Article pubs.acs.org/JPCC
Gradual Structural Evolution from Pyrochlore to Defect-Fluorite in Y2Sn2−xZrxO7: Average vs Local Structure Zhaoming Zhang,* Simon C. Middleburgh, Massey de los Reyes, and Gregory R. Lumpkin Institute of Materials Engineering, Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW 2234, Australia
Brendan J. Kennedy, Peter E. R. Blanchard, and Emily Reynolds School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia
Ling-Yun Jang Experiment Facility Division, National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan S Supporting Information *
ABSTRACT: We have studied the long-range average and local structures in Y2Sn2−xZrxO7 (x = 0−2.0) using synchrotron X-ray powder diffraction and X-ray absorption spectroscopy, respectively, and by theoretical methods. While the diffraction data indicate a clear phase transition from ordered pyrochlore to disordered defectfluorite at x ∼ 1.0−1.2, X-ray absorption near-edge structure (XANES) results at the Zr L3- and Y L2-edges reveal a gradual structural evolution across the whole compositional range. These findings provide experimental evidence that the local disorder occurs long before the pyrochlore to defect-fluorite phase boundary, as determined by X-ray diffraction, and the extent of disorder continues to develop throughout the defectfluorite region. The Zr and Y L-edge spectra are very sensitive to changes in the local structure; such sensitivity enables us to reveal the progressive nature of the phase transition. Experimental results are supported by ab initio atomic scale simulations, which provide a mechanism for disorder to initiate in the pyrochlore structure. Further, the coordination numbers of the cations in both the defect-fluorite and pyrochlore structures are predicted, and the trends agree well with the experimental XANES results. The calculations predict that the coordination of cations in the Y2Zr2O7 defect-fluorite (normally considered to be 7 for all cations) varies depending on the species with the average coordination of Y and Zr being 7.2 and 6.8, respectively.
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□, respectively). The local coordination environments of the cations are AO(1)6O(2)2 and BO(1)6□2 (Figure 1b), while the anions and vacancy are each surrounded by four cations (O(1) A2B2, O(2)A4, and □B4). Pyrochlore is an unusual example of a structure with both cation and anion ordering.1 The ordered arrangement of both cations and anions leads to the doubling of the pyrochlore cell parameter compared to that of the fluorite (ap ≈ 2af). In the ideal pyrochlore structure, the A and B cations occupy the 16d (1/2, 1/2, 1/2) and 16c (0, 0, 0) sites (in origin choice 2), respectively. The O(1) oxygen ions are located at the 48f (x48f, 1/8, 1/8) site and the O(2) at the 8b (3/8, 3/8, 3/8) site, whereas the 8a (1/8, 1/8, 1/8) sites are unoccupied. The pyrochlore stability field is generally related to the ionic radius ratio of the A and B cations (rA/rB) under ambient conditions. The III/IV pyrochlore structure is stabilized when rA/rB = 1.46−1.78, whereas the defect-fluorite structure (or anion deficient fluorite A0.5B0.5O1.75) is formed
INTRODUCTION Pyrochlore oxides with the general formula A2B2O7 are a class of materials that display diverse properties with a wide range of technological applications.1 The most common pyrochlore oxides are the III/IV pyrochlores containing trivalent A-site and tetravalent B-site cations, due to the fact that there are many A3+ and B4+ cations with suitable ionic radii to form the pyrochlore structure. Of particular interest are pyrochlore oxides with Zr, Ti, or Sn occupying the B-site as both ionic and electronic conductors in solid oxide fuel cells,2,3 and host matrixes for the immobilization of actinide-rich nuclear wastes.4−6 Certain lanthanide zirconate pyrochlores have also been considered as potential inert matrix fuel materials.7,8 Many of the properties of pyrochlore are sensitive to the degree of disorder and related changes in the structure.4,9,10 The ideal (or fully ordered) pyrochlore structure, A2B2 O(1)6O(2), is cubic in space group Fd3̅m with the larger cations occupying the A-site and the smaller ones the B-site, as shown in Figure 1a. It is derived from the ideal fluorite structure AO2 (space group Fm3m ̅ ), but with two cation sites and three oxygen sites (for O(1), O(2), and 12.5% vacancies © 2013 American Chemical Society
Received: August 30, 2013 Revised: November 20, 2013 Published: November 25, 2013 26740
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Figure 1. (a) Pyrochlore structure of general formula A2B2O7 showing the A-site (blue) and B-site (green) polyhedra and (b) the local coordination environment around the A- and B-site cations. The O(1) and O(2) oxygen atoms located at the 48f and 8b sites are depicted as gold and red balls, respectively.
