Exploiting the Chemical Shielding Anisotropy to Probe Structure and

Article pubs.acs.org/JPCC

Exploiting the Chemical Shielding Anisotropy to Probe Structure and Disorder in Ceramics: 89Y MAS NMR and First-Principles Calculations Martin R. Mitchell,† Diego Carnevale,†,∥ Robin Orr,‡ Karl R. Whittle,§ and Sharon E. Ashbrook*,† †

School of Chemistry and EaStCHEM, University of St Andrews, North Haugh, St Andrews KY16 9ST, U.K. National Nuclear Laboratory, Sellafield, Seascale, Cumbria, CA20 1PG, U.K. § Institute of Materials Engineering, ANSTO, PMB1, Menai, NSW 2234, Australia ‡

S Supporting Information *

ABSTRACT: The local structure and cation disorder in Y2(Sn,Ti)2O7 pyrochlores, materials proposed for the encapsulation of lanthanide- and actinide-bearing radioactive waste, is investigated using 89Y (I = 1/2) NMR spectroscopy and, in particular, measurement of the 89Y anisotropic shielding. Although known to be a good probe of the local environment, information on the anisotropy of the shielding interaction is removed under magic angle spinning (MAS). Here, we consider the feasibility of experimental measurement of the 89Y anisotropic shielding interaction using two-dimensional CSA-amplified PASS experiments, implemented for 89Y for the first time. Despite the challenges associated with the study of low-γ nuclei, and those resulting from long T1 relaxation times, the successful implementation of these experiments is demonstrated for the end member pyrochlores, Y2Sn2O7 and Y2Ti2O7. The accuracy and robustness of the measurement to various experimental parameters is also considered, before the approach is then applied to the disordered materials in the solid solution. The anisotropies extracted for each of the sideband manifolds are compared to those obtained using periodic first-principles calculations, and provide strong support for the assignment of the spectral resonances. The value of the span, Ω, is shown to be a sensitive probe of the next nearest neighbor (NNN) environment, i.e., the number of Sn and Ti on the six surrounding “B” (i.e., six-coordinate) sites, and also provides information on the local geometry directly, through a correlation with the average Y−O8b distance (where 8b indicates the Wyckoff position of the oxygen).

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utilize the application of several π pulses applied at timings synchronous with the MAS rotor (as in the phase adjusted spinning sideband (PASS)7 approaches), allowing the manipulation of the phase and intensity of the MAS sidebands. Although two-dimensional PASS-type experiments afford a simple yet efficient method for the site-specific determination of CSA interactions, provided a sufficient number of sidebands are observed, the measurement of small anisotropic interactions remains a challenge. Typically, the MAS rates required to achieve the necessary number of sidebands in the manifold are either prohibitively low or are simply insufficient to remove the dipolar interactions, compromising spectral resolution. More recently, a number of experiments have been proposed that achieve an effect termed “CSA amplification”, where the conventional MAS spectrum (with MAS rate, ωr) in the direct dimension is correlated with a sideband pattern in the indirect dimension with an effective MAS rate of ωr/NT.11−16 Hence, these approaches can be thought of as “amplifying” the CSA by a factor of NT, enabling an accurate measurement to be obtained at MAS rates sufficient to achieve high resolution.

INTRODUCTION The chemical shielding interaction is perhaps the most useful and informative probe of the local atomic environment exploited in NMR spectroscopy.1 Although information is more usually provided by measurement of the isotropic, or average, chemical shift, δiso, NMR spectra of solids also contain information relating to the anisotropy, or orientation dependence, of the shielding interaction, resulting in powder-pattern lineshapes. This anisotropic information is, however, removed by magic-angle spinning (MAS),2 routinely employed to improve the sensitivity and resolution of solid-state NMR spectra. A number of strategies have been employed to measure the chemical shift anisotropy (CSA), including rotation at slow MAS rates, producing not only an isotropic centerband but also an envelope of spinning sidebands with intensities that depend upon the magnitude and asymmetry of the interaction.3,4 This approach becomes significantly more complicated as the number of distinct species in the spectrum increases, with potential overlap of centerbands and sidebands for different sites at the slow MAS rates required. A number of twodimensional methods have been proposed to overcome this problem, resulting in spectra where the isotropic resonances in one dimension are correlated with their corresponding sideband manifolds in the second.5−10 Many of these methods © 2012 American Chemical Society

Received: November 2, 2011 Revised: January 18, 2012 Published: January 19, 2012 4273

dx.doi.org/10.1021/jp2105133 | J. Phys. Chem. C 2012, 116, 4273−4286

The Journal of Physical Chemistry C

Article

Notably, the isotropic spectrum is obtained in the direct dimension, where resolution can be achieved with little detriment to the overall acquisition time. To date, these approaches have been evaluated for, and applied to, 13C NMR of sugars, amino acids, and other small organic molecules and 31 P NMR of simple inorganic phosphates.11−19 The ability to measure both isotropic and anisotropic shielding parameters would significantly ease the challenge of spectral assignment in solid-state NMR. This is particularly true for disordered materials, where the range of local environments often results in complex spectra with overlapping resonances. However, it is often this “disorder”, i.e., the deviation (whether positional or compositional) from the regular, periodic structure of a crystalline solid, which produces the interesting physical and chemical properties that can be exploited industrially or commercially. Methods able to probe the local, rather than the long-range structure, such as NMR spectroscopy, are vital in obtaining a detailed understanding of these materials. In recent years, the interpretation of solid-state NMR spectra has been considerably assisted by the advances in methods for the calculation of NMR parameters from first principles, with both shielding and quadrupolar interactions now able to be calculated using periodic approaches.20 This has resulted in increased interest in the combination of experimental NMR spectroscopy and first-principles calculations to investigate structure, disorder, and dynamics in organic materials, dense ceramics, glasses, minerals, and microporous frameworks.17,18,21 Although much early work was concerned only with the calculation of δiso (and quadrupolar parameters where applicable), more recently, the shielding anisotropy has also been exploited.17,18 This additional information will prove vital in understanding the complex NMR spectra observed for disordered solids. Here, we aim to combine information on the 89Y isotropic and anisotropic shielding obtained by experiment with that predicted by planewave density functional theory (DFT) calculations, to investigate disorder in yttrium-containing pyrochlore ceramics. The considerable crystal chemical flexibility of the pyrochlore structure (general formula A2B2O7) has resulted in its proposed utility as a host phase for the immobilization of actinide- and lanathanide-bearing nuclear waste.22 In recent work, we have shown that 89Y and 119 Sn NMR spectra of the Y2Ti2−xSnxO7 solid solution displayed a variety of different Y and Sn environments.23−25 Although titanium-based pyrochlores are generally considered to have good chemical durability, the incorporation of Sn has recently been demonstrated to result in an increased tolerance to damage by radioactive decay, creating a growing interest in the local structural environment and cation disorder in these materials.26 Despite the more challenging acquisition, 89Y MAS NMR spectra were shown to provide more detailed information on the cation disorder in Y2Ti2−xSnxO7 than 119Sn NMR spectra, owing to the considerable overlap of resonances in the latter.23−25 The 89Y MAS NMR spectra (shown in Figure 1, for B0 = 14.1 T) were tentatively assigned using first-principles electronic structure calculations of the isotropic chemical shielding, and were consistent with the presence of a random distribution of Sn and Ti cations on the pyrochlore “B” (i.e., sixcoordinate) sites.24 Given the overlap of the spectral lines, the combination of information on both the isotropic and anisotropic shielding would offer considerably more confidence in this assignment. Although 89Y is a 100% abundant spin I = 1/2 nuclide, the very low gyromagnetic ratio results in a

