Thermal Variation of Structure and Electrical Conductivity in Bi4YbO7

Article pubs.acs.org/cm

Thermal Variation of Structure and Electrical Conductivity in Bi4YbO7.5 Marzena Leszczynska,† Xi Liu,‡ Wojciech Wrobel,† Marcin Malys,† Marcin Krynski,† Stefan T. Norberg,§ Stephen Hull,∇ Franciszek Krok,*,† and Isaac Abrahams*,‡ †

Faculty of Physics, Warsaw University of Technology, ul. Koszykowa 75, 00-662, Warsaw, Poland Materials Research Institute, School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom § Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden ∇ ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom ‡

S Supporting Information *

ABSTRACT: The thermal behavior of the oxide ion-conducting solid electrolyte Bi4YbO7.5 was investigated using a combination of variable temperature X-ray and neutron powder diffraction, thermal analysis (DTA and TGA), and ac impedance spectroscopy. The title compound shows a fluorite-type structure throughout the measured temperature range (20−850 °C), with a phase separation at ca. 600 °C into a cubic δ-type phase and an orthorhombic phase of assumed stoichiometry Bi17Yb7O36. This type of transition is a relatively common feature in bismuth oxide-based systems and can limit their practical application. Here, the transition was carefully studied using isothermal measurements, which showed that it is accompanied by changes in oxide-ion stoichiometry, as well as significant disorder in the oxide ion sublattice in the δ-type phase. These results correlate with the observed electrical behavior. Analysis of the total neutron scattering through reverse Monte Carlo (RMC) modeling reveals details of the coordination environments for both cations. The oxide-ion vacancy distribution seems to be consistent with a favoring of ⟨100⟩ vacancy pairs, although ⟨110⟩ vacancy pairs exhibit the highest frequency as they have the maximum likelihood. A vacancy ordering model based on three vacancies per cell is presented. KEYWORDS: bismuth oxide, bismuth ytterbium oxide, fluorite structure, defect structure, neutron diffraction, total scattering, X-ray diffraction, ac impedance spectroscopy The Bi2O3−Yb2O3 system has been studied by many authors. Datta and Meehan found that the face-centered cubic (fcc) fluorite phase could not be stabilized.15 However, later work by Iwahara et al.16 suggested that the fluorite fcc phase could indeed be obtained, depending on composition and thermal treatment. These authors found that the fcc phase was readily obtained at 30% substitution and 20% substitution could be quenched from high temperatures. In the subsolidus phase diagram reported by Chen et al.,17 the fcc solid solution was found to occur between 15% substitution and 35% substitution. Drache et al.18 reported the Bi2O3−Yb2O3 equilibrium phase diagram, which shows a mixture of α-Bi2O3 and a stable orthorhombic phase, Bi17Yb7O36, at compositions up to ca. 29%, which transforms to the fcc phase at high temperatures. They reported that the δ-phase is readily quenchable, but is, in fact, metastable. Wachsman and co-workers have extensively studied the rare-earth-substituted bismuth oxides and have readily obtained the ytterbium-substituted system in the fcc

1. INTRODUCTION Bismuth oxide-based solid electrolytes are an important class of materials, because of their exceptionally high oxide ion conductivities at intermediate and high temperatures.1−6 Much of the research on these systems is focused around compositions that exhibit the δ-Bi2O3-type structure, in particular, on the stabilization of this highly conducting structural form, which in the parent bismuth oxide is stable only above ca. 730 °C.7 This stabilization can be brought about through solid solution formation with other oxides. Substitution of Bi3+ by isolvalent cations, such as those of the rare-earth metals, leads to a variety of phases, depending on the radius of the substituting cation and the level of substitution. It has been argued that (i) the so-called “stabilized” δ-type phases are, in fact, metastable and (ii) prolonged annealing at temperatures ∼600 °C results in transitions to lower-symmetry stable phases.8,9 However, it has also been shown that low levels of a secondary dopant can lead to truly stable phases.10−13 Despite concern over the applicability of bismuth oxide-based electrolytes in solid oxide fuel cells (SOFCs), they have been shown to have genuine potential in this area.14 © 2013 American Chemical Society