when rA/rB < 1.46.1 The ordered pyrochlore structure can be transformed to the disordered defect-fluorite structure by a random distribution of both cations and anions onto their respective sublattices, with the A- and B-site coordination number (CN) changing from 8 and 6, respectively, to an average of 7 for both. Such a phase transition can be induced by temperature,11,12 pressure,13,14 composition,3,15,16 or ion irradiation.5,17,18 In addition to the fully ordered pyrochlore and completely disordered defect-fluorite, there is also increasing evidence for partial order/disorder in A2B2O7.2,10,15,19,20 However, it could be difficult to experimentally quantify the partially disordered state depending on the degree and length scale of the disorder. There have been quite a few studies of the effect of chemical substitution on the pyrochlore to defect-fluorite structural transformation in Y2B2−xZrxO7 (B = Sn or Ti).2,3,10,19,21−25 Most of these studies employed X-ray and/or neutron powder diffraction methods, which probe the long-range average structure. On the basis of their neutron and X-ray diffraction results, Wuensch et al.2,3,22,23 reported that disorder in the Y2Sn2−xZrxO7 and Y2Ti2−xZrxO7 solid solutions evolves progressively in both the anion and cation sublattices, but the disordering rates are independent of each other. Upon substitution of Zr for Ti (or Sn), the vacant 8a site starts to become partially occupied, initially solely by O(1) from the 48f site and later by O(2) from the 8b site as well. In both Y2Sn2−xZrxO7 and Y2Ti2−xZrxO7 systems, the anion disorder precedes the disordering in the cation sublattice, and complete disordering (i.e., transition to defect-fluorite) does not occur until the Zr content is x > 1.6. However, first-principles calculations of defect-formation energies in Y2B2O7 pyrochlore (B = Sn, Ti, or Zr) predicted that cation antisite disorder causes oxygen disorder.26 The local structure in Y2B2−xZrxO7 (B = Sn or Ti) was also investigated using Raman and NMR spectroscopies,19,24,25 which confirmed the progressive nature of the pyrochlore to defect-fluorite transition. A recent study of Y2Ti2−xZrxO7,10 using the neutron total scattering method, has revealed that, although the Zr4+ ions initially replace the Ti4+ ions on the B-sites, they prefer to adopt a cubic local environment (in contrast to the octahedral environment
around Ti4+), which in turn leads to disordering in the anion sublattice. Given the difference between the long-range average structure and short-range local structure as observed in the Y2Ti2−xZrxO7 system,10 we have revisited the closely related Y2Sn2−xZrxO7 series using synchrotron X-ray diffraction and Xray absorption near-edge structure (XANES) spectroscopy to study the average and local structures, respectively. These experimental studies have been supported by ab initio calculations. While diffraction is sensitive to long-range order and gives the structure averaged over thousands of unit cells, XANES probes the short-range local chemical environment including valence state, coordination, and site geometry. The combination of both types of techniques is required in order to provide a full description of systems with localized disorder, as some local distortions may be averaged out in diffraction measurements. For example, X-ray absorption spectroscopy was used to demonstrate that the local environment around Y is independent of the long-range crystal structure in tetragonal or cubic polymorphs of Y2O3 stabilized ZrO2.27 While Zr has a very different local structure in the different polymorphs in terms of the M−O bond distance and CN, the local structure around Y is practically the same in all the compositions studied with Y2O3 concentration ranging from 3 to 20 mol %.27 XANES has also been extensively used to study the local structures in various pyrochlore and defect-fluorite materials.20,28−34 The aim of the present study is to first demonstrate that the local structural evolution in Y2Sn2−xZrxO7 is more complex than that of the long-range average structure, second to determine whether there is a two-phase region near the pyrochlore to defect-fluorite boundary as reported for the similar Y2Ti2−xZrxO7 system,21 and finally to shed some light on the detailed disordering process with the substitution of Zr for Sn. We propose to use the crystal field splitting of the Zr and Y 4d orbitals as a key parameter to measure the local disorder in Y2Sn2−xZrxO7. It will be shown that the Zr and Y L-edge XANES spectra provide a very sensitive measure of the local chemical environment around Zr and Y in the pyrochlore and defect-fluorite materials, which differs from that implied by the global symmetry as determined by X-ray diffraction. We have also performed ab initio atomic scale calculations to predict the 26741
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Figure S1 in the Supporting Information, and calculations were carried out for each arrangement to provide a statistically accurate analysis. Static calculations to analyze the effect of defects on the volume of the unit cell were carried out using constant pressure periodic boundary conditions. Further analysis of the defect clusters in the static unit cells involved the calculation of defect energies, determined by taking the difference between a perfect supercell and a defective supercell (accounting for addition and/or removal of atoms by separating them to an isolated state).42 Molecular dynamics calculations used a 5 fs time step for all calculations with a canonical ensemble using a standard Nosé− Hoover thermostat43 (i.e., constant volume and temperature), in a similar manner to those used for the Y2Ti2O7 and Y2Zr2O7 systems.44 Each arrangement of the pyrochlore and defectfluorite structures was initially taken to 1800 K, held for 10 ps to allow oxygen migration to occur and to move into energetically preferential positions. This step is particularly important for the defect-fluorite calculations where the local oxygen ordering can be quite complicated. The cell temperature was then reduced in 50 K intervals for 0.5 ps at each step to 300 K. At this target temperature, the local ordering was examined by calculating the average coordination of each cation in the structure over a period of 2.5 ps (details are provided in the Supporting Information). The coordination of the cations in the ideal defect-fluorite system averages out to be 7, regardless of cation species. Any deviation from this value for a specific species provides evidence that there is some degree of local ordering. The duration of the simulations is considered adequate bearing in mind the high computational expense of the methods used.
pyrochlore unit cell volume change, and the cation coordination numbers in both the pyrochlore and defect-fluorite structures. A mechanistic understanding of the disordering process in pyrochlore can be achieved by matching the theoretical predictions with experimental observations.
