Structure of Zn and Na Borophosphate Glasses by X-ray and Neutron Diffraction

1. Introduction

The addition of B₂O₃ to phosphate glasses improves their chemical durability [1] and makes these glasses suitable for a variety of applications. Borophosphate glasses with alkali modifiers are of particular interest due to their promising ionic conductivities and large glass-forming ranges extending into the P₂O₅- or B₂O₃-rich compositional regions [2]. The observation of maxima in ionic conductivity, for example, in the glasses (M₂O)_0.35[(B₂O₃)_x(P₂O₅)_1-x]_0.65 at x = ~0.4, gave rise to the introduction of the term mixed network-former effect [3]. A striking feature of the mixed glassy networks with compositions rich in P₂O₅ is that the boron forms exclusively tetrahedral BO₄ units with the corners mostly linked to phosphate tetrahedra but also to some neighboring BO₄ units [4,5,6,7,8,9]. The higher cationic mobility with increasing x is accompanied by increasing cross-link densities of the borophosphate networks. At the B₂O₃-rich end, the BO₄ fractions decrease, replaced by BO₃ units, to those values known according to the boron anomaly of binary alkali borate glasses [10].

The BO₄ formation in the P₂O₅-rich glasses with mostly B−O−P bridges in the tetrahedral corners expresses the common use of all oxygen added to phosphate networks for disrupting P−O−P bridges [11]. The BPO₄ crystals [12,13] illustrate the mutual benefit for the PO₄ and BO₄ tetrahedra. They have balanced valences of 1.25 and 0.75 vu (valence units) in their four bonds with P−O and B−O bond lengths of ~0.152 and ~0.147 nm, respectively. The few known borophosphate crystals, e.g. Na₃BP₂O₈ [14], Na₅B₂P₃O₁₃ [15], and Zn₃BO₃PO₄ [16] have structures where the phosphate networks are already fully dissolved (no P−O−P bridges). Crystalline analogs for the glassy borophosphate networks are missing in the regions of samples that are rich in P₂O₅.

The present work is aimed at clarifying the structural role of ZnO in the borophosphate networks and comparing that role to the one played by Na₂O in two similar compositions. The glass-forming range of binary ZnO-B₂O₃ glasses is small [17] and ternary glasses with small P₂O₅ contents (< 30 mol%) are difficult to obtain [11,18,19,20]. Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), high-pressure liquid chromatography (HPLC), and ³¹P or ¹¹B MAS NMR have provided detailed information on the structural evolution of the Zn-borophosphate networks whose chemical compositions are given in Figure 1a. The presence of B−O−B bridges found together with P−O−P bridges contradicts the common scheme of the fully depolymerized phosphate networks [21]. This behavior was explained by the stronger acidity of the glass-former B₂O₃ [11], when compared, e.g., with Al₂O₃ in phosphate networks [22]. Most studies on the mixed network-former effect use a series of constant modifier content [4,8,9] as also shown in Figure 1a. Other series have fixed O/P ratios, e.g., for the Zn alumino- and borophosphate glasses [11,22]. The O/P ratios determine the mean number of PO₄ corners in P−O−P bridges provided that all oxygen belongs to at least one PO₄.

For describing the borophosphate networks, the labels ${\mathrm{P}}_{m\mathrm{B}}^n$ and ${\mathrm{B}}_{m\mathrm{P}}^n$ were introduced to describe the PO₄ and BO₄ (BO₃) units with the bridges P−O−P, B−O−B, and P−O−B [4,5,6]. The superscript n is the total number of bridging corners of the P- or B-centered units while the subscript m gives the number of heteroatomic bridges. The corresponding fractions of groups can be widely resolved by ³¹P and ¹¹B MAS NMR [4,5,6,7,8,9] and were useful for developing quantitative descriptions of the compositional dependence of the network structures. These models, however, are not used to analyze the Zn- and Na-centered oxygen polyhedra in the borophosphate glasses, the focus of the present work. Here, the critical parameter will be the number of P−O bonds that do not link to neighboring PO₄-tetrahedra that will ultimately determine the coordination environments of the Zn- and Na-ions. Therefore, besides the ${\mathrm{P}}_{m\mathrm{B}}^n$ and ${\mathrm{B}}_{m\mathrm{P}}^n$, the PO₄ units will be still characterized by the common Qⁿ nomenclature, where the superscript n gives the number of PO₄ corners in P−O−P bridges with possible n = 3, 2, 1, or 0 [21]. The oxygens of binary phosphate glasses are divided into O_B (bridging in P−O−P) and O_NB (non-bridging in other bonds). In detail, the O_Bs of the borophosphate glasses can form P−O−P, P−O−B, and B−O−B bridges where some of them have modifier cations in their vicinity. A complete description of all combinations of nearest neighbors is a challenging task. The knowledge of the binary systems is helpful to start.

In binary (ZnO)_x(P₂O₅)_1-x glasses with 0.33 ≤ x ≤ 0.5, the oxygen coordination number (N_ZnO) of the Zn ions decreases from six to four with increasing ZnO content [23,24,25]. The minimum N_ZnO of four is reached at 50 mol% P₂O₅ [26]. In this compositional range, the value N_ZnO follows the ratio O_NB/Zn = 2/x which indicates real Zn−O−P bridges [23]. The ratio O_NB/Zn of the binary system is given on the left axis of Figure 1. For glasses with x > 0.5, increasing fractions of O_NBs must share two Zn neighbors. The P−O_NB bonds of the Qⁿ with n = 3, 2, 1, and 0 show decreasing bond valences with 2.0, 1.5, 1.33, and 1.25 vu (valence unit) [21]. Thus, the electron charges on the O_NBs increase, to be balanced by the Zn-ions. The Q¹ and Q⁰ groups supply sufficient charge to their O_NBs to be shared by two Zn²⁺ that still form ZnO₄. For a given P−O_NB in a Qⁿ, the bond valence is not strictly fixed. The P−O_NB bond distances show variations according to the demands of their local environments. For example, the bond valence P−O_NB of the Q³ is a little less than 2.0 vu if this O_NB coordinates a Zn [24]. For x > 0.5, the O_NBs shared by two Zn cause some elongated Zn−O bonds if compared with those in Zn−O−P bridges. This effect broadens the peak of Zn−O distances. Also, the Zn−O coordination can exceed the number four as found for the binary glasses [27,28]. In the phosphate-rich compositions (x < 0.5), a broadening of the Zn−O peaks is expected, as well, because of longer bonds associated with the ZnO₅ or ZnO₆ that account for the increasing N_ZnO > 4 [23,24,25,28].

This work will mainly focus on the variations of the Zn−O distance peaks while the P and B environments and the borophosphate networks were characterized in a preceding work [11]. In addition to the glasses along a line from Zn(PO₃)₂ to BPO₄ with fixed 50 mol% P₂O₅, two series with fixed O/P ratios are chosen for the diffraction study. An earlier measured sample of a binary Zn borate glass is adopted for discussing the change in the ZnO_m units for a glass being free of P₂O₅. Two additional samples contain Na₂O instead of ZnO to investigate the different effects of the Na⁺ and Zn²⁺ cations on details of the P−O bond lengths.

