcaption>FIG. 22. The R dependence of (a) fNBO along the 50 mol. % silica tie-line, (b) fNBO along the 60 mol. % silica tie-line, and (c) the ratio N$_{NBO}$/ (N$_{Zn}$ + N$_{Almcc}$). The green broken vertical line marks the R = 1 composition. The datasets (solid symbols) were obtained from the $^{27}$Al MAS NMR results for fAl(IV) listed in Table I or reported in Ref. 9 using (a) and (b) Eq. (13) or (c) Eq. (14). The red curves show the predictions of the GYZAS model with p = 0.82.</figcaption></figure>

gen atoms connected to these species are bridging or non-bridging. The fraction of NBO atoms can be calculated from the glass composition and the value for $f_{Al(IV)}$ measured by $^{27}$Al MAS NMR using the expression¹⁶

$$f_{\text{NBO}} = 2 - \frac{c_{\text{Si}} z_{\text{Si}}^{\text{O}}}{c_{\text{O}}} - f_{\text{Al(IV)}} \frac{c_{\text{Al}} z_{\text{Al(IV)}}^{\text{O}}}{c_{\text{O}}} \quad (13)$$

where $\tilde{n}_{Si}^{O} = \tilde{n}_{Al(IV)}^{O} = 4$ and the NBO atoms can be associated with the Si and/or Al(IV) atoms. Equation (13) does not make allowance for the possibility of three-coordinated oxygen atoms in tricluster conformations:⁵⁰,⁵¹ All the oxygen atoms are assumed to be one- or two-coordinated to the four-coordinated network-forming cations.

According to the GYZAS model, $f_{NBO} = 2(x + y - 2py)/(2 - x + y)$ on the ZnO-rich side of the phase diagram where $R \ge 1$ or $f_{NBO} = 2(x + y - 2px)/(2 - x + y)$ on the alumina-rich side of the phase diagram where $R \le 1$. Figures 22(a) and 22(b) show that the predictions of this model for the R dependence of $f_{NBO}$ along the 50 and 60 mol. % silica tie-lines are in overall accord with the values calculated from Eq. (13) using the $f_{Al(IV)}$ values taken from $^{27}$Al MAS NMR experiments.

The GYZAS model also gives access to the ratio $N_{NBO}/(N_{Zn} + N_{Almcc})$, where $N_{\alpha}$ is the number of atoms of chemical species $\alpha$. This ratio measures two competing effects: The NBO atoms will break the connectivity of the network formed by the Si and Al(IV) centered tetrahedral units, whereas the high cation field strength $Zn^{2+}$ and Al$_{mcc}$ ions may help to bind together the pieces of the network thus fragmented. In the case of MgAS glasses, the composition dependence of the glass hardness appears to be correlated with this ratio, taking a minimal value when the ratio takes a minimal value.⁴⁴ The model gives $N_{NBO}/(N_{Zn} + N_{Almcc}) = 2(1 + R - 2p)/$

<figure><img src="image_35.png" /><figcaption>FIG. 23. The R dependence of $f_{Zn_m}$, $f_{Zn_{cc}}$, and $N_{NBO}/N_{Zn}$ predicted by the GYZAS model for ZnAS glasses with $p = 0.82$. The green broken vertical line marks the R = 1 composition.</figcaption></figure>

(1 + R - p) for R ≥ 1 compared to $N_{NBO}/(N_{Zn} + N_{Almcc}) = 2$ $[1 + R(1 - 2p)]/[1 + R(1 - p)]$ for R ≤ 1. Figure 22(c) shows that this prediction for the R dependence of the ratio is in overall accord with the values deduced from the expression

$$\frac{N_{\text{NBO}}}{N_{\text{Zn}} + N_{\text{Al}_{\text{mcc}}}} = \frac{f_{\text{NBO}} c_{\text{O}}}{c_{\text{Zn}} + [1 - f_{\text{Al(IV)}}] c_{\text{Al}}} \quad (14)$$

where Eq. (13) is used to find $f_{NBO}$ and the $f_{Al(IV)}$ values are taken from $^{27}$Al MAS NMR experiments.