Received: September 9, 2012 Revised: January 4, 2013 Published: January 8, 2013 326

dx.doi.org/10.1021/cm302898m | Chem. Mater. 2013, 25, 326−336

Chemistry of Materials

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Table 1. Crystal and Refinement Parameters for Bi4YbO7.5 at 20 and 800 °C Value T = 20 °C

property chemical formula formula weight crystal system space group unit-cell dimension volume Z density (calculated) sample description weight fraction secondary phase

R-factorsa (a) neutron backscattering (b) neutron low angle (c) X-ray total no. of variables no. of profile points used neutron backscattering neutron low angle X-ray a

T = 800 °C

Bi4YbO7.5 1128.96 cubic Fm3̅m a = 5.49271(4) Å 165.715(4) Å3 0.8 9.050 g cm−3 yellow powder 1.0 none

Bi4YbO7.5 1128.96 cubic Fm3̅m a = 5.5644(2) Å 172.29(2) Å3 0.8 8.705 g cm−3 yellow powder 0.97828(9) quartz-SiO2 space group = P3221 a = 4.9991(3) Å c = 5.4561(5) Å volume = 118.09(1) Å3 weight fraction = 0.022(5)

Rwp = 0.0120, Rp = 0.0181, Rex = 0.0031 Rwp = 0.0297, Rp = 0.0219, Rex = 0.0100 Rwp = 0.0590, Rp = 0.0388, Rex = 0.0238 94

Rwp = 0.0038, Rp = 0.0068, Rex = 0.0024 Rwp = 0.0184, Rp = 0.0137, Rex = 0.0080 Rwp = 0.0646, Rp = 0.0514, Rex = 0.0557 104

4396 3818 5984

4396 3818 2542

For a definition of R-factors, see ref 27.

form at 25% substitution.19−21 They have shown that, of the rare-earth-substituted systems, the Yb-containing phases exhibit the highest conductivity decay upon prolonged annealing at 500 °C, which can be associated with a redistribution of the oxide ions, as well as vacancy ordering. Yashima and Ishimura have used maximum entropy methods combined with Rietveld analysis to examine the conduction pathways in δBi1.4Yb0.6O3.22 Their results show significant positional disorder in the oxide ion sublattice, with oxide ions shifted in the ⟨111⟩ direction, with respect to the ideal tetrahedral site in the cubic close-packed (ccp) fluorite structure. Their results were consistent with an oxide ion conduction pathway in the ⟨100⟩ direction. In studies on the bismuth ytterbate system, Battle et al.23 found that diffuse elastic neutron scattering results were consistent with short-range anion/vacancy ordering and materials were described as possessing rhombohedral microdomains. In addition, these authors found evidence of cation ordering, in more bismuth-rich phases. We have previously shown that total neutron scattering methods, involving analysis of both Bragg and diffuse scattering, can lead to additional information regarding vacancy ordering in both disordered24 and ordered fluorite systems25 (δ-Bi3YO6 and Bi3Nb0.5Y0.5O6.5, respectively). In those studies, it was shown that ⟨110⟩ vacancy pair ordering predominates, but characterization of the cation coordination was hampered by the relatively poor neutron scattering contrast between the cations. In the present study, we use total scattering analysis to examine the thermal variation of oxide ion and vacancy distribution in the system Bi4YbO7.5, which has significantly better neutron scattering contrast between the cations (b =

8.532 and 12.43 barns for Bi and Yb, respectively26). These are examined with respect to the electrical behavior.