2. Materials and Methods

2.1. Samples

The zinc borophosphate glasses were prepared as described elsewhere [11]. The raw materials ZnO, H₃BO₃, and H₃PO₄ (85%) were mixed to obtain glasses with the nominal compositions as given in Fig. 1b and Table S1 (Supplementary material). The samples are labeled zbp01 and so on according to their numbers given in Fig. 1b. Two Na borophosphate glasses with labels nbp08 and nbp13 were prepared using Na₂CO₃ as a raw material. The mixtures were calcined in platinum crucibles for 16h at 350°C. The duration of melting was two hours at temperatures in the range of 1000-1225°C. The melts were quenched in preheated carbon molds. The clear glasses were annealed for one hour at temperatures 10°C below the glass transition temperature. The chemical analyses of the Zn borophosphate glasses of the preceding study [11] gave a loss of P₂O₅ content from 0 to 6 mol% with uncertainties of ~2.5 mol%. Here, it was decided to start the data analyses with the batch compositions. The mass densities were measured using the Archimedes method. Two samples (zbp04, zbp11) exceed the range of homogeneous glasses that was reported in [20].

2.2. X-ray Diffraction

The X-ray diffraction (XRD) experiments were performed at the synchrotron (storage ring PETRA III at DESY Photon Science Hamburg/Germany). The hard photons at the beamline P02.1 have fixed radiation energies of ~60 keV. The exact wavelength of the incident beam (0.02080 nm) and the sample-detector distance (249.9 mm) were calibrated with the diffraction pattern from CeO₂ powder. The beam size was 0.5 × 0.5 mm². Thus, the beam is narrower than the silica capillaries (diameter 1 mm and wall thickness ~10 µm) that contain the powdered sample material. The beam stop between the sample and detector was fixed on a Kapton foil. The image-plate detector (Perkin Elmer 1621) used in these experiments is sensitive to photons of radiation energies > 20 keV. The samples were irradiated five times for one second with a full duration of the measurement equal to one minute per sample. The two-dimensional scattering images were merged to functions of the scattering angle 2θ. Further details on the instrument and first data analysis are described elsewhere [29]. The scattering intensities were corrected for container scattering, background, and absorption. The final intensities I_corr(Q) were normalized to the structure-independent scattering which makes use of the chemical compositions of the samples and the tabulated atomic data of coherent and Compton scattering I_compt(Q) [30,31]. The final X-ray structure factors S_X(Q) are given by

$$S_X\left(Q\right)=\left[I_{\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}\left(Q\right)\bullet N-<f^2\left(Q\right)>-{ I}_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{t}}\left(Q\right)\right]/{<f\left(Q\right)>}^2$$

(1)

where <…> means the average of the sample composition and f(Q) is the coherent atomic scattering amplitude. The normalization factor N allows S_X(Q) to oscillate around unity. Smoothly changing corrections improve the behavior in the upper end of the Q-range. The scattering data of the sample zbp14 were obtained in an earlier laboratory experiment using Ag K_α radiation. A recent work [17] improved the knowledge of the range of binary Zn borate glasses from 54 to 70 mol% ZnO. Glasses of smaller ZnO content show the separation of a B₂O₃-rich phase during melting. The Raman spectrum of the clear part of the glass with a 50 mol% batch is identical to that of the 54 mol% glass [17]. Hence, 54 mol% ZnO is also used for analyzing the data of the sample zbp14 instead of its batch composition of 50 mol%.

2.2. Neutron Diffraction

The neutron diffraction experiments were performed at the GEM instrument of the neutron spallation source ISIS of the Rutherford Appleton Laboratory (Chilton/UK). Measurements were made for six of the 15 samples (zbp05, zbp07, zbp09, zbp11, zbp13, nbp13). The powdered sample material was loaded into thin-walled vanadium cylinders (diameter: 10.33 mm for all samples). The cylinder wall is a vanadium foil only 0.025 mm thick. The duration of data acquisition was at least 5 hours per sample. A vanadium rod was used to determine the incident energy spectrum that is needed for the data normalization in the time-of-flight regime. The data were corrected using standard procedures for container and background scattering, attenuation, multiple scattering, and inelasticity effects [32]. Since natural boron with 20% of the strongly absorbing isotope ¹⁰B was used a strong wavelength-dependent neutron absorption occurs. The corrections proved to be reliable even for up to 8% of boron atoms in sample zbp11. The differential scattering cross-sections of the detector groups 2, 3, 4, and 5 (scattering angles 14°–109°) are normalized to the mean scattering that is calculated from the sample compositions and tabulated neutron scattering lengths. Finally, the neutron structure factors S_N(Q) were obtained in analogy to Equation 1.

3. Results

The corrected and normalized X-ray structure factors of the borophosphate glasses are shown in Figure S1. The S_X(Q) data of the samples zbp04 and zbp11, which are close to the border of glass formation [20], show small Bragg reflections of tiny crystalline fractions. Statistical noise is no issue in the measurements using image plates. The neutron diffraction experiments of six samples cover large Q-ranges which bears the advantage of an excellent real-space resolution. The neutron diffraction results are shown in Figure 2 by the interference functions which are weighted by the factor Q. The experimental data are compared with model curves, which are composed of damped sinusoidal functions. These oscillating functions in the scattering intensities are the pendant to Gaussian peaks in the real-space correlation functions T(r). The model curves are calculated by the parameters given in Table S2 as obtained from the subsequently described Gaussian fitting. The T(r) functions are Fourier transforms of the experimental S(Q) data with

$$T\left(r\right)=4\pi r{\rho }_0+\frac{2}{\pi } {\int }_0^{Q_{\mathrm{m}\mathrm{a}\mathrm{x}}}Q\left[S\left(Q\right)-1\right]M\left(Q\right)\sin \left(Qr\right)dQ$$

(2)

The number densities of atoms, ρ₀, are calculated from the mass densities and glass compositions given in Table S1. The T(r) functions are calculated with Q_max = 183 nm^-1 (X-rays), 400 nm^-1 (neutrons), and M(Q) = 1. A damping M(Q) according to Lorch with Q_max = 200 nm^-1 (X-rays) and 500 nm^-1 (neutrons) was used for a second series of T(r) functions. The Gaussian fitting procedures of the first-neighbor peaks were applied to both series of T(r) functions where the effects of truncation at Q_max, M(Q) damping, and the Q-dependence of the partial weighting factors in the case of X-rays are taken into account [33,34]. Good fits for the first-neighbor peaks were obtained for all X-ray T(r) functions whereas the fits of the Zn−O (Na−O) peaks in the neutron T(r) functions were not as good for some cases. Several comparisons of the model T(r) functions with the experimental T(r) functions are exemplified in Figure 3 and Figure 4, Figures S2, S3, and S4. The resulting peak parameters are listed in Table S2.