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EXPERIMENTAL AND THEORETICAL METHODS Samples with the composition Y2Sn2−xZrxO7 (x = 0−2.0 in 0.2 steps) were prepared using the conventional mixed metal-oxide process. All starting materials, commercially available yttrium oxide, tin oxide, and zirconium oxide (all Aldrich, 99.5%), were heated to 1123 K for 10 h to completely remove adsorbed H2O and CO2. The stoichiometric mixture was then attrition milled for 12 h at room temperature using zirconia balls and cyclohexane as the milling media. After drying at 523 K, finely ground powders were pressed into 10 mm diameter pellets using a cold uniaxial press at 200 bar. Pellets were then sintered in air at 1773 K for 168 h. Finally, a small piece was broken off each pellet and crushed to fine powder for XRD and XANES measurements. Synchrotron X-ray diffraction (S-XRD) data were collected at room temperature in the angular range 5° < 2θ < 85°, using X-rays of wavelength 0.82518 Å on the powder diffractometer at BL-10 of the Australian Synchrotron.35 Each sample was placed in a 0.3 mm glass capillary that was rotated during the measurements to reduce the effects of preferred orientation and improve powder averaging. Structures were refined using the Rietveld method implemented in the program Rietica.36 The peak shape was modeled using a pseudo-Voigt function, and the background was estimated using a linear interpolation between a set of 40 background points, which were refined simultaneously with the other profile and structural parameters. All atomic displacement parameters (ADPs) were taken to be isotropic. The Zr L3- and Y L2-edge XANES spectra were collected on beamline 16A1 at the National Synchrotron Radiation Research Center (NSRRC) in Hsinchu, Taiwan.37 Finely ground powder samples were dispersed onto Kapton tape and placed in front of the X-ray beam at a 45° angle. Spectra were collected in bulksensitive fluorescence yield mode using a Lytle detector. Energy steps as small as 0.2 eV were employed near the absorption edges with a counting time of 2 s per step. The energy scale was calibrated using the L3-edge of a pure Zr foil with the maximum in the first derivative set to 2222.3 eV. Normalization and background subtraction were carried out using the Athena software program.38 Static and dynamic calculations were carried out on the Y2Sn2−xZrxO7 system where the atomic bonding was predicted using density functional theory (DFT) within the VASP code.39 A DFT approach was chosen to account for the variation in bonding expected to occur as the system composition is varied, which a standard empirical potential approach normally cannot do. A 450 eV cutoff energy was used with a 2 × 2 × 2 k-point grid. The GGA-PBE exchange correlation was employed with a PAW type pseudopotential.40 The compositions having the defect-fluorite structure were studied using a 2 × 2 × 2 supercell (containing 96 lattice sites). A single supercell, analogous to the 2 × 2 × 2 defect-fluorite supercell, was used for calculations of the pyrochlore samples. The defect-fluorite structure is not clearly defined due to the shared occupancy of the cations and the partial occupancy of the anions. As such, 20 random arrangements of cations were produced using a special quasirandom structure (SQS) approach,41 as illustrated in
