A high-resolution natural abundance 33S MAS NMR study of the cementitious mineral ettringite

Despite the widespread occurrence of sulfur in both natural and man-made materials, the S nucleus has only rarely been utilised in solid-state NMR spectroscopy on account of its very low natural abundance (0.76%), low NMR frequency (n0 = 30.7 MHz at B0 = 9.4 T), and significant nuclear quadrupole moment (spin I = 3/2, Q = 69.4 mb). Satellite-transition magic angle spinning (STMAS) is an NMR method for obtaining high-resolution spectra of half-integer quadrupolar nuclei (spin I 4 1/2) in solids and is notable for its intrinsic sensitivity advantage over the similar multiple-quantum (MQMAS) method, especially for nuclei with low NMR frequencies. In this work we demonstrate the feasibility of natural abundance S STMAS NMR experiments at B0 = 9.4 T and 20.0 T using a model sulfate sample (Na2SO4 + K2SO4 in a 1 : 1 molar ratio). Furthermore, we undertake a natural abundance S STMAS NMR study of the cement-forming mineral ettringite (Ca6Al2(SO4)3(OH)12 26H2O) at B0 = 9.4 T and 20.0 T, resolving a discrepancy in the literature between two previous conventional S MAS NMR studies and obtaining an alternative set of S NMR parameters that is simultaneously consistent with the MAS and STMAS data at both field strengths.


Introduction
Although sulfur is widespread in both nature and materials science, solid-state 33 S NMR spectroscopy has been relatively little used as a technique.This is largely due to the low natural abundance of 33 S nuclei (0.76%), combined with the high cost of isotopic enrichment, especially where this also involves finding new synthetic routes.In addition, with respect to its gyromagnetic ratio g, 33 S can be categorised as a low-g nucleus (NMR frequency n 0 = 30.7 MHz at B 0 = 9.4 T). 1 Since the intrinsic sensitivity of NMR signals is proportional to g 5/2 , this makes obtaining an acceptable signal-to-noise (S/N) ratio difficult.Furthermore, 33 S is a half-integer quadrupolar nucleus (spin I = 3/2) and its NMR spectrum is subject to anisotropic broadenings arising from quadrupolar interactions, where the additional linewidth is characterised by a coupling constant, C Q = e 2 qQ/h, and asymmetry parameter, Z = (V xx À V yy )/V zz .The presence of a quadrupolar interaction thus greatly increases the S/N problems.Recently, however, high-field NMR spectrometers have been employed to advantage to overcome some of the limitations associated with low-g quadrupolar nuclei.Not only does the intrinsic NMR sensitivity increase at higher magnetic fields but also there is a significant reduction in the linewidth arising from the second-order quadrupolar broadenings (proportional to 1/n 0 ).Therefore, with the increasing use of high-field (B 0 4 14.1 T) solid-state NMR spectrometers, solid-state 33 S NMR now shows greater potential for future applications.
Solid-state 33 S NMR investigations have been relatively scarce in the literature and it seems that only conventional (''one-dimensional'') spectra have been reported to date.  Mosf these 33 S NMR studies were performed with the 33 S nuclei at natural abundance, strongly reflecting the obstacles associated with 33 S isotopic enrichment.[4][5][6]8 In 1986, Eckert and Yesinowski 7 reported an extensive study of ''static'' solid-state 33 S NMR spectra recorded at B 0 = 11.7 T from a total of 27 inorganic compounds including sulfides, sulfates and alums.The first 33 S MAS NMR spectra were reported in 1996. 10In this study, natural abundance 33 S MAS NMR spectra of sulfides, sulfates and alums were recorded at B 0 = 14.1 T and this was followed by further 33 S MAS NMR studies of sulfides 11 and sulfates 12 recorded at B 0 = 17.6 T and thiosulfates at B 0 = 14.1 T. 13 Satellite-transition spinning sideband manifolds have been observed at B 0 = 14.1 T, where the temperature dependence and a sign change in C Q were investigated in two alums, 14 while extraction of unambiguous 33 S chemical shift anisotropy (CSA) parameters has been achieved for two tetrathiometallates. 16hese mainly medium-field 33 S MAS NMR studies were focused on the investigation of simple inorganic compounds owing to the relative ease of recording NMR spectra of S sites in highly symmetric environments with small quadrupolar broadenings.For anhydrous sulfates, long T 1 relaxation times have been reported as an additional limiting factor, 11,12 hampering efficient signal averaging to achieve reasonable S/N ratios for spectral analysis.
