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Cation Disorder in Pyrochlore Ceramics: 89Y MAS NMR and First-Principles Calculations Simon W. Reader,† Martin R. Mitchell,† Karen E. Johnston,† Chris J. Pickard,‡ Karl R. Whittle,§ and Sharon E. Ashbrook*,† School of Chemistry and EaStCHEM, UniVersity of St Andrews, St Andrews KY16 9ST, United Kingdom; Department of Physics and Astronomy, UCL, London WC1E 6BT, United Kingdom; and Institute of Materials Engineering, ANSTO, PMB1, Menai, NSW 2234, Australia ReceiVed: July 17, 2009; ReVised Manuscript ReceiVed: September 10, 2009
The use of first-principles DFT calculations to interpret solid-state 89Y MAS NMR spectra of Y2Ti2-xSnxO7 pyrochlores, materials with applications for the encapsulation of actinide-bearing radioactive waste, is investigated. Although NMR is a sensitive probe of local structure, which does not rely on the presence of long-range order, spectra of disordered materials are often complex and difficult to interpret. We show how calculations can be used alongside experiment to confirm that Y occupies only the eight-coordinate pyrochlore A site in these materials and that the 89Y isotropic chemical shift is primarily affected by the number of Sn/Ti on the neighboring B sites. Small changes in local geometry and more distant B-site cation substitutions are shown to have a smaller effect on the chemical shift, and will result in broadening, shoulders, and small splittings in the NMR spectrum. In general, the results confirm the validity of the assumptions made in the previous spectral analysis, although in a very small minority of cases, chemical shifts are calculated which lie outside the expected ranges. However, these are shown to result from significant deviations in local geometry (O-Y-O bond angles and Y-O bond distances) and are thought to arise from the periodicity (and, therefore, long-range order) which is imposed in the calculations. Using our calculated results we can confirm that there is a random distribution of Sn/Ti on the six-coordinated pyrochlore B sites in Y2Ti2-xSnxO7, and also demonstrate that an equilibrium structure has been achieved by studying materials which have been annealed for different durations. Introduction Solid-state nuclear magnetic resonance (NMR) spectroscopy has long been an important tool for the investigation of structure and dynamics in a range of materials. One distinct advantage of NMR, a local probe that does not require the presence of any long-range order, is its ability to investigate disorder, be it positional or compositional in nature, within a solid.1 Disorder plays an important role in determining many of the physical and chemical properties of materials, and knowledge of its exact nature is, therefore, crucial in developing a detailed understanding of a solid. In general, each different local environment an atom experiences within a solid will result in a different chemical shift. If the environment is significantly different, e.g., a change in coordination number, then the difference in chemical shift can be considerable,1,2 and well-resolved resonances are observed in a magic-angle spinning (MAS) NMR spectrum, enabling the number and nature of environments to be easily determined. Less significant changes in environment, e.g., a change in the occupancy of neighboring (or next nearest neighboring, NNN) sites, can result in smaller shift changes, and often in composite resonances where the different contributions may have to be determined through analytical fitting.1,2 In addition, NMR lineshapes can also exhibit broadening as a result either of smaller changes in the local environment (e.g., differences in bond angles or bond lengths) or of more significant, but more remote, changes to the structure. The * To whom correspondence should be addressed. E-mail:
[email protected]. † School of Chemistry and EaStCHEM, University of St Andrews. ‡ Department of Physics and Astronomy, UCL. § Institute of Materials Engineering, ANSTO, PMB1.
resulting line width provides information on the distribution of chemical shifts and, therefore, on the distribution of environments present. (It should be noted that NMR lines may also be broadened as a result of dynamics, although typically, variable temperature measurements are able to distinguish these two effects). Despite this possible complexity in spectral appearance for disordered materials, NMR has been extremely successful in providing insight into a wide range of disordered materials, including Si/Al disorder in zeolites,3 Mg/Al disorder in spinels,4 cation distribution in ionic conductors5 and battery materials,6 and bond angle distributions in glasses.7,8 One approach to interpreting the potentially complex NMR spectra of disordered systems is the use of first-principles calculations. There has long been interest in using calculations to help interpret, assign, and even predict NMR spectra of solids, revitalized in recent years by the introduction of codes which exploit the inherent periodicity and translational symmetry of many solids.9,10 Such an approach can have significant advantages over the more conventional “cluster” approaches, as there is no need to terminate (and therefore perturb) the periodic structure, and a range of applications using this technique have recently been demonstrated.11-14 For disordered materials, however, the “perfect” translational symmetry of a material is disrupted either by variations in position, composition, or occupancy. While there is still a strong incentive to use a periodic approach (thereby retaining the overall three-dimensional structure), it is often difficult to carry out such calculations using a single unit cell. Instead, the creation of “supercells” may be necessary, allowing a wider range of defects and structural variations able to be studied. In general, a computational approach provides an easy and flexible way to monitor
10.1021/jp906764e CCC: $40.75 2009 American Chemical Society Published on Web 10/05/2009
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Figure 1. (a) View of a typical pyrochlore structure along [110]. Large red spheres denote O, green spheres denote Y, and small blue spheres denote the six-coordinated B site, occupied by either Sn or Ti. (b, c) Expansions showing the nearest and next nearest neighbor environment of the eight-coordinated A-site Y species.
