Pyrochlore to Fluorite Transition: The Y2(Ti1–xZrx)2O7 (0.0 ≤ x ≤ 1.0

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Pyrochlore to Fluorite Transition: The Y2(Ti1−xZrx)2O7 (0.0 ≤ x ≤ 1.0) System Stefan T. Norberg,*,†,‡ Stephen Hull,† Sten G. Eriksson,‡ Istaq Ahmed,‡,∥ Francis Kinyanjui,‡ and Jordi Jacas Biendicho†,§ †

ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, United Kingdom Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden § Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden ‡

S Supporting Information *

ABSTRACT: The structural properties of the system Y2(Ti1−xZrx)2O7 have been investigated using the neutron powder diffraction technique, including a detailed analysis of the “total scattering” using reverse Monte Carlo modeling to probe the short-range ion−ion correlations over sample range 0.0 ≤ x ≤ 1.0. The average crystal structure shows a continuous transformation from the long-range ordered pyrochlore structure (Fd3̅m, a = 10.0967(1) Å, Z = 8, for x = 0.00, Y2Ti2O7) to a disordered fluorite structure (Fm3̅m, a = 5.2042(1) Å, Z = 1, for x = 1.00, Zr2Y2O7) in agreement with previous reports. However, on increasing x the disordering of both the cation and the anion sublattices occurs in stages, with the Zr4+ initially only substituting onto the Ti4+ site and adopting a cubic, rather than octahedral, local anion environment. At concentrations in excess of x ≈ 0.4 there is a gradual disordering of the Y3+, Ti4+, and Zr4+ species over all the cation sites, coupled with a redistribution of the O2− which initially only involves those anions on the O1 sites. The relationship between the composition dependences of the structure properties and the ionic conductivity is discussed. KEYWORDS: RMC modeling, oxygen vacancy ordering, SOFC electrolytes method and reaction conditions.14−17 Particular attention has focused on the line represented by Y2(Ti1−xZrx)2O7 which joins the pyrochlore structured Y2Ti2O7 compound (x = 0) to the disordered fluorite Zr2Y2O7 (x = 1).18−25 The relationship between the fluorite structure of a compound of stoichiometry AO2 (space group Fm3̅m) and the pyrochlore structure of a compound with the ideal formula of A2B2O7 (a = 2 × aflourite, space group Fd3m ̅ ) is illustrated in Figure 1. In the former, the A4+ cations occupy alternate centers of cubes of O2− (see Figure 1a), while in the latter the two cation species, conventionally A3+ and B4+, are ordered into rows in ⟨100⟩ directions (in 16(c) positions at 0,0,0, etc. and 16(d) positions at 1/2,1/2,1/2, etc.). As shown in Figure 1b, the 64 anion positions within the equivalent fluorite arrangement then comprise a 48-fold set (48( f) in xO1,1/8,1/8, etc., labeled O1), plus two 8-fold sets (8(a) in 1/8,1/8,1/8, etc. and 8(b) in 3 3 3 /8, /8, /8, etc., labeled O2 and O3, respectively). Both the O1 and O2 positions are fully occupied within an “ideal” pyrochlore, while the O3 sites are completely empty. As a consequence, the O1 anions relax in ⟨100⟩ directions toward the vacant O3 sites, such that their positional parameter xO1 is

1. INTRODUCTION The structural and transport properties of zirconia doped with yttria, Zr1−xYxO2−x/2, have been extensively studied at elevated temperatures, since it is currently the most widely used material for the role of solid electrolyte within Solid Oxide Fuel Cells (SOFCs).1 A key property for this application is the high oxideion conductivity shown by these materials at temperatures in excess of 1000 K, which is a consequence of a high concentration of charge-compensating mobile anion vacancies induced by Y3+ doping onto the Zr4+ sites. However, the redox reactions which take place on the fuel (anode) and air (cathode) sides of the SOFC electrolyte requires the use of electrode materials which combine a high oxide-ion conductivity with a high electronic conductivity, coupled with good chemical and thermal expansion matching to the Zr1−xYxO2−x/2 electrolyte. In the case of the anode, a cermet of nickel and Zr1−xYxO2−x/2 is commonly employed, though a number of alternatives have also been proposed.2−7 Of these, the addition of TiO2 to Zr1−xYxO2−x/2 has been shown to enhance the electronic contribution under the strongly reducing conditions experienced at the anode,8−10 because of electron hopping between Ti 4+ and Ti 3+ species via a small polaron mechanism.11−13 The reported phase diagrams of the ternary ZrO2−TiO2−Y2O3 system show a number of discrepancies, with the phases formed being rather sensitive to the synthesis © 2012 American Chemical Society

