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

Abstract

Despite the widespread occurrence of sulfur in both natural and man-made materials, the ³³S nucleus has only rarely been utilised in solid-state NMR spectroscopy on account of its very low natural abundance (0.76%), low NMR frequency (ν₀ = 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 > 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 ³³S 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 ³³S 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 ³³S MAS NMR studies and obtaining an alternative set of ³³S NMR parameters that is simultaneously consistent with the MAS and STMAS data at both field strengths.

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Introduction

Although sulfur is widespread in both nature and materials science, solid-state ³³S NMR spectroscopy has been relatively little used as a technique. This is largely due to the low natural abundance of ³³S 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 γ, ³³S can be categorised as a low-γ nucleus (NMR frequency ν₀ = 30.7 MHz at B₀ = 9.4 T).¹ Since the intrinsic sensitivity of NMR signals is proportional to γ^5/2, this makes obtaining an acceptable signal-to-noise (S/N) ratio difficult. Furthermore, ³³S 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 = e²qQ/h, and asymmetry parameter, η = (V_xx − 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-γ 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/ν₀). Therefore, with the increasing use of high-field (B₀ > 14.1 T) solid-state NMR spectrometers, solid-state ³³S NMR now shows greater potential for future applications.

Solid-state ³³S NMR investigations have been relatively scarce in the literature and it seems that only conventional (“one-dimensional”) spectra have been reported to date.^1–26 Most of these ³³S NMR studies were performed with the ³³S nuclei at natural abundance, strongly reflecting the obstacles associated with ³³S isotopic enrichment. The earliest solid-state ³³S NMR studies date back to 1968 and the immediately ensuing investigations were performed exclusively on sulfides.^2–6,8 In 1986, Eckert and Yesinowski⁷ reported an extensive study of “static” solid-state ³³S NMR spectra recorded at B₀ = 11.7 T from a total of 27 inorganic compounds including sulfides, sulfates and alums. The first ³³S MAS NMR spectra were reported in 1996.¹⁰ In this study, natural abundance ³³S MAS NMR spectra of sulfides, sulfates and alums were recorded at B₀ = 14.1 T and this was followed by further ³³S MAS NMR studies of sulfides¹¹ and sulfates¹² recorded at B₀ = 17.6 T and thiosulfates at B₀ = 14.1 T.¹³ Satellite-transition spinning sideband manifolds have been observed at B₀ = 14.1 T, where the temperature dependence and a sign change in C_Q were investigated in two alums,¹⁴ while extraction of unambiguous ³³S chemical shift anisotropy (CSA) parameters has been achieved for two tetrathiometallates.¹⁶ These mainly medium-field ³³S 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 T₁ 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 ³³S NMR as a reliable tool for structural investigations. One of the first high-field ³³S NMR studies was carried out at B₀ = 19.6 T on cementitious materials containing ³³S nuclei as sulfates.¹⁵ Central-transition (CT) enhancement techniques via population transfer have been successfully implemented in ³³S NMR,^17,19 and observation of three crystallographically distinct S sites in ettringite with C_Q values of up to 1 MHz was possible at B₀ = 14.1 T. The Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence is known to boost the S/N ratio by accumulating signal intensity into “spikelets” and, following its success in signal enhancement of ³³S-enriched disordered silicates,¹⁸ the CPMG pulse sequence has been frequently employed in high-field solid-state ³³S NMR, especially where only a single S site is present.^{20–22,24–26} For example, acquisition using the CPMG pulse sequence at B₀ = 21.1 T has enabled the observation of large C_Q values (9 to 16 MHz) for a single S site at natural ³³S abundance.^22,24 First-principles calculations of ³³S NMR parameters accompany many of the latest solid-state ³³S NMR studies^20,22–26 to predict and guide assignment of the experimental spectra. Prior knowledge of the magnitudes of quadrupolar broadenings, combined with acquisition at high B₀ fields, has been expanding the range of materials accessible for study by experimental solid-state ³³S NMR. For example, a very large C_Q value of 43 MHz was predicted and experimentally observed in elemental sulfur (S₈), owing to the combination of ³³S isotopic enrichment, CPMG sensitivity enhancement and first-principles NMR calculations.²³

