2.1 Synthesis

High-purity crystalline ZrP₂O₇ was prepared from ZrOCl₂ and H₃PO₄ (85%), which were mixed in a 2:1 molar ratio in a platinum crucible and heating to 350 °C for 1 h. The resultant powder was washed with distilled water, and heated to 750 °C then 1000 °C for a 12-h period. The high purity of the ZrP₂O₇ sample was confirmed by X-ray and neutron powder diffraction.

The PbO_x(P₂O₅)_1–x glasses (x = 0.52, 0.59, 0.66) were prepared from reagent-grade PbO and (NH₄)₂HPO₄. The glass samples were melted in Pt crucibles for 1 h under air at temperatures varying from 700 to 850 °C depending on composition and quenched by partly immersing the crucible in water. Glass compositions were checked by microprobe (1 mol% uncertainties).

2.2 Solid-state NMR

The solid-state NMR experiments were performed at room temperature on a Bruker DSX 300 spectrometer (7.0 T) with a 4-mm MAS probehead operating at a Larmor frequency of 121.4 MHz for ³¹P. The one-dimensional (1D) ³¹P MAS spectra of the crystalline and glassy samples were recorded at various spinning frequencies (from 3 to 15 kHz) using single-pulse (π/8) acquisition. The recycle delay varied from 80 to 20 s for the crystalline sample and the glasses, respectively, to ensure no saturation.

The two-dimensional (2D) ³¹P through-bond single-quantum-double-quantum (SQ–DQ) MAS NMR correlation spectra were acquired using the refocused INADEQUATE [24] sequence [12] (Fig. 1a). The π/2 pulse duration was 2.3 μs. The delay τ in the excitation and reconversion periods was synchronized with the rotor period and was set to 10 ms for ZrP₂O₇, and 5 ms for the glassy samples. For ZrP₂O₇, the spinning frequency was 12 kHz and 70 t₁ increments, with 32 transients each, were collected using a recycle delay of 20 s. For the PbO_x(P₂O₅)_1–x glasses, 64 t₁ increments, with 32 transients each, were recorded at 14 kHz spinning frequency using a recycle delay of 20 s. For all the samples, a presaturation sequence was applied to ensure equivalent conditions for each transient.

The 2D ³¹P through-space SQ–DQ MAS NMR correlation spectrum of ZrP₂O₇ was acquired at 10 kHz spinning frequency. The POSTC7 recoupling sequence [7] (Fig. 1b) was used to reintroduce the ³¹P–³¹P homonuclear dipolar interaction and to achieve the excitation and reconversion of double quantum coherences. The rf-field strength was ~70 kHz. Short excitation and reconversion periods of 600 μs were used. 80 t₁ increments, with 16 transients each, were collected using a recycle delay of 30 s and a presaturation sequence.

The 2D homonuclear J-resolved MAS NMR spectra were recorded using a z-filtered spin-echo sequence (Fig. 1c) [25–26]. The π/2 pulse duration was 2.3 μs. For the ZrP₂O₇ sample, the spinning frequency was 12 kHz and 64 t₁ increments with 32 transients each were collected using a recycle delay of 20 s. For the PbO_x(P₂O₅)_1–x glasses, 70 t₁ increments, with 32 transients each, were recorded at 14 kHz spinning frequency, with a recycle delay of 20 s. In both cases, a presaturation sequence was applied to ensure equivalent conditions for each transient.

All the two-dimensional pure absorption phase spectra were obtained using a hypercomplex acquisition [27]. To avoid spinning sidebands in the ω₁ dimension, the t₁ time increment was synchronized with the rotor period. The spinning frequency was stabilized to ±10 Hz for all experiments. ³¹P chemical shifts were referenced relative to 85% H₃PO₄ aqueous solution using the high-frequency positive convention. Simulations of the 1D MAS and 2D MAS correlation spectra were performed using the dmfit software [28].

3.1 Space-group selection in MP₂O₇ crystalline compounds

The ³¹P 1D MAS NMR spectra of ZrP₂O₇ obtained at different spinning rates are shown in Fig. 2 (isotropic region only). These spectra exhibit at least 13 partially overlapping ³¹P isotropic resonances, indicating that the asymmetric unit of ZrP₂O₇ contains at least 13 crystallographically different P sites. This allows the exclusion of the possibility of a cubic symmetry with $\mathrm{Pa}\overline{3}$ space group, for which only 11 independent phosphorus sites are expected. It can be noted that the positions and linewidths of these resonances vary to different extents with the spinning frequency. In particular, the single resonance located at –44.8 ppm for a spinning frequency of 10 kHz gives rise to a doublet at lower spinning rate, with a spinning-frequency-dependent splitting. Such unusual line shape effects have first been observed in ³¹P MAS NMR spectra of homonuclear spin pairs with two chemically equivalent spins [29–32]. They are due to the ³¹P–³¹P homonuclear dipolar interaction, which lead to a second-order perturbation term in the average Hamiltonian, inversely proportional to the spinning frequency [29–32]. More recently, similar lineshape behaviours have been reported for P₂O₇ units with two inequivalent P sites having a weak isotropic chemical shift difference, as in the case of TiP₂O₇ [19] and Cd₂P₂O₇ [33].