Figure 23 shows the prediction of the GYZAS model for the R dependence of the fraction of zinc ions that are network modifiers $f_{Zn_m}$, the fraction of those that are charge compensators $f_{Zn_{cc}} = 1 - f_{Zn_m}$, and the ratio $N_{NBO}/N_{Zn}$. According to the model, $f_{Zn_m} = 1 - (p/R)$ when $R \ge 1$ or $f_{Zn_m} = 1 - p$ when $R \le 1$¹⁶ and $N_{NBO}/N_{Zn} = 2(1 + R - 2p)/R$ when $R \ge 1$ or $N_{NBO}/N_{Zn} = 2$ $[1 + R(1 - 2p)]/R$ when $R \le 1$.⁴⁴ As $R \to 1$ from its largest value, $N_{NBO}/N_{Zn}$ decreases and takes its minimum value at $R = 1$, whereas $f_{Zn_{cc}}$ increases and first takes its maximum value at $R = 1$. In the limit of the standard model when $p = 1$, $N_{NBO}/N_{Zn} = 0$ and $f_{Zn_{cc}} = 1$ at $R = 1$, i.e., all the $Zn^{2+}$ ions are charge-compensating and all their nearest-neighbors are BO atoms. In contrast, $N_{NBO}/N_{Zn} \to 2$ in the limit as $R \to \infty$ when all the $Zn^{2+}$ ions would take a network-modifying role. The observed change in the Zn-O coordination number as $R \to 1$ from high-R [Fig. 15(b)] is, therefore, related to the availability of NBO atoms. Overall, there is a greater propensity for the network-modifying $Zn^{2+}$ ions to be connected to NBO atoms and the charge-compensating $Zn^{2+}$ ions to be connected to BO atoms, where the higher charge associated with the NBO atoms favors a more compact coordination environment for the network-modifying species.

### C. $Zn^{2+}$ vs $Mg^{2+}$ ions in aluminosilicate glasses

Diffraction experiments on glassy MgAS materials show that the $Mg^{2+}$ ions also adopt a broad and asymmetric distribution of oxygen nearest-neighbors, with a coordination number that depends on the glass composition.⁴⁴,⁵³ Table III compares the M-O (M = Zn or Mg) coordination numbers and bond distances for the network-modifying and charge-compensating species. These parameters are comparable for the cations in a predominantly network-modifying
<figure><img src="image_36.png" /><figcaption>**FIG. 24.** The nearest-neighbor M–O (M = Zn or Mg) partial pair-distribution function for MAS_25_50 and MAS_20_60 glasses. The functions were obtained by summing the Gaussian peaks fitted to the measured $D'_N(r)$ functions reported in this work (M = Zn) and Ref. 44 (M = Mg). The glass compositions correspond to R = 1 where the majority of M$^{2+}$ ions take a charge-compensating role. The mean $\bar{r}_{ZnO}$ distances are 2.051(20) and 2.046(20) Å for the ZnAS_25_50 and ZnAS_20_60 glasses, respectively, corresponding to $\bar{n}_{Zn}^O$ values of 5.29(4) and 5.62(4), respectively. The mean $\bar{r}_{MgO}$ distance is 2.075(20) Å for both the MgAS_25_50 and MgAS_20_60 glasses, corresponding to $\bar{n}_{Mg}^O$ values of 5.13(4) and 5.30(4), respectively.</figcaption></figure>

<table><caption>**TABLE IV.** Cation field strength $F_M$ for Mg$^{2+}$, Zn$^{2+}$, and Ca$^{2+}$ ions with different coordination numbers (CNs). The ionic radii are taken from the work of Shannon.⁵²</caption><thead><tr><th>Ion</th><th>CN</th><th>r<sub>M</sub> (Å)</th><th>F<sub>M</sub> (Å<sup>-2</sup>)</th></tr></thead><tbody><tr><td rowspan="5">Mg<sup>2+</sup></td><td>4</td><td>0.57</td><td>6.16</td></tr><tr><td>5</td><td>0.66</td><td>4.59</td></tr><tr><td>6</td><td>0.72</td><td>3.86</td></tr><tr><td>8</td><td>0.89</td><td>2.52</td></tr><tr><td>4</td><td>0.60</td><td>5.56</td></tr><tr><td rowspan="5">Zn<sup>2+</sup></td><td>5</td><td>0.68</td><td>4.33</td></tr><tr><td>6</td><td>0.74</td><td>3.65</td></tr><tr><td>8</td><td>0.90</td><td>2.47</td></tr><tr><td>6</td><td>1.00</td><td>2.00</td></tr><tr><td>7</td><td>1.06</td><td>1.78</td></tr><tr><td>Ca<sup>2+</sup></td><td>8</td><td>1.12</td><td>1.59</td></tr></tbody></table>