In 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.³¹ The 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-γ quadrupolar nuclei, where the required high radiofrequency field strengths (ν₁) are intrinsically difficult to achieve. The sensitivity of the MQMAS method is known to decrease considerably unless high ν₁ field strengths are employed for the reconversion of multiple- to single-quantum coherences.³³ Largely owing to the single-quantum nature of satellite transitions, STMAS exhibits an inherent sensitivity advantage over MQMAS and relative enhancement factors of three or more are commonly observed for NMR-sensitive nuclei such as ²³Na, ⁸⁷Rb (I = 3/2) and ²⁷Al (I = 5/2).³³ Previously, the suitability of the STMAS method in preference to MQMAS for the study of low-γ nuclei has been demonstrated,³⁴ using numerical calculations and ³⁹K (I = 3/2, ν₀ = 18.7 MHz at B₀ = 9.4 T, 93% natural abundance) and ²⁵Mg (I = 5/2, ν₀ = 24.5 MHz at B₀ = 9.4 T, 10% natural abundance) STMAS experiments at B₀ = 9.4 T. Therefore, it is tempting to investigate what can be achieved using STMAS by means of an extreme case study, such as ³³S NMR at the natural ³³S abundance of 0.76%.

The purpose of this paper is to demonstrate the feasibility of natural abundance ³³S STMAS NMR experiments at B₀ = 9.4 T and 20.0 T under favourable conditions. We discuss the technicalities with respect to successful implementation of ³³S STMAS experiments at ³³S natural abundance before applying the STMAS method to the NMR investigation of the cementitious mineral, ettringite. Ettringite (Ca₆Al₂(SO₄)₃(OH)₁₂·26H₂O) 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 ²⁷Al MAS NMR studies³⁹ have been reported previously. There have been two previous ³³S solid-state NMR studies of ettringite,^15,17 both at natural isotopic abundance: one at a field B₀ = 19.6 T and using conventional single-pulse acquisition¹⁵ and the other at B₀ = 14.1 T and employing CT enhancement techniques.¹⁷ These two studies disagree as to the number of crystallographically distinct S sites observed: the higher field study simulates a spectrum with a single S site¹⁵ while the lower field study suggests three S sites¹⁷ in accordance with the diffraction studies. Our aim is to apply the high-resolution ³³S STMAS method to ettringite and resolve the ambiguity over the number of crystallographically different S sites observed by solid-state ³³S NMR.

Materials and experimental methods

Na₂SO₄, K₂SO₄ and AlNH₄(SO₄)₂·12H₂O 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 (3CaO·Al₂O₃), which was prepared from a 3 : 1 molar ratio of CaCO₃ and Al₂O₃ at 1400 °C. Anhydrite CaSO₄ was prepared by dehydration of gypsum in a muffle furnace at 550 °C overnight. Ettringite was then prepared by suspending a 1 : 3 molar mixture of tricalcium aluminate and anhydrite CaSO₄, respectively, with a water-to-solid ratio of 20 using double-distilled CO₂-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 N₂ atmosphere in a glove box and subsequently aged at 25 °C for two months inside hermetic glass bottles equilibrated at 8% relative humidity using a NaOH-saturated salt solution.⁴⁰

³³S MAS NMR spectra were acquired at Larmor frequencies (ν₀) of 30.7 and 65.2 MHz using Bruker Avance spectrometers equipped with B₀ = 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 (ν_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 ³³S MAS spectra. The use of ¹H decoupling was investigated and found to be unnecessary. The ³³S chemical shift scales are given with respect to neat CS₂, calibrated using AlNH₄(SO₄)₂·12H₂O as a secondary reference (δ_iso = 331 ppm).¹² Spectral fitting and simulations of one-dimensional ³³S MAS spectra were performed using Bruker TopSpin 3.2. Simulated two-dimensional ³³S 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 Na₂SO₄ and K₂SO₄ 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 ν₁ frequency outweighing those of the reduced sample volume.³⁴ However, after concluding our preliminary experiments with the mixture of Na₂SO₄ and K₂SO₄, we discovered that the ν₁ 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 B₀ = 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 ³³S radiofrequency field strengths (ν₁ = |γB₁|/2π) estimated to be around 55 kHz on both the 9.4 T and 20.0 T instruments.