Received: May 29, 2012 Revised: November 1, 2012 Published: November 2, 2012 4294

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Figure 1. Crystal structures of (a) the cubic fluorite structure (space group Fm3̅m) of a compound of stoichiometry AO2, with the A cations surrounded by a cube of O anions, (b) the “filled pyrochlore” structure (space group Fd3̅m) of a compound of stoichiometry A2B2O8, showing the long-range ordering of the A and B cation species and the three symmetry independent anion sites O1, O2 and O3, (c) the pyrochlore structure of a compound of stoichiometry A2B2O7, in which the O3 sites are empty and the O1 anions relax in ⟨100⟩ directions toward the vacant positions, such that the anion co-ordination around the A and B cations become distorted cubic and distorted octahedral, respectively.

typically greater than the ideal value of 3/8.26 The smaller B4+ cations then sit at the center of an octahedron of 6 × O1 anions (which is ideal at xO1 = 7/16), while the larger A3+ adopt a distorted cubic environment comprised of 6 × O1 plus 2 × O2 (see Figure 1c). The respective ionic radii of the cations (rY3+ = 1.02 Å, rTi4+ = 0.74 Å and rZr4+ = 0.84 Å for 8-fold co-ordination)27 means that the effective radii of the A and B sites within the Y2(Ti1−xZrx)2O7 system become more similar as x increases, providing a simple explanation for the change from the (ordered) pyrochlore arrangement to the (disordered) fluorite structure observed experimentally.18−20,22,23 However, it follows from the discussion in the previous paragraph that the transformation from the Y2Ti2O7 compound at x = 0 to the Zr2Y2O7 compound at x = 1 involves a gradual loss of longrange order within both the cation and the anion sublattices. Moon and Tuller23 showed that the disorder increases continuously with x, with a random arrangement of cations reached at x ∼ 0.8, but assumed that the disordering processes occur equally over both the cation sites and the three anion positions. However, a subsequent more detailed neutron powder diffraction study showed that, while the pyrochlore to disordered fluorite transformation within Y2(Ti1−xZrx)2O7 is continuous, the cation and anion disordering processes are more complex, and possibly distinct.19 The onset of disorder of the anion sublattice occurs at x ≈ 0.3 and is characterized by filling of the empty O3 sites with O2− ions displaced from the nearest neighbor anion shell of O1 sites, with the O2 sites only participating in the disorder for x > 0.45. The substitutional Zr4+ species were suggested to replace the Ti4+ in the 6-fold coordinated B sites for much of the solid solution, with complete mixing of all three cation species occurring over the range 0.60 ≤ x ≤ 0.90. These conclusions are broadly consistent with Raman and 17O NMR studies,18,20 with the latter showing evidence of local pyrochlore-like ordering within the Zr2Y2O7 end member. However, X-ray and electron diffraction studies showed evidence of a subtle two-phase region separating pyrochlore-type (0.0 ≤ x ≤ 0.54) and disordered fluorite (≈0.68 ≤ x ≤ 1) solid solutions, with the presence of one or two phases dependent on the synthesis method and temperature.22 Conductivity measurements showed that, in common with the majority of compositions in the ZrO2−TiO2−Y2O3 system, ionic conductivity dominates

under normal atmospheres,24,25 with the variation of the ionic conductivity, σ, with x correlating well with the factor mO1(1− mO1), where mO1 is the mean occupancy of the pyrochlore O1 sites obtained by neutron powder diffraction studies.19 However, it is not clear whether anion diffusion occurs between O1 sites via direct hops in ⟨100⟩ directions28 or in ⟨111⟩ directions29 through the octahedral interstices within the f.c.c. cation array. In this study, the structural properties of the system Y2(Ti1−xZrx)2O7 are investigated using the neutron powder diffraction technique. Samples with x = 0.00, 0.15, 0.30, 0.40, 0.50, 0.65, 0.80, and 1.00 are investigated, to probe the disordering of both the cation and anion sublattices as a function of x. In contrast to previous studies18−23 we analyze the total neutron scattering (i.e., Bragg plus diffuse scattering components) to probe the changes in both the average and the local structures and their influence on the composition dependence of the ionic conductivity.