Figure 1. 89Y (14.1 T) MAS NMR spectra of Y2Ti2−xSnxO7 with x = 0, 0.4, 0.8, 1.2, 1.6, and 2. The spectra are the result of averaging 584 (x = 0, 2), 848 (x = 0.4, 1.6), and 1080 (x = 0.8, 1.2) transients, with recycle intervals of 10 (x = 0, 2) and 300 s (x = 0.4, 0.8, 1.2, 1.6) and a preacquisition interval of 80 μs. The MAS rate was 14 kHz.

molar receptivity ∼10000 times less than 1H. When coupled with typically long relaxation times (often many thousands of seconds), this can often limit the use of more complex twodimensional experiments. Our aims, therefore, are (i) to assess whether accurate experimental measurement of 89Y CSA parameters is feasible (with reasonable sensitivity and within a reasonable time frame), (ii) to evaluate the accuracy of CSA parameters calculated using periodic planewave DFT calculations for a series of simple model compounds, (iii) to determine whether the CSA is a sufficiently sensitive probe of the local Y environment, and (iv) to combine information from experiment and calculation to assign the 89Y NMR spectra and 4274



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Table 1. Experimental and Calculated 89Y NMR Parameters, Including Principal Components of the Shielding Tensor (δii and δiicalc), Span (Ω and Ωcalc), and Skew (κ and κcalc) for a Range of Simple Inorganic Compoundsa experimental compound Y2O333 Y2O333

Y1 Y2

Y2Sn2O734 Y2Ti2O735 Y2O2S36 YAlO337 Y3Al5O1238 Y4Al2O939 Y1 Y4Al2O939 Y2 Y4Al2O939 Y3 Y4Al2O939 Y4 YScO340 a

calculated

δ11

δ22

δ33

Ω

κ

ref

δ11calc

δ22calc

δ33calc

Ωcalc

κcalc

336 383 223 270 378 293 317 234 333 300 312 358

234 283 212 250 218 245 204 172 184 221 240 295

234 266 15 −325 218 107 142 147 131 64 141 136

102 117 208 595 160 86 175 86 202 236 171 221

−1 −0.7 0.9 0.9 −1 0.5 −0.3 −0.4 −0.5 0.3 0.2 0.4

41, 42 41, 42 25 25 41 42 42 42 42 42 42 40

351 406 219 244 416 329 380 256 355 305 325 377

231 286 219 244 241 309 259 194 170 257 244 322

231 255 56 −415 235 139 175 150 128 70 131 145

120 151 163 689 182 190 205 105 227 236 194 232

−1 −0.6 1 1 −0.9 0.8 −0.2 −0.2 −0.6 0.6 0.2 0.6

Values of δii and Ω are quoted in ppm. See original references for a discussion of experimental errors.

tables and plotted in figures is that output by SIMPSON, as described in the SIMPSON manual.28 Further details are given in the relevant figure captions. 119Sn MAS NMR experiments were performed for SnO2 using a conventional double resonance HX probe, a maximum rf field strength of ∼108 kHz, and powdered samples packed into 4 mm ZrO2 rotors. Chemical shifts are given relative to (CH3)4Sn. CSA-amplified PASS experiments were carried out using the pulse sequence in Figure S1.1b in the Supporting Information. Further details are given in the relevant figure captions. Calculations. Calculations of the shielding tensors were carried out using the CASTEP DFT code,29 employing the GIPAW algorithm20 which allows the reconstruction of the allelectron wave function in the presence of a magnetic field. The generalized gradient approximation (GGA) PBE functional30 was used, and core−valence interactions were described by ultrasoft pseudopotentials.31 A planewave energy cutoff of 50 Ry (680 eV) was used, and integrals over the Brillouin zone were performed using a k-point spacing of 0.04 or 0.05 Å−1. All calculations were converged as far as possible with respect to both k-point spacing and cut off energy. Initial structural parameters (unit cell size and shape, and all atomic positions) for model compounds were obtained from literature diffraction studies. The crystal structure was reproduced from these parameters using periodic boundary conditions. Where necessary, geometry optimization of the crystal structures was also performed within CASTEP (using the same conditions as described above). Calculations were performed on the EaStCHEM Research Computing Facility, which consists of 148 cores running at 2.4 GHz, partly connected by Infinipath high-speed interconnects. Calculation wallclock times ranged from 24 to 48 h using 16 cores, depending on the size of the calculation. Calculations generate the absolute shielding tensor (σ) in the crystal frame. Diagonalization of the symmetric part of σ yields three orthogonal principal components, σ11, σ22, and σ33. The principal components of the chemical shift tensor, δ11, δ22, and δ33, are related by

provide insight into the cation disorder in yttrium-containing pyrochlore ceramics.

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EXPERIMENTAL AND COMPUTATIONAL DETAILS Sample Preparation. Y2Ti2−xSnxO7 pyrochlores were prepared by grinding together stoichiometric amounts of Y2O3 (Aldrich 99.5%), SnO2 (Alfa-Aesar, 99.5%), and TiO2 (Alfa-Aesar 99.9%) in an agate ball mill using acetone as the mobile phase. The resultant powders were then pressed into pellets using a uniaxial press, heated at 1500 °C for 48 h (at 10 K min−1), cooled, reground, repressed, and heated for a further 96 h at 1500 °C. Samples were characterized by X-ray diffraction and electron microscopy and all determined to be single-phase pyrochlore. See ref 23 for further details. NMR Spectroscopy. NMR spectra were acquired using a Bruker Avance III 600 MHz spectrometer equipped with a 14.1 T widebore magnet, at Larmor frequencies of 29.4 MHz for 89Y and 223.8 MHz for 119Sn. For 89Y, experiments were performed on a commercial “low-γ” probe, using a radiofrequency (rf) field strength of 23 kHz and with powdered samples packed into 4 mm ZrO2 or Si3N4 rotors. Chemical shifts are given relative to 1 M YCl3 (aq) and were measured using Y2Ti2O7 as a secondary reference (δ = 65 ppm). Preacquisition intervals of ∼80 μs were used to eliminate problems resulting from probe ringdown. MAS spectra were acquired using a single π/2 pulse (of ∼11 μs) at a variety of rotation rates. Recycle intervals are given in the relevant figure captions. CSA-amplified PASS experiments were performed using the pulse sequence of Orr et al.,13,14 shown in Figure S1.1 of the Supporting Information. The total scaling factor is given by NT = (nPASS + 1)N, where N is the scaling factor determined by the timing of the five π pulses and nPASS is the additional number of π pulse blocks. Cogwheel phase cycling is used to reduce the length of the phase cycle required.27 In many cases, the experiment was modified to include a saturation train prior to the initial π/2 pulse, typically consisting of 32 pulses separated by 50 ms, allowing shorter recycle intervals, typically 10 s, to be employed. For more details on the two-dimensional experiments, see the Supporting Information. Fitting of the sideband patterns in the indirect dimension was carried out using SIMPSON,28 either by comparison to a one-dimensional MAS spectrum (assuming ideal pulses) or by complete simulation of the two-dimensional experiment (and an estimated rf field strength), as described in the text. The “rms” error quoted in

δii = −(σii − σref )/(1 − σref ) ≈ −(σii − σref )

(1)

where σref (assumed to be ≪1) is a reference shielding, determined in previous work to be 2646.5 ppm for 89Y.24 There are a number of different conventions for describing the shielding anisotropy. In this work, to enable a clear comparison 4275



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with the experimental data, the principal components of the shielding tensor are ordered such that δ11 ≥ δ22 ≥ δ33

(2)

The isotropic shift, δiso, is given by δ iso = (δ11 + δ22 + δ33)/3

(3)

while the shielding anisotropy is defined by the span Ω = δ11 − δ33

(4)

and the skew (a measure of the asymmetry of the tensor) κ = 3(δ22 − δ iso)/Ω

(5)

such that κ lies between −1 and +1. Alternative conventions for describing the shielding interaction, in terms of the anisotropy and asymmetry, are described in the Supporting Information.