As well as the number of individual ³¹P sites, the number of P₂O₇ groups in the asymmetric unit can be used for space group assignment. To characterize the number of unique P₂O₇ groups in the ZrP₂O₇ structure, we have used the refocused INADEQUATE experiment, which allows determination of the through-bond P–O–P connectivities in crystalline and disordered phosphates [13]. The 2D ³¹P through-bond SQ–DQ correlation MAS spectrum of ZrP₂O₇, obtained using the refocused INADEQUATE sequence [12], is depicted in Fig. 3. This 2D spectrum clearly exhibits 11 pairs of resolved cross-correlation peaks (A to K) that reflect the through-bond intra-P₂O₇ connectivity. The paired cross-peaks A show significantly broader linewidths and integrated intensities about three times higher than those of the remaining correlations (B to J), suggesting the presence of several overlapping contributions. In contrast, the paired cross-peaks K exhibit strongly reduced intensities, as expected from the overlap and the weak chemical shift difference of the coupled resonances. This 2D refocused INADEQUATE spectrum thus indicates that the room temperature structure of ZrP₂O₇ contains more than 11 P₂O₇ groups with two inequivalent P sites. This makes unlikely the possibility of P2₁3 space group, for which only 11 P₂O₇ groups with two inequivalent P sites are expected and suggests that the most probable symmetry of ZrP₂O₇ is Pbca, which gives rise to 13 P₂O₇ groups with two inequivalent P sites. It should be remarked that, for Pbca symmetry, a single P₂O₇ groups with two crystallographically equivalent P sites related by a centre of inversion is also expected (see Table 1). Such P₂O₇ groups with two magnetically equivalent ³¹P nuclei are not observable in a through-bond correlation spectrum, but they give rise to diagonal auto-correlation peaks in a through-space dipolar correlation spectrum. The 2D through-space SQ–DQ correlation spectrum of ZrP₂O₇ obtained using the POSTC7 sequence [7] is shown in Fig. 4 [34]. In addition to the 11 pairs of intense cross-correlation peaks characteristic of P₂O₇ groups with two inequivalent P sites previously/proved, this spectrum clearly shows a single intense auto-correlation peak along the diagonal (L), arising from a P₂O₇^4– group containing two equivalent P sites. It should be noted that this spectrum, obtained using short excitation and reconversion periods, displays some additional correlation peaks of weaker intensities, due to the presence of weaker longer-range dipolar couplings. These weak-intensity peaks reflect the inter-P₂O₇ spatial proximities, providing additional structural information, but they can damage the spectral resolution in more complex cases [35]. Analysis of the peak intensities in Fig. 4 shows again that the paired cross-peaks A have approximately triple integrated intensities, suggesting the presence of three overlapping cross-correlation peaks corresponding to three P₂O₇^4– groups. Good fits (not shown) of the quantitative 1D MAS and 2D correlation spectra were obtained with 27 distinct ³¹P resonances of approximately equal intensity corresponding to 13 P₂O₇^4– units (A to K) with two inequivalent P sites and one P₂O₇^4– group (L) with two equivalent P sites. This indicates that the room temperature structure of ZrP₂O₇ adopts Pbca space-group symmetry, which requires 13 P₂O₇^4– groups in general positions and one lying on an inversion centre.

As observed for other crystalline phosphates, the weak through-bond ²J(P–P) coupling that drives the coherence transfer in the refocused INADEQUATE experiment is significantly smaller than the line width of the ³¹P resonances and is not resolved in 1D MAS and 2D correlation spectra. This through-bond J coupling can be clearly proved from the 2D J-resolved experiment [25], which has been previously used to measure weak ²J(P–P) couplings in metal phosphine complexes [9,36]. The 2D J-resolved MAS spectrum of ZrP₂O₇, recorded using a z-filtered spin-echo sequence [26], is depicted in Fig. 5. In this 2D spectrum, the characteristic doublets due to the weak ²J(P–P) couplings are clearly resolved in the indirect ω₁ dimension and are correlated to the individual ³¹P resonances in the ω₂ dimension. From the observed splitting, the magnitude of the intra-P₂O₇ ²J(P–P) coupling constants is measured to range between 10 and 14 Hz. As expected, the resonance associated with the P₂O₇ group with two P sites related by a centre of inversion (located at –42.1 ppm in the ω₂ dimension) gives rise to a single peak in the ω₁ dimension, since there is no observable J-coupling for magnetically equivalent spins. It should be mentioned that the magnitude of the coupling constant measured here is slightly smaller than those reported for other pyrophosphates which range between about 16 and 25 Hz [18,19,33,35,37] and that the absolute sign of the ²J(P–P) coupling in P–O–P units is known to be negative [37].