2. EXPERIMENTAL METHODS 2.1. Sample Preparation. Y2(Ti1−xZrx)2O7 powder samples with x = 0.00, 0.15, 0.30, 0.40, 0.50, 0.65, and 0.80 of typical volumes of 5 cm3 were prepared by mixing stoichiometric amounts of the previously dried binary oxides Y2O3, rutile TiO2 and ZrO2 supplied by the Aldrich Chemical Co. and of stated purities 99.99%, 99.995%, and 99.99%, respectively. High purity HfO2-free zirconia powder was used to avoid the significant neutron absorption caused by hafnium contamination. The starting powders were mixed and thoroughly ground by a planetary ball mill using zirconia balls and a zirconia jar for roughly 8 h (in continuous sequences of 20 min milling at 150 rpm followed by 5 min cooling), except for the x = 0.00 sample for which a Teflon milling jar was used. The resulting powders were then pressed into pellets and heated at 1473 K for 72 h. The first sintering step was followed by two intermediate sintering steps, each lasting for 48 h at a temperature of 1773 K, with the pellets crushed, ball milled, and pressed into pellets before each sintering step. The sintered pellets were subsequently crushed, ball milled again, pressed and sintered at 1823 K for another 24 h to obtain homogeneous samples. Samples used for neutron diffraction were subsequently crushed and ground into a fine powder. After the neutron diffraction experiments the samples were resintered into pellets at 1823 K for 36 h and used for impedance spectroscopy studies. The measured densities of these pellets were 65−70% of that expected theoretically. Additional structural and conductivity data for the x = 1.00 composition were taken from the results of a previous 4295

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2.5. RMC Modeling Details. RMC analysis35 of the total neutron scattering data (Bragg peaks plus diffuse scattering components) was performed using the RMCProfile software.36 Each RMC model, one for each sample stoichiometry, used a configuration box of 10 × 10 × 10 unit cells (i.e., contains a total of 4000 Y3+/Ti4+/Zr4+ cations in their stoichiometric ratio and 7000 O2− anions). A bond valence sum (BVS) soft constraint37 was used to ensure that individual cation− anion coordination environments remain chemically reasonable, with parameters taken from Brese and O’Keeffe.38 The RMC modeling used both reciprocal space data, S(Q), and real space data, G(r). The former emphasizes the long-range ordering while the G(r) focuses on the short-range interactions. Additionally, the S(Q) is broadened by convolution with a box function to reflect the finite size of the configuration box (for details, see Tucker et al.36). The broadened Sbox(Q) is used in the RMC method, and the comparison between the calculated functions and the experimental data is assessed using an agreement factor given by