2. EXPERIMENTAL SECTION 2.1. Sample Preparations. Samples of the title compound were prepared using stoichiometric amounts of Bi2O3 (Sigma−Aldrich, 99.9%), and Yb2O3 (Sigma−Aldrich, 99.9%). In each case, the starting mixture was ground in ethanol using a planetary ball mill. The dried mixture was heated at 750 °C for 24 h, then cooled and reground. Samples were then heated at 800 °C for 24 h, cooled, reground, and reheated to 850 °C for an additional 24 h, before slow cooling in air to room temperature over a period of ca. 5 h. For electrical measurements, prepared samples were pelletized, pressed isostatically at a pressure of 400 MPa and sintered at 900 °C for 10 h, before slow cooling in air to room temperature over a period of ca. 5 h. Sintered pellets had densities of ∼98.7% of the theoretical value, as determined by the Archimedes method. Sample stoichiometry was monitored through weight loss measurements at every stage. No significant changes in weight were observed. 2.2. Diffraction Measurements. Powder X-ray diffraction (XRD) data were collected on a Philips X’Pert Pro diffractometer, fitted with an X’Celerator detector, using Ni-filtered Cu Kα radiation (λ1 = 1.54056 Å and λ2 = 1.54439 Å). Data were collected in flat plate θ/θ geometry and calibrated against an external Si standard. Roomtemperature data suitable for detailed Rietveld refinement were collected in the 2θ range of 5°−125°, in steps of 0.0167°, with an effective scan time of 250 s per step (long scan). For elevated temperature measurements, data were collected using an Anton-Paar HTK 1200 camera at selected temperatures from 100 °C to 850 °C upon heating and cooling. Data were collected in the 2θ range of 5°− 125°, in steps of 0.033°, with an effective scan time of 50 s per step 327



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Table 2. Refined Structural Parameters for Bi4YbO7.5 at (a) 20 °C and (b) 800 °C atom

site

x

y

z

occ.

Uiso (Å2)

4a 4a 8c 32f 48i

0.0 0.0 0.25 0.3058(6) 0.5

0.0 0.0 0.25 0.3058(6) 0.1798(12)

0.0 0.0 0.25 0.3058(6) 0.1798(12)

0.8 0.2 0.290(7) 0.094(2) 0.014(1)

0.0490(2) 0.0490(2) 0.0697(6) 0.0697(6) 0.0697(6)

4a 4a 8c 32f 48i

0.0 0.0 0.25 0.3073(14) 0.5

0.0 0.0 0.25 0.3073(14) 0.1691(11)

0.0 0.0 0.25 0.3073(14) 0.1691(11)

0.8 0.2 0.250(18) 0.097(4) 0.018(1)

0.0718(2) 0.0718(2) 0.078(1) 0.078(1) 0.078(1)

(a) 20 °C Bi Yb O(1) O(2) O(3) (b) 800 °C Bi Yb O(1) O(2) O(3)

Figure 1. Diffraction profiles for Bi4YbO7.5 fitted using conventional Rietveld analysis at (a) 20 °C and (b) 800 °C. Neutron backscattering data are shown. Observed (+) and calculated (line) profiles are shown, as well as the difference profile (lower), with reflection positions indicated by markers (upper markers correspond to quartz in the 800 °C plot). (short scan) for all but the data at 800 °C, where the roomtemperature scan parameters were used. In order to assess phase stability, a further experiment was carried out, including an isothermal step at 600 °C. The sample was first heated on the diffractometer to 850 °C, cooled to room temperature, then heated to 600 °C and held at this temperature for 24 h. The sample was subsequently cooled to room temperature. After 48 h at room temperature, the sample was subjected to a further heating and cooling cycle between room temperature and 850 °C. During the thermal cycling, diffraction data were collected using the short scan parameters at selected temperatures, with longer scans at room temperature and 800 °C. During the annealing step at 600 °C, short scans were carried out at approximate intervals of 2 h. Powder neutron diffraction measurements were made on the Polaris diffractometer at the ISIS Facility at the Rutherford Appleton Laboratory in the United Kingdom. Data were collected on backscattering (130°−160°), 90° (85°−95°), low-angle (28°−42°), and very low angle (13°−15°) detectors, over the respective time-offlight ranges 1.0−20 ms, 0.8−19.2 ms, 0.5−20 ms, and 2.0−18.6 ms. Measurements were performed at room temperature and from 300 °C to 800 °C in steps of 50 °C. For the room-temperature measurements, the sample was contained in a thin-walled 8 mm diameter vanadium can and a dataset of 1000 μA h obtained, suitable for total scattering analysis. To avoid significant volatilization and reduction of bismuth oxide during the extended data collections at high temperatures, a sample of Bi4YbO7.5 was sealed in a silica tube and placed in an 11 mm diameter vanadium can located in an evacuated furnace. Data collections of 30 μA h were obtained from 300 °C to 750 °C, while at 800 °C, a longer data collection of 1000 μA h was carried out for total scattering analysis. For correction of the total scattering data, diffraction patterns for an empty thin-walled 8 mm diameter vanadium can and an empty silica tube inside an 11 mm diameter vanadium can were collected for ca. 700 μA h, each under identical conditions to the sample.