During the last decade, the development of sensitivity enhancement techniques for half-integer quadrupolar nuclei and the widespread use of high-field spectrometers have been expanding the use of solid-state 33 S NMR as a reliable tool for structural investigations.One of the first high-field 33 S NMR studies was carried out at B 0 = 19.6 T on cementitious materials containing 33 S nuclei as sulfates. 15[24][25][26] For example, acquisition using the CPMG pulse sequence at B 0 = 21.1 T has enabled the observation of large C Q values (9 to 16 MHz) for a single S site at natural 33 S abundance. 22,24First-principles calculations of 33 S NMR parameters accompany many of the latest solid-state 33 S NMR studies 20,[22][23][24][25][26] to predict and guide assignment of the experimental spectra.Prior knowledge of the magnitudes of quadrupolar broadenings, combined with acquisition at high B 0 fields, has been expanding the range of materials accessible for study by experimental solid-state 33 S NMR.For example, a very large C Q value of 43 MHz was predicted and experimentally observed in elemental sulfur (S 8 ), owing to the combination of 33 S isotopic enrichment, CPMG sensitivity enhancement and first-principles NMR calculations. 23n solid-state NMR spectroscopy of half-integer quadrupolar nuclei with overlapping quadrupolar-broadened lineshapes, high-resolution methods such as dynamic angle spinning (DAS), 27 double rotation (DOR), 28 multiple-quantum magic angle spinning (MQMAS), 29 and satellite-transition magic angle spinning (STMAS) 30 NMR experiments are often performed for complete spectral analysis.While the DAS and DOR methods require specialist probes, MQMAS and STMAS are performed using conventional MAS probes.Owing to its robustness and ease in implementation, MQMAS has been applied to investigations of a wide variety of materials containing half-integer quadrupolar nuclei. 31The STMAS method, on the contrary, is known to be more difficult to implement, 32 owing to experimental requirements such as a stable spinning frequency, accurate setting of the spinning axis to the magic angle, and the virtual necessity of a pneumatic insert and eject system for MAS rotors.One area where MQMAS has had limited applications is in the study of low-g quadrupolar nuclei, where the required high radiofrequency field strengths (n 1 ) are intrinsically difficult to achieve.The sensitivity of the MQMAS method is known to decrease considerably unless high n 1 field strengths are employed for the reconversion of multipleto single-quantum coherences. 33Largely owing to the singlequantum nature of satellite transitions, STMAS exhibits an inherent sensitivity advantage over MQMAS and relative enhancement factors of three or more are commonly observed for NMRsensitive nuclei such as 23 Na, 87 Rb (I = 3/2) and 27 Al (I = 5/2). 33reviously, the suitability of the STMAS method in preference to MQMAS for the study of low-g nuclei has been demonstrated, 34 using numerical calculations and 39 K (I = 3/2, n 0 = 18.7 MHz at B 0 = 9.4 T, 93% natural abundance) and 25 Mg (I = 5/2, n 0 = 24.5 MHz at B 0 = 9.4 T, 10% natural abundance) STMAS experiments at B 0 = 9.4 T. Therefore, it is tempting to investigate what can be achieved using STMAS by means of an extreme case study, such as 33 S NMR at the natural 33 S abundance of 0.76%.
