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While it is usually straightforward to obtain one- and two-dimensional ³¹P MAS NMR spectra of polycrystalline inorganic phosphates, extraction of physically meaningful parameters from such spectra is considerably less straightforward, owing to the NMR properties of the 100% naturally abundant spin-1/2 nucleus ³¹P under MAS conditions. Recently developed new pulse sequences, designed for quantitative investigations of homonuclear coupled spin systems under MAS conditions, in conjunction with suitable numerical methods for data analysis offer new possibilities also for in-depth characterisation of polycrystalline inorganic phosphates. Some examples of applications of such new NMR experiments to ortho- and pyro-phosphates of known single-crystal X-ray structure will be given.

Cd₃(PO₄)₂

Cd₃(PO₄)₂ crystallises in space group P2₁/c with six crystallographically independent P-sites in the asymmetric unit, giving rise to six resolved ³¹P resonances. Application of a so-called single quantum - double quantum 2D correlation ³¹P MAS experiment allows unique assignment of these six ³¹P resonances to the corresponding six crystallographic P-sites from qualitative inspection of the connectivity pattern as is shown in Fig. 3.8-8. Double quantum coherence is created via homonuclear dipolar coupling, the excitation efficiency is proportional to the dipolar coupling strength and is thus a sensitive measure of internuclear distances. Comparison with known distances from X-ray diffraction yields the unique assignment from NMR on a polycrystalline powder - which would otherwise require NMR experiments on oriented single crystals.
 

Fig. 3.8-8: 31P MAS single quantum - double quantum correlation experiment (in collaboration with M. Feike and I. Schnell/Mainz) on Cd3(PO4)2. On the diagonal "self-correlation" peaks occur; the numbers assigned to the individual 31P resonances A-F in the single-quantum projection refer to the numbering scheme of the X-ray crystal structure.

Double quantum MAS NMR experiments offer the advantage of also displaying "self-connectivities", but suffer the disadvantage that quantification in terms of internuclear distances is problematic for coupled spin systems of more than two spins. Broadbanded rf-driven ³¹P MAS spin diffusion experiments, in turn, do not directly reveal "self-connectivities" but may be quantitatively analysed also for larger spin systems. Figure 3.8-9 shows such a 2D ³¹P MAS spin diffusion experiment with a mixing time of 12 ms for Cd₃(PO₄)₂; Figure 3.8-10 (top) shows the intensities of all diagonal and off-diagonal peaks as a function of mixing time. The best fit of all experimental ³¹P spin diffusion data is compared to the spin diffusion build-up curves as calculated from the X-ray crystal structure (Fig. 3.8-10 bottom), showing excellent agreement. Furthermore, these spin diffusion experiments
fully corroborate the assignment of the ³¹P resonances to specific P-sites in the crystal structure. Such (and related) ³¹P MAS NMR experiments have now been sufficiently carefully explored so that in a next step these methods can be exploited for the investigation of, for instance, solid solutions or, more generally, for solids of unknown crystal structure.

Based on the complete assignment of all ³¹P resonances in the ³¹P spectra of Cd₃(PO₄)₂ it is now possible to use ³¹P-¹¹³Cd double resonance MAS techniques in order to also assign all ¹¹³Cd resonances to the respective nine independent Cd-sites in the crystal structure. Only the combined use of selective ³¹P excitation schemes, followed by cross polarisation ³¹P-¹¹³Cd from a selected ³¹P resonance, using short contact times, yields sufficient site discrimination. This is illustrated in Fig. 3.8-11. Also two-dimensional ³¹P-¹¹³Cd MAS correlation experiments are feasible for such assignment purposes.
 

Fig. 3.8-9: 121 MHz 31P rf-driven MAS spin diffusion on Cd3(PO4)2. Intensities of off-diagonal peaks are a function of mixing times used, the build-up behaviour is characteristic for a given coupled network (see Fig. 3.8-10).

Fig. 3.8-10: Top: experimental 31P spin diffusion build-up curves for Cd3(PO4)2 as a function of mixing time where data from left to right and from top to bottom refer to peaks A -F in the 31P MAS spectrum. Bottom: comparison of best fit of all experimental NMR spin diffusion build-up data (solid line) with build-up curves calculated from the single-crystal X-ray structure, illustrating excellent agreement (with an estimated error in absolute distances of less than 5%).