The combination of X-ray and neutron diffraction does allow the separation of the B−O and P−O bonds due to the different changes in scattering contrast. Nevertheless, N_BO = 4 was fixed in this analysis, consistent with previous ¹¹B MAS NMR studies that showed that BO₄ units were dominant in the structures of the full compositional range of the investigated borophosphate glasses [6,11,19,20]. In diffraction experiments, the limit of detection for the presence of any BO₃ fractions is of poorer certainty (±10 %). The bond length of 0.147 nm for the BO₄ is taken from related crystals [12,13,14,15] and is used together with a reasonable peak width to fit the diffraction data.

For the binary ZnO-P₂O₅ glasses (zbp01, zbp05), the P−O peak is based on two bond lengths, P−O_NB and P−O_B, which differ by ~0.010 nm [24,27]. These fractions are directly determined from the P−O peaks in the T(r) of zbp05 from neutron diffraction (Figure 3). The bond fractions are also calculated from the O/P ratio that corresponds to the average n of the Qⁿ distribution [21]. Here, the corresponding relation is applied to the ternary glasses, as well, assuming that the P−O bonds in the P−O−B bridges are only insignificantly longer than those in the P−O−Zn bridges. Only small changes in the bond fractions were needed to achieve excellent fits for the P−O peaks of all samples. However, the use of the O/P ratio could not be accurate for glasses with B−O−B bridges because some additional P−O−P bridges must also form [11]. The observed P−O bonds of the Na borophosphate glasses show slightly different behavior. Both deviations are discussed in Chapter 4.3.

Finally, the assumed P−O distances give a satisfactory approximation of the P−O peaks for all samples. Two samples have an N_PO value of 3.6 which differs from the expected 4.0 by more than the common uncertainty. That can be due to a slightly changed composition for sample zbp11 because also its N_ZnO appears quite large. The situation is unclear for zbp06. In the case of all other samples, the N_PO values are quite reasonable which gives support to the use of the batch compositions for these analyses. The O−O peaks at 0.25 nm belong to the edges of the BO₄ and PO₄ units. The numbers of the tetrahedral edges were calculated from the fractions of the BO₄ and PO₄ units according to the batch compositions (Table S1). The calculation of the N_OO value of the Zn borate glass zbp14 takes into account the fractions of the BO₄ and BO₃ units according to N_BO = 3.3 which equals the result from ¹¹B MAS NMR [17]. The successful fits of the huge O−O peaks in the case of the neutron T(r) functions support the choice of this approach. The edge length of the BO₄ tetrahedron was fixed to 0.241 nm as taken from a crystal [14], and that of the PO₄ close to 0.252 nm was adjusted a little for each case.

The scattering weight of the Zn−O partial correlation is larger for X-rays than for neutrons. Therefore, T(r) fitting in the range of the Zn−O distances was forced to the X-ray correlation functions independent of the neutron data. The use of high-energy XRD has several advantages, including low absorption, and thus little demand for precise sample positioning. On the other hand, the real-space resolution of the neutron data is so good, that termination effects are nearly vanishing. Oscillations caused by termination at Q_max in Equation 2 are visible only for the narrow B−O and P−O peaks, but not for the others (cf. Figure 3). The positions and shapes of the obtained Zn−O peaks are reproduced in the neutron data. The full peak heights are not reached for the samples zbp11 and zbp13 (Figure S3). The Zn−O partial of zbp11 has a small scattering weight for neutrons (only 5%) and large corrections for the highly absorbing boron content were needed. Note, that the fits to the T(r) functions obtained with Lorch damping gave equivalently good results. Figure S4 shows the fits of the sodium borophosphate glass nbp13. The Na−O distances overlap with the O−O peaks. The X-ray data show a good fit for the broad Na−O peak with four oxygen neighbors at distances centered at 0.238 nm (Table S2). The neutron T(r) function shows some unphysical features at ~0.20 nm.

The goal of the present work is to understand how the glass composition affects the Zn−O environment. At first glance, the results are disappointing in that interesting changes are not observed. The Zn−O coordination numbers shown in Figure S5 are almost constant ~4.4 with a slight increase toward smaller ZnO contents. The values N_ZnO of zbp06 and zbp11 are considered outliers. Note, that these are also the samples with the small values N_PO = 3.6. Commonly, the bond lengths increase with N_ZnO and the mean distances can be used as a criterion for the N_ZnO values. The ZnO₄, ZnO₅, and ZnO₆ units have mean bond lengths of 0.194, 0.205, and 0.209 nm, respectively, as found in related crystal structures [35,36,37]. The Zn−O distances in the glasses have been reported with 0.194 nm for ZnO₄ [26] and 0.209 nm for ZnO₆ units [24]. In the present work, the Zn−O distances vary from 0.196 to 0.199 nm with changes only a little outside the uncertainty interval (cf. Figure 5), consistent with the obtained coordination numbers that were found to be a little larger than four. Careful inspection of the bond lengths of the series with constant O/P = 3.25 (Figure 5b) identifies the shortest bonds for sample zbp09. This sample belongs also to the series of constant 50 mol% P₂O₅ (Figure 5a) where systematic distance changes were not observed. The Zn borate glass (zbp14) has an N_ZnO value of 4.3 and the largest detected Zn−O bond length of all samples at 0.200 nm (cf. Table S2). The Gaussian fit of this sample was repeated using the batch composition of 50 mol% ZnO instead of the 54 mol% taken from [17]. The observed N_ZnOs do not change which is explained by a compensation of the compositional Zn decrease and O increase in the calculation of the Zn−O weighting factors. In the case of using 50 mol% ZnO, however, an N_BO of only 2.9 was obtained.

The Zn−O peaks in the total X-ray T(r) functions (Figure 4) do not show significant changes. A further way to compare is by considering the model peaks, here presented by the radial distribution functions. These Zn−O model peaks were calculated with the parameters obtained from Gaussian fitting and these peaks are compared with the bond lengths in the related crystals. This approach was recently used for binary phosphate glasses [25], where it was shown that the termination effects of the Fourier transformation (broadening and oscillations) and the influence of the changed scattering weights as the ZnO content changes are widely eliminated. The full widths at half maximum (fwhm) of these model peaks are shown in Figure 6. Again, a minimum is found for sample zbp09 in the series in Figure 6b whereas the values in Figure 6a do not show any clear trend. The Zn−O model peaks of all samples are shown for the three series of constant P₂O₅ content or constant O/P ratio (cf. Figure 7). For better comparability, the peaks of the glasses are given with identical heights. The peaks of the ZnO₄, ZnO₅, and ZnO₆ units from the crystals show significant differences in the bond lengths. For all three series, the peaks of the glasses are close to that of the ZnO₄ units known from the β-ZnP₂O₆ crystal [35]. The ZnO₄ polyhedron of the β-ZnP₂O₆ [35] has a fifth oxygen nearby. Hence, the small contributions at ~0.230 nm found for all samples can be interpreted as real distances. Significant differences exist at ~0.215 nm. The peaks of the glasses with a constant 50 mol% P₂O₅ content shown in Figure 7a have small numbers of such distances and change very little. The samples outside the line of 50 mol% (cf. Figure 1) have significantly more Zn−O bonds at ~0.215 nm as becomes visible in Figure 7b and 7c. The differences appear very pronounced for the samples shown in Figure 7c. The samples zbp12, zbp13, and zbp14 have visibly more distances at ~0.215 nm than zbp04, due to bond lengths that belong to fractions of ZnO₅ or ZnO₆ units or shared O_NBs. This behavior is also found for zbp05, zbp06, zbp07, and zbp11 in Figure 7b. Among them, zbp11 is the only sample with a P₂O₅ content >50 mol% (cf. Figure 1b). According to the large uncertainties of the measured coordination numbers, the behavior shown by the bond lengths is a better basis for discussing the Zn−O environments in the Zn borophosphate glasses. To support this statement, the fractions of the long bonds are calculated with N_long/(N_short+N_long) and given in Figure S6. The values N_short and N_long are the numbers of oxygen neighbors at 0.194 and ~0.212 nm as given in Table S2. Similar to the fwhm in Figure 6, the N_long fractions for the series with constant 50 mol% P₂O₅ (Figure S6a) do not show systematic changes whereas the minimum of long bonds in the series with the O/P ratio of 3.25 is found for sample zbp09 (Figure S6b).