the effect upon the NMR parameters of changes to the local environment, and its combination with high-resolution NMR offers great promise for understanding the structure of disordered materials. Recently, we have studied the local yttrium environment in a series of pyrochlores (Y2Ti2-xSnxO7) using 89Y (I ) 1/2) MAS NMR.15 The great chemical flexibility of the pyrochlore structure and its ability to incorporate a large variety of cations, has resulted in its utility as a host for the immobilization of nuclear waste.16 In particular, the use of pyrochlores within ceramic wasteforms such as SYNROC (a synthetic wasteform that also includes materials such as hollandite, zirconolite, and perovskite) has focused attention upon the incorporation of actinides and lanthanides, with the ultimate aim being the safe disposal and long-term storage of Pu.17 While titanate-based pyrochlores are generally considered to have good chemical durability, it has recently been shown that the incorporation of Sn into such systems results in an increased tolerance to radiation damage.18 For the Y2Ti2-xSnxO7 solid solution, diffraction and microscopy were used to confirm the presence of a single phase pyrochlore structure, while NMR was able to probe directly the cation local environments.15 The 89Y chemical shifts observed suggested that Y3+ occupied only the eight-coordinated A site in the structure, with Sn4+ and Ti4+ distributed on the six-coordinated B site. Although a reasonably large change in the 89Y chemical shift was observed upon the substitution of Sn or Ti into the Y NNN environment, the presence of broad and sometimes overlapping resonances hindered the ease with which detailed information could be extracted. The challenges associated with 89Y NMR, including a very low gyromagnetic ratio and long T1 relaxation times (often many 1000s of seconds), not only hinder spectral acquisition and sensitivity, but also preclude the use of more complex two-dimensional correlation experiments typically employed to provide more information.2 In order to interpret the relative intensities of the 89Y spectral resonances in terms of the distribution of yttrium environments present (and therefore, the nature of the order/disorder of the B-site cations) a number of assumptions and simplifications had to be made when assigning the NMR spectra. Once assigned, the relative intensity of the spectral resonances was shown to be consistent with that expected from a random distribution of Sn and Ti on the B site.15 In this work, we exploit the power and flexibility of firstprinciples density functional theory (DFT) calculations to
interpret 89Y MAS NMR spectra of the Y2Ti2-xSnxO7 solid solution and to test the validity of the assumptions made in the previous analysis.15 In addition to considering previous experimental results, we also present new work to determine whether the cation distribution and ordering is affected by the synthesis method and, in particular, the duration for which materials are annealed. First, the accuracy of our computational approach is evaluated using a series of model compounds (including the end members of the pyrochlore solid solution), before the changes to the NMR parameters resulting from substitution of Sn/Ti into the pyrochlore structure are investigated. In addition to considering the changes resulting from different numbers of Sn/Ti in the NNN environment and their spatial arrangement, the effects of more remote substitution are also considered. The assumption that Y occupies only the A cation sites within the pyrochlore is also examined by considering structures where A and B cations are exchanged. Finally, the implications of our results for the previous analysis and for the ordering of the B-site cations in pyrochlores are discussed. Experimental Details Sample Preparation. Three sets of Y2Ti2-xSnxO7 samples were prepared by grinding stoichiometric amounts of Y2O3, SnO2, and TiO2 (all obtained commercially) in a ball mill using acetone/ethanol as the mobile phase. Sample set A, with x ) 0, 0.4, 0.8, 1.2, 1.6, and 2, were pressed into pellets in a uniaxial press and heated at 1500 °C for 48 h, cooled, repressed into pellets, and heated for a further 96 h at 1500 °C (See ref 15 for further details). Sample sets B and C, with x ) 0.8 and 1.6, were pressed using a uniaxial press, prior to cold isostatic pressing to ensure a high sample density. Both samples were then heated at 1500 °C for 48 h, before cooling. For sample set C, pellets were then heated for a further 48 h at 1500 °C. Once cooled, all pellets were ground into powders using an agate pestle and mortar. Samples were characterized by X-ray diffraction and electron microscopy and all determined to be single-phase pyrochlore.11 NMR. For full details on the acquisition of the spectra shown in Figure 2 (sample set A), see ref 15. All other spectra were acquired using a Bruker Avance III 600 spectrometer, equipped with a 14.1 T widebore magnet, operating at a Larmor frequency of 29.4 MHz for 89Y. Powdered samples were packed into a 4-mm ZrO2 rotor and rotated at an MAS rate of 14 kHz using a commercial “low-γ” probe. Typically, spectra were acquired
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Figure 2. 89Y (B0 ) 11.7 T) MAS NMR spectra of Y2Ti2-xSnxO7 (sample set A) with x ) 0, 0.4, 0.8, 1.2, 1.6, and 2. Spectra are the result of averaging 80 transients with a recycle interval of 5000 s and a preacquisition delay of 100 µs. The MAS rate was 6 kHz. Reproduced from ref 15.