The phase-modulated split-t₁ STMAS pulse sequence^32,41 was used in all the ³³S STMAS experiments in this study as it seems to be the most sensitive basic implementation of the technique.^32,34 For sensitive NMR nuclei (such as ²³Na, ⁸⁷Rb and ²⁷Al), 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 ³³S it is impractical to perform such pulse length optimisations unless ³³S-enriched samples suitable for STMAS experiments are available (and generally these will not be, as they were not to us). Previously, numerical calculations³⁴ 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 90° and 60°, respectively; the third pulse (p3) is a CT-selective “180°” 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 2πν₁τ_p1 and 2πν₁τ_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 90°, with the selective nutation rate increased by a factor of I + 1/2. Our approach is then to calibrate the ³³S radiofrequency field strength and then to calculate the corresponding STMAS pulse durations.³⁴ For the calibration we employed the ³³S MAS NMR signal of AlNH₄(SO₄)₂·12H₂O. The negligible value of C_Q (resulting in linewidth at half height of 18 Hz) and short T₁ relaxation time (0.27 s)¹² of this solid makes it ideal as a setup sample for ³³S MAS experiments.¹ For the first two STMAS pulses, the maximum available ³³S radiofrequency field strength (ν₁) of 55 kHz was employed, while for the CT-selective 180° pulse, ν₁(³³S) = 15 kHz was appropriate. The actual pulse lengths used for p1, p2 and p3 were 4.5, 3.0 and 17.0 μs, respectively, in all our ³³S 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.⁴² However, excitation of double-quantum coherences is inefficient for spins with small C_Q values³² (<1 MHz for I = 3/2 nuclei, for example), as we are expecting with ³³S. Furthermore, since for I = 3/2 the optimum flip angle of 90° for the ST excitation pulse (p1) corresponds to a CT-selective “180°”, 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-t₁ STMAS experiment and not the DQF-STMAS sequence was used for the ³³S NMR experiments in this work.

In STMAS, accurate setting of sample spinning axis to 54.736 ± 0.002° is a prerequisite.³² Prior to our ³³S STMAS experiments, phase-modulated split-t₁⁸⁵Rb (spin I = 5/2) DQF-STMAS experiments⁴² were performed on RbNO₃ for accurate spinning axis calibration. There are several advantages associated with the use of ⁸⁵Rb DQF-STMAS experiments performed on RbNO₃: ⁸⁵Rb is easily observable (72% natural abundance), the ⁸⁵Rb Larmor frequency is close enough to ³³S to lie within the same tuning range of an MAS probe (ν₀(⁸⁵Rb) = 38.6 MHz and ν₀(³³S) = 30.7 MHz at B₀ = 9.4 T), efficient ⁸⁵Rb spin–lattice relaxation (T₁ ≈ 60 ms)⁴³ saves considerable time during the stepwise adjustment of the spinning axis, the magnitude of the ⁸⁵Rb 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.⁴² In practice, we record a one-dimensional DQF-STMAS spectrum, corresponding to a single t₁ 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 ⁸⁵Rb (but note that they are insignificant for I = 3/2 nuclei such as ³³S) and their presence should be taken into account, especially at lower B₀ fields as they are proportional to 1/ν₀².^32,45

Once the magic angle is achieved with the RbNO₃ setup sample, changing the sample, even using the Bruker pneumatic insert-eject system, has the potential to alter the spinning angle if not performed carefully. On the B₀ = 9.4 T spectrometer, 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 B₀ = 20.0 T 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 RbNO₃ was added to the powdered ettringite for experiments at B₀ = 20.0 T, thus avoiding the ejection and insertion procedure normally associated with the spinning axis calibration. To maximise the ³³S sensitivity, powdered RbNO₃ 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 ³³S MAS spectra, one recorded with a 7 mm rotor full of ettringite and one recorded with a 7 mm rotor also containing RbNO₃ at the bottom, the resulting ³³S MAS spectra were confirmed to be identical except for a small difference in sensitivity proportional to the sample volume inside each rotor.

At B₀ = 20.0 T, we acquired ³³S 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 STMAS sequence, attempting to avoid truncation of STMAS signals while retaining sensitivity; a value of 12 ms was used in our experiments. At B₀ = 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 ³³S STMAS experiments on a model system with known and undisputed NMR parameters, a 1 : 1 molar mixture of Na₂SO₄ and K₂SO₄, with experiments performed at B₀ = 20.0 T. The ³³S MAS spectrum of each sulfate has been reported previously,^12,17,26 and the ³³S NMR parameters from ref. 26 are summarised in Table 1. Both sulfates have similar isotropic chemical shifts (δ_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 ³³S MAS spectrum of the equimolar sulfate mixture at B₀ = 20.0 T (Fig. 1a) indicates the presence of overlapping second-order broadened lineshapes and this was confirmed by the experimental ³³S MAS spectrum of the sulfate mixture at B₀ = 20.0 T shown in Fig. 1b. A simulated ³³S STMAS spectrum of the sulfate mixture at B₀ = 20.0 T using quadrupolar parameters previously reported for each sulfate is shown in Fig. 2a. The two STMAS ridges are expected to be resolved in the δ₁ (isotropic) dimension and this was confirmed by our experimental natural abundance ³³S STMAS spectrum of the sulfate mixture recorded at B₀ = 20.0 T, 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 T₁ relaxation times of these anhydrous sulfates (T₁ = 30 s for Na₂SO₄ and 16 s for K₂SO₄).¹² The poor S/N in the δ₂ cross sections from Fig. 2b made any lineshape fitting unreliable but, using the δ₁ and δ₂ 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-t₁ STMAS experiments to obtain the isotropic chemical shift, δ_iso, and the isotropic I = 3/2 second-order quadrupolar shift, δ_Q = (250C_Q/ν₀)²(1 + η²/3):^32,34