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RESULTS AND DISCUSSION Long-Range Average Structure. The synchrotron X-ray powder diffraction patterns were obtained from all 11 samples in the Y2Sn2−xZrxO7 series (x = 0−2.0 in 0.2 steps). Parts a and b of Figure 2 show the patterns of Y2Sn1.8Zr0.2O7 and Y2Sn0.2Zr1.8O7 as an example of the pyrochlore and defectfluorite phase, respectively. As mentioned above, the pyrochlore structure can be described as a cation and anion/vacancy ordered derivative of the fluorite structure. Therefore, X-ray diffraction patterns of the pyrochlore phase contain weak superlattice reflections in addition to the main reflections observed from the defect-fluorite phase. On the basis of the presence or absence of these superlattice reflections, patterns corresponding to samples with Zr content (x) below 1.0 were refined to the pyrochlore structure (space group Fd3m ̅ ), and those obtained from samples with x above 1.2 were refined to the defect-fluorite structure (space group Fm3̅m). The crystallographic parameters obtained from Rietveld refinements are listed in Table 1 for Y2Sn1.8Zr0.2O7 and Y2Sn0.2Zr1.8O7. The relatively high ADPs for the anions in the defect-fluorite phase are a result of the vacancies. The S-XRD patterns obtained from Y2Sn1.0Zr1.0O7 and Y2Sn0.8Zr1.2O7 show clear evidence of coexisting pyrochlore and defect-fluorite phases, in the form of resolved peak splitting. A representative diffraction pattern is shown in Figure 3 for Y2Sn1.0Zr1.0O7; a satisfactory fit to the data was only obtained when both phases were included in the refinements. In addition, the main peaks also have a small very broad feature at higher angles (see inset of Figure 3), which is attributed to strain-induced peak asymmetry.45 This residual intensity was 26742
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Table 1. Crystallographic Parameters for Y2Sn1.8Zr0.2O7 and Y2Sn0.2Zr1.8O7 at Room Temperaturea Y2Sn1.8Zr0.2O7, pyrochlore in Fd3̅m, a = 10.38564(2) Å, Rp = 3.69%, Rwp = 5.24% atom
x
site
y
z
Uiso (10−2 Å2)
Y 16d 0.5 0.5 0.5 0.31(1) Sn/Zr 16c 0 0 0 0.37(1) O(1) 48f 0.3398(2) 0.125 0.125 1.94(6) O(2) 8b 0.375 0.375 0.375 1.47(11) Y2Sn0.2Zr1.8O7, defect-fluorite in Fm3̅m, a = 5.21068(1) Å, Rp = 6.22%, Rwp = 8.90% atom
site
x
y
z
Uiso (10−2 Å2)
Y/Sn/Zr O
4a 8c
0 0.25
0 0.25
0 0.25
1.61(1) 5.90(7)
a
The number in parentheses beside each entry indicates the estimated standard deviation (ESD) referred to the last digit shown. The displacement parameters for cations occupying the same crystallographic site were constrained to be equal.