using a radiofrequency field strength of 32 kHz, and small (π/ 4) flip angle pulses, enabling shorter recycle intervals (typically 300 s) to be employed. A preacquisition interval of 80 µs was used to reduce probe ringdown. Chemical shifts are displayed in ppm relative to 1 M YCl3 (aq), measured using Y2Ti2O7 as a secondary reference (δiso ) 65 ppm).19 Spectral analysis was performed using the dmfit20 program. Further experimental details can be found in the relevant figure captions. Calculations. Calculations were carried out using the CASTEP10 density functional theory code, with the gauge including projector augmented wave (GIPAW) formalism.21 The generalized gradient approximation (GGA) PBE functional was used, with core-valence interactions described by ultrasoft pseudopotentials.22 Integrals over the Brillouin zone were performed using a Monkhorst-Pack grid with a k-point spacing of 0.05 or 0.04 Å-1 and wave functions were expanded in planewaves with a kinetic energy smaller than the cutoff energy of 50 Ry. All calculations were converged as far as possible with respect to both k-point spacing and cutoff energy. Structural parameters (unit cell 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 those described above). Calculations were performed on the EaStCHEM Research Computing Facility, which consists of 152 AMD Opteron processing cores partly connected by Infinipath high speed interconnects. Typical NMR calculation times were between 24 and 48 h using 16 cores. To assess the accuracy of this approach for the computation of 89Y NMR parameters, calculations were performed for a series of simple compounds whose isotropic chemical shifts had been previously determined experimentally. Given the difficulties associated with 89Y NMR, this was necessarily a fairly small set of materials, involving 12 Y species in 8 different compounds (Y2O3, Y2Sn2O7, Y2Ti2O7, Y2O2S, YF3, YAlO3, R-Y2Si2O7, and
β-Y2Si2O7). The agreement between calculated and experimental isotropic shifts was good and further details of these calculations can be found in the Supporting Information. In each case, from the absolute shielding tensor, σ, the isotropic chemical shift, δiso, was obtained by (σref - σiso), where σiso, the isotropic shielding, is (1/3) Tr{σ}. A reference shielding, σref, of 2646.5 ppm was used, determined from calculations on Y2O3, as described in detail in the Supporting Information. The chemical shielding anisotropy (CSA), ∆CSA, and asymmetry, ηCSA, can be determined (according to the Haeberlen convention) from the principal values of the shielding tensor using (σzz - σiso) and (σyy - σxx)/(σzz - σiso), respectively. The best agreement with experiment was found when the structures obtained from diffraction measurements were geometry optimized, allowing all atomic positions and the unit cell dimensions to vary. In general, this resulted in an expansion of the unit cell dimensions between 1 and 1.5% (as perhaps expected for the GGA functional which is generally recognized to underbind, resulting in increased cell dimensions). As shown in the Supporting Information, the agreement between experimental and calculated shifts was good, suggesting that this approach is of suitable accuracy for the interpretation of 89Y NMR spectra of disordered materials. Results and Discussion The general pyrochlore (A2B2O7) structure, with the cubic space group Fd3jm,23 is shown in Figure 1a, and is derived from that of fluorite (AO2) through the ordered removal of 1/8 of the oxygen atoms. This results in two distinct cation sites; the eightcoordinate A site (typically occupied by 2+ or 3+ cations) and the six-coordinate B site (occupied by 5+ or 4+ cations). The entire structure can be described simply by two parameters, the cubic unit cell length (a) and the position of the 48f oxygen species (which has atomic coordinates (x, 1/8, 1/8)). The stability range is determined by the relative sizes of the A and B cations, with the pyrochlore phase formed when 1.46 < (rA/rB) < 1.78.23 As the ratios for both of the end members of the Y2(Ti, Sn)2O7
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Figure 3. 89Y (B0 ) 14.1 T) MAS NMR spectra of Y2Ti2-xSnxO7 with x ) 0.8 and 1.6 for sample set B and C (heated for a total of 48 and 96 h, respectively). Spectra are the result of averaging 512 transients with a recycle interval of 300 s. The MAS rate was 14 kHz. The deconvolution of the NMR spectra are also shown (by red and blue lines) for the samples in set C.
solid solution, Y2Sn2O7 and Y2Ti2O7, fall within this range, the solid solution remains single phase pyrochlore throughout the full compositional range. However, there is a difference in the location of the 48f oxygen position and unit cell size between the two end members, with x ) 0.338, a ) 10.48 Å for the stannate24 and x ) 0.327, a ) 10.15 Å for the titanate,25 reflecting the smaller size of the Ti4+ cation. In both cases, Y3+ is expected to occupy the eight-coordinate A site with, as shown in Figure 1, parts b and c, six A- and six B-site next nearest neighbors. The large electronegativity difference between Sn and Ti results in very different 89Y isotropic chemical shifts (150 and 65 ppm for stannate and titanate, respectively), as shown in Figure 2, parts a and f.15,19 89 Y MAS NMR spectra across the compositional range of the Y2(Ti, Sn)2O7 solid solution (sample set A) are shown in Figure 2. As described in detail in ref 15, each spectrum exhibits a spread of resonances within the 60-160 ppm range, characteristic of chemical shifts usually associated with eightcoordinated yttrium. A separation in chemical shift of ∼15 ppm is observed between resonances, which is attributed to the incorporation of Sn/Ti into the NNN coordination environment.15,19 There are seven different local environments possible considering only the number of Sn/Ti occupying the six NNN B sites (i.e., it is possible