role. In comparison, the Zn–O coordination number is larger than the corresponding Mg–O value for the cations in a predominantly charge-compensating role, although the associated bond distance $\bar{r}_{Mg_{cc}O}$ is ≈2.5% longer than $\bar{r}_{Zn_{cc}O}$. The latter reflects a different distribution of M–O distances for Zn$^{2+}$ vs Mg$^{2+}$ and a more compact Zn$_{cc}$–O coordination environment (Fig. 24).

An average M–O coordination number of less than five supports the existence of four-coordinated M$^{2+}$ ions. For example, if only four- and five-coordinated species are present, then $\bar{n}_{M}^{O} = 4f_{M(IV)} + 5f_{M(V)}$, where $f_{M(IV)}$ and $f_{M(V)} = 1 - f_{M(IV)}$ denote the fractions of four- and five-coordinated M$^{2+}$ species, respectively. In glassy MgSiO$_3$ and CaMgSi$_2$O$_6$, the measured Mg–O coordination numbers of 4.46(4) and 4.40(4)⁵³ would then imply that 54(4) or 60(4)% of the magnesium is four-coordinated, respectively. There is, however, no evidence in support of these species playing a network-forming role. For example, $^{29}$Si MAS NMR experiments on these materials and glassy CaSiO$_3$ show a similar network connectivity, as expressed by the Q$^n$ speciation.⁵⁴⁻⁵⁹ In addition, the measured entropy of mixing associated with the replacement of

Ca$^{2+}$ by Mg$^{2+}$ in a variety of silicate and aluminosilicate melts is consistent with an ideal mixing hypothesis.⁶⁰,⁶¹ Hence, the results do not indicate any substantial difference between the structural roles played by Ca$^{2+}$, which is a conventional network modifier, and Mg$^{2+}$.

Four-coordinated Zn$^{2+}$ ions are indicated in several of the ZnAS glasses by the observation of Zn–O coordination numbers $\bar{n}_{Zn}^O < 5$. The cation field strength $F_M$ of the Zn$^{2+}$ ion sits in between that of the Ca$^{2+}$ and Mg$^{2+}$ ions (Table IV). A structural role for Zn$^{2+}$ that is markedly different from Mg$^{2+}$ is not, therefore, anticipated, i.e., a network-forming role for four-coordinated zinc is not expected.

## VII. CONCLUSIONS

The structure of ZnAS glasses across a broad range of compositions was investigated by combining neutron and x-ray diffraction with $^{27}$Al MAS NMR spectroscopy. The results for the Al$^{3+}$ coordination environment were interpreted using the GYZAS model for aluminosilicate glasses¹⁶ and give Al(IV)–O and Al(V)–O bond distances consistent with those found from other experiments and the predictions of bond-valence theory (Table III). The coordination number of Zn$^{2+}$ is not four and invariant as reported in other work on zinc containing aluminosilicate glasses,¹⁴ and it is unlikely that any four-coordinated zinc species play a network-forming role (Sec. VI G). Instead, the Zn$^{2+}$ ions play a predominantly network-modifying or charge-compensating role, the proportions of which change with the glass composition. The network-modifying zinc species take a smaller coordination number than their charge-compensating counterparts and are associated with a greater fraction of NBO atoms. The results, therefore, reveal and quantify the structural role of a key element that is often classified as an “intermediate” in glass science (Sec. I).