Figure 2. S-XRD patterns recorded from (a) pyrochlore Y2Sn1.8Zr0.2O7 (superlattice reflections indicative of the pyrochlore structure are indicated by “*” or the subscript “p”) and (b) defect-fluorite Y2Sn0.2Zr1.8O7. The black crosses represent the observed data, and the solid red line is the fit obtained by the Rietveld method using the cubic structure in Fd3̅m (pyrochlore) or Fm3̅m (defect-fluorite). The blue vertical markers show the peak positions expected in the structure, and the green line beneath the pattern records the difference between the observed and calculated patterns. The insets highlight the difference between the pyrochlore and defect-fluorite structures. Note that, due to the doubling of the pyrochlore cell parameter compared to that of the defect-fluorite (ap ≈ 2af), the (h k l) reflection in defectfluorite corresponds to (2h 2k 2l) in pyrochlore; i.e., (111) and (002) peaks in defect-fluorite correspond to (222) and (004) in pyrochlore.
Figure 3. S-XRD pattern recorded from Y2Sn1.0Zr1.0O7. The black crosses represent the observed data, and the red solid line is the fit to the model described in the text. The green line beneath the pattern records the difference between the observed and calculated patterns. The inset shows resolved peak splitting of the pyrochlore (448)p and defect-fluorite (224)f peaks, as well as the asymmetry at higher angles which was modeled by a fluorite “phase” (as indicated by the lowest set of markers).
octahedral B-site.47 Our results are in general agreement with those reported by Ku et al.,22 except for the pyrochlore to defect-fluorite transition occurring at slightly higher Zr content in their study (x ∼ 1.6 with a larger composition step of Δx = 0.4). As shown in Figure 4, the lattice parameters in each phase region were fitted with a linear function, and those from the pyrochlore phase seem to be in better agreement with Vegard’s law. It is also interesting to note that the lattice parameter of the pyrochlore phase is noticeably larger than twice that of the defect-fluorite phase; this increased volume of the pyrochlore phase was also observed for La2−xYxZr2O7,15 Ho2−xNdxZr2O7,16 and Y2Ti2−xZrxO721 (the reason for this phenomenological observation is unclear). The positional parameter of O(1) oxygen, x(48f), appears to increase in a linear fashion with increasing Zr content (x), ranging from 0.3370 at x = 0 to 0.3487 at x = 1.0. Due to limited X-ray scattering power for oxygen (especially in the presence of much heavier cations), we have not explored the possibility of oxygen partially occupying the nominally vacant 8a sites. However, the increase in the
modeled using a fluorite “phase”, similar to that employed in the studies of Gd2Zr2O7.20,34 Although the coexistence of pyrochlore and defect-fluorite phases is common in similar systems,16,21,46 a two-phase region has not been reported for Y2Sn2−xZrxO7 (x = 0−2.0) in previous studies using laboratory X-ray and neutron powder diffraction.2,22,25 This demonstrates that the superior resolution of synchrotron XRD is necessary for the detection of two-phase regions, especially when the lattice parameters of the two phases are very close (i.e., ap ≈ 2af). Figure 4 illustrates the compositional dependence of the unit cell parameter (ap or 2af) and the positional parameter of O(1), x(48f), for Y2Sn2−xZrxO7 as obtained by Rietveld refinements against the S-XRD data. The lattice parameter increases with the increase of Zr content, as a result of replacing smaller Sn4+ ions (IR = 0.69 Å) with larger Zr4+ ions (IR = 0.72 Å) on the 26743