When compared with the silicate and borate glasses the ratio of O_NBs per Na is large for phosphate glasses (O_NB/Na = 2 for the NaPO₃ glass). A comparably narrow Na−O peak with N_NaO = 4.2 was found for this glass [38] whereas broader peaks exist in silicate glasses with smaller values of O_NB/Na [39]. The Na borophosphate samples nbp08 and nbp13 have O_NB/Na ratios less than two and, thus show the transition to the Na−O environments in sodium borate glasses. Na−O coordination numbers of 4.5 and 4.0 with mean distances of 0.238 nm were determined (Table S2). The distributions of the Na−O distances of the three glasses (nbp08, nbp13, and NaPO₃ glass [38]) are similar to each other. The Na−O peaks of the related crystals [14,15] show a little larger distances for the five- and sixfold coordinated Na⁺ cations (cf. Figure S7).

4. Discussion

4.1. Fully Tetrahedral Networks and the Ratio O_NB/Zn

The Zn borophosphate glasses have the potential to form continuous disordered networks of corner-connected tetrahedra with all oxygen atoms being two-fold coordinated. The Zn metaphosphate glass (50 mol% P₂O₅) has been considered a continuous tetrahedral network for a long time now [40], which is manifested in its properties [41]. This classification is not entirely accurate because the Zn−O coordination number is slightly larger than four, which is also reflected in the corresponding bond lengths (Figure S4 and Figure 5). The ZnO₄ units of the β-Zn(PO₃)₂ crystal [35] show a fifth Zn−O bond of 0.28 nm length. Similarly, a few longer distances exist for the investigated glasses. Nevertheless, the metaphosphate glass zbp01 and the borophosphate glasses of 50 mol% P₂O₅ (zbp02, zbp09, zbp03, and zbp04) show the most narrow Zn−O peaks together with the smallest distance contributions at ~0.212 nm (Figure 7a and Figure S6), evidence that a great majority of Zn ions are in tetrahedral units that have the four corners in Zn−O−P linkages.

The Zn−O peaks of the samples having less than 50 mol% P₂O₅ show increased contributions at ~0.212 nm that indicate O_NBs shared by two Zn. A significant increase in the corresponding N_ZnOs is not detected. Two samples (zbp10, zbp11) of the series with the fixed O/P ratio of 3.25 have more than 50 mol% P₂O₅. Sample zbp11 shows significantly increased values of N_ZnO, r_ZnO, and peak width (fwhm). In this case, the ratio O_NB/Zn is larger than four, and some larger units than ZnO₄ are formed. Similar to the binary ZnO-P₂O₅ system [23,24,42], the borophosphate networks behave in such a way that avoids PO₄ units (Q³, Q²) with terminal P=O double bonds. The possible second bond partner of this oxygen is Zn but not B for reasons of bond valences. This is in contrast to what has been found for the Zn aluminophosphate glasses, where the Al³⁺ cations form AlO₅ and AlO₆ units for the P₂O₅-rich and ZnO-poor compositions [22]. This structural flexibility of Al allows the glass-forming range to reach the binary Al₂O₃-P₂O₅ border. However, similar to the BPO₄, the range of the AlPO₄ composition is excluded for its strong crystallization tendency.

On the side of the binary B₂O₃-P₂O₅ system, BPO₄ crystals [12,13] are known but disordered networks of PO₄ and BO₄ units are not formed. The structure of BPO₄ consists of ${\mathrm{P}}_{4\mathrm{B}}^4$ and ${\mathrm{B}}_{4\mathrm{P}}^4$ units, each connected via their four corners by P−O−B bridges. Figure 8a shows the bond valences in the BPO₄ crystals formed by these units. The tetrahedral network in the Zn(PO₃)₂ metaphosphate glass consists of ${\mathrm{P}}_{0\mathrm{B}}^2$ and ZnO₄ units (Figure 8b). If one connects the Zn(PO₃)₂ and the BPO₄ compositions (50 mol% P₂O₅) in Figure 1, their mixture could create networks of ZnO₄, BO₄, and PO₄ units whose corners are connected exclusively by twofold coordinated oxygens. That behavior gets support from the detected narrow Zn−O distance peaks (Figure 7a). However, the question arises as to how the structures made of Zn(PO₃)₂ and BPO₄ with mixed ${\mathrm{P}}_{0\mathrm{B}}^2$ and ${\mathrm{P}}_{4\mathrm{B}}^4$ groups can be constructed, whereby the isolated ZnO₄ and BO₄ units must be provided with the necessary bond valences. Starting from the side of the ZnO-rich glasses, the problem is solved using a structural speciation reaction

$${\mathrm{P}}_{0\mathrm{B}}^2+{\mathrm{P}}_{4\mathrm{B}}^4\leftrightarrow 2{\mathrm{P}}_{2\mathrm{B}}^3$$

(3)

where the oxygens of the ${\mathrm{P}}_{2\mathrm{B}}^3$ (a Q¹ unit) are shared with one ZnO₄, one PO₄, and two BO₄ units as shown in Figure 8c. The Q¹ groups terminate the phosphate chains. Most ZnO₄ corners interact with the remaining Q² groups while the BO₄ tetrahedra connect the Q¹ and Q⁰ groups. Neither the ZnO₄ nor the BO₄ could exist in isolated sites alone with only Q¹ neighbors (with ${\mathrm{P}}_{0\mathrm{B}}^1$ or ${\mathrm{P}}_{3\mathrm{B}}^4$ respectively). The ZnO₄ would have to share O_NBs and the BO₄ would not get sufficient bond valence. Approaching the composition of sample zbp04, nearly all Q² have changed to Q¹ groups. A high ordering of the ZnO₄ and BO₄ is required that both groups get the needed bond valences. Fortunately, a further solution exists for the bond valences, which stabilizes the disordered borophosphate networks, whereby some of the oxygens that, for example, would form P−O−B bonds instead are incorporated into B−O−B bonds, necessitating the concomitant formation of new P−O−P bond to produce a weak polymerization of the phosphate network [11]. This rearrangement is described by

$${\mathrm{P}}_{4\mathrm{B}}^4+{\mathrm{B}}_{4\mathrm{P}}^4\leftrightarrow {\mathrm{P}}_{3\mathrm{B}}^4+{\mathrm{B}}_{3\mathrm{P}}^4$$