Average structure refinement was carried out by conventional Rietveld analysis with the GSAS suite of programs,27 using a combination of equally weighted X-ray and neutron datasets. A cubic model in space group Fm-3m was used for these refinements. Bi and Yb were located on the ideal 4a site (0,0,0), with oxide ions distributed over three sites; 8c at (0.25, 0.25, 0.25); 32f at approximately (0.3, 0.3, 0.3) and 48i at around (0.5, 0.2, 0.2).28 A total oxygen occupancy constraint was applied in all refinements. Isotropic thermal parameters were refined for all atoms, with those for the cations tied to a single value and those for anions also tied to a single value. For the data obtained at 600 °C, the orthorhombic fluorite, Bi17Yb7O36, was included as a secondary phase, using the parameters of Drache et al. in space group Pmmm.29 For the data collected at 800 °C, a small amount of crystalline quartz was modeled as a secondary phase, in space group P3221, using a starting model based on that of Antao et al.30 Crystal and refinement parameters for the fits at room temperature and 800 °C are given in Table 1, with the final refined parameters in Table 2 and the corresponding fitted diffraction profiles in Figure 1 and Figure S1 in the Supporting Information. 2.3. Neutron Total Scattering Analysis. Neutron total scattering analysis was carried out on the neutron diffraction data collected at room temperature and at 800 °C. Details of this method are given elsewhere;31 here, only a brief description of the basic methodology is given. Short-range ion-pair correlations were examined using reverse Monte Carlo (RMC) modeling of the neutron total scattering data. The program Gudrun32 was used to apply corrections for background scattering and beam attenuation and the resulting normalized total scattering structure factors, S(Q), were then used to obtain the corresponding total radial distribution function, G(r), via Fourier transformation. RMC simulations were carried out using the RMCProfile software,33 with a configuration box of 10 × 10 × 10 unit cells in P1 symmetry. The initial model was based on the ideal fluorite structure in space group Fm3̅m, with a random distribution of cations and anions over their respective sites in the supercell, 328



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Figure 2. Fitted total scattering S(Q) {(a) and (c)} and total radial distribution G(r) {(b) and (d)} functions for Bi4YbO7.5 at 20 °C {(a) and (b)} and 800 °C {(c) and (d)}. Observed (points) and calculated (line) profiles are shown, as well as the difference profiles (lower). concentration cell O2(pO2 = 1.01 × 105 Pa);Pt|oxide|Pt;O2 (pO2 = 0.2095 × 105 Pa), as described in detail elsewhere.36 Measurements were performed upon cooling between 800 °C and 450 °C at stabilized temperatures. 2.5. Thermal Analysis. Differential thermal analysis (DTA) was carried using a TA Instruments Q600 scanning differential thermal analyzer. Approximately 30 mg of powdered sample in an alumina crucible was monitored over heating and cooling runs in air, between ambient temperature and 950 °C, at a rate of 20 °C min−1. Thermogravimetric analysis was carried out on the same instrument for comparison with the X-ray phase stability measurements. The temperature ranges of the heating and cooling cycles were identical to those in the X-ray experiments. A heating/cooling rate of 20 °C min−1 was used, with the isothermal annealing at 600 °C carried out for 24 h as in the X-ray experiment.