for any Y to have 0, 1, 2,. .. Six Sn NNN). However, the presence of shoulders and even splittings (notably around ∼110 ppm) suggests that the chemical shift is also sensitive to more subtle changes in environment, perhaps including the spatial arrangement of the Sn/Ti NNN. It is also interesting to note that the position of the resonance assigned to 6 Sn NNN in the spectrum of Y2Ti0.4Sn1.6O7 (i.e., the most deshielded) is slightly shifted downfield from the resonance found in Y2Sn2O7, probably as a result of the change in unit cell size.15,19 Although present throughout the range of samples, this effect is more pronounced for the Sn rich compositions. Figure 3 shows similar 89Y MAS NMR spectra (for sample sets B and C) recorded with B0 ) 14.1 T, for compositions with x ) 1.6 and 0.8. In general, the spectra appear very similar to those in Figure 2, demonstrating that the distribution of local
environments is reproducible between experiments. The intensity distributions in all three sets of samples is very similar, despite the differences in total heating time (ranging from 48 to 144 h), indicating that the distribution of B-site cations appears to be an inherent or “thermodynamic” result and not the result of any “kinetic” effect. It has previously been reported that the structure and ordering of many pyrochlore and defect fluorite phases is dependent upon the synthesis approach owing to slow cation diffusion rates.26,27 It would appear, however, that in this case an equilibrium structure and order has been achieved. The spectral resolution in Figure 3 is only slightly better than that in Figure 2, despite the use of a higher B0 field strength as, although the peak separation (in Hz) has increased, there is also a corresponding increase in line width. This inhomogeneous contribution to the line width results from a distribution of chemical shifts and reflects the long-range disorder present when Sn and Ti both occupy the B cation sites. Indeed, as observed in Figure 2, the resonances for the end members are generally narrower than those observed throughout the solid solution. In principle, the relative intensities of the 89Y spectral resonances (extracted as shown in Figure 3) reflects the range of local environments present and, ultimately, the distribution of Sn and Ti on the pyrochlore B site. In order to extract this information, however, the resonances must be assigned. Given the spectral complexity, this is nontrivial unless a few simplifying assumptions are made. As described in detail in ref 15, it is assumed that (i) Y occupies only the eight-coordinate A site, (ii) the 89Y chemical shift is determined only by the number of Sn/Ti NNN, (iii) the chemical shift is not affected by the spatial arrangement of the Sn/Ti, and (iv) there are no longer range effects that alter the chemical shift.15 Once assigned, the relative spectral intensities can be compared to those predicted for a random distribution of Sn/Ti. This can be determined from simple statistics, with the probability of finding n Sn NNN given by P(n Sn) ) Ω pn (1 - p)6-n, where Ω is the number of possible permutations.15 Figure 4 compares this theoretical distribution with the experimental (integrated) spectral intensities for Y2Ti0.4Sn1.6O7 and Y2Ti1.2Sn0.8O7 compositions in sample sets
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Figure 4. Plot of signal intensities (expressed as %) for Y2Ti2-xSnxO7 with (a) x ) 1.6 and (b) x ) 0.8. Plots include values derived from a statistical model assuming a random distribution of Sn/Ti on the pyrochlore B site (red filled squares), and those extracted from the 89Y MAS NMR spectra of Y2Ti2-xSnxO7 (sample set A) in Figure 2 (blue circles) or the 89Y MAS NMR spectra of Y2Ti2-xSnxO7 (sample sets B and C) in Figure 3 (green triangles and black diamonds, respectively).
TABLE 1: Calculated and Experimental 89Y NMR Parameters (Isotropic Chemical Shift, δiso, Chemical Shift Anisotropy, ∆CSA, and Asymmetry, ηCS) for Y2Sn2O7 and Y2Ti2O7 Pyrochloresa,b δiso (ppm)
∆CSA (ppm)
ηCS
150 174 175 165
-135 -111 -104 -112
0.08 0.00 0.00 0.00
65 27 26 26
-390 -443 -443 -430
0.05 0.00 0.00 0.00
28
Y2Sn2O7 experimental15,19 calculated I calculated II calculated III Y2Ti2O729 experimental15,19 calculated I calculated II calculated III
a Calculations were performed using (I) the structure as determined by diffraction, (II) after geometry optimization of the atomic coordinates and (III) after geometry optimization of atomic coordinates and unit cell dimensions. In all cases, the energy cut-off was 50 Ry and the k-point spacing was 0.04 Å-1. b Estimated experimental errors are (0.5 ppm (δiso), (3 ppm (∆CSA), and (0.1 (ηCS).
A, B, and C. Given the assumptions made (and the experimental challenges of 89Y NMR) there is good agreement between theory and experiment, with the largest disagreement found for 3 Sn NNN (x ) 1.6) and 2 Sn NNN (x ) 0.8). However, the long preacquisition interval used for B0 ) 14.1 T (to reduce the effects of probe ringing) results in difficulties when phasing the experimental spectra and, in particular for x ) 1.6, this leads to a large uncertainty (estimated to be up to 10%) for the 3 Sn NNN environment owing to the broad, low intensity nature of this resonance. Consequently, of course, this increases the uncertainty for the other resonances in this spectrum, indicating the origin of the small differences between the 11.7 and 14.1 T data. However, in all cases, there is no evidence that the distribution of Sn and Ti on the B site is anything other than random, i.e., there is no ordering or clustering of cations. To investigate the validity of the assumptions made in the course of spectral analysis, and to confirm the origin of the chemical shift changes observed in the 89Y experimental spectra, a range of DFT calculations were performed. First, the accuracy of the approach (GIPAW calculations using CASTEP) was tested for a series of simple yttrium-containing model samples, with the parameters needed for convergence and a reference shielding also determined (see Supporting Information for further details). Table 1 gives the calculated 89Y NMR parameters for the stannate and titanate end members of the Y2(Ti, Sn)2O7 solid solution (along with corresponding experimental values from the literature). As there is only a single Y species