study, in which it forms the end member of the solid solution (Y3−xNb1−xZr2x)O7.30 2.2. Impedance Spectroscopy. The bulk and grain boundary ionic conductivities of the Y2(Ti1−xZrx)2O7 samples were measured on sample pellets of approximately 10 mm diameter and 2 mm thickness using platinum electrodes. Platinum paste was used to ensure good contact between the electrodes and the sample. The samples were heated to 1673 K in air at around 5 K min−1 and the complex impedance spectroscopy was performed during cooling at 25 K intervals, using a Solartron SI-1260 Frequency Response Analyzer over a frequency range from 0.1 Hz to 1 MHz and a voltage of 0.1 V. The bulk and grain boundary contributions to the conductivity were determined by least-squares equivalent circuit fitting to the frequency dependent impedance data using the program ZVIEW and a model based on two series RC elements. Previous studies of the ZrO2− TiO2−Y2O3 system show that significant electronic conductivity only appears at oxygen partial pressures, pO2, less than around 10−10 atm at temperatures in the region of 1273 K.24,25 The measured data are, therefore, assumed to arise purely from motion of the O2− ions. Additional neutron diffraction studies of selected samples after their use for measurements of the ionic conductivity showed no significant structural changes from the results attained beforehand. 2.3. Neutron Powder Diffraction. Neutron diffraction experiments were performed at the Polaris diffractometer of the ISIS facility, Rutherford Appleton Laboratory, U.K.,31 using the backscattering detector bank (covering scattering angles of 130° < 2θ < 160°), the ∼90° detector bank (85° < 2θ < 95°), and the low angle detector bank (28° < 2θ < 42°). These cover approximate ranges of scattering vector Q (where Q = 2π/d and d is the interplanar spacing) of 2−30 Å−1, 1.5−20 Å−1, and 0.8−12 Å−1, respectively. Each powder sample was encapsulated in a cylindrical 6 mm diameter thin-walled (40 μm) vanadium can and measured for approximately 12 h to obtain counting statistics of sufficient statistical quality to allow analysis of the total neutron scattering. Rietveld analysis of the averaged structures using only the Bragg scattering was performed using the GSAS software.32 2.4. Total Neutron Scattering. After correction for the effects of background scattering and beam attenuation, the diffraction data from each detector bank was merged to form a single spectrum covering a wide Q range using the program Gudrun.33 This process also puts the scattered intensity onto an absolute scale of scattering cross-section. The resultant normalized total scattering structure factor, S(Q), was used to generate the corresponding total radial distribution function, G(r), via a Fourier transform,

G(r ) =

1 (2π )3 ρ0

∫0

∞

4πQ 2S(Q )

sin Qr dQ Qr

2 χRMC =

j

is the individual agreement factor for data type j. Multiple where RMC runs (typically 10) were used to estimate the uncertainties in the resulting structural information.

(1)

Figure 2. Temperature dependence of (a) the bulk ionic conductivity and (b) the grain boundary conductivity of the Y2(Ti1−xZrx)2O7 samples, plotted as log10 σ (in Ω−1 cm−1) versus 1000/T (in K−1). The compositions are x = 0.0 (●), x = 0.15 (○), x = 0.30 (▲), x = 0.40 (Δ), x = 0.50 (▼), x = 0.65 (∇), and x = 0.80 (■).

where ρ0 is the average atom number density in atoms Å (for details, see Keen34). The G(r) can also be expressed in terms of the individual partial radial distribution functions, gij(r), weighted by the concentrations of the two species, ci and cj, and their coherent bound neutron scattering lengths, b̅i and b̅j, so that

3. RESULTS AND DISCUSSION 3.1. Ionic Conductivity. Figure 2 shows the temperature dependence of the bulk and grain boundary ionic conductivities of the Y2(Ti1−xZrx)2O7 samples as an Arrhenius plot of log10 σ versus 1000/T. For all samples, the grain boundary conductivities lie in the range 1−3 × 10−6 Ω−1 cm−1 and are largely independent of temperature (Figure 2b), while the bulk conductivities show a linear behavior, except for the samples with 0.3 ≤ x ≤ 0.8 at temperatures in excess of around 1000 K (Figure 2a). Activation energies for oxygen migration, obtained by least-squares fits to the linear regions, decrease from 2.1 eV (x = 0.0) to 1.4 eV (x = 0.15) before reaching a roughly constant value of around 1.0 eV at higher x values. The variation of the bulk ionic conductivity with composition x is shown for a series of temperatures in Figure 3. After an initial

n

∑i , j = 1 cicjbi̅ bj̅ gij(r ) n

∑i = 1 (cibi̅ )2

(2)

where n is the number of ionic species. The partial radial distribution function is in turn given by gij(r ) =

nij(r ) 1 2 4πr Δr ρj

(4)

χ2j

−3

G(r ) =

∑ χj2

(3)

with nij(r) equal to the number of atoms of type j located at a distance between r and r + Δr from an atom of type i and ρj is the number density of atoms of type j, given by ρj = cjρ0. These individual partial distribution functions, gij(r), can be obtained from RMC modeling, which simultaneously probes both the long-range and the short-range structural properties. 4296

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Figure 3. Variation of the bulk ionic conductivity, log10 σ (in Ω−1 cm−1), with composition x in Y2(Ti1−xZrx)2O7 samples at temperatures of 1273K (●), 1173K (▲), 1073K (▼), and 1023K (■). The data for the x = 1.0 sample are taken from our previous study of Zr2Y2O7.30 For comparison, the open symbols are taken from the study of Moon et al.23, for temperatures of 1273K (○), 1173K (Δ), 1073K (∇), and 973K (□).