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RESULTS AND DISCUSSION Calculation of the 89Y Shielding Anisotropy. Despite considerable recent work evaluating periodic planewave DFT approaches for calculating isotropic shieldings, relatively little attention has been focused on the shielding anisotropy, principally owing to the difficulty of experimental measurement for all but the simplest compounds.17,18,32 For 89Y NMR, this problem is exacerbated by the low sensitivity of NMR spectra in general, and in particular, of the broader lines associated with anisotropic interactions. However, a small number of 89Y shielding anisotropies have been measured experimentally, and these are given in Table 1 along with corresponding values calculated using DFT. Figure 2a shows a plot comparing the principal components (δ11, δ22, and δ33) of the experimental and calculated shielding tensors (defined as in eq 2). An ideal (i.e., 1:1) correlation is shown by the dotted line. Good agreement is obtained between experiment and calculation, with a strong linear correlation observed. However, some of the calculated components appear to be slightly underestimated, and this can also be seen in Figure 2b, where the experimental and calculated spans are compared. The experimental and calculated skew are also in good agreement, as shown in Figure 2c, although the greater degree of scatter here probably reflects (i) the increased difficulty in accurate experimental measurement and (ii) the dependence of κ on all three calculated principal tensor components. For the two pyrochlore end members, Y2Sn2O7 and Y2Ti2O7, the agreement between calculation and experiment is relatively good, as shown in Table 1.24 The calculated skew, κcalc, in both cases is +1, in agreement with the axial point symmetry expected from the crystal structure. The experimental values differ slightly from this, probably owing to the relatively poor sensitivity of the experimental spectra, and the possible presence of dipolar (and J) couplings in NMR spectra of static samples. In general, the agreement between calculation and experiment is similar to that found for the calculation of 89Y isotropic chemical shifts.24 Having established the general accuracy of the planewave periodic DFT approach for the calculation of 89Y shielding tensors, attention can be turned to the specific case of the Y2(Sn,Ti)2O7 solid solution. The values of Ω for the two end members, Y2Sn2O7 and Y2Ti2O7, highlighted in Figure 2b, although in good agreement with the general trend, appear to be slightly underestimated and overestimated, respectively, by the calculations. If these two points are considered in isolation, this would result in a correlation that does not have the “ideal”

Figure 2. Plot comparing experimental and calculated (a) principal components, δ11, δ22, and δ33, (b) span, Ω, and (c) skew, κ, of the 89Y shielding tensor for a range of yttrium-containing compounds. In each case, the dashed line shows a 1:1 correlation as a guide to the eye. In parts b and c, the points for the two end member pyrochlores Y2Sn2O7 and Y2Ti2O7 are highlighted.

gradient of 1. As subsequent calculations will focus only on the solid solution between these two, calculated spans (Ωcalc) have been systematically “corrected” or scaled (Ωcalc,scaled) to take account of this, simply for easier comparison between the experimental and calculated data. Similar scaling factors have also been used in previous work, where 13C experimental and calculated anisotropic shieldings were compared.17 Further details on this correction can be found in the Supporting Information. For ordered solids, the calculation of the shielding tensor is relatively straightforward, as shown above. The investigation of disordered materials is considerably more challenging, as the translational symmetry is disrupted by variations in either position, composition, or occupancy. For the Y2(Sn,Ti)2O7 pyrochlore solid solution, the major changes in the 89Y local environment concern the nature of the cations occupying the surrounding atomic positions. Hence, the preservation of the long-range positional periodicity and the three-dimensional nature of the material provide a strong incentive to retain a 4276



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Figure 3. (a) Cluster showing the nearest and next nearest neighbor (NNN) environment of the eight-coordinated A-site in the pyrochlore structure, occupied by Y. Red spheres denote O, green spheres denote Y, and small dark and light blue spheres denote (B site) Sn and Ti, respectively. (b) Possible arrangements of Sn/Ti on the six NNN B sites that surround the pyrochlore A site.

periodic approach for the calculations. In general, the investigation of disordered materials may be assisted by the use of “supercells”, allowing a wider range of structural modifications to be studied, although it is clearly not possible to consider directly the full disordered material, as an impractically large calculation would be required. Here, we utilize the simplified approach described in previous work,24,25 for the calculation of δiso in pyrochlore solid solutions, where the local environment of just one Y species in a single Y2B2O7 pyrochlore unit cell is modified systematically, altering both the number of the surrounding cations and their spatial arrangement. The Y3+ cation occupies the eight-coordinated A site of the pyrochlore structure (space group Fd-3m), and is surrounded by six B-site next nearest neighbors (NNN), as shown in Figure 3a, in principle occupied by either Sn4+ or Ti4+, although the exact distribution of these cations in the real materials is not known. The environment of one of the 16 Y species within the unit cell was modified systematically to include all the possible NNN arrangements shown in Figure 3b. In each case, the geometry of the structure was optimized (with atomic coordinates and unit cell parameters allowed to vary), prior to calculation of the NMR parameters. Figure 4a shows a plot of the calculated span, Ωcalc,scaled, as a function of the number of Sn NNN for each of the Y environments shown in Figure 3b, for both initial Sn-based and Ti-based pyrochlore cells. There is a systematic increase in Ωcalc,scaled as the number of Sn NNN decreases,24 reflecting the differences observed for the two end members, as Ω is significantly larger for the titanate than the stannate. This appears to reflect the variation in the 48f oxygen (O48f) x position, which differs from the ideal value (0.375) found in fluorite, with x = 0.338 for yttrium stannate and 0.327 for yttrium titanate.24−26 Any deviation of x away from the ideal value results in a distortion of the oxygen coordination environment around the Y from the ideal cube found in fluorite, to that shown in Figure 3a, decreasing the two Y−O8b bond lengths relative to the six Y−O48f distances, thereby resulting in a greater anisotropy. The introduction of one Ti into the NNN environment results in an increase of ∼80 ppm in Ωcalc,scaled. The effect of the longer-range environment is also apparent, with a difference in Ωcalc,scaled also of ∼80 ppm between Ti-based and Sn-based cells, although a similar trend with Ti substitution is observed in each case. Although the environment of only one Y species has been modified systematically in the calculations, the local environments of the remaining 15 Y cations within the unit cell are also modified by these changes, with different NNN arrangements or with longer-range differences. The calculated spans for all Y species are plotted as a function of the number of Sn NNN in Figure 4b, along with additional data extracted from a series of

Figure 4. Plots showing the 89Y calculated span, Ωcalc,scaled, as a function of the number of Sn NNN, n, for each of the local environments shown in Figure 3b, with initial cells of Y2Sn2O7 and Y2Ti2O7. In part a, only Ωcalc,scaled for the Y species at the center of the modified cluster is shown, while in part b, Ωcalc,scaled for all Y species within the unit cell are plotted. Also included in part b are 89Y Ωcalc,scaled extracted from a series of similar calculations from previous work.24

similar calculations in previous work.24 The differences in the longer-range environment and small changes in local geometry result in distributions of Ωcalc,scaled (of ∼90 ppm) associated with a coordination type, with an increase in the average Ωcalc,scaled (of ∼70 ppm) with Ti substitution. Notably, the ranges of the span observed for different spatial arrangements of a fixed number of Sn/Ti NNN (e.g., 1,2-, 1,3-, and 1,4Sn4Ti2 environments) overlap and so are not expected to be distinguished experimentally. It is possible to correlate the changes in Ωcalc,scaled directly to local structure, as shown in Figure 5, where the dependence upon the (average of the two) Y−O8b bond distances is plotted. A strong, almost linear, correlation (of ∼ −109 ppm/0.02 Å) is observed, highlighting the sensitivity of the anisotropic shielding to small changes in geometry. Although the variation in the (six) Y−O48f bond distances has a much smaller effect upon Ωcalc,scaled, a weak correlation is observed with the Y−O48f bond distance (see the Supporting Information). 4277