(4)

Figure 8d illustrates an arrangement of a ${\mathrm{P}}_{3\mathrm{B}}^4$ with a ${\mathrm{B}}_{3\mathrm{P}}^4$ unit. ¹¹B MAS NMR has determined the fractions of the ${\mathrm{B}}_{3\mathrm{P}}^4$ besides the ${\mathrm{B}}_{4\mathrm{P}}^4$ units [11]. Hence, the O/P ratio is no longer exactly related to the Qⁿ distribution. Four of the Zn borophosphate glasses used in [11] have ~50 mol% P₂O₅. The glass with the highest B₂O₃ fraction (18.5 mol%) was found with the highest ${\mathrm{B}}_{3\mathrm{P}}^4$ fraction (88%). The other samples had ~35% ${\mathrm{B}}_{3\mathrm{P}}^4$ besides the ${\mathrm{B}}_{4\mathrm{P}}^4$ units. Reactions according to Equation 3 take place in glasses of high Q² fractions (high ZnO content) whereas reactions according to Equation 4 dominate when the Q² units are already in the minority (equal amounts of ZnO and B₂O₃). The fraction of oxygens that are available for coordinating the Zn²⁺ cations is preserved when the fraction of ${\mathrm{B}}_{3\mathrm{P}}^4$ units changes. Equation 4 does not change the numbers of P−O and B−O bonds as illustrated in Figure S8. That allows us to calculate the accurate O_NB/Zn without knowing the accurate ${\mathrm{B}}_{3\mathrm{P}}^4$ fraction and this ratio O_NB/Zn largely determines the Zn−O environments.

and ${\mathrm{B}}_{4\mathrm{P}}^4$ units, (d) Zn borophosphate glass with ${\mathrm{P}}_{3\mathrm{B}}^4$ and ${\mathrm{B}}_{3\mathrm{P}}^4$ units. The numbers indicate the bond valences given in valence units (vu). Bond valences of 1.0 represent P−O−P or B−O−B bridges. The values of bond valences are not repeated for equivalent bonds.

Now it is discussed how one can divide the oxygen fractions to coordinate the Zn and B. Simply knowing the sample composition of the ternary phosphate glasses is not sufficient for that. The available amount of oxygens is derived by subtracting the number of P−O−P bonds per PO₄ and that is calculated from the total O/P ratio. In analogy to the structural behavior of the Zn phosphate glasses (cf. Introduction), all oxygens will find two neighbors with decreasing P₂O₅ content (P, B, Zn) before threefold coordinated oxygen sites occur. Sophisticated considerations have to take into account the different properties of the two sorts of cations besides the P⁵⁺ such as charge balance, field strength, preference of definite oxygen polyhedra, or threefold coordinated oxygen sites.

A general model (model 1) takes into account the different requirements for charge compensation of the Zn²⁺ and B³⁺ cations. It is assumed, that the two cationic species act independently of each other and are linked with the different Qⁿ by equal probability which is reasonable for a simple approach. The corresponding values O_NB/Zn and O_B/B are obtained with

$${\mathrm{O}}_{\mathrm{N}\mathrm{B}}/\mathrm{Z}\mathrm{n}=4(c_{\mathrm{O}}-2 c_{\mathrm{P}})/(2c_{\mathrm{Z}\mathrm{n}}+3c_{\mathrm{B}})$$

(5)

$${\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{O}}_{\mathrm{B}}/\mathrm{B}=6(c_{\mathrm{O}}-2 c_{\mathrm{P}})/({2c}_{\mathrm{Z}\mathrm{n}}+{3c}_{\mathrm{B}})$$

(6)

where the c_i are the concentrations of the four sorts of atoms. This approach produces O_B/B ratios that are too high (> 4) for all samples as shown in Figure 9 where the ratios are considered for the series with constant P₂O₅ contents of 50 mol% (a) and constant O/P ratios of 3.25 (b). The boron cannot meet this coordination behavior. In other words, the Zn−O environments and BO₄ units cannot form independently of each other. Preferences for special Qⁿ neighbors as shown in Figure 8c,d must be effective. In the range of the glasses studied, the situation is quite simple because ¹¹B MAS NMR detected only BO₄ (no BO₃) [11]. When N_BO is fixed to the number four for BO₄ units, a well-defined fraction of oxygens is used as bridging ones by the borons. Then, the oxygens formed as non-bridging in the PO₄ units are used for the coordination of the zinc (model 2) with a ratio

$${\mathrm{O}}_{\mathrm{N}\mathrm{B}}/\mathrm{Z}\mathrm{n}=\left[2\left(c_{\mathrm{O}}-2 c_{\mathrm{P}}\right)-N_{\mathrm{B}\mathrm{O}}{ c}_{\mathrm{B}}\right]/c_{\mathrm{Z}\mathrm{n}}$$

(7)

For glasses with P₂O₅ contents of 50 mol%, model 2 predicts that O_NB/Zn = 4. This value is exactly what is necessary for isolated ZnO₄ units and a fully tetrahedral network (filled squares in Figure 9a). Differently, the fixed O/P ratios of 3.25 produce a continuous increase of O_NB/Zn with increasing B₂O₃ content (cf. Figure 9b). For completeness, the ratios O_NB/Zn according to model 2 are calculated for the samples zbp12 and zbp13 with 3.10 and 3.27, respectively.

The ratio O_NB/Zn becomes smaller than four for glasses with P₂O₅ contents less than 50 mol%. Then, two ZnO₄ units must share some of their O_NBs. The obtained ratios O_NB/Zn are still larger than three, which means a few connected ZnO₄ units, but not any interconnected ZnO₄ substructures. If one looks at the binary ZnO-B₂O₃ glasses [17] that are obtained with 54 to 70 mol% ZnO, the ratios O_NB/Zn reach only 1.5 to 1.9 (Table S3). That means for the ZnO₄ units existing in these glasses each O_NB is shared by at least two Zn and extended substructures of interconnected ZnO₄ exist. Octahedral Zn−O units were proposed for these glasses [17]. However, EXAFS and X-ray diffraction suggest that ZnO₄ units are the dominant moiety [43]. The N_ZnO value of 4.3 for our Zn borate glass is similar to those of the borophosphate glasses. The mean bond length of 0.200 nm is the largest among those of the other glasses (cf. Fig. 7c). The Zn−O distances of zbp14 show large variations due to the massive need for shared O_NBs. Highly distorted ZnO₅ polyhedra co-exist beside the ZnO₄.

Fig. 9b shows strongly increasing ratios O_NB/Zn > 4 in the direction of increasing B₂O₃ contents. Thus, a significant increase in N_ZnO is forced. According to the Zn−O distances (Figure 5b and Figure 7b), the N_ZnO of sample zbp11 must be increased but it is still expected to be below five. Otherwise, in the case of N_ZnO < O_NB/Zn, some terminal P=O double bonds must occur. According to the other limitations of sample zbp11 (N_PO = 3.6), its P₂O₅ content should be a little less than the nominal value. The formation of homogeneous glasses reaches the limit for this sample as reported for such compositions [20].