The purpose of this paper is to demonstrate the feasibility of natural abundance 33 S STMAS NMR experiments at B 0 = 9.4 T and 20.0 T under favourable conditions.We discuss the technicalities with respect to successful implementation of 33 S STMAS experiments at 33 S natural abundance before applying the STMAS method to the NMR investigation of the cementitious mineral, ettringite.Ettringite (Ca 6 Al 2 (SO 4 ) 3 (OH) 12 Á26H 2 O) is a hydrous sulfate that is found naturally and also synthetically during the production of cements.Its crystal structure is known from diffraction studies, 35-38 and 27 Al MAS NMR studies 39 have been reported previously.There have been two previous 33 S solidstate NMR studies of ettringite, 15,17 both at natural isotopic abundance: one at a field B 0 = 19.6 T and using conventional single-pulse acquisition 15 and the other at B 0 = 14.1 T and employing CT enhancement techniques. 17These two studies disagree as to the number of crystallographically distinct S sites observed: the higher field study simulates a spectrum with a single S site 15 while the lower field study suggests three S sites 17 in accordance with the diffraction studies.Our aim is to apply the high-resolution 33 S STMAS method to ettringite and resolve the ambiguity over the number of crystallographically different S sites observed by solid-state 33 S NMR.

Materials and experimental methods
Na 2 SO 4 , K 2 SO 4 and AlNH 4 (SO 4 ) 2 Á12H 2 O were obtained commercially as powdered solids and used as received.Ettringite was synthesised from analytical grade reagents.The main precursor in the synthesis of ettringite was tricalcium aluminate (3CaOÁAl 2 O 3 ), which was prepared from a 3 : 1 molar ratio of CaCO 3 and Al 2 O 3 at 1400 1C.Anhydrite CaSO 4 was prepared by dehydration of gypsum in a muffle furnace at 550 1C overnight.Ettringite was then prepared by suspending a 1 : 3 molar mixture of tricalcium aluminate and anhydrite CaSO 4 , respectively, with a water-to-solid ratio of 20 using double-distilled CO 2 -free water.The mixture was stirred using a magnetic stirrer for three days and then periodically agitated over the period of a fortnight.Once purity was confirmed by X-ray diffraction, the solid was vacuum filtered under an N 2 atmosphere in a glove box and subsequently aged at 25 1C for two months inside hermetic glass bottles equilibrated at 8% relative humidity using a NaOH-saturated salt solution. 40n 0 ) of 30.7 and 65.2 MHz using Bruker Avance spectrometers equipped with B 0 = 9.4 and 20.0 T magnets, respectively.Powdered samples were packed into either 4 mm or 7 mm MAS rotors and conventional Bruker MAS probes were employed.Spinning frequencies (n R ) of 14 286 and 5000-6400 Hz were used with 4 mm and 7 mm rotors, respectively.Single-pulse and rotor-synchronised spin-echo experiments were used to record one-dimensional 33 S MAS spectra.The use of 1 H decoupling was investigated and found to be unnecessary.The 33 S chemical shift scales are given with respect to neat CS 2 , calibrated using AlNH 4 (SO 4 ) 2 Á12H 2 O as a secondary reference (d iso = 331 ppm). 12Spectral fitting and simulations of one-dimensional 33 S MAS spectra were performed using Bruker TopSpin 3.2.Simulated two-dimensional 33 S STMAS spectra and the corresponding isotropic projections were generated in the frequency domain using a home-written Fortran code.Further experimental and computational details are provided in the figure captions.
A powdered mixture of Na 2 SO 4 and K 2 SO 4 was packed into a 4 mm MAS rotor, while powdered ettringite was packed into a 7 mm rotor.The most efficient manipulation of satellite-transition (ST) coherences is achieved with high radiofrequency field strengths and, as has been shown previously, this can result in a smaller diameter rotor producing the highest STMAS sensitivity, with the beneficial effects of the higher n 1 frequency outweighing those of the reduced sample volume. 34However, after concluding our preliminary experiments with the mixture of Na 2 SO 4 and K 2 SO 4 , we discovered that the n 1 frequencies yielded by the 4 mm and (single-channel) 7 mm MAS probes on the 20.0 T spectrometer were similar and so we used a 7 mm rotor for all the ettringite experiments at both B 0 = 9.4 and 20.0 T. Obviously, whatever the rotor diameter, the use of the highest radiofrequency power available is recommended for the efficient manipulation of ST coherences, i.e., for the first two pulses in the STMAS pulse sequence.In our work, the 1 kW amplifiers produced 33 S radiofrequency field strengths (n 1 = |gB 1 |/2p) estimated to be around 55 kHz on both the 9.4 T and 20.0 T instruments.