## SUPPLEMENTARY MATERIAL

In the supplementary material, Table S1 lists the fitted peak parameters, interatomic distances, and coordination numbers for crystalline Zn$_2$SiO$_4$; Table S2 lists the parameters obtained from the Czjzek fits to the $^{27}$Al MAS NMR spectra shown in Fig. 5; Figs S1–S4 show the $S(k)$ functions measured in the neutron and x-ray diffraction experiments on the ZnAS glasses with 60, 65, or 70 mol. % silica; Figs. S5–S8 show the fits to the associated $D'_N(r)$ or $D'_X(r)$ functions; Table S3 lists the $k_{max}$ value used to Fourier transform each $S(k)$ function, the range used to fit the corresponding real-space function, and the associated goodness-of-fit parameter $R_X$; and Tables S4–S7 list the fitted Si–O, Al–O, and Zn–O peak parameters obtained from all the real-space functions measured in the diffraction work on the ZnAS glasses.

## ACKNOWLEDGMENTS

We thank Gabriel Cuello (Grenoble) for help with the D4c experiment. R.M.D.S. was supported by the Royal Society (Grant No. RGF/EA/180060). A.Z. was supported by a Royal Society-EPSRC Dorothy Hodgkin Research Fellowship. H.M. was supported
by Corning, Inc. (Agreement No. CM00002159/SA/01). L.V.D.G. acknowledges the funding and support from the EPSRC Centre for Doctoral Training in Condensed Matter Physics (CDT-CMP), Grant No. EP/L015544/1, and the Science and Technology Facilities Council (STFC) and Diamond Light Source, Ltd. (Reference No. STU0173). E.G.L. was supported by the funding from the European Union's Horizon 2020 Research and Innovation Program under Marie Skłodowska-Curie Grant Agreement No. 847439 and from Corning Inc. (Agreement No. CM00003814). P.S.S. and A.Z. are grateful to Corning Inc. for the award of Gordon S. Fulcher Distinguished Scholarships during which this work was conceived. We acknowledge use of the Inorganic Crystal Structure Database accessed via the Chemical Database Service funded by the Engineering and Physical Sciences Research Council (EPSRC) and hosted by the Royal Society of Chemistry. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

B.G.A., P.S.S., R.E.Y., and A.Z. designed the project. B.G.A. and H.M. prepared the samples. R.M.D.S., L.V.D.G., A.Z., A.C.H., and P.S.S. performed the neutron diffraction experiments and R.M.D.S. and A.Z. analyzed the results. C.J.B. performed the 6-ID-D experiments and R.M.D.S. analyzed the results. E.G.L. and G.B.M.V. performed the ID15A experiments and E.G.L. analyzed the results. R.E.Y. performed the NMR experiments and analyzed the results. L.V.D.G. and P.S.S. devised the structural model and P.S.S. processed the experimental results. P.S.S. wrote the paper with input from all coauthors.

**Rita Mendes Da Silva:** Formal analysis (equal); Investigation (equal); Writing – review & editing (supporting). **Anita Zeidler:** Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (lead); Writing – review & editing (supporting). **Hesameddin Mohammadi:** Formal analysis (supporting); Investigation (supporting); Methodology (supporting); Writing – review & editing (supporting). **Lawrence Vincent Daniel Gammond:** Investigation (supporting); Methodology (supporting); Software (supporting); Writing – review & editing (supporting). **Esther Giron Lange:** Formal analysis (supporting); Investigation (supporting); Software (supporting); Writing – review & editing (supporting). **Randall E. Youngman:** Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (supporting); Resources (supporting); Supervision (supporting); Validation (equal); Visualization (supporting); Writing – review & editing (supporting).

**Bruce Aitken:** Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Resources (supporting); Supervision (supporting); Writing – review & editing (supporting). **Alex C. Hannon:** Investigation (supporting); Software (supporting). **Chris J Benmore:** Investigation (supporting); Writing – review & editing (supporting). **Gavin Vaughan:** Investigation (supporting); Writing – review & editing (supporting). **Philip Stephen Salmon:** Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead).

## DATA AVAILABILITY

The datasets created during this research are openly available from the University of Bath Research Data Archive at https://doi.org/10.15125/BATH-01200.⁶² The neutron diffraction datasets are available from Refs. 63 and 64.

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