Model 1 was introduced assuming equal preferences of B and Zn for the oxygens of the different Qⁿ. That means the B and Zn would form their environments independently of each other which is not possible with the limit N_BO ≤ 4. For the ZnO-Al₂O₃-P₂O₅ glasses, the Al−O coordination number can increase up to six and the changes of N_AlO according to model 1 are possible in a large concentration range. The fractions of AlO₄, AlO₅, and AlO₆ units were obtained by ²⁷Al MAS NMR, and N_AlO values were calculated [22]. One of the glasses is a compositional analog to that of sample zbp11. That Al−O coordination number was found to be 5.2 which is close to 5.0 as resulting from model 1 (Figure 9b). The structural analysis of Na₂O-Al₂O₃-P₂O₅ glasses has shown that all oxygen is used for the breakage of the P−O−P bridges [44]. The compositional dependence of N_AlO was found to follow other rules than simply a continuous increase with the O_NB fractions. Abrupt changes from N_AlO = 4 to 6 were found [44] which indicates the greater stability of the AlO₄ and AlO₆ polyhedra if compared with the AlO₅ [45]. The Na⁺ coordinating the oxygens in Al−O−P bridges is essential for this behavior. Certainly, special preferences with the different Qⁿ groups exist.

In this work, the different preferences for the oxygens of the Q², Q¹, and Q⁰ units with the Zn and B polyhedra are due to the restrictions of the B to BO₄ units (model 2). The different field strengths of Zn²⁺ and B³⁺ are not essential in this context. The maximum limit N_BO = 4 made the model considerations comparably simple for the borophosphate glasses of this study. As long as the value N_BO = 4 is less than the ratio O_B/B of model 1, the ratio O_NB/Zn can be calculated and it determines the Zn−O environments. The success of model 2 became obvious in the predicted behavior of the Zn−O distances with the narrow peaks along the line of 50 mol% P₂O₅.

4.2. The Stabilization of the BO₄ Units and the Boron Anomaly

BO₄ tetrahedra and planar BO₃ triangles are the units in the crystalline forms of B₂O₃ [46,47]. The BO₄ unit is the variant of the densest packing and it is formed provided its bond valencies can be balanced. In the corresponding high-pressure B₂O₃ crystal [46], the charge compensation is realized with threefold-linked oxygens. Usually, glasses are only formed when there is no or little threefold connected oxygen in the network. Other mechanisms cause also the required depletion of electron density from the B−O bonds in the BO₄ unit which then results in four bonds with the necessary valencies of ~0.75 vu. The occurrence of BO₄ tetrahedra in binary borate glasses was identified as the origin of non-continuous property changes [10] which is widely known as the boron anomaly.

For the borophosphate glasses, the BPO₄ crystals [12,13] show the mutual benefit for the B and P atoms with a deficit and excess valence electron density in the B−O−P bridges of the tetrahedral networks (cf. Figure 8a). This type of valence transfer is effective throughout the Zn borophosphate glasses studied whereby the BO₄ units do not form B−O−Zn bridges. The typical PO₄ – Zn interactions are shown in Figure 10a,b which were discussed above. The interaction of the Zn with the oxygen sites in P−O−B bridges is rather improbable. Each Zn−O bond of a ZnO₄ needs a bond valence of ~0.50 vu which value cannot be shared with these oxygens. Similarly, the oxygen corner of a ZnO₄ unit cannot be that oxygen between two BO₃ units or a pair of BO₃ and BO₄ (analogously to Figure 10g). These circumstances suggest a relation to the lack of glass formation in the B₂O₃-rich and P₂O₅-poor regions of the Zn borophosphate system. There is one exception, the oxygen sites in B−O−B between BO₄ pairs can coordinate a Zn (cf. Figure 10d) as found in several Zn borate crystals [48,49,50,51]. However, this feature is not sufficient to stabilize any glasses poor in P₂O₅ but it can occur in the glasses of moderate P₂O₅ content until not quite 50 mol%.

Binary Zn borate glasses are obtained in a small range rich in ZnO [17] where already a significant fraction of O_NBs in BO₃-triangles exists (O_NB/Zn ≥ 1.5). Two Zn²⁺ cations share each O_NB (Figure 10c) which means the ZnO₄ or ZnO₅ use three such O_NB corners at minimum. Our diffraction results of the Zn borate glass (zbp14) suggest a fraction of ZnO₅ units besides the ZnO₄. The ZnO₅ have bonds of unequal lengths whose two more distant corners can coordinate the oxygens in any B−O−B bridge. The corner of a ZnO₄ can coordinate only the oxygen in a bridge between two BO₄ units (cf. Figure 10d).

Similar to the ZnO₄ units, the Na⁺ cations have total coordination numbers close to four (Table S2). The cation oxygen distance is larger for Na⁺ and the width (fwhm) of the Na−O peak (Figure S6) is ~0.042 nm, much more than the ~0.017 nm of the Zn−O peak (Figure 6). These parameters express the large flexibility of the Na⁺ cations to form distorted oxygen environments. Figure 10e,h show the interaction of the Na⁺ with the O_NBs of the P or B atoms which is similar to the Zn−O bonds in Figure 10a,b,c. Here, the Na−O bonds are marked with bond valences of ~0.25 vu as belonging to a NaO₄ tetrahedron. This value can vary according to the distortions of the NaO_m polyhedra including the variations in m. The Na−O bonds are dominantly ionic but it is better not to mix the bond valences and electronic charges in the schematic presentations. The weak Na−O interaction allows the Na⁺ to approach the bridging oxygens in the P−O−B and B−O−B bridges (cf. Figure 10f,g). The corresponding oxygens are still quasi-twofold linked. The third partner Na⁺ forms a flexible bond that maintains sufficient flexibility to the disordered network as needed for glass formation.

It was emphasized that the BO₄ units in the Zn borophosphate glasses with P₂O₅ contents ≥50 mol% are charge-balanced by PO₄ units (Figure 8). The Zn²⁺ cations can approach oxygens in B−O−B bridges only for glasses of P₂O₅ content <50 mol% and then contribute also to the BO₄ stabilization. Of course, the BO₄ fractions in the binary Zn borate glasses [17] are charge-balanced by the Zn²⁺ cations only. What about the Na borophosphate glasses? One can compare with the known crystal structures. The Na₂B₈O₁₃ crystal free of phosphate [52] shows two mechanisms for BO₄ stabilization through Na⁺. The lengths of the B−O bonds suggest that the surplus negative charge of the BO₄ is not only balanced by the Na⁺ coordinating the BO₄ corners but it is also transferred to the neighboring BO₃ triangles. The bond lengths in the BO₃ units are strengthened in B−O−B bridges to the BO₄ (~0.134 nm) whereas they are elongated in bridges to other BO₃ (~0.138 nm). Thus, the Na⁺ cations act also across the BO₃ triangles as neighbors of the BO₄. It is to be presumed that there is no serious difference between the depletion effects of electron density from the bonds in the BO₄ in the direction of the PO₄ units or the Zn²⁺ and Na⁺ cations.