The phase-modulated split-t 1 STMAS pulse sequence 32,41 was used in all the 33 S STMAS experiments in this study as it seems to be the most sensitive basic implementation of the technique. 32,34For sensitive NMR nuclei (such as 23 Na, 87 Rb and 27 Al), it is possible to optimise the durations of each pulse experimentally and obtain the highest S/N ratio on the sample of interest.However, for low sensitivity nuclei such as 33 S it is impractical to perform such pulse length optimisations unless 33 S-enriched samples suitable for STMAS experiments are available (and generally these will not be, as they were not to us).Previously, numerical calculations 34 have shown that, for spin I = 3/2, the optimum flip angles for the first ST excitation pulse (p1) and second ST reconversion pulse (p2) are 901 and 601, respectively; the third pulse (p3) is a CT-selective ''1801'' inversion pulse, as in the second pulse of the spin-echo sequence.It should be noted that the flip angles quoted for the first two STMAS pulses are intrinsic values; e.g., the values of 2pn 1 t p1 and 2pn 1 t p2 .In contrast, the third pulse is a ''soft'' inversion or refocusing pulse that acts only on the central transition and, for I = 3/2, has an intrinsic flip angle of 901, with the selective nutation rate increased by a factor of I + 1/2.Our approach is then to calibrate the 33 S radiofrequency field strength and then to calculate the corresponding STMAS pulse durations. 34or the calibration we employed the 33 S MAS NMR signal of AlNH 4 (SO 4 ) 2 Á12H 2 O.The negligible value of C Q (resulting in linewidth at half height of 18 Hz) and short T 1 relaxation time (0.27 s) 12 of this solid makes it ideal as a setup sample for 33 S MAS experiments. 1 For the first two STMAS pulses, the maximum available 33 S radiofrequency field strength (n 1 ) of 55 kHz was employed, while for the CT-selective 1801 pulse, n 1 ( 33 S) = 15 kHz was appropriate.The actual pulse lengths used for p1, p2 and p3 were 4.5, 3.0 and 17.0 ms, respectively, in all our 33 S STMAS experiments.
It is well known that a double-quantum filtered (DQF) version of the STMAS pulse sequence simplifies the resulting spectrum by the removal of the CT-CT autocorrelation peaks. 42owever, excitation of double-quantum coherences is inefficient for spins with small C Q values32 (o1 MHz for I = 3/2 nuclei, for example), as we are expecting with 33 S. Furthermore, since for I = 3/2 the optimum flip angle of 901 for the ST excitation pulse (p1) corresponds to a CT-selective ''1801'', the CT-CT autocorrelation peaks are anticipated to be of low intensity even without use of a double-quantum filter.For this reason, the basic phase-modulated split-t 1 STMAS experiment and not the DQF-STMAS sequence was used for the 33 S NMR experiments in this work.