δ_iso = (17δ₁ + 10δ₂)/27 (1a)

δ_Q = 85(δ₁ − δ₂)/54 (1b)

The isotropic I = 3/2 quadrupolar shift was then used to obtain the composite quadrupolar product P_Q = C_Q (1 + (η²/3))^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.

Table 1 Experimental ³³S NMR parameters for sodium sulfate and potassium sulfate taken from ref. 26 and this work (Fig. 2). The magnetic field dependent shifts δ₁ and δ₂ were measured at B₀ = 20.0 T. The P_Q values in brackets were calculated from the C_Q and η values in ref. 26 for comparison with the values determined in this work

	δ iso (ppm)	C Q (kHz)	η	δ 1 (ppm)	δ 2 (ppm)	P Q (kHz)
Na2SO4
Ref. 26	340.1 ± 1.0	655 ± 50	0.0 ± 0.1			(655 ± 50)
This work (Fig. 2)	340.6 ± 0.5			342.1 ± 0.5	338.1 ± 0.5	650 ± 80
K2SO4
Ref. 26	335.7 ± 0.5	959 ± 30	0.42 ± 0.05			(988 ± 37)
This work (Fig. 2)	336.4 ± 0.7			339.8 ± 0.5	330.6 ± 1.0	990 ± 80

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Fig. 1 (a) Simulated and (b) experimental ³³S MAS spectra of a 1 : 1 molar mixture of sodium sulfate (Na₂SO₄) and potassium sulfate (K₂SO₄) at B₀ = 20.0 T. In (a) the ³³S NMR parameters (δ_iso, C_Q and η) were taken from ref. 26 (see Table 1). 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 (a) Simulated and (b) experimental ³³S STMAS spectra of a 1 : 1 molar mixture of sodium sulfate (Na₂SO₄) and potassium sulfate (K₂SO₄) at B₀ = 20.0 T, with the corresponding isotropic projections. In (a) the ³³S NMR parameters (δ_iso, C_Q and η) were taken from ref. 26 (see Table 1). In (b) 192 transients were averaged for each of 67 t₁ increments of 132.22 μs with a relaxation interval of 20 s. An echo interval (τ) 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).

Following on from this successful feasibility study, our investigations of ettringite in a 7 mm MAS rotor using natural abundance ³³S NMR were conducted at, initially, B₀ = 20.0 T and, subsequently, B₀ = 9.4 T. A set of three experiments (single-pulse, spin-echo, and STMAS) was performed each field strength. Previously, two studies reported natural abundance ³³S MAS spectra of ettringite,^15,17 one at B₀ = 19.6 T using conventional single-pulse acquisition,¹⁵ and the other at B₀ = 14.1 T employing CT enhancement techniques.¹⁷ The higher B₀ field study simulates a spectrum with a single site¹⁵ while the lower B₀ field study proposes three S sites¹⁷ 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 ³³S 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 B₀ = 20.0 T). It was this efficient relaxation that encouraged us to attempt experiments at the relatively low field strength of B₀ = 9.4 T.

Table 2 Experimental ³³S NMR parameters for ettringite taken from ref. 15 and 17 and this work (Fig. 3 and 4). The magnetic field dependent isotropic shifts δ₁ in brackets were calculated at B₀ = 9.4 T and B₀ = 20.0 T from the C_Q and η values given in ref. 15 and 17 and determined in this work to allow comparison with the experimental STMAS spectra

	δ iso (ppm)	C Q (kHz)	η	δ 1 at 9.4 T (ppm)	δ 1 at 20.0 T (ppm)
Ref. 15	331	700	0.45	(339.2)	(332.8)
Ref. 17	331.1	516 ± 5	0.50 ± 0.05	(335.6)	(332.1)
	329.8	591 ± 5	0.72 ± 0.05	(336.2)	(331.2)
	329.6	810 ± 5	0.97 ± 0.05	(343.0)	(332.6)
This work	331.8	620 ± 20	0.1 ± 0.1	337.8	(333.1)
(Fig. 3 and 4)	332.1	660 ± 20	0.3 ± 0.1	339.1	(333.7)
	331.0	800 ± 20	0.1 ± 0.1	341.0	(333.2)