corresponding to the regular 4a and 8c crystallographic sites in the subcell. Vacancies were therefore distributed randomly within the starting configuration. A set of 10 parallel calculations were carried out to ensure satisfactory statistics on the radial distribution functions. Fitting was carried out against S(Q), G(r), and the Bragg profile data to provide a constraint for the long-range crystallinity. The S(Q) data were broadened by convolution with a box function to reflect the finite size of the simulation box (eq 1): ∞

1 S box(Q ) = π

∫ −∞

(

sin Sexpt(Q ′)

L(Q − Q ′) 2

Q − Q′

) dQ ′ (1)

where L/2 is the smallest dimension of the RMC configuration and, as such, defines the upper limit of G(r). Bond valence summation (BVS) constraints34 and an O−O closest approach constraint (to avoid unrealistically short O−O contacts) were applied during calculations. Cation swapping (one random cation swapping positions with a random cation of another species) was tested and found to have no significant influence on the fit. Therefore, in the final calculations, only translational moves were permitted. The final fits to the Sbox(Q) and G(r) data at room temperature and 800 °C are shown in Figure 2. 2.4. Electrical Measurements. Electrical parameters were determined by a.c. impedance spectroscopy up to ca. 840 °C, using a fully automated Solartron 1255/1286 system in the frequency range from 1 Hz to 5 × 105 Hz. Samples for impedance measurements were prepared as rectangular blocks (ca. 6 mm × 3 mm × 3 mm) cut from slowly cooled sintered pellets, using a diamond saw. Platinum electrodes were sputtered by cathodic discharge on the two smallest faces. Impedance spectra were acquired over two cycles of heating and cooling at stabilized temperatures. Impedance at each frequency was measured repeatedly until consistency (2% tolerance in drift) was achieved or a maximum number of 25 repeats had been reached. Drift of impedance was monitored during measurement using an algorithm described earlier.35 The ionic and electronic contributions to the total conductivity were measured using a modified electromotive force (EMF) method, with an external adjustable voltage source in the

3. RESULTS AND DISCUSSION 3.1. Thermal Behavior of Bi4YbO7.5. The variabletemperature X-ray and neutron diffraction patterns for Bi4YbO7.5 (Figure 3 and Figure S2 in the Supporting Information) clearly show that the fluorite structure is maintained throughout the temperature range studied, with no evidence of superlattice reflections. Note that the neutron patterns at elevated temperatures have been corrected for the silica tube background. The neutron patterns at 800 °C show weak additional peaks of quartz due to a degree of crystallization of the silica glass tube during the extended heating time at this temperature, for the total scattering study. It is also evident upon heating that, at ∼600 °C, there is an apparent peak broadening phenomenon, in both X-ray and neutron diffraction patterns (Figure 3b), associated with a degree of phase separation, into a cubic δ-type phase and a phase approximating to Bi17Yb7O36. However, above this temperature, a single δ-type phase reappears. The occurrence of this phase separation is lower in temperature than that 329



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corresponding to the temperature where phase separation is observed in the diffraction patterns (Figure 3). Upon cooling, a linear decrease in volume is observed, following the values obtained upon heating, but extending further down to ca. 550 °C. Below this temperature, in the low-temperature region, the curve generally follows that obtained upon heating. Figure 5

Figure 5. DTA thermogram for Bi4YbO7.5, with heating and cooling directions indicated by arrows. Figure 3. Variable-temperature powder diffraction patterns for Bi4YbO7.5 showing (a) neutron backscattering data on heating and (b) detail of X-ray (upper) and neutron backscattering (lower) profiles.