in these well-ordered crystalline materials, both the isotropic and anisotropic shielding parameters can be easily determined experimentally.15,19 Calculations were performed for (I) the structures as determined by diffraction,28,29 (II) after geometry optimization of the atomic coordinates, and (III) after geometry optimization of atomic coordinates and unit cell dimensions. The experimental and calculated parameters are in relatively good agreement (particularly when the chemical shift range of 89 Y, which is ∼4000 ppm, is considered, with errors of only 15-40 ppm or 0.3-1% of the shift range observed).2 The agreement is better for the stannate than the titanate, although as described in the Supporting Information, this may well result from inaccuracy in the Ti pseudopotential. The larger CSA of the titanate, resulting from the larger deviation of the 48f oxygen from its position in ideal fluorite (where x ) 0.375), is well reproduced, and the asymmetry in each case is zero, as predicted from the point symmetry of the Y site (-3m).23 The initial assumption made in the spectral analysis for the Y2(Ti, Sn)2O7 solid solution is that the Y3+ cation occupies only the eight-coordinated A site in the pyrochlore structure, and is not also found on the six-coordinate B site. While this may seem reasonable given the relative sizes and charges of Y3+, Sn4+, and Ti4+, it should be noted that as the (rA/rB) ratio decreases, a transition to a defect fluorite phase (space group Fm3jm) is observed, which exhibits both anion and cation disorder.19 The presence of only A-site Y seems to be supported, however, by the 89Y MAS NMR spectra shown in Figures 2 and 3, where the resonances observed all lie within a chemical shift range of 60-160 ppm, typical of Y in an 8-fold coordination environment. A general relationship of increasing chemical shift with decreasing coordination number has been observed for 89Y, and it may be expected, therefore, that six-coordinate Y species would be found with considerably higher chemical shifts (previously, shifts between 200 and 400 ppm have been observed).30,31 However, the large chemical shift range of 89Y and the sensitivity to local environment changes means that care must be taken in applying this general principle to specific cases. Calculations were therefore performed to investigate the change in the chemical shift when Y occupies the B site in the pyrochlore structure, by exchanging one A- and one B-site cation in Y2Sn2O7 and Y2Ti2O7. Owing to the need for charge balancing within the unit cell (unless a defect is also created), cations were exchanged rather than the conceptually simpler replacement of Sn4+/Ti4+ by Y3+. However, this does have important consequences for the local environments of the remaining A-site Y species, which now have differing numbers of Y and Sn or Ti on the surrounding A and B sites, leading to a distribution of chemical shifts. This can be seen in Figure 5, where the
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Figure 5. Plot of calculated 89Y isotropic chemical shifts for Y2Sn2O7 and Y2Ti2O7 (denoted by blue diamonds and red squares, respectively) after exchange of an A-site (Y) and B-site (Sn or Ti) cation, as a function of the number of Sn/Ti NNN. The values for the sixcoordinated Y species are shown by filled symbols, and those for the eight-coordinated species by open symbols.
calculated 89Y chemical shifts for all species within the unit cell are plotted against the number of Sn or Ti in the NNN coordination environment. (Note that no distinction is made between whether the Sn/Ti occupies the A or B NNN sites). Although a range of shifts are seen for the eight-coordinate B-site cations, the values observed for the six-coordinate Y species (denoted by filled symbols) are much higher, with a δiso of over 200 ppm in each case, larger than the shifts observed experimentally. To determine the effects of substitution of Sn/Ti into the pyrochlore structure, it is necessary to generate a simple model system, as it is not possible to directly calculate the disordered material, owing to the impractically large number of atoms which would be required to generate the range of possible environments. Therefore, the effect of NNN substitution was investigated systematically using a single unit cell of Y2Sn2O7 or Y2Ti2O7 and initially considering the chemical shift of just one yttrium species as increasing numbers of Ti/Sn are substituted into the NNN coordination sphere. In each case, structures were geometry optimized (with atomic coordinates and unit cell dimensions allowed to vary) before NMR parameters were calculated. Figure 6 shows a schematic of the variety of local environments considered, with a central yttrium species (not shown) surrounded by six NNN B sites occupied by Sn/Ti. The number of Sn/Ti and their spatial distribution (denoted by relative positions 1 to 6) are indicated in each case. The isotropic chemical shift of the central Y species for each of these local environments substituted into both Y2Ti2O7 and Y2Sn2O7 pyrochlore unit cells is given in Table 2 and plotted in Figure 7, parts a and b, respectively. For Y2Ti2O7, there appears to be a systematic change in the 89Y chemical shift as Sn is substituted onto the NNN B sites, as shown in Figure 7a. The change is ∼26 ppm per Sn NNN, larger than the shift change observed between distinct 89Y resonances in the experimental spectra (∼15 ppm). Different chemical shifts are also observed for different spatial arrangements (but the same number) of Sn/Ti, e.g., 91, 99, and 94 ppm for the 1,2,3-, 1,2,4and 1,3,5-Sn3Ti3 arrangements, respectively. However, in general, the differences are smaller (∼8-11 ppm) than those produced by a change in the number of Sn NNN. Similarly, for Ti substitution into Y2Sn2O7 a systematic change in chemical shift is observed as the number of Sn/Ti NNN varies (as shown in Figure 7b), although the magnitude of the change is slightly smaller (∼18 ppm). However, the difference between these two cases highlights that the exact chemical shift observed is certainly sensitive to longer range effectssbe it the nature of the more distant B-site cations (Sn in one case and Ti in the