In STMAS, accurate setting of sample spinning axis to 54.736 AE 0.0021 is a prerequisite. 32Prior to our 33 43 saves considerable time during the stepwise adjustment of the spinning axis, the magnitude of the 85 Rb quadrupolar interactions is large enough (P Q = 3.7-4.7 MHz) 44 to observe the effect of angle misset easily, and the DQF version of the STMAS pulse sequence (which works well here) simplifies the resulting spectrum by the removal of CT-CT autocorrelation peaks. 42In practice, we record a one-dimensional DQF-STMAS spectrum, corresponding to a single t 1 value and maximise the signal amplitude, followed by acquisition of full two-dimensional DQF-STMAS spectra to ensure the removal of any residual splitting arising from spinning angle misset.Residual splittings due to third-order quadrupolar interactions can be significant for I = 5/2 nuclei such as 85 Rb (but note that they are insignificant for I = 3/2 nuclei such as 33  we used a low flow of bearing or eject gas to cushion the rotor during the insertion.However, with a 7 mm rotor on the B 0 = 20.0T magnet this still produced a change in the spinning angle, perhaps due to the greater height that the rotor has to fall in the larger magnet.Consequently, a layer of RbNO 3 was added to the powdered ettringite for experiments at B 0 = 20.0T, thus avoiding the ejection and insertion procedure normally associated with the spinning axis calibration.To maximise the 33 S sensitivity, powdered RbNO 3 was first packed into the bottom of a 7 mm rotor (about 20% of the total volume) and the rest of the rotor was filled with the ettringite.Upon comparison of two 33 S MAS spectra, one recorded with a 7 mm rotor full of ettringite and one recorded with a 7 mm rotor also containing RbNO 3 at the bottom, the resulting 33 S MAS spectra were confirmed to be identical except for a small difference in sensitivity proportional to the sample volume inside each rotor.
At B 0 = 20.0T, we acquired 33 S spin-echo MAS spectra of ettringite with various intervals between the two pulses (3-12 ms) to determine the optimum length of the echo interval in the    1).In (b) 192 transients were averaged for each of 67 t 1 increments of 132.22 ms with a relaxation interval of 20 s.An echo interval (t) of 12 ms was used.Total experimental time was 72 h.The MAS frequency was 14 286 Hz.A 4 mm MAS rotor was used.Contour levels are drawn at 16, 32, 48, 64, 80, and 96% of the maximum value.No weighting functions were applied in (b).
Table 2 Experimental 33 S NMR parameters for ettringite taken from ref. 15  and 17 and this work (Fig. 3 and 4).The magnetic field dependent isotropic shifts d 1 in brackets were calculated at B 0 = 9.STMAS sequence, attempting to avoid truncation of STMAS signals while retaining sensitivity; a value of 12 ms was used in our experiments.At B 0 = 9.4 T, a short echo interval (4 ms) was employed for maximum sensitivity (the optimum is possibly longer than 8 ms but the effect of signal truncation was not obvious in the resulting spectrum due to the low S/N ratio).

Results and discussion
We first demonstrate the feasibility of natural abundance 33 S STMAS experiments on a model system with known and undisputed NMR parameters, a 1 : 1 molar mixture of Na 2 SO 4 and K 2 SO 4 , with experiments performed at B 0 = 20.0T. The 33 S MAS spectrum of each sulfate has been reported previously, 12,17,26 Fig. 3 (a-c 1.Both sulfates have similar isotropic chemical shifts (d iso shifts of 340 ppm and 336 ppm) and small quadrupolar broadenings (C Q coupling constants of 0.655 MHz and 0.988 MHz).Our simulated 33 S MAS spectrum of the equimolar sulfate mixture at B 0 = 20.0T (Fig. 1a) indicates the presence of overlapping second-order broadened lineshapes and this was confirmed by the experimental 33 S MAS spectrum of the sulfate mixture at B 0 = 20.0T shown in Fig. 1b.A simulated 33 S STMAS spectrum of the sulfate mixture at B 0 = 20.0T using quadrupolar parameters previously reported for each sulfate is shown in Fig. 2a.The two STMAS ridges are expected to be resolved in the d 1 (isotropic) dimension and this was confirmed by our experimental natural abundance 33 S STMAS spectrum of the sulfate mixture recorded at B 0 = 20.0T, shown in Fig. 2b.A total acquisition time of three days was required to obtain this spectrum, although the major limiting factor here was the long T 1 relaxation times of these anhydrous sulfates (T 1 = 30 s for Na 2 SO 4 and 16 s for K 2 SO 4 ). 12The poor S/N in the d 2 cross sections from Fig. 2b made any lineshape fitting unreliable but, using the d 1 and d 2 peak positions in the two-dimensional STMAS spectrum, a centre-of-mass analysis was carried out using the appropriate equations for I = 3/2 split-t 1 STMAS experiments to obtain the isotropic chemical shift, d iso , and the isotropic I = 3/2 second-order quadrupolar shift, d Q = (250C Q /n 0 ) 2 (1 + Z 2 /3): 32,34 d iso = (17d 1 + 10d 2 )/27 (1a) The isotropic I = 3/2 quadrupolar shift was then used to obtain the composite quadrupolar product P Q = C Q (1 + (Z 2 /3)) 1/2 : This procedure yielded the chemical shift and quadrupolar parameters summarised in Table 1, which are in satisfactory agreement with the previously reported NMR parameters.