shows the DTA thermogram for Bi4YbO7.5. Both heating and cooling curves are featureless, indicating the absence of firstorder transitions. However, upon heating, there is a clear change of baseline slope in the approximate range of 500−600 °C, which is consistent with a second-order phase transition. The absence of a significant thermal event upon heating does not reflect the phase separation observed in the diffraction experiments. This difference is probably associated with the difference in heating rates between the thermoanalytical and diffraction studies. The data in Table 2 show that oxide ions are found to be distributed over three crystallographically distinct sites: 8c, 32f, and 48i (O(1), O(2), and O(3), respectively). This type of distribution is common in the bismuth oxide-based fluorites.19,28 Figure 6 shows the thermal evolution of the oxide ion

reported by Drache et al. of ca. 700−800 °C.18 Apart from this phase separation at 600 °C, there is little obvious variation in the diffraction patterns with temperature other than the expected temperature shift. Upon cooling, the cubic δ-type phase is maintained throughout, with no evidence of phase separation at intermediate temperatures. The thermal variation of the cubic unit cell volume is shown in Figure 4. The plot can be divided into two regions, one at low temperature and one at high temperature. Upon heating, the volume is seen to increase throughout the measured temperature range, with a sharp increase above 600 °C,

Figure 6. Thermal evolution of oxide ion distribution in δ-Bi4YbO7.5, showing values for (□) 8c, (●) 32f, and (▲) 48i). Values are plotted as fractions of the total oxide ion content. Error bars correspond to ± twice the estimated standard deviation.

Figure 4. Thermal variation of unit-cell volume in Bi4YbO7.5 upon heating (●, from combined X-ray and neutron data) and cooling (○, from X-ray data only). Error bars are smaller than symbols used. 330



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distribution in Bi4YbO7.5. It is evident that, in the region of 450−600 °C, there is a significant change in oxide ion distribution between the 8c and 32f sites. The site occupancy of the 32f site begins to increase significantly above 400 °C, at the expense of that of the 8c site, and at ca. 550 °C, the latter site is unoccupied. Between 600 °C and 650 °C, the occupancy of the 8c site returns to a value similar to that seen below the transitional region. These results are consistent with those of Boyapati et al. on Bi3YbO6,20 where similar changes in the relative occupancies of the 32f and 8c sites were observed upon prolonged annealing at 500 °C. Although the 32f and 8c sites are crystallographically distinct, they are very close to each other and both lie within the tetrahedral site of the ccp lattice (Figure 7). Indeed, ions on the 32f site are related to those on

Figure 9. Variation of weight fraction (filled symbols) of the cubic δphase (squares) and orthorhombic Bi17Yb7O36 (circles) and variation in fluorite cell volume (open symbols) for the δ-phase (squares) and orthorhombic Bi17Yb7O36 (circles) on annealing Bi4YbO7.5 at 600 °C over 24 h. For Bi17Yb7O36, the fluorite cell volume was taken as onesixth of the unit cell volume. Error bars correspond to ± twice the estimated standard deviation. Figure 7. Structure of Bi4YbO7.5, showing location of oxide ion sites O(1), O(2), and O(3) (8c, 32f, and 48i, respectively). For clarity, only one position is shown for O(2) and O(3) sites. Large and small open circles represent Bi/Yb atoms and O atoms, respectively.