Figure 4. Evolution of the neutron powder diffraction pattern with composition x in Y2(Ti1−xZrx)2O7 at ambient temperature. The gradual disappearance of some of the Bragg peaks with increasing x is consistent with the transition from an ordered pyrochlore structure (space group Fd3̅m) to a disordered fluorite structure (space group Fm3̅m). In addition, there is clear evidence of diffuse scattering in the x = 0.65 and x = 0.80 samples arising from short-range order within the lattice.

increase over the range 0.0 ≤ x ≤ 0.4, the ionic conductivity reaches a plateau, except for a small increase at x = 1.0. These data are in broad agreement with those reported previously for the total conductivity.23 3.2. Rietveld Refinement. Rietveld refinement of the neutron powder diffraction data collected from the samples of Y2(Ti1−xZrx)2O7 started with the x = 0.0 material (i.e., Y2Ti2O7) and a structural model based on a fully ordered cubic structure pyrochlore with a lattice parameter a ∼ 10.1 Å in space group Fd3̅m.39 With reference to Figure 1, the larger Y3+ occupy the A sites with distorted cubic environment, while the Ti4+ sit in the B sites and adopt a distorted octahedral co-ordination to O2−. The anions then fully occupy the O1 and O2 positions, while the O3 are completely empty. The refined parameters comprised a scale factor, the cubic lattice parameter, a, isotropic thermal vibration parameters for the A and B site cations and O1 and O2 anions, uA, uB, uO1, and uO2, the positional parameter for the O1 anions, xO1, plus 20 coefficients of a shifted Chebyshev polynomial describing the undulating background scattering and 4 coefficients describing Gaussian and Lorentzian contributions to the Bragg peak shapes. The evolution of the powder neutron diffraction pattern with increasing x in Y2(Ti1−xZrx)2O7 is illustrated in Figure 4 and shows a gradual reduction in the intensity of some of the Bragg peaks, which become rather broad at x = 0.65 and virtually absent for the x = 0.80 sample. This behavior is consistent with a transition from a pyrochlore structure to a disorder fluorite arrangement. However, as discussed previously by Heremans et al.,19 structural characterization of the samples with x > 0.0 is problematic, since a single diffraction experiment is unable to determine the distribution of three ionic species (Y3+, Ti4+, Zr4+) over the two crystallographically distinct A and B cation sites. Instead, it is only possible to determine the average scattering lengths of the two positions, bA and bB. Rietveld refinement of the data included variation of these scattering lengths and allowed the occupancies of the three anion sites, mO1, mO2, and mO3, to vary (subject to the constraint that the total number of anions per unit cell remained fixed at the value given by the stoichiometry, that is, 48mO1 + 8mO2 + 8mO3 = 56). It was not possible to independently determine the isotropic thermal vibration parameters uO2 and uO3, and these were constrained to be equal. For consistency, the diffraction

data for the x = 0.00 sample were refined using this structural model including the possibility of disorder, giving evidence for limited disorder within the anion sublattice (with mO3 = 0.064(6)). The refined weighted R-factors ranged from 0.0323 to 0.0397, except for Rwp = 0.0623 in the case of the x = 0.65 sample which contained significant diffuse scattering and, as a consequence, possessed a slightly poorer fit to the measured background. The results from the Rietveld refinement provided no clear evidence for a two phase behavior within the Y2(Ti1−xZrx)2O7 system for 0.0 ≤ x ≤ 1.0 in agreement with the findings of Heremans et al.19 However, the presence of significant diffuse scattering produced rather unsatisfactory Rietveld refinements (see Supporting Information, Figures S1 and S2 for Rietveld fits to x = 0.30 and x = 0.80 neutron data), and we do not present detailed results here. Instead, the structural model obtained from the Rietveld analysis was used to generate starting models for a detailed reverse Monte Carlo analysis of the total neutron scattering data. This reveals further details of the pyrochlore (x = 0.00, Y2Ti2O7) to disordered fluorite (x = 1.00, Zr2Y2O7) phase transition, including the local ion−ion correlations which cannot be probed by conventional Rietveld methods. 3.3. Total Scattering Analysis. The evolution of the total radial distribution function, G(r), obtained by Fourier transform of the structure factor, S(Q), (eq 1) with composition x in Y2(Ti1−xZrx)2O7 is shown in Figure 5. The negative scattering length of the Ti nucleus is an advantage in the analysis of the total scattering data, since the gTiO(r) contribution is negative (see eq 2) and can be easily distinguished from the other cation−anion terms. In addition to displacements of the ions to minimize the χ2RMC factor (eq 4) during the RMC fitting procedure, the cations were allowed to swap positions to determine the extent of disorder within the cation sublattice providing the best agreement with the experimental neutron diffraction data. At the end of the fitting process, each cation within each configuration was assigned to its nearest A or B position and the fractional occupancy of the Y3+, Ti4+, and Zr4+ determined 4297