Fig. 3.8-11: 31P-113Cd CP/MAS on Cd3(PO4)2. top left: 31P-113Cd CP/MAS, with polarising 113Cd from all 31P's (corresponding 31P MAS shown on top right); bottom left: 31P-113Cd CP/MAS, polarising 113Cd only from P C = P 1 (corresponding selectively prepared 31P MAS shown on bottom right). A full set of selective excitation CP/MAS experiments will yield assignment of all 113Cd resonances to the corresponding nine crystallographic Cd-sites.

Cd₂P₂O₇

³¹P MAS spectra of Cd₂P₂O₇ serve as an example that the - usual - treatment of ³¹P MAS spectra of solid pyro-phosphates within the framework of a single-spin approximation is insufficient: the NMR interactions for solid P₂O₇ compounds are such that at least a two-spin approximation should be used for the simulation of ³¹P MAS spectra of pyro-phosphates in order to correctly account for the MAS frequency and external magnetic field strength dependent higher order effects in such MAS spectra. Extraction of the NMR parameters characterising a P₂O₇ unit requires spectral simulations using the full Hamiltonian of a homonuclear spin pair under MAS. This approach affords considerably more involved numerical data analysis than does the usual single-spin treatment, but has the beneficial side-effect that the Euler angles, describing the orientation of the ³¹P shielding tensor(s) within the P₂O₇ fragment, are obtained from easily accessible, simple ³¹P MAS spectra of polycrystalline powders. Again, this is information which would otherwise only be obtainable from ³¹P NMR experiments on oriented single crystals. Experimental and simulated ³¹P MAS spectra of Cd₂P₂O₇ are shown in Fig. 3.8-12; the electronically least shielded component of both ³¹P shielding tensors is oriented nearly coincident with the direction of the respective P-O_bridge bond.
 

Fig. 3.8-12: Experimental and simulated (two-spin approximation) 31P MAS spectra of Cd2P2O7 at different external magnetic field strengths and MAS frequencies.

SiP₂O₇ (in collaboration with R. Miletich, and with M. Baldus, R. Iuliucci and B.H. Meier/ Nijmegen)

A refinement of the single-crystal structure of the cubic phase of SiP₂O₇ in space group Pa3 has been proposed in the literature. This refinement has been questioned since space group Pa3 requires the presence of (some) strictly linear P-O-P units in the structure; the existence or non-existence of linear P₂O₇ units being the point of disagreement, refinement of the structure in space groups of lower symmetry has been proposed (which then would no longer require the presence of linear P-O-P units). Space group Pa3 requests the presence of 11 crystallographically inequivalent P-sites of the following arrangement and relative amount: one linear P-O-P group with equivalent P atoms, two linear P-O-P groups formed by non-equivalent P atoms, and four different bent P₂O₇ units made up from inequivalent P-atoms and each unit of a relative amount three. Other conceivable space groups for refinement of the structure would require differing numbers and relative amounts of P sites in the asymmetric unit. Hence, ³¹P MAS NMR being able (in principle) to quantitatively identify the number of crystallographically inequivalent P sites in the asymmetric unit, should be able to resolve this space group ambiguity. At first glance, simple ³¹P MAS spectra of SiP₂O₇ appear to be more or less in agreement with the requirements of space group Pa3, except that the integrated intensities of the various ³¹P resonances slightly deviate form the predicted values, beyond experimental error. A ³¹P MAS NMR experiment, undisturbed by the presence of multiple dipolar interactions and considerable ³¹P shielding anisotropies and which would be able to - somehow - "count" the number of P₂O₇ units, each made up from inequivalent P atoms, would also immediately resolve the space group ambiguity.

Recently, the NMR-group in Nijmegen has introduced such an NMR experiment (TOBSY): this pulse experiment achieves polarisation transfer solely by homonuclear J-coupling. J-coupling is a through-bond interaction, hence represents a strictly intra-P₂O₇-unit interaction and will lead, in a two-dimensional TOBSY experiment, to correlations only for ³¹P resonances belonging to the same P₂O₇ unit and thus allows "counting" of the number of P₂O₇ units in the asymmetric unit. A 2D ³¹P TOBSY experiment on SiP₂O₇ is shown in Fig. 3.8-13, the number of correlations found (5) is consistent with the requirements of space group Pa3, but there remains the problem of the not quite perfect agreement of the integrated intensities in the ³¹P MAS spectra to be solved / explained. Lower symmetry space groups, in turn, do not seem compatible with the small number of TOBSY correlations observed.
 

Fig. 3.8-13: 2D 31P TOBSY experiment on a sample of the cubic phase of SiP2O7 (sample courtesy of R.Glaum/Giessen).