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significantly increase the confidence in any assignment. Although the skew, κ, is more difficult to measure experimentally, it is also possible to calculate the effect upon this of NNN substitution. For both end members, the Y3+ cation sits at a point of axial symmetry, with κ = +1. As Sn/Ti are substituted onto the six NNN B sites, this symmetry will be broken and a variation in κ is expected. The exact value will depend upon (i) the number and spatial arrangement of the Sn/Ti cations, (ii) the nature of the more remote cations, and (iii) any resulting changes/distortions in the local geometry. Figure S5.1 in the Supporting Information shows a plot of κcalc as a function of the number of Sn/Ti NNN. A deviation from axial symmetry is observed as the number of Sn/Ti NNN is varied, although the presence of a range of contributions to κcalc makes it difficult to relate directly to local structure. Experimental Measurement of the 89Y Shielding Anisotropy. The challenges associated with experimental 89Y NMR are amplified for lineshapes broadened by anisotropic interactions, and particular attention must be given to efficient methods for spectral acquisition and the accuracy of the information extracted. It is often implicitly assumed that wideline spectra of static samples produce the “best”, i.e., most accurate, measurement of the shielding anisotropy. However, the sensitivity of such spectra can be poor, compromising the reliability of the information extracted. In contrast, the sensitivity of MAS spectra is considerably higher, and spinning at a moderate rate offers the compromise of increased

Figure 5. Plot showing the dependence of the 89Y calculated span, Ωcalc,scaled, on the average of the two Y−O8b bond distances, ⟨Y−O8b⟩. The NNN environments are as shown in Figure 3b.

It is notable that the variation in Ωcalc,scaled in Figure 4b for any one number of Sn/Ti NNN is such that the ranges for different environments overlap, particularly when the number of Sn and Ti NNN are similar. This was also observed to be the case for the 89Y δiso in previous work.24 Thus, while both the isotropic and anisotropic shielding are sensitive probes of the local environment, it can be difficult to assign NMR spectra unambiguously by considering just one of these parameters. The measurement of both, however, could provide a considerably more robust method for spectral analysis and

Figure 6. (a) 89Y (14.1 T) slow MAS NMR spectra of Y2Ti2O7 (left) and Y2Sn2O7 (right) with MAS rates of 2 and 0.9 kHz, respectively. Overlaid (in red) are the sideband intensities extracted from two-dimensional CSA-amplified PASS experiments, acquired using the pulse sequence in Figure S1.1a in the Supporting Information and a recycle interval of 180 s. In part b, experimental parameters are as in part a, but in all experiments, a prior saturation train consisting of 32 pulses separated by 50 ms was employed, and recycle intervals of 10 s were used. Also shown (by the blue line) in parts a and b are ideal spectra (shifted slightly for ease of comparison), simulated using the CSA parameters extracted from previous experiments (for static samples) in the literature.24 Part c shows the differences between the (normalized) two slow MAS (solid lines) and two CSA-amplified PASS sideband intensities (red data points) shown in parts a and b, i.e., with and without a saturation train. Other experimental parameters: Y2Ti2O7 [MAS (a) 72 (b) 1296 transients; PASS 16 t1 increments, MAS rate = 10 kHz, NT = 5, nPASS = 1, (a) 52 (b) 442 transients]. Y2Sn2O7 [MAS (a) 196 (b) 3528 transients; PASS 16 t1 increments, MAS rate = 6 kHz, NT = 6.67, nPASS = 1, (a) 52 (b) 442 transients]. 4278



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Table 2. Experimental 89Y NMR Anisotropic Shielding Parameters (Span, Ω, and Skew, κ) and Corresponding Root-MeanSquare (rms) Deviation Resulting from Fits of 89Y Slow MAS (MAS) and Two-Dimensional CSA-Amplified PASS (PASS) Spectra for Y2Ti2O7 and Y2Sn2O7a Y2Ti2O7 b

experiment

static24 c Figure 6a MAS (2 kHz) PASS [10, 5, 1] (2)

Y2Sn2O7

Ω (ppm)

κ

595

0.9

a a b

597 561 604

0.9 0.5 0.6

0.4 6.9 3.4

MAS (0.9 kHz) PASS [6, 6.67, 1] (0.9)

a a b

594 562 603

0.9 0.5 0.7

0.4 5.1 3.3

a a a b a b

602 593 595 609 543 603

0.8 0.8 0.6 0.7 0.6 0.7

0.3 2.4 4.2 3.2 14.0 12.7

a a b a b

597 589 597 561 603

0.9 0.7 0.8 0.5 0.7

0.4 1.1 1.2 5.1 3.3

fitting

rms

Ω (ppm)

κ

208

0.9

a a b

166 214 218

1 0.5 0.5

3.4 2.8 2.7

SATMAS

(0.9 kHz) PASS [6, 6.67, 1] (0.9) SAT

a a b

171 204 209

0.8 0.5 0.5

5.3 2.1 2.1

MAS (0.9 kHz) [3, 3.33, 0] (0.9)

a a b a b

166 208 209 204 209

1 0.7 0.7 0.5 0.5

3.4 2.6 2.5 2.1 2.1

experiment

b

fitting

static24 c

rms

Figure 6b SATMAS

(2 kHz) PASS [10, 5, 1] (2) SAT Figure 7a MAS (2.4 kHz) MAS (1.2 kHz) SATPASS [8, 3.33, 0] (2.4) SATPASS

[8, 6.67, 1] (1.2)

Figure 7b MAS (2 kHz) SATPASS [5, 2.5, 0] (2) SATPASS

[10, 5, 1] (2)

SATPASS

SATPASS

[6, 6.67, 1] (0.9)

a

Fits were carried out using either (a) simulation of the MAS spectrum or (b) a complete simulation of the two-dimensional PASS spectrum. Experiments with a prior saturation train are denoted SATMAS/PASS. For MAS experiments, parameters are denoted MAS (F2 MAS rate in kHz). For PASS experiments, parameters are denoted PASS [F2 MAS rate in kHz, NT, nPASS] (F1 MAS rate in kHz). cNote that axial symmetry is expected from the crystal structure, i.e., κ = 1. b

to ±30 Hz on the hardware used. This results in a broadening of the spinning sidebands in the experimental spectrum (the isotropic peak remains relatively unaffected), variation in the sideband intensities, and inaccuracy in the extracted parameters. This effect is more pronounced for Y2Sn2O7 owing to the smaller Ω, and is a fundamental limitation in the extraction of information from slow MAS experiments. The two end member pyrochlores provide an excellent test for the evaluation of two-dimensional PASS-based experiments for measuring the 89Y anisotropic shielding interaction, with simple isotropic spectra obtained in a reasonable time scale, and different anisotropy in each case. At first sight, it appears that the low sensitivity and long T1 relaxation times associated with 89 Y NMR will limit, or even preclude, the use of twodimensional experiments. However, experiments based on the PASS approach require only a small number of increments in the indirect dimension (equivalent to the number of sidebands desired), enabling such experiments to be feasible within a reasonable time scale. Two-dimensional 89Y CSA-amplified PASS spectra were acquired using the pulse sequence introduced by Orr et al.,13,14 shown in Figure S1.1a in the Supporting Information. This experiment yields a two-dimensional spectrum, correlating the spectrum under rapid MAS (at rate ωr) in the direct dimension with one at an apparent spinning rate of ωr/NT, in the indirect dimension. The total scaling factor NT depends upon the timing of the five π pulses and the number of additional π pulse blocks (nPASS) used. Note that any spinning sidebands observed in the direct dimension must also be included when considering the (sum) projection in the indirect dimension. Under ideal conditions, the sideband