Following on from this successful feasibility study, our investigations of ettringite in a 7 mm MAS rotor using natural abundance 33 S NMR were conducted at, initially, B 0 = 20.0T and, subsequently, B 0 = 9.4 T. A set of three experiments (singlepulse, spin-echo, and STMAS) was performed each field strength.Previously, two studies reported natural abundance 33 S MAS spectra of ettringite, 15,17 one at B 0 = 19.6 T using conventional single-pulse acquisition, 15 and the other at B 0 = 14.1 T employing CT enhancement techniques. 17The higher B 0 field study simulates a spectrum with a single site 15 while the lower B 0 field study proposes three S sites 17 in accordance with the diffraction studies.The chemical shift and quadrupolar parameters determined in these two studies are summarised in Table 2.Both studies employed a relaxation interval of 1 s and we have qualitatively verified this very efficient 33 S spin-lattice relaxation in ettringite (the use of 0.2 s as a recycle interval gave rise to a 10% loss in sensitivity compared with the use of 0.4 s at B 0 = 20.0T).It was this efficient relaxation that encouraged us to attempt experiments at the relatively low field strength of B 0 = 9.4 T.
Fig. 3 and 4 show the natural abundance33 S single-pulse, spin-echo and STMAS spectra of ettringite in a 7 mm MAS rotor at B 0 = 20.0T and 9.4 T, respectively.It is apparent from the B 0 = 20.0T STMAS spectrum in Fig. 3d, which took 92 h to record, that, although there is some evidence of the presence of more than one two-dimensional lineshape, multiple S sites are not fully resolved.Recognising that this was likely to be the result of small second-order quadrupolar shifts at B 0 = 20.0T, we were encouraged to record the B 0 = 9.4 T 33 S STMAS spectrum of ettringite shown in Fig. 4d, which took 262 h to complete.Although the S/N ratio is poor and there are strong truncation artefacts at d 1 E 0, the d 1 projection of the spectrum appears to show isotropically resolved S sites.
Centre-of-mass analyses were performed on the two-dimensional STMAS spectra using the appropriate equations for I = 3/2 split-t 1 experiments 34 (eqn (1)-( 2)).These provided initial estimates for the chemical shift and quadrupolar parameters for ettringite that were This journal is © the Owner Societies 2017 then used in an iterative fitting of the one-dimensional MAS spectra at the two field strengths.Further refinement of the NMR parameters was then achieved by comparing the simulated d 1 projections of the STMAS spectra at the two field strengths with the experimental projections.In this way we obtained a consistent set of chemical shift and quadrupolar parameters at B 0 = 20.0T and 9.4 T for the three crystallographically distinct S sites in ettringite, as summarised in Table 2.
Fig. 5 compares the simulated d 1 projections at B 0 = 20.0T and 9.4 T using the parameters obtained in this work with those using the parameters from ref. 17 and with the experimental 33 S STMAS d 1 projections.It is apparent that the 33 S NMR parameters from ref. 17 do not reproduce the experimental STMAS d 1 projections obtained in this work.With respect to this, we note that the spectra in ref. 17 were recorded with the assistance of a CT enhancement method, which may have distorted the 33 S MAS lineshapes, and were subjected to significant line broadening (up to 50 Hz) 17 during processing.