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Fig. 3 and 4 show the natural abundance ³³S single-pulse, spin-echo and STMAS spectra of ettringite in a 7 mm MAS rotor at B₀ = 20.0 T and 9.4 T, respectively. It is apparent from the B₀ = 20.0 T 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 B₀ = 20.0 T, we were encouraged to record the B₀ = 9.4 T ³³S 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 δ₁ ≈ 0, the δ₁ projection of the spectrum appears to show isotropically resolved S sites.

Fig. 3 (a–c) Experimental and simulated ³³S MAS and (d and e) experimental and simulated STMAS spectra of ettringite with corresponding isotropic projections at B₀ = 20.0 T. 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 ³³S MAS and STMAS spectra using the NMR parameters (δ_iso, C_Q and η) determined in this work and given in Table 2. In (d) 11 040 transients were averaged for each of 64 t₁ increments of 377.78 μs with a relaxation interval of 0.45 s. An echo interval (τ) of 6 ms was used. Total experimental time was 92 h. The MAS frequency was 5 kHz. A 7 mm MAS rotor containing both RbNO₃ 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 (a–c) Experimental and simulated ³³S MAS and (d and e) experimental and simulated STMAS spectra of ettringite with corresponding isotropic projections at B₀ = 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 ³³S MAS and STMAS spectra using the NMR parameters (δ_iso, C_Q and η) determined in this work and given in Table 2. In (d) 40 960 transients were averaged for each of 85 t₁ increments of 295.14 μs with a relaxation interval of 0.25 s. An echo interval (τ) 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.

Centre-of-mass analyses were performed on the two-dimensional STMAS spectra using the appropriate equations for I = 3/2 split-t₁ experiments³⁴ (eqn (1)–(2)). These provided initial estimates for the chemical shift and quadrupolar parameters for ettringite that were 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 δ₁ 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 B₀ = 20.0 T and 9.4 T for the three crystallographically distinct S sites in ettringite, as summarised in Table 2.

Fig. 5 compares the simulated δ₁ projections at B₀ = 20.0 T and 9.4 T using the parameters obtained in this work with those using the parameters from ref. 17 and with the experimental ³³S STMAS δ₁ projections. It is apparent that the ³³S NMR parameters from ref. 17 do not reproduce the experimental STMAS δ₁ 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 ³³S MAS lineshapes, and were subjected to significant line broadening (up to 50 Hz)¹⁷ during processing.

Fig. 5 (a and b) Simulated and (c) experimental isotropic projections of two-dimensional ³³S STMAS spectra of ettringite at B₀ = 20.0 T and 9.4 T. ³³S NMR parameters (δ_iso, C_Q and η) were taken from (a) ref. 17 and (b) this work, as summarised in Table 2.

Conclusions

We have demonstrated the feasibility of high-resolution ³³S STMAS NMR experiments at B₀ = 9.4 and 20.0 T and at the natural abundance of ³³S (0.76%). We judge that, at ³³S natural abundance in the presence of multiple S sites, ³³S STMAS is feasible at B₀ = 20.0 T for quadrupolar coupling constants up to 1 MHz in magnitude. If the ³³S spin–lattice relaxation times are particularly short, as in the case of ettringite, then our results indicate that ³³S STMAS becomes possible at lower field strengths, such as the B₀ = 9.4 T used here. Total acquisition times can be very long, a week or more, and we were fortunate that our B₀ = 9.4 T magnet was particularly stable. Using ³³S STMAS at ³³S natural abundance, we have resolved the disagreement in the ³³S 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 ³³S NMR parameters (δ_iso, C_Q and η) for ettringite that are in consistent agreement with ³³S MAS and STMAS spectra recorded at field strengths of B₀ = 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 ³³S T₁ relaxation times, is expected to complicate attempts to calculate the ³³S NMR parameters using first-principles methods such as WIEN2k or CASTEP, as we have confirmed in preliminary DFT studies.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors are grateful to Bruker UK Ltd and the University of Glasgow for the award of a PhD studentship (AS). The UK 850 MHz Solid-State NMR Facility used in this research was funded by EPSRC and BBSRC (contract reference PR140003), as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF). We are very grateful to Dr Dinu Iuga for collaborative assistance at the 850 MHz Facility and to Dr Tom Ball for preliminary ³³S STMAS NMR work at B₀ = 9.4 T.

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