J. Phys. Chem. C, Vol. 113, No. 43, 2009 18879 other) or the difference in unit cell size which results from this. In reality, a distribution of both Sn/Ti on all remote B sites is expected in a disordered material. As was observed in Figure 7a, different chemical shifts are also found in Figure 7b for the different spatial arrangements of the Sn/Ti NNN. However, in contrast to the previous case, two of the values calculated are very different (appearing anomalously high) to those found for the other related environments. A series of similar calculations showed that this was a reproducible result and, as indicated by comparison with Figure 7a, is not a consequence of the symmetry of a particular spatial arrangement, as a similar result is not observed for the same spatial arrangement of Sn substituted into Y2Ti2O7. Given the apparent sensitivity of the 89Y chemical shift to the exact local environment and also to longer range changes, it is instructive to also consider the chemical shifts of all of the 89 Y species in the unit cell, rather than the single species around which substitution occurs. For any particular substitution, the remaining 15 yttrium species in the cell will have different numbers of Sn/Ti cations on the NNN B sites and a range of more distant coordination environments, the latter producing a distribution of isotropic chemical shifts. These shifts are plotted in Figure 7, parts c and d, for substitutions into Y2Ti2O7 and Y2Sn2O7, respectively. Shift ranges between 10 and 20 ppm are typically observed for each environment type, with a distinct and systematic increase in the average chemical shift as the number of Sn NNN increases. This is reminiscent of the chemical shift ranges previously observed for 29Si (I ) 1/2) NMR in aluminosilicate zeolites, where a variation in the number of Al NNN also results in a significant change in the 29 Si chemical shift.2,3 Owing to the initial starting compositions for the calculations, relatively few points are observed for Snrich environments in Y2Ti2O7 and Ti-rich environments in Y2Sn2O7, respectively. The results are generally consistent with the previous interpretation of the experimental spectrum, i.e., that the distinct resonances observed result from a change in the number of Sn NNN, while the broadenings, shoulders and even small splittings result from smaller (or more distant) changes to the environment.15 Figure 7d shows that the unexpectedly high chemical shifts discussed for some of the local environments in Figure 7b still appear anomalous, even when the possible ranges of chemical shift are taken into account. Furthermore, a small number of anomalous shifts are now also observed for Sn substitution into Y2Ti2O7, as seen in Figure 7c, notably for some of the Sn1Ti5 environments, with δiso of ∼95 ppm. These deviations from the “expected” shifts could pose problems for the interpretation of the experimental spectra if they occurred with significant frequency, as they would result in the increased intensity of spectral resonances attributed to a different local environment, and ultimately, therefore, produce an inaccurate picture of the cation distribution and ordering. In order to understand the origin of these effects, it is necessary to look in more detail at the local yttrium coordination environment. As shown in Figure 1, parts b and c, each yttrium is coordinated by 8 oxygens; six 48f oxygens (O48f), which are also bonded to B-site cations, and two 8b oxygens (O8b) bonded to three other yttrium.23 In the end members, Y2Sn2O7 and Y2Ti2O7, the two Y-O8b bond lengths are equal, as are the six Y-O48f bond lengths, although the exact values are different for the two chemical compositions owing to the size difference between Sn and Ti. The O8b-YsO8b bond angle in both cases is also exactly 180°.23,24 As a different B-site cation is substituted onto the NNN sites, a range of Y-O48f bond lengths is produced, as shown in Table
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Figure 6. Possible arrangements of Sn/Ti on the six NNN B sites which surround the eight-coordinate pyrochlore A site. (See also Figure 1).
TABLE 2: Calculated 89Y NMR Parameters (Isotropic Chemical Shift, δiso, Chemical Shift Anisotropy, ∆CSA, and Asymmetry, ηCS) for the Local Environments Shown in Figure 6, within Unit Cells of Y2Sn2O7 and Y2Ti2O7a δiso (ppm) Y2Sn2O7 Sn6 Sn5Ti 1,2-Sn4Ti2 1,3-Sn4Ti2 1,4-Sn4Ti2 1,2,3-Sn3Ti3 1,2,4-Sn3Ti3 1,3,5-Sn3Ti3 1,2-Sn2Ti4 1,3-Sn2Ti4 1,4-Sn2Ti4 Ti5Sn Ti6 Y2Ti2O7 Sn6 Sn5Ti 1,2-Sn4Ti2 1,3-Sn4Ti2 1,4-Sn4Ti2 1,2,3-Sn3Ti3 1,2,4-Sn3Ti3 1,3,5-Sn3Ti3 1,2-Sn2Ti4 1,3-Sn2Ti4 1,4-Sn2Ti4 Ti5Sn Ti6
∆CSA (ppm)
ηCS
161 139 119 120 124 98 134 103 86 132 94 73 51
-109 -183 -253 -247 -250 -325 -294 -304 -391 -355 -368 -449 -524
0.00 0.12 0.13 0.12 0.15 0.02 0.06 0.00 0.05 0.00 0.16 0.06 0.00
178 159 121 121 132 91 99 94 68 71 78 47 24
-30 -100 -171 -168 -176 -240 -236 -229 -307 -301 -296 -370 -438
0.11 0.26 0.28 0.30 0.28 0.00 0.31 0.00 0.12 0.13 0.30 0.11 0.00
a All structures were geometry optimized prior to the calculation of the NMR parameters. In all cases, the energy cut-off was 50 Ry and the k-point spacing was 0.05 Å-1.