4.3. Different Effects of Zn and Na on the P−O Bond Lengths

The lengths of the P−O bonds in the glasses zbp13 and nbp13 of equivalent compositions with an O/P ratio of 3.5 reveal the different effects of the Zn²⁺ and Na⁺ cations. Binary phosphate glasses of the same O/P ratio (pyrophosphates with O_NB/O_B = 6:1) show usually two different lengths of P−O bonds, the P−O_NB and P−O_B bonds with a frequency ratio of 3:1 [21,27,53]. The neutron diffraction results of zbp13 and nbp13 also show two different types of P−O bonds (cf. Figures S3, S4). Their P−O model peaks composed of two Gaussians are compared in Figure 11 with that of a phosphate glass (ZnPbP₂O₇ [53]) of the same O/P ratio. The frequency numbers of the two P−O bonds are obtained with 2.8 and 1.0 for zbp13 and 2.5 and 1.3 for nbp13 (cf. Table S2). For sample zbp13, the ratio is close to 3:1, and the P−O peak agrees with that of the ZnPbP₂O₇ glass. The sample nbp13 has a significantly larger fraction of P−O bonds with lengths of ~0.160 nm. An effect that could increase this P−O fraction is the formation of B−O−B bridges between two BO₄ according to Equation 4 which is accompanied by additional P−O−P bridges. A borophosphate glass of composition close to that of zbp13 has 27.7% boron in ${\mathrm{B}}_{3\mathrm{P}}^4$ units [11]. According to the glass composition of zbp13 and excluding B−O−B bridges, the P−O bonds can be divided into 25% in P−O−P bridges, 30% in P−O−B bridges, and 45% in P−O_NB. 27.7% of the B in ${\mathrm{B}}_{3\mathrm{P}}^4$ units means an increase of the bonds in P−O−P bridges from 25% to 27%. Hence, the corresponding increase in the number of the longer P−O_B bonds is insignificant (<0.1).

The Na borophosphate glass nbp13 should be almost free of B−O−B bridges as it was reported for a similar glass (sample x = 0.125 in [6]). The structures of the related Na₃BP₂O₈ [14] and Na₅B₂P₃O₁₃ [15] crystals help to understand the larger fraction of the longer P−O bonds although the crystal’s compositions differ somewhat from that of nbp13 (cf. Figure 1). The Na borophosphate crystals have isolated PO₄ units (Q⁰). From the point of view of binary phosphates [21], a single P−O distance should occur. However, two distances become obvious. Half of the oxygens of the PO₄ units participate in P−O−B bridges and these oxygens have a Na⁺ cation in their close vicinity as illustrated in Figure 10f. These Na⁺ stabilize the BO₄ but also reduce the bond valence in the adjacent PO₄ (elongation of the P−O bond). The other two PO₄ corners coordinate only Na⁺ cations as shown in Figure 10e and the corresponding short P−O bonds carry the surplus bond valence taken over from the others. The difference in both P−O bond strengths in these crystals is a little smaller than that in the zbp13 and ZnPbP₂O₇ glasses, the latter with bond valences of 1.33 and 1.0 vu (cf. Figure 11). For the glass nbp13, the changes in bond lengths appear less pronounced than in the crystals. Again, 25% of the P−O bonds are in P−O−P bridges, 30% in P−O−B bridges, and 45% in P−O_NB. To achieve the right ratio of the short and long P−O bonds of sample nbp13 (2.5:1.3), the fraction of the P−O−B bridges is split into two parts, those with a Na⁺ close nearby and those free of any Na⁺ neighbor. Then, 30% of the P−O bonds in the P−O−B bridges are elongated indicating the effect of a Na⁺ cation. The other 70% of P−O bonds in P−O−B bridges are not affected by any Na⁺ cations and have lengths similar to those of typical P−O_NB bonds. This difference to zbp13 means that the BO₄ units in the glass nbp13 undergo charge compensation equally by Na⁺ cations and PO₄ tetrahedra. The ZnO₄ units in zbp13 are less contributing because their corners do not participate in P−O−B bridges.

Two species of P−O−B bridges have been suggested for nbp13 that seem to be distinguishable easily. One is coordinated to a Na⁺ cation, and the other is not. On the other hand, a clear separation of the P−O−B bridges into those with and without a Na⁺ neighbor might be questionable due to the large width of the Na−O distance peak. Both P−O peak components overlay with each other. The analyses of the O 1s spectra (XPS) did not distinguish two different types of P−O−B bridges in the Na and Zn borophosphate glasses [6,18]. Nevertheless, the effect of the Na⁺ on the P−O−B is real and it is not effective for Zn²⁺. Another approach supports the fact that only part of the P−O−B bridges of nbp13 can have Na⁺ neighbors. The total Na−O coordination number is calculated assuming all oxygens in the P−O_NB bonds or P−O−B bridges with three or one Na⁺ neighbors as shown in Figure 10e,f, respectively. Then for nbp13, a value N_NaO of ~6.0 is obtained which noticeably exceeds the value (4.0) obtained from diffraction. Accordingly, only part of the P−O−B can have a Na⁺ neighbor (30% as estimated for nbp13). Also, the O_NBs shown in Figure 10e can have only 2.3 Na⁺ neighbors on average instead of three. These conditions mean that only a third of the Na⁺ can coordinate the oxygen in a P−O−B bridge. All other oxygens in the Na−O bonds belong to the P−O_NB bonds. Here, only the behavior of a single sample is discussed. The corresponding relations will strongly change with the glass compositions.

The weak forces of the Na⁺ are not sufficient to take profit from the maximum capabilities of the modifier cation’s coordination. The Na−O distance peaks in Figure S7 show that the values N_NaO of the glasses are smaller than those of the related crystals [14,15], accompanied by smaller bond lengths. Similarly, the number and bond valences of the P−O_NB bonds in zbp13 (cf. Figure 10b) would allow the Zn²⁺ to form ZnO₆ octahedra, which does not occur. The strong bonds in the PO₄ and BO₄ units together with the comparably high cross-link density of the borophosphate networks prevent the modifier cations from forming compact oxygen polyhedra.

The relation between the network structure and the modifier environments was also used to interpret the mixed network-former effect. The average number of O_Bs per glass-forming unit, BO, calculated for the yNa₂O-xB₂O₃-(1-x)P₂O₅ glasses characterizes the stiffness of the network [4,8]. This value’s behavior correlates well with the T_g values. A larger BO means an increasing network stiffness, that is accompanied by more disordered modifier environments, here the NaO_m polyhedra. In addition, the ratio O_NB/Na decreases (Equation 7). These changes explain the reduced activation energies for ionic transport when the B₂O₃ content increases while the Na₂O content is constant [4,8]. The average number of bridging corners per glass-forming unit, BC_GFU, is a more plausible value with BC_GFU = 2 BO [45]. For the borophosphate glasses, it is calculated with

$${BC}_{\mathrm{G}\mathrm{F}\mathrm{U}}=2\left(4c_{\mathrm{P}}+N_{\mathrm{B}\mathrm{O}}{ c}_{\mathrm{B}}-c_{\mathrm{O}}\right)/\left(c_{\mathrm{P}}+c_{\mathrm{B}}\right)$$

(8)

The BC_GFU value is two for the ${\mathrm{P}}_{0\mathrm{B}}^2$ chain units in the NaPO₃ glass. It increases for sample nbp13 to 2.6. Maximum values of ≥3 are reached for larger B₂O₃ content till the potential of the PO₄ units to stabilize the BO₄ is exhausted and BO₃ triangles occur. The Na−O distances of three glass compositions are shown in Figure S7. A significant change in the Na−O peak is not observed. The small scattering power of Na if compared with Zn and the overlap with the O−O distances at 0.25 nm impede an accurate distance analysis.