sensitivity, while retaining enough information for the anisotropy to be extracted with reasonable accuracy. The reliability of the shielding parameters extracted from MAS spectra (the reduced anisotropy, δ, and asymmetry, η, rather than Ω and κ) as the number of MAS sidebands varied was discussed by Hodgkinson and Emsley.43 A summary of their results (and a similar investigation of 89Y MAS NMR of Y2Ti2O7) is shown in the Supporting Information. The 89Y MAS NMR spectra for the end members of the solid solution of interest both exhibit a single sharp resonance, as shown in Figure 1, although there is a difference in anisotropy between them (as described above) owing to the different 48f oxygen positions.23,24 Figure 6a shows 89Y NMR spectra of Y2Sn2O7 and Y2Ti2O7, acquired under slow MAS conditions. For Y2Ti2O7, the NMR parameters extracted are in good agreement with previous data in the literature from experiments on static samples (see Table 2).23,24 This can also be seen in Figure 6a, where a MAS spectrum simulated using the values given in the literature is shown in blue (shifted slightly for ease of comparison). It should be noted that as κ = +1 (and η = 0) it is difficult to extract reliable information on the shape of the shielding tensor without a large number of sidebands present. For Y2Sn2O7, there is a discrepancy between the shielding parameters extracted from the slow MAS spectrum and those reported previously in the literature, as shown in Table 2.23,24 This is clearly seen in the spectrum shown by the blue line in Figure 6a, simulated using the values given in the literature. This difference appears due to inherent instabilities in the MAS rate, which becomes more difficult to control accurately at slower MAS rates (∼900 Hz in this case), with deviations of up 4279



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Figure 7. (a) 89Y (14.1 T) slow MAS NMR spectra of Y2Ti2O7 with MAS rates of 2.4 (left) and 1.2 (right) kHz. Overlaid are sideband intensities extracted from two-dimensional CSA-amplified PASS experiments, acquired using the pulse sequence in Figure S1.1b in the Supporting Information, with apparent spinning rates (ωr/2πNT) in the indirect dimension of 2.4 (left) and 1.2 (right) kHz. (b) 89Y (14.1 T) slow MAS NMR spectra of Y2Ti2O7 (left) and Y2Sn2O7 (right), with MAS rates of 2 kHz and 900 Hz. Shown overlaid are sideband intensities extracted from two-dimensional CSA-amplified PASS experiments, acquired using the pulse sequence in Figure S1.1b in the Supporting Information, with apparent spinning rates in the indirect dimension of 2 (left) and 0.9 (right) kHz. In each case, the blue line shows an ideal spectrum (shifted slightly for ease of comparison), simulated using the CSA parameters extracted from previous experiments (for static samples) in the literature.24 Other experimental parameters: (a) [MAS (left) 650 (right) 1000 transients, recycle interval 10 s; PASS (left) 392 transients, 16 t1 increments, NT = 3.33, nPASS = 0, recycle interval 10 s, MAS rate = 8 kHz (right) 442 transients, 32 t1 increments, NT = 6.67, nPASS = 1, recycle interval 10 s, MAS rate = 8 kHz]. (b) Y2Ti2O7 [MAS 72 transients, recycle interval 180 s; PASS (green) 448 transients, 16 t1 increments, NT = 2.5, nPASS = 0, recycle interval 10 s, MAS rate = 5 kHz; PASS (red) 442 transients, 16 t1 increments, NT = 5.0, nPASS = 1, recycle interval 10 s, MAS rate = 10 kHz], Y2Sn2O7 [MAS 196 transients, recycle interval 180 s; PASS (green) 448 transients, 16 t1 increments, NT = 3.33, nPASS = 0, recycle interval 10 s, MAS rate = 3 kHz; PASS (red) 442 transients, 16 t1 increments, NT = 6.67, nPASS = 1, recycle interval 10 s, MAS rate = 6 kHz].

intensities should match the manifold when spinning at ωr/NT. Sideband intensities extracted from 89Y NMR experiments performed for Y2Sn2O7 and Y2Ti2O7 using amplification factors NT of 6.67 and 5 are shown overlaid on the slow MAS spectra in Figure 6a. These were acquired in 42 h, in contrast to the slow MAS spectra obtained in 9.8 and 3.6 h for the stannate and the titanate, respectively. Relatively good agreement is observed for each material, despite the extremely challenging nature of the two-dimensional experiments, demonstrating the success of this approach for 89Y. For the stannate, the agreement is best between the simulated slow MAS spectrum and the CSA-amplified PASS data, highlighting the benefits of using the amplified PASS-type approach over traditional slow MAS for compounds with smaller Ω, where the accuracy is limited by mechanical instabilities at slow MAS rates. In general, however, the agreement between MAS and CSAamplified PASS data is poorer for the titanate, where Ω is considerably larger. NMR parameters extracted from fitting these intensities are given in Table 2. Although the spectra in Figure 6a demonstrate that 89Y CSAamplified PASS experiments are possible for simple compounds, sensitivity remains a major challenge, with unfeasibly long experiments required when more complex (and disordered) materials are studied. It is common in cases

where experimental times are limited by slow T1 relaxation rates to employ a short recycle interval in conjunction with a prior saturation train, ensuring that any necessary phase cycling remains efficient. As Y2Ti2O7 and Y2Sn2O7 contain only a single distinct Y species, nonuniform relative relaxation between resonances is not a concern; however, it is necessary to ensure that the relative intensities of the sideband manifold (and the accuracy of the parameters extracted) is not affected by the use of a saturation train. Figure 6b shows 89Y slow MAS spectra acquired using a saturation train (and a recycle interval of 10 s) for Y2Ti2O7 and Y2Sn2O7. The relative sideband intensities in each case are very similar to the corresponding MAS spectra in Figure 6a. This is more clearly seen in Figure 6c, where the traces show the difference in the sideband intensities between the slow MAS spectra recorded with and without a saturation train. In terms of overall signal, for this sample, the conventional MAS spectrum has more signal per transient (by a factor of ∼3.2), but greater signal intensity per unit time is observed when a saturation train (with a recycle interval of 10 s) is used (by a factor of ∼5.5). Clearly, the exact enhancements observed will depend upon the T1 relaxation time for the sample used and the chosen recycle interval. Also shown in Figure 6b are the sideband intensities extracted from two-dimensional CSA-amplified PASS experi4280



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infinitely strong, infinitesimally short, accurately synchronized on-resonance π pulses. In reality, experimental limitations and imperfections will result in deviations in the intensities of the sideband manifold and contribute to inaccuracies in the shielding parameters. For 89Y, a low-γ nucleus, the strength of the rf field available (ν1 = ω1/2π = −γB1), and in particular its relation to the span (expressed in Hz), ΩHz, may be a fundamental limitation in the accuracy of the shielding parameters extracted. For Y2Ti2O7, the sideband manifold is considerably larger than for Y2Sn2O7, with ν1/ΩHz = ∼1.3 and ∼3.7, respectively, perhaps explaining the poorer agreement between the one- and two-dimensional experiments in Figures 6 and 7 for the titanate pyrochlore. It is difficult to investigate the effect of low rf field strength on the 89Y sideband intensities in a two-dimensional CSA-amplified PASS spectrum directly, as the maximum mutation rate that can be achieved experimentally is already very low. It is possible to gain some insight into this effect using an alternative nucleus. Figure 8 shows