3, where this range (the difference between largest and smallest distances) is given for possible NNN substitutions into Y2Sn2O7. Table 3 also shows that, in contrast, the two Y-O8b bonds, while decreasing in length with increasing Ti NNN occupation, always remain equal. In most cases, the O8b-Y-O8b bond angle remains at or close to 180°. However, it is noticeable that where anomalously high chemical shifts are observed (see Table 2), e.g., 1,2,4-Sn3Ti3 and 1,3-Sn2Ti4 environments, there is a
significant deviation of the O8b-Y-O8b bond angle away from 180°. This is also accompanied by a significant lengthening of one or more of the Y-O48f distances, reflected in the increase in the range of Y-O48f distances given in Table 3, although the average Y-O48f distance remains similar. The high chemical shift, therefore, appears to result from a distortion of the local geometry (both in bond angles and bond distances). From the plots in Figure 7, parts a and b, (through a linear regression to obtain a line of best fit) it is possible to define an “ideal” or “expected” chemical shift for an environment with a given number of Sn NNN in Y2Sn2O7 and Y2Sn2O7, respectively. (Note any anomalous points are discounted when performing such a fit). The difference between this shift and the calculated chemical shift, denoted ∆δiso, then provides some measure of a deviation from “ideality”, i.e., a measure of how “anomalous” a particular calculated chemical shift is considered. Figure 8a plots the correlation of this shift difference with the deviation of the O48f-Y-O48f bond angle from 180°, for all calculated 89 Y chemical shifts. Although some scatter is present (reflecting the ranges of shifts observed in Figures 7, parts c and d), there is a distinct correlation between chemical shifts which are very different from the ideal values and the distortion of the O48f-Y-O48f bond angle. A similar correlation is also observed in Figure 8b between ∆δiso and the range of Y-O48f bond distances present. While it seems that unexpectedly high chemical shifts result from significant distortions in the local coordination geometry, the origin of such distortions is not quite so clear. The two B-site cations, Sn and Ti, are very different sizes and it might be expected that particular NNN geometrical arrangements may be less favorable and impose more strain on the system, which subsequently undergoes a distortion. However, the differences shown in Table 2 between substitution into Y2Sn2O7 and Y2Ti2O7, suggest that the distortion is not a result of the NNN environment alone. For example, for the 1,2,3-Sn3Ti3 substitution in Y2Sn2O7 an anomalously high chemical shift is observed, while the same local environment in Y2Ti2O7 results in a chemical shift well within the expected range. The difference between these two cases is the nature of the more remote B-site cations, all Sn in one case and all Ti in the other. This may well pose more restrictions on the type of distortions which are possible in order to accommodate the structural changes and,
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Figure 7. Plots showing calculated 89Y isotropic chemical shifts (δiso) as a function of the number, n, of Sn NNN for the local environments shown in Figure 6 for (a, c) Y2Ti2O7 and (b, d) Y2Sn2O7. In (a, b) only the chemical shift of the central Y species is shown, while in (b, d) the chemical shifts of all Y species in the unit cell are given.
Figure 8. Plots of the difference between an “ideal” shift for a particular number of Sn NNN (obtained by fitting the plots in Figure 7, parts a and b) and the calculated 89Y isotropic chemical shift (denoted ∆δiso) against (a) the deviation from 180° of the O8b-Y-O8b bond angle and (b) the range of Y-O48f bond distances. Calculations involving substitution into Y2Ti2O7 and Y2Sn2O7 are denoted by red squares and blue diamonds, respectively.
TABLE 3: Local Geometry (O8b-Y-O8b Bond Angle, Y-O8b Bond Distance and Range of Y-O48f Bond Distances) for the Local Environments Shown in Figure 6 and an Initial Unit Cell of Y2Sn2O7, after Full Geometry Optimization
Y2Sn2O7 Sn6 Sn5Ti 1,2-Sn4Ti2 1,3-Sn4Ti2 1,4-Sn4Ti2 1,2,3-Sn3Ti3 1,2,4-Sn3Ti3 1,3,5-Sn3Ti3 1,2-Sn2Ti4 1,3-Sn2Ti4 1,4-Sn2Ti4 Ti5Sn Ti6
O8b-Y-O8b bond angle
Y-O8b bond distance (Å)
average Y-O48f bond distance (Å)
range of Y-O48f bond distances (Å)
180.0° 178.8° 180.0° 178.7° 180.0° 178.9° 173.8° 180.0° 180.0° 171.9° 180.0° 180.0° 180.0°
2.269 2.255 2.239 2.240 2.241 2.227 2.225 2.228 2.212 2.215 2.213 2.201 2.188
2.507 2.512 2.524 2.523 2.526 2.527 2.547 2.533 2.547 2.564 2.544 2.556 2.565
0.000 0.046 0.088 0.051 0.126 0.062 0.409 0.000 0.121 0.401 0.126 0.103 0.000
in particular, on the overall size and shape of the unit cell. In reality, the more remote B sites will be occupied by a mixture of both Sn and Ti, which may lift some of the geometrical
constraints on the system and prevent some of the more extreme distortions. Furthermore, in order to study the changes in chemical shift in a systematic way our model contains a local
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cluster or “defect” in a three-dimensional framework. However, this defect is reproduced regularly by the periodic nature of the calculations, and could, if the unit cell was not sufficiently large, pose additional (but longer range) geometrical constraints for the system. If this was the case, then this could be relieved by the formation of supercells where the local structural changes would be distant enough that they can be assumed to have no effect upon each other. Unfortunately, the number of atoms and electrons involved for calculations of supercells of Y2(Ti, Sn)2O7 is impractically large for local computational resources. A preliminary investigation using a (2 × 1 × 1) supercell showed little change in the local geometry or the chemical shift for the 1,2,3-Sn3Ti3 substitution in Y2Sn2O7, which exhibited a large ∆δiso, but it is perhaps expected that, as the cell is cubic, at least a (2 × 2 × 2) supercell would be required. In summary, the extreme distortions and anomalous shifts that result from these, may well be imposed by the simplifications required in our model and perhaps may be alleviated if larger and more complex models could be used, and would then not be expected to be experimentally present. However, even for the simpler systems considered here, these large differences occur in only a small fraction of cases (500 Y species considered) and, even if these did occur in reality, they would result in only a very small change to the spectral