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Figure 5. Pyrochlore unit cell volume change as a function of increasing concentration of Zr in Y2Sn2−xZrxO7, calculated using density functional theory under constant pressure, along with experimental S-XRD data (x = 0−0.8). nZrSn× denotes isovalent defects with n Zr substituting for Sn, while {ZrY•:YSn′} represents an aliovalent defect and {ZrY•:YSn′} + (n−1)ZrSn× is a defect cluster incorporating (n − 1) isovalent defects and one aliovalent defect.
Figure 4. The appropriately scaled unit cell parameter of Y2Sn2−xZrxO7 (x = 0−2.0) as a function of Zr content (x). The black squares correspond to the unit cell parameter of the pyrochlore phase (ap), and the red circles denote twice the unit cell parameter of the defect-fluorite phase (2af). The inset shows the positional parameter of O(48f) as a function of Zr content (x); the value for the x = 1.2 sample was fixed in the final refinements (based on linear extrapolation of the values obtained for x = 0−1.0)otherwise, the refinements yielded a value larger than the allowable upper limit of 0.375. Note the EDSs are smaller than the symbols.
{ZrY•:YSn′} defect formation alone increases the volume of the unit cell too severely and is therefore not expected to be the sole mechanism by which Zr is accommodated into the Y2Sn2O7 lattice. It is necessary to combine both mechanisms in order to match the observed rate of volume increase with increasing Zr content, which suggests that Zr would form defects on the Y sublattice while displacing the Y cations onto the Sn sublattice in conjunction with forming the simple ZrSn× substitutional defects. The relative stability of the defect clusters presented in Figure 5 has also been investigated by considering the defect energy, and it was found that, although the ZrSn× defect is clearly more favorable than the {ZrY•:YSn′} defect cluster (accommodating a single Zr in each case), further clustering of Zr defects leads to the arrangement of incorporating the {ZrY•:YSn′} cluster with ZrSn× defects becoming the more favored mechanism to accommodate Zr in Y2Sn2O7. The defect energy results are presented in Figure 6 as a function of the total number of Zr (n). One can see that the energy per defect for the nZrSn× bound defects varies very little with n. This is to be expected, as there are no Coulombic interactions nor any significant strain binding effects that can occur. This is in stark
x(48f) value with increasing Zr content does provide a measure of the anion disordering progress from pyrochlore toward defect-fluorite (recall that when x = 0.375 the anions are at the equivalent position for the defect-fluorite structure). In summary, our synchrotron diffraction data indicate a clear transition from single-phase pyrochlore to single-phase defectfluorite with the two phases coexisting at x = 1.0−1.2. A number of defects and defect clusters in the pyrochlore structure have been investigated using atomic scale modeling to understand the effect of Zr additions on the volume of the unit cell. These defect clusters can be placed in one of two categories: those involving Zr atoms occupying either the isovalent Sn site (ZrSn×) or the aliovalent Y site (ZrY•), using the Kröger−Vink notation48 (where the superscript “×” and “•” denote neutral and singular positive charge, respectively). Three different isovalent bound defects are considered: 1ZrSn× (i.e., one Zr atom replacing Sn), 2ZrSn×, and 3ZrSn× (i.e., two or three Zr atoms substituting for Sn, which are clustered together in the most energetically favorable arrangement). In addition, four different clusters that incorporate aliovalent bound defects are considered, all incorporating the defect cluster {ZrY•:YSn′} where a Zr ion sits on a Y lattice site with singular positive charge in conjunction with a Y ion sitting on a Sn site with singular negative charge (where the prime symbol denotes singular negative charge). The defect volumes are calculated and compared to