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Figure 7, in the pyrochlore-structured material with x = 0.00 the Y3+ and Ti4+ cations possesses co-ordination numbers close

Figure 5. Evolution of the total radial distribution function, G(r), obtained by Fourier transform of the structure factor, S(Q), with composition x in Y2(Ti1−xZrx)2O7. The data for the x = 1.0 sample are taken from our previous study of the disordered fluorite Zr2Y2O7.30 The dashed lines show the zero levels, to illustrate the first negative peak, corresponding to the contribution from the partial radial distribution function gTiO(r).

Figure 7. Variation of the anion co-ordination numbers for the Y3+ (●), Ti4+ (▲), and Zr4+ (▼) with composition x in Y2(Ti1−xZrx)2O7. The data for the x = 1.0 sample are taken from our previous study of the disordered fluorite Zr2Y2O7.30

to 8 and 6, as expected for the distorted cubic and distorted octahedral environments surrounding on the A and B sites, respectively (see Figure 1c). With increasing x, the coordination number of the Ti4+ increases only slowly, while that of the Y3+ gradually decreases. The co-ordination number of the Zr4+, which are initially located on the same B sites as the Ti4+, increases steadily from close to 6 to a value slightly lower than that of the Y3+ at x = 1.00. The latter is probably associated with the tendency of anion vacancies to be preferentially located as nearest neighbor to the smaller cation species within zirconia based oxides.40−43 To further investigate the geometry of the anion coordinations surrounding the various cation species it is instructive to generate angular distribution functions for the O-M-O bond angles using the RMC generated configurations. As illustrated in Figure 8 for the example of the x = 0.40 sample, the resultant distributions for the three cation species are rather different. In the case of the Y3+ cations, the distribution is consistent with the distorted cubic environment found in the pyrochlore-structured end member, where the shorter Y3+-O2− bond distance to the two O2 anions than the

for each site as a function of composition x. As illustrated in Figure 6, the added Zr4+ initially exclusively enter the B sites to

Figure 6. Variation of (a) the Y3+ content, (b) the Ti4+ content, and (c) the Zr4+ content over the A (○) and B (●) cation sites with composition x in Y2(Ti1−xZrx)2O7. The lines correspond to the structural models in which the Zr4+ exclusively enter the A sites (dotdash line) or the B sites (solid line), while the dashed line corresponds to a random distribution of the three cation species over the A and B sites.

replace the Ti4+, though at x = 0.40 there is some evidence of Zr4+ occupancy of the A positions. Over the range 0.50 ≤ x ≤ 0.85 there is an increasing tendency toward complete disorder of all three cation species over both sites, which is virtually complete at x = 0.85. The major advantage of the RMC analysis of the total scattering data is the ability to probe the short-range correlations between the nearest neighbor cations and anions and obtain the preferred co-ordination around the former as a function of composition x in Y2(Ti1−xZrx)2O7. As illustrated in

Figure 8. Average O-M-O bond angle distribution for the case of M = Y3+ (solid line), M = Ti4+ (dashed line), and M = Zr4+ (dash-dot line) obtained by RMC simulations of the neutron powder diffraction data for Y2(Ti1−xZrx)2O7 with x = 0.4. These distributions are consistent with distorted cubic, distorted octahedral, and cubic environments, respectively. 4298