the experiment. Figure 9 also shows the change in fluorite cell volume for the two phases during the isothermal experiment. It is evident that both phases decreased in volume over the duration of the experiment. Most of this decrease occurred within the first few hours. Upon cooling from 600 °C, XRD patterns still exhibited the same degree of phase separation. This phase separation was fully reversed upon heating above 600 °C, to 850 °C; upon subsequent cooling to room temperature, the pure cubic phase was obtained. The observed reduction in fluorite cell volume upon annealing is inconsistent with the change in volume predicted from phase separation. If the stoichiometry of the second phase is indeed Bi17Yb7O36, as suggested by Drache et al.,18 then the residual cubic fluorite phase would be expected to be more bismuth-rich. This should result in an increase in the fluorite cell volume as the average cation radius increases (ionic radii: Yb3+ = 0.868 Å, Bi3+ = 1.03 Å for 6 coordinate geometry37). Therefore, an alternative explanation is required to account for the observed reduction in fluorite cell volume. Figure 10 shows the TGA thermogram obtained during the isothermal experiment at 600 °C. The sample is seen to gain mass rapidly (ca. 0.06%) in the first 2 h of annealing, reaching a steady state after ca. 5 h. These results suggest that the phase separation at this temperature is accompanied by a change in oxygen stoichiometry. This can be explained by considering that a small degree of reduction of the cations can occur in the initial heating step to 850 °C, which would only partially be reversed upon cooling in air, because of the kinetics of the oxidation process. Upon reheating to 600 °C, followed by annealing, the sample has sufficient thermal energy and time to reach equilibrium. These results are consistent with the observed reduction in fluorite cell volume, which can be explained by considering two effects of the oxidation process. An increase in the oxide ion content would be expected to result in an increase in cell volume, while oxidation of the cations would be expected to result in a decrease in volume as the average ionic radius of the cations decreases. Since the structures contain large vacancy concentrations, the former

the ideal 8c site by a small displacement in the ⟨111⟩ direction (0.531(6) Å at room temperature) and can therefore be considered as being disordered within the tetrahedral site. The results suggest that the transition at intermediate temperatures is accompanied by an increase in disorder on the tetrahedral sites. Figure 8 shows detail of the XRD patterns obtained on annealing Bi4YbO7.5 at 600 °C over 24 h and reveal the

Figure 8. Detail of XRD patterns obtained upon annealing Bi4YbO7.5 at 600 °C over 24 h.

evolution of the phase separation at this temperature. The corresponding variation of weight fraction of the cubic δ-phase and orthorhombic Bi17Yb7O36 is shown in Figure 9 and reveals that the separation occurred relatively rapidly and, within ca. 3 h, was already extensive, continuing slowly over the duration of 331



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first heating, a linear low-temperature region with higher activation energy (1.209(2) eV) is observed up to ca. 500 °C, with a second linear region of lower activation energy (0.595(4) eV) above ca. 650 °C. At intermediate temperatures, a transitional region is observed as a “knee”-shaped feature, with a sharp increase in conductivity at ca. 600 °C. Upon cooling, the high-temperature region extends to ∼550 °C, but between ca. 650 °C and ca. 550 °C, a degree of nonlinearity is observed. At ca. 550 °C, a sharp transition is observed to a linear low-temperature region, of lower conductivity than in the first heating run, with an activation energy of 1.068(1) eV. Upon a second heating, the data follow those from the first cooling curve up to ca. 500 °C, where, again, a knee-shaped feature is observed, but is less pronounced than upon the first heating. As in the first heating run, a sharp transition occurs at ca. 600 °C and, from this point, the remainder of the second cycle follows the first. The observed features in the first heating run correlate well with those seen in the diffraction and thermal analysis experiments. The characteristic values of total conductivity, corresponding to the second cooling run, at 300 and 800 °C are 1.31(6) × 10−5 S cm−1 and 6.49(2) × 10−1 S cm−1, respectively. The activation energies for the lowtemperature and high-temperature regions in the second cooling run were 1.068(2) and 0.512(9) eV, respectively. Arrhenius plots for the separate contributions of ionic and electronic conductivity are shown in Figure 11b. The electronic conductivity shows linear Arrhenius type behavior throughout the studied temperature range. In contrast, the ionic contribution shows two linear regions in the Arrhenius plot, with a transition at ∼600 °C. The results indicate that the jump seen in the temperature dependence of total conductivity is entirely associated with changes in the ionic contribution. 3.2. Defect Structure of Bi4YbO7.5. From the relative site occupancies and the intersite contact distances (Table 2 and Table S1 in the Supporting Information), some of which preclude simultaneous occupancy, it is possible to propose models for the local coordination environments for Bi and Yb, using methodology that we have described previously for other systems.38−40 Since occupation of the 48i site only occurs in doped bismuth oxides, it can be reasonably assumed that oxide ions in this site are exclusively associated with the Yb3+ ions and allow this ion to adopt a distorted octahedral coordination, with the octahedral geometry completed through bonds to oxide ions on O(1) or O(2) sites. The Yb:O(3) site occupancy ratio varies from 1:0.84 at 25 °C to 1:1.08 at 800 °C. Since oxide ions on the 48i site coordinate only two cations, Yb:O(3) ratios close to 1:1 indicate clustering of ytterbate polyhedra. The observed ratios suggest the cluster sizes and/or ytterbium coordination number may vary with temperature. The proposed clustering of ytterbate polyhedra does not lead to long-range order, as evidenced by the absence of superlattice reflections. This is in contrast to the situation in Bi3NbO7 and Bi3TaO7, where clustering of niobate/tantalate polyhedra does indeed lead to the formation of an incommensurate superlattice.39,41 Analysis of the Bi−O contact distances indicate the association of Bi with oxide ions on O(1) and O(2) sites. Since O(1) coordinates 4 cations and O(2) coordinates 3 cations, the average bismuth coordination numbers can be readily calculated as follows. If, at room temperature, 0.672 Yb atoms per cell are in octahedral coordination (since each octahedral Yb requires O(3) atoms shared with one other cation, i.e., 0.672 × 2 × 1/2) then they would require 0.672 O(1) atoms (i.e., 0.672 × 4 × 1/4O(1) atoms shared with three