Previous diffraction work on Na₂O-B₂O₃-P₂O₅ glasses [54,55] did not reach that large Q_max which is needed to resolve different P−O bonds. The structural analysis was made by the Reverse Monte Carlo (RMC) method which was aimed at the elucidation of the mixed network former effect. A main point was the description of the medium-range order which includes the migration pathways for the Na⁺ cations. The analysis of the Na−O environments in the model configurations gave total N_NaO values of ~4.5 with very broad distributions of the distinct Na sites ranging from two- to eightfold coordination. The two distances of 0.152 and 0.156 nm given in [55] for the P−O_NB and P−O_B bonds are simply calculated from the RMC configurations but are not resolved in the measuring results and thus cannot be compared with our data.

4.4. The Evolution of the Properties of the Zn Borophosphate Glasses

The figures with the mass densities ρ of the ZnO-B₂O₃-P₂O₅ glasses in [20] show a continuous increase with fixed ZnO and increasing B₂O₃ contents. Glass transition temperatures T_g show similar trends while the expansion coefficients α change in opposite directions. The values of ρ and T_g in [11] show similar trends though the comparisons are made along constant O/P ratios. It needs to be remembered that the Zn phosphate glasses have been classified as showing anomalous behavior [40]. Minima of mass density at 50 mol% ZnO [23,40,56] or T_g values [11,27,56] at ~60 mol% ZnO are characteristic of the binary Zn phosphate glasses. Below, the mass densities that were published for the full range of glass formation in the ZnO-B₂O₃-P₂O₅ system are discussed [20]. Packing densities are better suited for comparisons whereby the influence of atomic size and mass is widely eliminated. Such comparisons were made for the ZnO-P₂O₅ glasses recently [25] by using the ionic radii from [57].

A packing density is the filled volume fraction assuming the atoms as spheres of known ionic radii. Since the BO₄ tetrahedra have small O−O distances there is some overlap of the oxygen spheres with the ionic radius of 0.135 nm, to a lesser extent also for the PO₄ tetrahedra. A correction was made for this overlap. The packing densities of the Zn borophosphate glasses obtained from the mass densities given in [20] are shown in Figure 12 as numbers close to the sample positions in the concentration triangle. The absolute minimum at 50 mol% ZnO is found with 46.4% packing density. This behavior was attributed to being caused by the network of corner-connected PO₄ and ZnO₄ tetrahedra with all oxygens in bridges (Figure 8b), a network that fills the space quite inefficiently [23,27].

Above, it was shown that the tetrahedral character of the network does not change when B₂O₃ replaces the ZnO while 50 mol% P₂O₅ is fixed. A plateau of ~51% packing density is reached with 10% B₂O₃ (Figure 12). This increase is due to the exchange of the rather open ZnO₄ unit for the more compact BO₄ unit. There exists a further subtle increase of the packing density up to ~52.5% in the direction of decreasing P₂O₅ contents. This fact is interpreted with the change from P−O−Zn bridges (Figure 10a) to the first O_NBs shared by two Zn (Figure 10b) and the exchange of PO₄ for BO₄ units. When finally only isolated PO₄ units exist then also BO₃ units with O_NBs shared by two Zn are formed (Figure 10c) and the packing densities are still increasing. The (ZnO)_x(B₂O₃)_1-x glasses with 0.54 ≤ x ≤ 0.67 [17] with few BO₄ connected with BO₃ have packing efficiencies of 55% to 53.5% where the O_NBs of the BO₃ are shared by two Zn. For the reachable glass compositions, the BO₃ units of the Zn borate glasses have one or two O_NBs.

5. Conclusions

The atomic structures of the Zn and Na borophosphate glasses were investigated by diffraction methods. Neutron diffraction was successfully made on glasses with up to 8 atom% boron, which includes the highly absorbing ¹⁰B isotope in natural abundance. X-ray diffraction by high-energy photons with the image-plate technique was crucial for determining the Zn−O distances, while neutron diffraction at a spallation source offered a large measuring range to achieve excellent spatial resolution to determine details of the P−O bond lengths.

The Zn−O coordination numbers were found to be a little larger than four and did not change significantly when changing the glass compositions. What is striking, however, the glasses along a line connecting the BPO₄ and Zn(PO₃)₂ compositions (50 mol% P₂O₅) showed the narrowest peaks of Zn−O distances. This indicates the formation of tetrahedral networks of PO₄, BO₄, and ZnO₄ with mostly isolated ZnO₄ units and no B−O−Zn bridges. The calculated amount of the O_NBs that is available for the Zn−O coordination supports this interpretation. For smaller P₂O₅ contents, the Zn share O_NBs which leads to distances of ~0.212 nm and thus, a broadening of the Zn−O peaks. The one sample of a P₂O₅ content larger than 50 mol% shows a subtle increase of N_ZnO that is accompanied by a broadened Zn−O peak, as well. The two investigated Na borophosphate glasses have Na−O distances similar to those of a NaPO₃ glass with coordination numbers of 4 to 4.5 while NaO₅ and NaO₆ polyhedra exist in the related crystals with a little larger Na−O distances. The first-neighbor distances of the B−O, P−O, and O−O pairs in the real-space correlations confirm that only BO₄ units co-exist with the PO₄ in the borophosphate networks.

As common, two peaks of P−O bonds are visible for the binary phosphate glasses. They are assigned to the short P−O_NB and the longer P−O_B bonds. This behavior also exists for the ZnO-B₂O₃-P₂O₅ glasses whereby, however, the first peak component includes the ordinary P−O_NB bonds together with the bridging bonds of the P−O−B linkages, according to their similar lengths. Though some B−O−B bridges exist, the concomitant increase in the fraction of the longer P−O_B bonds is small. On the other hand, significantly larger fractions of the long P−O_B bonds are found for the Na₂O-B₂O₃-P₂O₅ glasses. Some Na⁺ cations coordinate oxygens in a part of the P−O−B bridges which elongates the corresponding P−O bonds. Thus, BO₄ units formed in the Zn borophosphate glasses are charge-balanced by mainly PO₄ units while the charge balance of the BO₄ in the Na borophosphate glasses is realized by the neighboring PO₄ and the Na⁺ cations equally.

The property changes of the ZnO-B₂O₃-P₂O₅ glasses seem to be complex. However, the changes with the B₂O₃ additions interfere with the known anomalies of the ZnO-P₂O₅ glasses that have a minimum packing density at 50 mol% and a minimum glass transition temperature at ~40 mol% P₂O₅.