experimental data from Figure 4 that provides the pyrochlore lattice parameter of Y2Sn2−xZrxO7. The comparison is limited to x = 0−0.8, corresponding to the pyrochlore single phase region. The change in the pyrochlore unit cell volume with different defect types is presented in Figure 5 as a function of Zr content. As evident from Figure 5, the ZrSn× substitutional defect alone does not produce the change in volume observed as the concentration of Zr is increased. Increasing the number of ZrSn× defects clustered together subtly reduces the expansion of unit cell volume, although the difference between 2ZrSn× and 3ZrSn× is negligible. Figure 5 also illustrates that lone
Figure 6. Defect energy per zirconium in a defect cluster populated by simple nZrSn× defects (black squares) and {ZrY•:YSn′} + (n − 1)ZrSn× defect clusters (red dots). 26744
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contrast to the {ZrY•:YSn′} + (n − 1)ZrSn× cluster, which shows a marked drop in defect energy per defect when n is increased from 1 to 2. For both mechanisms, the defect energies with three Zr atoms in the defect cluster are extremely close (within 0.05 eV), and can probably be considered equal within error. When four Zr atoms are considered, there is a small but clear preference to form a {ZrY•:YSn′} + 3ZrSn× cluster over forming a 4ZrSn× cluster. Combining these results with those presented in Figure 5, the formation of {ZrY•:YSn′} + 2ZrSn× and/or {ZrY•:YSn′} + 3ZrSn× defect clusters is believed to be the preferred mechanism considered in this work for cation disorder to initiate in the pyrochlore Y2Sn2−xZrxO7 system. Note that defect cluster−defect cluster interactions have not been taken into account but would play a key role in the eventual complete disordering into the defect-fluorite structure. It is possible that the ratio of Zr defects residing on the Y and Sn sublattices in larger clusters would remain around 1:2−1:3 (i.e., one {ZrY•:YSn′} for every two or three ZrSn×), as this has provided a good match to the experimentally observed unit cell volume change. Finally, it should be mentioned that the presence of an antisite defect in Y2Sn2O7, {SnY•:YSn′}, has also been investigated. The antisite defect is predicted to proceed with an energy of 2.25 eV, and hence, the concentration is expected to be extremely low (1.26 × 10−19 at 300 K) using the laws of mass action.49 The defect volume change associated with {SnY•:YSn′} is very positive; therefore, such defects were not included when considering the lattice response to accommodate Zr in Y2Sn2O7. Short-Range Local Structure. Parts a and b of Figure 7 plot the Zr L3- and Y L2-edge XANES spectra for the Y2Sn2−xZrxO7 series, resulting primarily from the Zr 2p3/2 → 4d and Y 2p1/2 → 4d dipole transitions, respectively; in both cases, the contribution to the s final state is negligible, as it is ca. 50 times weaker than that to the final d state.50 Consequently, these spectra provide direct information on the occupancy and energy distribution of the final Zr(4d) or Y(4d) states, which is determined mainly by the local crystal field exerted by the surrounding oxygen ligands. As shown in Figure 7, each L-edge spectrum displays a bimodal feature (labeled peaks α and β), which is caused by the crystal field splitting of the unoccupied 4d orbitals of the Zr or Y cations. The energy gap between peaks α and β, ΔE, is directly related to the crystal field splitting, which increases with increased interaction between the cation 4d and the ligand 2p orbitals. It was demonstrated in the recent studies of Ln2Zr2O720 and Nd2−yYyZr2O751 that both the splitting (ΔE) and the peak intensity ratio (Iα/Iβ) are sensitive to the local environment around Zr and Y. Furthermore, the coordination number (CN) of Zr can be deduced