Conclusions
We have demonstrated the feasibility of high-resolution 33 S STMAS NMR experiments at B 0 = 9.4 and 20.0 T and at the natural abundance of 33 S (0.76%).We judge that, at 33 S natural abundance in the presence of multiple S sites, 33 S STMAS is feasible at B 0 = 20.0T for quadrupolar coupling constants up to 1 MHz in magnitude.If the 33 S spin-lattice relaxation times are particularly short, as in the case of ettringite, then our results indicate that 33 S STMAS becomes possible at lower field strengths, such as the B 0 = 9.4 T used here.Total acquisition times can be very long, a week or more, and we were fortunate that our B 0 = 9.4 T magnet was particularly stable.Using 33 S STMAS at 33 S natural abundance, we have resolved the disagreement in the 33 S NMR literature as to the number of distinct S sites in the mineral ettringite in favour of ref. 17: we also find 3 distinct S sites, in further agreement with diffraction studies.We have obtained a set of 33 S NMR parameters (d iso , C Q and Z) for ettringite that are in consistent agreement with 33 S MAS and STMAS spectra recorded at field strengths of B 0 = 9.4 and 20.0 T. The importance of working at more than one magnetic field strength cannot be overstated in a challenging study such as that presented here.Finally, we note that the highly dynamic nature of the ettringite structure, as evidenced by the unusually short 33 S T 1 relaxation times, is expected to complicate attempts to calculate the 33 S NMR parameters using first-principles methods such as WIEN2k or CASTEP, as we have confirmed in preliminary DFT studies.
S STMAS experiments, phase-modulated split-t 1 85 Rb (spin I = 5/2) DQF-STMAS experiments 42 were performed on RbNO 3 for accurate spinning axis calibration.There are several advantages associated with the use of 85 Rb DQF-STMAS experiments performed on RbNO 3 : 85 Rb is easily observable (72% natural abundance), the 85 Rb Larmor frequency is close enough to 33 S to lie within the same tuning range of an MAS probe (n 0 ( 85 Rb) = 38.6MHz and n 0 ( 33 S) = 30.7 MHz at B 0 = 9.4 T), efficient 85 Rb spin-lattice relaxation (T 1 E 60 ms) S) and their presence should be taken into account, especially at lower B 0 fields as they are proportional to 1/n 0 This journal is © the Owner Societies 2017 Phys.Chem.Chem.Phys., 2017, 19, 24082--24089 | 24085

Fig. 1
Fig.1(a) Simulated and (b) experimental33 S MAS spectra of a 1 : 1 molar mixture of sodium sulfate (Na 2 SO 4 ) and potassium sulfate (K 2 SO 4 ) at B 0 = 20.0T. In (a) the 33 S NMR parameters (d iso , C Q and Z) were taken from ref.26 (see Table1).In (b) a spin-echo pulse sequence was used.The MAS frequency was 14 286 Hz.A 4 mm MAS rotor was used.4928 transients were averaged with a relaxation interval of 30 s.Total experimental time was 41 h.The complete simulated lineshape from (a) is overlaid (red) on the experimental lineshape (black).

Fig. 2
Fig.2(a) Simulated and (b) experimental33 S STMAS spectra of a 1 : 1 molar mixture of sodium sulfate (Na 2 SO 4 ) and potassium sulfate (K 2 SO 4 ) at B 0 = 20.0T, with the corresponding isotropic projections.In (a) the 33 S NMR parameters (d iso , C Q and Z) were taken from ref.26 (see Table1).In (b) 192 transients were averaged for each of 67 t 1 increments of 132.22 ms with a relaxation interval of 20 s.An echo interval (t) of 12 ms was used.Total experimental time was 72 h.The MAS frequency was 14 286 Hz.A 4 mm MAS rotor was used.Contour levels are drawn at 16, 32, 48, 64, 80, and 96% of the maximum value.No weighting functions were applied in (b).