The use of the through-bond SQ–DQ correlation NMR spectra for space-group selection in MP₂O₇ compounds has also been recently illustrated in more complex cases. As an example, the refocused INADEQUATE spectrum obtained for SnP₂O₇ [35] is shown in Fig. 6. This 2D spectrum clearly exhibits a spectacular gain in resolution relative to the 1D MAS spectrum, and shows 49 pairs of distinct cross-correlation peaks (some of them having significantly stronger intensities than others). In this case, this shows that the asymmetric unit contains at least 49 P₂O₇ units with two inequivalent P sites and suggests that the room-temperature structure of SnP₂O₇ is monoclinic, with P2₁ or Pc symmetry [35].

3.2 Through-bond connectivities in PbO_x–P₂O₅ glasses

The ³¹P 1D MAS NMR spectra of the PbO_x(P₂O₅)_1–x glasses (x = 0.52, 0.59, 0.66) are shown in Fig. 7. These MAS NMR spectra exhibit several broad isotropic resonances that can be attributed to the different types of PO₄ tetrahedra forming the glass network, corresponding to the ³¹P isotropic chemical shift range in crystalline lead phosphates (Qⁿ units, with n the number of bridging oxygen atoms) [23]. In agreement with previous work [23,38], the MAS spectrum of the glass with x = 0.52 shows an intense isotropic peak at about –24 ppm, which corresponds to Q² middle-chain groups involved in long phosphate chains or cycles, and a weaker intensity peak at about –9 ppm assigned to Q¹ end-chain groups. As the PbO content increases up to x = 0.65, the intensity of the Q¹ resonance increases, indicating a progressive depolymerisation of the phosphate network with PbO addition. For the glass with x = 0.66, the MAS spectrum exhibits a third isotropic resonance at 1.4 ppm, indicating the presence of Q⁰ units. For each Qⁿ unit, the broadening of the resonance comes from a large distribution of ³¹P chemical shifts that reflect the structural disorder in the glass, such as bond angles, bond-length variations and higher coordination-sphere disorder.

Although the quantitative analysis of these 1D MAS spectra provides a determination of the Qⁿ unit distribution as a function of the glass composition, information about pair connectivities between the Qⁿ units remains highly desirable for a better description of the disordered glassy network. Over the last few years, several homonuclear dipolar recoupling MAS NMR methods have been used to probe these Qⁿ pair connectivities [21–23]. These experiments allow the determination of nearest-neighbour spatial proximities between Qⁿ units in 2D through-space NMR correlation spectra, from which information about chemical connectivities is derived. A more convenient way to determine these Qⁿ connectivities is to use the weak through-bond ²J(P-P) coupling. Through-bond homonuclear correlation NMR spectra have already been obtained in disordered solids [12,39] and we have recently shown that the refocused INADEQUATE experiment applies very efficiently to glassy phosphates [13].

The possibility of directly determining the P–O–P through-bond connectivities between Qⁿ units in disordered phosphate networks is clearly illustrated in Fig. 8, which shows the through-bond SQ–DQ correlation spectra of the PbO_x(P₂O₅)_1–x glasses obtained using the refocused INADEQUATE experiment. These correlation spectra clearly show several broad correlation peaks that reflect the through-bond connectivities between the Qⁿ units. As shown in Fig. 8a, the refocused INADEQUATE spectrum of the glass with x = 0.52 exhibits an intense Q²–Q² auto-correlation peak and Q¹–Q² cross-correlation peaks of weaker intensities, revealing the Q²–Q² and Q²–Q¹ connectivities involved in long phosphate chains. For the glass with x = 0.59, the 2D correlation spectrum shows the intense Q¹–Q² and Q²–Q² correlations expected for phosphate chains of moderate length and an additional Q¹–Q¹ auto-correlation peak. This Q¹–Q¹ correlation peak gives evidence of the through-bond connectivity between two Q¹ end-chain units and is characteristic of P₂O₇ groups. This spectrum thus reveals the presence of a chain-length distribution in the glass network and confirms the results previously obtained from the interpretation of through-space dipolar correlation spectra [23]. It should be noted that, in a dipolar correlation experiment, the auto-correlation characteristic of P₂O₇ groups and the correlations between nearby (but not bonded) Q¹ groups of different chains overlap strongly, making the interpretation of the 2D spectrum more ambiguous. The 2D correlation spectrum of the glass with x = 0.66 is mainly composed of Q¹–Q¹ and Q¹–Q² correlations (Fig. 8c). As expected, the Q⁰ resonance corresponding to isolated [PO₄]^3– groups, for which there is clear evidence in the 1D MAS spectrum, is filtered out of the 2D through-bond correlation spectrum.