ments acquired using the modified pulse sequence shown in Figure S1.1b in the Supporting Information (and a recycle interval of 10 s) for Y2Ti2O7 and Y2Sn2O7. In each case, the sideband manifold is relatively unaffected by the use of a saturation train, as shown by the data points in Figure 6c. Little difference is observed in the shielding parameters extracted, as shown in Table 2. As was observed for the MAS spectra, the use of a saturation train results in less signal per transient (by a factor of ∼3.3) but more signal per unit time (by a factor of ∼5.4). It is probable that experimental duration, rather than sensitivity, will be the limiting factor when two-dimensional experiments are utilized for more complex materials. All further two-dimensional CSA-amplified PASS experiments have, therefore, been acquired using the modified pulse sequence in Figure S1.1b in the Supporting Information. The choice of scaling factor in a CSA-amplified PASS experiment (along with the actual MAS rate) governs the sideband spacing in the indirect dimension and the accuracy with which shielding parameters can be extracted. Figure 7a shows sideband intensities extracted from 89Y CSA-amplified PASS spectra of Y2Ti2O7, acquired with NT = 3.33 and 6.67. In each case, the actual MAS rate was 8 kHz, resulting in MAS rates in the indirect dimensions of 2.4 and 1.2 kHz, respectively. The corresponding slow MAS spectra are also shown for comparison. Assuming each spectrum can be acquired with sufficient sensitivity, the presence of a greater number of sidebands might be expected to result in more accurate anisotropic shielding parameters.43 For the slow MAS spectra, Table 2 shows that the shielding parameters extracted are similar for the two experiments, demonstrating that both sensitivity and number of sidebands play a role in the accuracy of the values extracted. It can be seen that the agreement between the sideband intensities in the CSA-amplified PASS experiments and those in the slow MAS spectrum is significantly poorer with the higher scaling factor, shown both in Figure 7a and in the values given in Table 2. This is also accompanied by a significantly higher rms deviation in the fitting process, suggesting a poorer quality of fit. In general, in the experiment of Orr et al.,13,14 scaling factors up to 3.4 can be obtained by altering the pulse timings within one block of five π pulses (i.e., nPASS = 0); however, larger scaling factors can only be achieved by the concatenation of π pulse blocks. Any errors or inefficiencies in the inversion pulses may then be amplified, and can potentially lead to less accurate results. This is demonstrated in Figure 7b, where sidebands extracted from 89Y CSA-amplified PASS spectra of Y2Ti2O7 and Y2Sn2O7 with apparent MAS rates in the indirect dimension of 2 kHz and 900 Hz, respectively, are shown. Scaling factors of 2.5 and 5 (with 1 and 2 total blocks of π pulses, respectively) are used for Y2Ti2O7, while factors of 3.33 and 6.67 (with 1 and 2 total blocks of π pulses, respectively) have been employed for Y2Sn2O7. Also shown for comparison are the corresponding slow MAS spectra. Shielding parameters extracted from the spectra are given in Table 2. For the stannate, the sideband intensities from the PASS experiments are similar to those in the (simulated) slow MAS spectra for experiments using either 1 or 2 (i.e., nPASS = 0 or 1) blocks of π pulses, and the NMR parameters extracted are in good agreement in all cases. For Y2Ti2O7, the agreement is considerably poorer when two blocks (i.e., nPASS = 1) of π pulses are used. The CSA-amplified PASS experiment of Orr et al.,13,14 and indeed the other related experiments of Crockford et al.11 and Shao et al.,12 were designed assuming “ideal conditions”, i.e.,

Figure 8. 119Sn (14.1 T) slow MAS NMR spectrum of SnO2 with an MAS rate of 3.5 kHz. Shown overlaid are sideband intensities extracted from two-dimensional CSA-amplified PASS experiments, acquired using the pulse sequence in Figure S1.1b in the Supporting Information, with a range of rf field strengths from 11 to 109 kHz, resulting in values of ν1/ΩHz between 0.4 and 3.9. Data are shown (a) before and (b) after normalization (to the isotropic resonance). Other experimental parameters: [MAS 64 transients, recycle interval 15 s; PASS 392 transients, 16 t1 increments, NT = 2, nPASS = 0, recycle interval 5 s, MAS rate = 7 kHz].

sideband intensities extracted from 119Sn CSA-amplified PASS experiments on SnO2 (Ω = ∼125 ppm, κ = ∼1),44 at a variety of rf field strengths, along with a slow MAS spectrum for comparison. In Figure 8a, where the spectra are shown without normalization, it can be seen that (as expected) the overall signal intensity decreases as the rf field strength decreases. More importantly, there is a significant difference in the relative intensities of the sidebands within the manifold at lower rf field strengths, particularly obvious when ν1/ΩHz is less than 1. This is more clearly shown in Figure 8b, where the spectral 4281



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intensities have been normalized (to the isotropic resonance). This suggests that low rf field strength is the most probable cause of the poorer agreement observed in the 89Y CSAamplified PASS spectra of Y2Ti2O7. In principle, this observation could be of considerable significance, suggesting that the maximum rf field strength is a limiting factor on the accuracy of the shielding parameters for 89 Y (and other low-γ nuclei), particularly for compounds where the anisotropy is large. It may be possible to obtain higher rf field strengths using home-built equipment, or to utilize probes with smaller rotor diameters; however, in the latter case, the reduced sample volume will lead to significant losses in sensitivity and perhaps unfeasibly long two-dimensional experiments. The fitting procedures we have used so far have compared the sideband manifold obtained from the twodimensional PASS spectra to the sideband intensities in a simulated MAS spectrum, implicitly assuming the use of ideal pulses. A more accurate fit can be obtained by comparison to a projection of the spectrum from a complete simulation of the two-dimensional experiment, using the rf field strength estimated from the experiment. Although slightly more timeconsuming to perform, this results in a considerable improvement in the accuracy of the NMR parameters, as seen in Table 2, where Ω and κ extracted from the 89Y spectra of Y2Ti2O7 in Figures 6 and 7 using the more sophisticated fitting procedure (labeled b) are given (see also the Supporting Information for a comparison of experimental and fitted data using the two different procedures). In each case, the agreement with the parameters extracted from the MAS spectrum is better, demonstrating that, while deviations in the sideband manifold are present when the rf field strength is low, this can largely be accounted for by a modified fitting procedure. The agreement for κ, although better using the new fitting procedure, is noticeably poorer than that for Ω; this reflects the inaccuracies predicted when κ is close to ±1, unless a very large number of sidebands is used, as discussed previously. All further experimental spectra have been fitted using procedure b. As previous CSA amplification experiments in the literature have exploited nuclei such as 13C and 31P with reasonably high γ,11−19 the rf field strength is not likely to have been a concern. The consequences of rf inhomogeneity and off resonance effects have, however, been the subject of investigation. Composite pulses45 (trains of simple pulses with varying flip angle and phase that are designed to exhibit an increased tolerance to experimental imperfections yet achieve the same overall result as a single pulse) have been utilized in some twodimensional approaches to compensate, for example, for B1 inhomogeneity.12,16 For 89Y, where the low rf field strength results in long pulse durations, composite pulses may not be beneficial, with the resulting pulse durations typically a significant proportion (>60%) of the rotor period. It is possible to investigate the effect that any rf inhomogeneity may be having on the relative sideband intensities by restricting the volume of the rotor occupied by the sample. Figure 9 shows the sideband manifold extracted from 89Y CSA-amplified PASS experiments on Y2Ti2O7 where the sample has been restricted to ∼60% of the rotor volume at the (i) top, (ii) middle, and (iii) bottom, respectively. There is a decrease in the overall signal intensity when the sample sits at the top or bottom of the rotor (although this is slightly different in the two cases, despite the presence of similar amounts of sample) and, notably, a much smaller decrease when the sample is restricted to the center, demonstrating that B1 inhomogeneity does appear to be