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six O1 anions predicts peaks at positions with cos θ = 0.452, 0.179, −0.179, −0.452, and −1.0. Similarly, the environment surrounding the Ti4+ is close to that expected for the distorted octahedral configuration, with values of cos θ = 0.097, −0.097, and −1.0 for the x 0.00 end member. Interestingly, the result for the Zr4+ cation differs significantly from that of the Ti4+, despite the fact that they occupy the same crystallographic site at low x values, and is consistent with a cubic environment (which in the ideal case would have peaks at cos θ = 0.333, −0.333, −1.0). However, since the anion co-ordination for the Zr4+ cation is less than 8 (see Figure 7), some of the vertices must be vacant. Overall, with increasing x the anion environments surrounding the Y3+ and Ti4+ retain their distorted cubic and distorted octahedral character, though the co-ordination number of the former decreases as some of the vertices become vacant as anions are transferred to the O3 sites. Even though the increasing concentration of Zr4+ cations initially shares the same B sites with the Ti4+, their preference for a cubic environment (with some of the vertices vacant) leads to a significant increase in the degree of disorder within the anion sublattice. This is demonstrated in Figure 9 by the broadening

sites and a displacement of significant numbers of anions from the O1 and O2 sites to the vacant O3 positions, has relatively little influence on the ionic conductivity. It is planned to perform Molecular Dynamics simulations of the Y2(Ti1−xZrx)2O7 system in the future to further explore the relationship between the disordering processes and the anion diffusion mechanisms. This approach has previously proved very valuable in the study of such systems as (Y3−xNb1−xZr2x)O7,30,44 (Zr1−xSc(1−y)xYyxO2−x/2,42,43 (Ce1−xYx)O2−x/2,45 and is likely to be relevant to other fluorite related systems, such as the weberite structured compounds of stoichiometry A2B2O7.46

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ASSOCIATED CONTENT

S Supporting Information *

Figure 1. The Rietveld fit for the x = 0.30 sample (pyrochlore phase) with dots indicating experimental data and the solid line the calculated profile. The vertical lines indicate allowed Bragg reflections (space group Fd3̅m), and the difference between observed and calculated data is plotted in the bottom. Figure 2. The Rietveld fit for the x = 0.80 sample (fluorite phase) with dots indicating experimental data and the solid line the calculated profile. The vertical lines indicate allowed Bragg reflections (space group Fm3̅m), and the difference between observed and calculated data is plotted in the bottom. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +48 31 7722876. Fax: +46 31 7722853. Present Address ∥

Volvo Group Trucks Technology, Advanced Technology & Research, Gothenburg, Sweden. Author Contributions

Figure 9. Evolution of the anion−anion partial radial distribution function, gOO(r), obtained from the RMC simulations of the neutron powder diffraction data for the Y2(Ti1−xZrx)2O7 samples. The data for the x = 1.0 sample are taken from our previous study of the disordered fluorite Zr2Y2O7.30

The manuscript was written with contributions of all authors. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The U.K. Science and Technology Facilities Council (STFC) is thanked for allocating beamtime at the ISIS Facility. S.T.N. and S.G.E. wish to thank Vetenskapsrådet (Swedish Research Council) for financial support.

of the peaks in the anion−anion partial radial distribution function, gOO(r), at values of x lower than that at which the redistribution of the three cation species occurs to form the fluorite structured phase.

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4. CONCLUSIONS Neutron powder diffraction studies of the structural properties of the system Y 2 (Ti 1−x Zrx ) 2 O 7 confirms the previous reports18−20,22,23 of a transition from an ordered pyrochlore structure at x = 0.00 to a disordered fluorite arrangement at x = 1.00. However, analysis of the “total scattering” using Rietveld analysis and reverse Monte Carlo simulations indicates that the transition occurs in distinct stages. With increasing composition up to x ≈ 0.4, the Zr4+ cations replace the Ti4+ on the B sites, with little influence on the Y3+ filled A positions. However, the former’s preference for a cubic local environment leads to a degree of disorder within the anion sublattice, and, with reference to Figure 3, this process is associated with a significant increase in the ionic conductivity. By contrast, the more dramatic disordering process observed at higher concentrations, with an increasing tendency for the Y3+, Ti4+, and Zr4+ species to be randomly distributed over all the cation

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