A notable feature revealed by these SQ–DQ through-bond correlation spectra is that the auto- and cross-correlation peaks of each Qⁿ unit appear at significantly different frequencies in the single-quantum dimension. For example, the centres of gravity of the broad auto- and cross-correlation peaks of the Q¹ resonance are located at about –8.4 and –9.7 ppm in the SQ dimension of the 2D maps. This was first observed from through-space dipolar correlation spectra [21–23] and suggests that the Qⁿ units linked to different types of PO₄ tetrahedra can be distinguished by their average isotropic chemical shift. As suggested by Witter et al. [22], the Qⁿ species are classified according to their connectivities, Q^n,ij, where the additional superscripts describe the type of the bonded PO₄ groups. Following this notation, the number of additional superscripts depends on n. For example, the Q¹ units forming P₂O₇ groups are labelled Q^1,1 and the Q¹ end-chain groups linked to Q² units are labelled Q^1,2, while a Q² group bonded to two Q¹ units (forming a trimer) is labelled Q^2,11. From the simulation of the 2D refocused INADEQUATE spectra, assuming a Gaussian line shape for each Q^n,ij group, we have determined the ³¹P isotropic chemical shifts and linewidths of the various Q^n,ij units. To reduce the number of fitting parameters, the experimental SQ–DQ correlation spectra were sheared along the ω₁ dimension to obtain symmetric SQ–SQ correlation spectra with two equivalent dimensions [25]. The simulation of the 2D correlation spectrum obtained for the PbO_0.59(P₂O₅)_0.41 glass is shown in Fig. 9a. For each glass composition, the relative concentrations of the Q^n,ij units were obtained from the fit of the quantitative 1D MAS spectrum (Fig. 9b), using the parameters determined from the 2D spectra and an additional intensity constraint, [Q^1,2] = 2[Q^2,11] + [Q^2,21], required by the stoichiometry. The ³¹P isotropic chemical shifts, linewidths and relative intensities of the Q^n,ij groups obtained from these simulations are reported in Table 2. As pointed out previously [22], the phosphate chain-length distribution can be obtained from the Q^n,ij concentrations for glasses with low P₂O₅ content.

As in the case of crystalline samples, the very weak isotropic ²J(P–P) coupling used in the through-bond correlation experiment can be demonstrated using the 2D J-resolved experiment. As shown in Fig. 10a, the 2D J-resolved spectrum of the PbO_0.66(P₂O₅)_0.34 glass allows the clear resolution of characteristic multiplet patterns due to the ²J(P–P) couplings. As expected, the Q¹ and Q² resonances are correlated in the indirect ω₁ dimension to doublet and triplet structures, respectively. A single resonance at zero-frequency is observed for the Q⁰ resonance, since there is no ²J(P–P) coupling. The cross-sections extracted along the indirect ω₁ dimension at the centres of gravity of the various Qⁿ resonances are depicted in Fig. 10b. Clearly, this 2D experiment provides an unambiguous attribution of the various Qⁿ resonances in glasses according to their J-multiplet structures and confirms the previous assignments based on the ³¹P isotropic chemical shift range. Importantly, this 2D spectrum reveals a strong correlation between the distributions of ³¹P isotropic chemical shifts and the distribution of ²J(P–P) coupling constants of the Qⁿ resonances. We observe that, as the ³¹P isotropic chemical shift varies from –6 to –11 ppm across the broad Q¹ resonance, the magnitude of the ²J(P–P) coupling constants determined from the observed splitting increases continuously from 17 to 20.5 Hz. It should be noted that such a strong correlation between isotropic chemical shifts and J-coupling values is not observed for crystalline lead phosphates or for the MP₂O₇ compounds (see Fig. 5). Further experiments, allowing the measurement of the distributions of ²J(P–P) coupling constants for each Q^n,ij units from 3D NMR spectra, are in progress.