Figure 9. 89Y (14.1 T) slow MAS NMR spectrum of Y2Ti2O7 with an MAS rate of 2.4 kHz. Shown overlaid are sideband intensities extracted from two-dimensional CSA-amplified PASS experiments, acquired using the pulse sequence in Figure S1.1b in the Supporting Information. Points shown in green, purple, dark green, and red result from sample restricted to the top, middle, and bottom 60% of the rotor volume, respectively, while the light green data points represent the result from a full rotor. Data are shown (a) before and (b) after normalization (to the isotropic resonance). Other experimental parameters: [MAS 88 transients, recycle interval 10 s; PASS 392 transients, 16 t1 increments, NT = 3.33, nPASS = 0, recycle interval 10 s, MAS rate = 8 kHz].

significant. However, the relative sideband intensities (most clearly seen in Figure 9b after normalization of the spectral intensities) are almost identical, suggesting that any errors resulting from inhomogeneity are either smaller than those resulting from low rf field strength or are compensated by the use of cogwheel phase cycling.45 A similar result was also observed when the π pulses used were artificially mis-set by up to ±30°. Although the overall signal intensity varied, the relative sideband intensities were largely unaffected. See the Supporting Information. Application to the Disordered Pyrochlore Solid Solution. From the results above, it appears that, despite the practical difficulties, 89Y CSA-amplified PASS experiments are possible for simple pyrochlores, and enable shielding parameters to be extracted with reasonably good accuracy. The use of a saturation train is vital for ensuring that the experiment can be completed on a feasible time scale, and appears to have little effect upon the relative sideband intensities and the accuracy of the NMR parameters. The accuracy does, however, decrease with increasing shielding anisotropy, primarily as a result of the low rf field strength available, although improvements can be obtained by including the rf field strength in the fitting procedure. Furthermore, it is noticeable that Ω is more consistently reproduced than κ, 4282



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sional experiment) and the rms deviation for a range of Ω and κ plotted, as shown in Figure 10b. The minimum rms deviation is given in Table 3, along with the value of Ω associated with the

although this may be a result of the latter being close to 1. However, the extension of this method to the Y2(Sn,Ti)2O7 solid solution, where the more complicated spectra exhibit a larger number of broadened resonances, poses an immense experimental challenge, and will result in very lengthy experimental acquisition times to obtain sufficient sensitivity. For this reason, only the more reliable measurement of Ω will be considered. Figure 10a shows an example of an 89Y two-dimensional CSA-amplified PASS spectrum of Y2Ti2−xSnxO7 (x = 1.6),

Table 3. Values of the 89Y Isotropic Shift, δiso, and Span, Ω, Extracted from MAS and Two-Dimensional CSA-Amplified PASS Experiments for the Y2(Sn,Ti)2O7 Solid Solution and Corresponding Root-Mean-Square (rms) Deviationa compound Y2Sn2O7 Y2Ti0.4Sn1.6O7

Y2Ti0.8Sn1.2O7

Y2Ti1.2Sn0.8O7

Y2Ti1.6Sn0.4O7

Y2Ti2O7

NNN environment

δiso (ppm)

Ω (ppm)

rms

Y−O8b (Å)

Sn6 Sn6 Sn5Ti Sn4Ti2 Sn6 Sn5Ti Sn4Ti2 Sn3Ti3(a) Sn3Ti3(b) Sn2Ti4 SnTi5 Sn5Ti Sn4Ti2 Sn3Ti3(a) Sn3Ti3(b) Sn2Ti4 SnTi5 Ti6 Sn3Ti3(a) Sn3Ti3(b) Sn2Ti4 SnTi5 Ti6 Ti6

148 153 136 121 158 140 124 113 105 94 80 146 127 115 106 93 81 63 118 108 96 81 64 65

209 230 276 341 194 241 327 398 453 399 419 288 312 350 335 423 521 581 334 303 425 513 572 603

2.1 2.6 2.3 11.6 12.2 1.9 2.4 3.1 11.4 38.6 58.9 20.3 4.9 4.8 12.6 10.5 10.6 50.4 28.6 32.9 6.5 2.3 6.5 3.3

2.27 2.27 2.26 2.25 2.27 2.27 2.25 2.24 2.23 2.24 2.23 2.26 2.25 2.25 2.25 2.23 2.21 2.20 2.25 2.25 2.23 2.22 2.20 2.20

a

Also shown are (average) Y−O8b bond lengths for each environment, estimated using the correlation shown in Figure 5.

best fit. It can be seen for Y2Ti0.4Sn1.6O7 that the rms deviation of the fits of the spectral resonances assigned in previous work to Sn6 and Sn5Ti NNN is considerably lower than that for the Sn4Ti2 NNN environment, reflecting a better quality of fit. This is a result of the lower spectral intensity (and therefore signal-to-noise ratio) of this latter resonance (see Figure 1). The contour plots show that, despite different rms values, the confidence associated with the extraction of Ω is fairly similar in all three cases. Although κ is not considered in any great detail here, the contour plots also show that the uncertainty associated with its determination is largest for the most deshielded resonance, as it has the smallest value of Ω and the lowest number of sidebands. Two-dimensional spectra (and contour plots) for other members of the solid solution are shown in the Supporting Information, with Ω and the lowest rms deviation given in Table 3. For each spectral resonance in all 89Y NMR spectra of the Y2Ti2−xSnxO7 solid solution, the experimental δiso and Ω are plotted in Figure 11. Also shown are 89Y δisocalc and Ωcalc,scaled calculated for the range of disordered structural models discussed previously. Each parameter appears to be a sensitive probe of the local environment, and there is a strong (positive) correlation between the two. The agreement between the calculated and experimental shielding parameters for the Y2(Sn,Ti)2O7 solid solution is good, despite the challenging

Figure 10. (a) 89Y (14.1 T) two-dimensional CSA-amplified PASS spectrum of Y2Ti0.4Sn1.6O7, acquired using the pulse sequence in Figure S1.1b in the Supporting Information, with a total experiment time of 299 h (∼12.5 days). (b) Two-dimensional contour plots showing the rms deviation of an analytical fitting of each sideband manifold (using SIMPSON28) for values of the span, Ω, and the skew, κ. The intensity scale of the plots has been (arbitrarily) limited to 50. Other experimental parameters: [5746 transients, 16 t1 increments, NT = 6, nPASS = 1, recycle interval 10 s, MAS rate = 10 kHz].

recorded using the pulse sequence in Figure S1.1b in the Supporting Information, with a MAS rate of 10 kHz and NT = 6. For each of the resonances resolved in the direct (i.e., fast MAS) dimension, a sideband manifold is extracted in the indirect dimension, with an apparent MAS rate of 1.67 kHz. A lengthy total acquisition time of 299 h (∼12.5 days) was required to obtain sufficient sensitivity for the extraction of information on the anisotropic shielding. (Note that without the use of a saturation train it would require ∼70 days to acquire a two-dimensional spectrum with similar sensitivity.) For each of the sideband manifolds, analytical fitting was performed (using a complete simulation of the two-dimen4283



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Figure 11. Plot showing the calculated 89Y shielding parameters (isotropic shift, δisocalc, and span, Ωcalc,scaled) for the range of disordered pyrochlore model structures shown in Figure 3b. Points are colored to denote the number of Sn and Ti in the NNN environment. Overlaid are the experimental 89 Y shielding parameters (δiso and Ω) extracted from two-dimensional CSA-amplified PASS spectra for materials in the Y2(Sn,Ti)2O7 solid solution. Also shown in each case is the rms deviation associated with the best fit. See the Supporting Information for all two-dimensional spectra and contour plots showing the variation in rms deviation with fitting parameters.