4 T and B 0 = 20.0T from the C Q and Z values given in ref. 15 and 17 and determined in this work to allow comparison with the experimental STMAS spectra d iso (ppm) C Q (kHz) 331.1 516 AE 5 0.50 AE 0.05 (335.6)(332.1)329.8 591 AE 5 0.72 AE 0.05 (336.2) (331.2) 329.6 810 AE 5 0.97 AE 0.05 (343.0)(332.6)This work 331.8 620 AE 20 0.1 AE 0.1 337.8 (333.1) (Fig. 3 and 4) 332.1 660 AE 20 0.3 AE 0.1 339.1 (333.7)331.0 800 AE 20 0.1 AE 0.1 341.0 (333.2)Thisjournal is © the Owner Societies 2017 Fig.3 (a-c) Experimental and simulated33 S MAS and (d and e) experimental and simulated STMAS spectra of ettringite with corresponding isotropic projections at B 0 = 20.0T. In (a) a single pulse and (b) a spin-echo pulse sequence was used.In both (a) and (b) 92 160 transients were averaged with a relaxation interval of 0.6 s.Total experimental time was 16 h in each case.The MAS frequency was 6.4 kHz.A 7 mm MAS rotor filled only with ettringite was used.No weighting functions were applied.(c and e) Simulated 33 S MAS and STMAS spectra using the NMR parameters (d iso , C Q and Z) determined in this work and given in Table2.In (d) 11 040 transients were averaged for each of 64 t 1 increments of 377.78 ms with a relaxation interval of 0.45 s.An echo interval (t) of 6 ms was used.Total experimental time was 92 h.The MAS frequency was 5 kHz.A 7 mm MAS rotor containing both RbNO 3 and ettringite was used.Contour levels are drawn at 32, 44, 56, 68, 80, and 92% of the maximum value.No weighting functions were applied.

Fig. 4
Fig.4 (a-c) Experimental and simulated33 S MAS and (d and e) experimental and simulated STMAS spectra of ettringite with corresponding isotropic projections at B 0 = 9.4 T. In (a) a single pulse and (b) a spin-echo pulse sequence was used.In both (a) and (b), 524 288 transients were averaged with a relaxation interval of 0.25 s.Total experimental time was 44 h in each case.The MAS frequency was 6.4 kHz.A 7 mm MAS rotor filled only with ettringite was used.No weighting functions were applied.(c and e) Simulated 33 S MAS and STMAS spectra using the NMR parameters (d iso , C Q and Z) determined in this work and given in Table 2.In (d) 40 960 transients were averaged for each of 85 t 1 increments of 295.14 ms with a relaxation interval of 0.25 s.An echo interval (t) of 4 ms was used.Total experimental time was 262 h.The MAS frequency was 6.4 kHz.A 7 mm MAS rotor filled only with ettringite was used.Contour levels are drawn at 32, 44, 56, 68, 80, and 92% of the maximum value.No weighting functions were applied.

Fig. 5
Fig. 5 (a and b) Simulated and (c) experimental isotropic projections of two-dimensional 33 S STMAS spectra of ettringite at B 0 = 20.0T and 9.4 T.

Table 1
33perimental33S NMR parameters for sodium sulfate and potassium sulfate taken from ref.26and this work (Fig.2).The magnetic field dependent shifts d 1 and d 2 were measured at B 0 = 20.0T.The P Q values in brackets were calculated from the C Q and Z values in ref.26for comparison with the values determined in this work

Table 2 .
In (d) 40 960 transients were averaged for each of 85 t 1 increments of 295.14 ms with a relaxation interval of 0.25 s.An echo interval (t) of 4 ms was used.Total experimental time was 262 h.The MAS frequency was 6.4 kHz.A 7 mm MAS rotor filled only with ettringite was used.Contour levels are drawn at 32, 44, 56, 68, 80, and 92% of the maximum value.No weighting functions were applied.and the 33 S NMR parameters from ref. 26 are summarised in Table