from the Zr L3-edge of XANES spectra as ΔE decreases with increasing CN.20,52 In the pyrochlore structure, as shown in Figure 1b, the smaller B cation is coordinated to six equally distant O48f anions within a trigonal antiprism (distorted octahedron), while the larger A cation is in a scalenohedron (distorted cube) formed by six O48f anions situated at equal distances and two O8b anions at slightly shorter distances. The shape of the coordination polyhedra changes with the positional parameter of 48f oxygen anions, which can vary within the range 0.3125− 0.375.1 The B-site cation has a perfect octahedral coordination when x(48f) = 0.3125, while the A-site cation sits in a perfect cubic environment when x(48f) = 0.375 (corresponding to the ideal fluorite arrangement). For convenience, we will use the
Figure 7. Normalized (a) Zr L3-edge and (b) Y L2-edge XANES spectra of the Y2Sn2−xZrxO7 solid solution (the spectra have been offset vertically to enhance visibility). Next to the XANES spectra, the metal d-orbital splitting in the octahedral (MO6) and cubic (MO8) coordination environment is also shown to illustrate the Zr 4d and Y 4d level splitting in the pyrochlore structure (under the simplistic assumptions of crystal field theory).
octahedral and cubic symmetry to approximate the actual (lower) local symmetry in pyrochlore around the B- and A-site cations, respectively, and discuss the XANES results within the framework of crystal field theory (CFT). Note that given the disorder of the anion vacancies it is not possible to identify the precise geometry, and hence the d-orbital splitting, of the 7coordinate cations in the defect-fluorite structure. For an octahedral MO6 unit (where M is at the origin and O ligands are positioned on the Cartesian axes), the triply degenerate t2g orbitals (dxy, dxz, and dyz) are located at lower energy than the doubly degenerate eg orbitals (dx2−y2 and dz2), as the latter point toward the ligand orbitals and hence are subject to a stronger electrostatic repulsion from the ligands. In contrast, the three dt2g orbitals lie higher in energy with respect to the two d-eg orbitals for a cubic MO8 unit (where M is at the origin and O ligands are situated at the cube corners), as the t2g orbitals are now oriented with their lobes much closer to the ligands than the eg orbitals. The energy difference between the t2g and eg orbitals is defined as the crystal field splitting, Δ. For a given ligand at the same metal−ligand distance, the magnitude of splitting in cubic coordination is 8/9 times the octahedral splitting (Δc = 8/9Δo) with reversed energy order of the orbitals.53 At the Sn-rich pyrochlore end (where the cation antisite disorder is negligible), Zr and Y are situated in the center of a 26745
dx.doi.org/10.1021/jp408682r | J. Phys. Chem. C 2013, 117, 26740−26749
The Journal of Physical Chemistry C
Article
distorted octahedron and cube, respectively. Therefore, the two structures displayed at the Zr L3-edge can be attributed to the splitting of the Zr(4d) orbitals into the t2g and eg orbitals at an octahedral site (see the XANES spectrum for Y2Sn1.8Zr0.2O7 in Figure 7a with the triply degenerate t2g orbitals at lower energy), whereas the two features at the Y L2-edge are due to the splitting of the Y(4d) orbitals into the eg and t2g orbitals at a cubic site (see the XANES spectrum for Y2Sn2O7 in Figure 7b doubly degenerate eg orbitals at lower energy). It should be noted that the above description is only rigorous under the simplistic assumptions of crystal field theory which ignores the covalency nature of the M−O bonds, and does not apply to samples with the defect-fluorite structure. At the Sn-rich pyrochlore end, the ratio between the low- and high-energy peak intensities (Iα/Iβ) is >1 at the Zr L3-edge and