intensities, and pose little problem for the interpretation of the experimental spectra. In addition to the systematic sets of substitutions described above, a number of additional calculations were undertaken for a material with composition Y2TiSnO7, i.e., with 8 Sn and 8 Ti B-site cations in the unit cell. These cations were arranged into a number of ordered structures, where the Sn/Ti occupy planes or layers of B sites for example, or alternatively were introduced into the structure entirely at random. While containing only a few of the possible NNN environments, these structures possess a more disordered long-range structure. The calculated 89Y chemical shifts all fall within the chemical shift ranges shown in Figure 7, although no anomalous shifts or significant structural distortions were observed. Full details of these calculations and the exact structures considered are given in the Supporting Information. Although the isotropic chemical shift provides an excellent probe of the local environment an atom experiences, detailed information about local structure is also available from the CSA.32 Typically, information on the anisotropic part of the shielding interaction is removed by MAS, and can only be extracted when MAS rates are sufficiently slow that a number of spinning sidebands are observed. However, such an approach may also lead to the incomplete removal of dipolar interactions, broadening spectral resonances and, furthermore, for cases where a number of distinct species are present, the spectral overlap may be such that the accuracy of the measurement is compromised. More recently, there have been a number of twodimensional MAS NMR experiments introduced which allow the CSA parameters to be determined at fast MAS rates while producing (in the indirect dimension) a sideband pattern which would be observed at much slower spinning rates.33 Accurate measurement of the CSA could provide an alternative approach to spectral assignment, which may be of particular use for the complex spectra obtained for disordered materials. The 89Y ∆CSA and ηCSA parameters for the range of NNN substitutions in Y2Sn2O7 and Y2Ti2O7 are given in Table 2. The two end members have very different ∆CSA values (as discussed above, that for Y2Ti2O7 is larger owing to the larger distortion of the 48f O species away from the position in ideal fluorite).23 As shown in Table 2, there is a systematic increase in ∆CSA as the
Reader et al.
Figure 9. Plot showing calculated 89Y ∆CSA as a function of the number, n, of Sn NNN for substitution into Y2Ti2O7 (red squares), Y2Sn2O7 (blue diamonds), and the Y2TiSnO7 compositions discussed in more detail in the Supporting Information (green triangles).
number of Ti NNN increases. The exact values observed for the Y2Sn2O7 and Y2Ti2O7 series are different, reflecting the different longer range environments and unit cell sizes, but the same general trend is observed. This trend is perhaps seen more clearly in Figure 9, which plots all calculated 89Y ∆CSA values (including substitutions into Y2Sn2O7 and Y2Ti2O7 and the additional Y2TiSnO7 compositions discussed in more detail in the Supporting Information). For any number of Sn NNN a range of ∆CSA values are observed owing to smaller differences in the local environment, but there is a systematic decrease in the average ∆CSA as the number of Sn NNN decreases. The differences in ηCSA are more difficult to relate to any single structural parameter. As seen in Table 2, ηCSA is 0 for the two end members, reflecting the axial symmetry of the Wyckoff position.23 As Sn/Ti are substituted into the NNN environment, this symmetry is lowered and ηCSA is typically between 0.1 and 0.3. Notable exceptions to this are the 1,3,5-Sn3Ti3 environments where axial symmetry is maintained. These results indicate that the CSA would be a sensitive probe of local environment and an additional tool for enabling spectral assignment if it can be experimentally measured easily and accurately. Conclusions The sensitivity of NMR parameters (in particular, the isotropic chemical shift) to environment provides a useful probe of local structure in disordered solids, although the complexity of the NMR spectra that may result, owing to the variety of different environments a nucleus experiences, can hinder the ease with which this information can be extracted. However, the use of first-principles calculations to aid spectral interpretation and assignment provides a powerful complementary approach and enables a more detailed structural insight. Here, we have demonstrated that such calculations can be used to investigate cation disorder in the Y2Ti2-xSnxO7 pyrochlore solid solution. Previous experimental results showed complex 89Y MAS NMR spectra containing composite resonances, which were only able to be analyzed in any detail once a number of assumptions were made concerning spectral interpretation. Using DFT calculations, we have been able to investigate the validity of these assumptions and the accuracy of the previous analysis. First, we have shown that the chemical shifts which result from Y occupation of the six-coordinate B site are significantly higher than those associated with eight-coordinated Y, and also higher than those observed experimentally, confirming Y is found only on the A site in our synthetic pyrochlores. A systematic change in the calculated 89Y isotropic chemical shift
Cation Disorder in Pyrochlore Ceramics was observed upon substitution of Sn/Ti into the NNN coordination sphere of a particular Y species, the magnitude of which was in good agreement with experiment. However, the chemical shift was also shown to be sensitive to more remote structural changes (e.g., in the occupancy of the more distant B-site cations) and the small changes in local geometry which result. For any number of Sn/Ti NNN, a range in chemical shift of 20-30 ppm was observed, but with a systematic increase in the average chemical shift as the number of Sn NNN increases. In a very small minority of cases, chemical shifts were calculated which lie outside the usual ranges, and these were shown to result from significant distortions in local geometry (notably, a deviation of the O8b-YsO8b bond away from 180° and an increase in the difference between the six Y-O48f bond distances). However, these anomalous results could well result from the periodicity imposed on the system, and may well be alleviated by the use of larger supercells (although this would require the use of large scale computing facilities). Even if this is not the case, these anomalies occurred rarely (