measured. Such measurements should prove possible for more sensitive nuclei such as 31P or 119Sn in disordered materials, and will enable the distributions of isotropic and anisotropic shielding to be correlated and, hopefully, related to the local geometry. One possible solution to address the sensitivity challenge of low-γ nuclei is the use of higher external magnetic fields, as the signal-to-noise ratio can be shown to depend upon B03/2.46 Moreover, in many cases, the increased shift dispersion also results in a concomitant increase in resolution. However, experiments carried out for Y2Sn0.8Ti1.2O7 with B0 = 20 T resulted in little resolution gain (see the Supporting Information). The linewidths of the spectral resonances shown in Figure 1 result from a distribution of chemical shifts (reflecting the distribution of local environments), and so are independent (in ppm) of B0, providing no resolution gain at higher field, merely a lowering of the peak height signal. Furthermore, the increased shielding anisotropy (in Hz) results

nature of the experiments and the relatively low sensitivity obtained for some of the resonances. While the measured values of Ω shown in Figure 11 are certainly not accurate to within a few ppm, they give a good indication of the relative sizes of this interaction for the different resonances and the variation between them. The higher level of accuracy achieved previously for more sensitive nuclei (such 31P and 13C)11−19 is sufficient to measure both Ω and κ with high reliability, and to consider very small changes in these parameters; however, this is not possible for 89Y, owing to the low sensitivity and the low rf field strength. Furthermore, the distribution of local environments in the disordered materials results in a range of NMR parameters, and only an average value is plotted in Figure 11. In principle, the distribution in Ω for any one resonance could be obtained by fitting a range of cross sections parallel to δ1 taken at different δ2 positions. In practice, however, the signal-to-noise (even after nearly 2 weeks of acquisition time) is not sufficient to enable the small changes to be reliably 4284



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PASS experiments can be successfully implemented to obtain the anisotropic shielding parameters. However, in order to ensure an experiment with sufficient sensitivity is obtained in a reasonable time, it is necessary to use a prior saturation train. This was shown to have little effect upon the relative sideband intensities and upon the accuracy of the NMR parameters extracted. The choice of scaling factor and the number of sidebands requires careful consideration of sensitivity, overall experimental time, and accuracy of the result. The use of smaller scaling factors (with a single block of π pulses) appears advantageous, although the deviations in sideband intensities relative to the MAS spectra are larger when the sideband manifold is broader. This appears to be due to the low rf field strength available but can be accounted for when a complete simulation of the two-dimensional experiment (with an estimated rf field strength) is used in a more sophisticated fitting procedure. In contrast, B1 inhomogeneity, although present, appears to have a small effect upon the spectrum, as does any flip-angle mis-set, most likely owing to compensation by the cogwheel phase cycling employed. In general, Ω is more consistently reproduced than κ, although this may be a result of the latter being close to 1 in the end member pyrochlores. We have also shown that the 89Y anisotropic shielding can be accurately calculated for a series of simple inorganic solids, using a periodic planewave DFT approach. For the disordered pyrochlore materials, it was also possible to calculate the shielding tensors for a range of possible NNN environments by substituting Sn/Ti onto the B sites surrounding a central Y species. The value of Ω was shown to be a sensitive probe of the NNN environment, i.e., the number of Sn and Ti on the six surrounding B sites. Furthermore, Ω provides information on the local geometry directly, through a correlation with the average Y−O8b distance. Although it was possible to use the CSA-amplified PASS experiment to measure the anisotropic shielding for the disordered Y2(Sn,Ti)2O7 pyrochlores, the significantly lower sensitivity, resulting from the presence of many broadened spectral resonances, results in long experimental times (∼12− 14 days) at B0 = 14.1 T. No significant improvement in sensitivity was obtained at higher B0, owing to an increase in the spectral line width and the larger ΩHz. As a result of the lower signal-to-noise obtained even with the lengthy acquisition times, it was only possible to consider Ω, as determination of κ is more difficult to perform reliably. Although the results are perhaps not as accurate as those obtained for more sensitive nuclei, the measurement of two parameters (rather than just one) aids the interpretation and assignment of the 89Y NMR spectra, and offers potential for future applications in the study of disordered materials.

in more spinning sidebands under MAS, and can decrease the signal further if Ω is large compared to the MAS rate. The overall sensitivity, and the accuracy of the NMR parameters extracted from the PASS-based experiments, is dependent upon ν1/ΩHz (see above), which is also lower in this case at higher B0, with an increase in ΩHz but no significant improvement in ν1. The lack of any significant gain in sensitivity, and the timelimited access to national facilities, suggest that this is not necessarily a promising route for the future investigation of the shielding anisotropy in these disordered materials. The results shown in Figure 11 confirm the spectral assignment tentatively proposed on the basis of only δiso in previous work.24 This parameter is a sensitive probe of the local environment, but its dependence on both the electronegativity of the surrounding B-site cations (producing an upfield shift of ∼80 ppm per Ti NNN) and upon the change in unit cell size (resulting in a corresponding but smaller downfield shift) hinders the straightforward extraction of information. The measurement of both δiso and Ω (even in cases such as 89Y, where the experimental challenges are considerable) aids in this process and increases significantly the confidence in the assignment. For example, it can be seen that resonances with similar chemical shift (e.g., at ∼146 ppm for Y2Sn0.8Ti1.2O7 and at ∼148 ppm for Y2Sn2O7) may have very different anisotropic interactions (a difference of ∼79 ppm in this case), a difference which can be used to confirm the assignment of the NNN environment. The validation of the spectral assignment also confirms the suggestion in previous work of the presence of an essentially random distribution of Sn and Ti on the pyrochlore B sites.24,25 Not only has Ω been shown to be a sensitive probe of the local structure, Figure 5 shows that it can be correlated directly to the local geometry, specifically to the Y−O8b bond distance. It would be difficult to measure such detailed geometrical parameters by diffraction for a disordered material, as information on the average structure is obtained by refinement. In the 89Y MAS NMR spectra of Y2(Sn,Ti)2O7 pyrochlores, the resonances resulting from the differing NNN environments are resolved and Ω can be measured for each independently. In principle, therefore, the average Y−O8b distances can then be determined from Figure 5, and are given in Table 3. It should be noted that the calculations were performed for optimized structures (necessary owing to the substitutions in the unit cell), and it is known that the use of (GGA) DFT calculations can result in a systematic increase in the size of the unit cell, potentially leading to a (systematic) error in the distance. However, the magnitude of this error can be estimated by comparing the bond distances before and after geometry optimization for the end members, Y2Sn2O7 and Y2Ti2O7. In each case, a very small change in distance is observed (∼1− 2%), suggesting that any error is relatively small, and probably smaller than the error associated with accurate measurement of Ω.

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ASSOCIATED CONTENT

S Supporting Information *

CONCLUSIONS In this work, we have considered the feasibility of experimental measurement of the 89Y anisotropic shielding interaction, and the use of this in the assignment and interpretation of NMR spectra of disordered materials, through the combination of experiment and DFT calculations. For simple model systems (i.e., Y2Sn2O7 and Y2Ti2O7, with only a single spectral resonance), we have demonstrated that, despite the considerable practical challenges, two-dimensional CSA-amplified

Information on the pulse sequence and experimental parameters for the two-dimensional experiments, various conventions used to describe the shielding tensor, a discussion of the scaling factors applied to the calculated results, additional analysis of both the DFT results and the experimental investigations of the model compounds, and full experimental results for the disordered materials. This material is available free of charge via the Internet at http://pubs.acs.org. 4285



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

∥ Institute des Sciences et Ingenierie Chimiques, Ecole Polytechnique Federale de Lausanne, EPFL Batochime, 1015 Lausanne, Switzerland.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to EPSRC for support (Grant No. EP/ E041825/1) and for a studentship (M.R.M.) and to EaStCHEM for the award of a studentship (D.C.). This research made use of the EaStCHEM Research Computing Facility (http://www.eastchem.ac.uk/rcf); this facility is partially supported by the eDIKT initiative. The UK 850 MHz solidstate NMR Facility used in this research was funded by EPSRC and BBSRC, 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 (EDRF).

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