Figure 10. TGA thermogram obtained on annealing Bi4YbO7.5 at 600 °C over 24 h (the first 10 h are shown).

effect is relatively small, with additional oxide ions filling vacant sites and, hence, the latter effect dominates. Figure 11a shows the Arrhenius plots of total conductivity for Bi4YbO7.5 obtained over two successive heating and cooling cycles. Thermal hysteresis is clearly evident between heating and cooling runs and between first and second cycles. Upon

Figure 11. Arrhenius plots of conductivity for Bi4YbO7.5 showing (a) total conductivity obtained over two cycles of heating and cooling and (b) ionic (○) and electronic (■) conductivities upon cooling. 332



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other cations) to complete their coordination geometry. This leaves 1.648 O(1) atoms per cell, as well as 3.008 O(2) atoms. Therefore, the remaining cations have an average coordination number of 4.69 at 20 °C (i.e. {(1.648 × 4) + (3.008 × 3)}/{4 − 0.672}). Similar calculations can be performed assuming Yb is coordinated to O(2), but the result is equivalent. At 800 °C, the average Bi coordination number decreases to 4.42. These values suggest a predominantly four pyramidal coordination environment for Bi, which is consistent with stereochemical activity of the Bi 6s2 lone pair of electrons. The final RMC model for Bi4YbO7.5, based on the total neutron scattering data, gave bond valence sums for Bi, Yb, and O of +2.99, +2.86, and −1.98 at room temperature, and +2.95, +2.76, and −1.94 at 800 °C, respectively. An iso-surface representation of the atom density in the final configuration collapsed to a single unit cell is given in Figure 12 for the room-

Figure 13. Selected pair correlation functions gij(r) for Bi4YbO7.5 at (a) 20 °C and (b) 800 °C.

Table 3. Cation Coordination Numbers and Average Bond Lengths (BLs) from Rietveld Analysis and RMC Models of Bi4YbO7.5 at (a) 20 °C and (b) 800°C

Figure 12. Iso-surface plot of final RMC configuration for Bi4YbO7.5 at 20 °C collapsed onto a single unit cell, showing Bi/Yb (blue semitransparent) and O (red) atom density.

Rietveld analysis

temperature model. Figure 13 shows ion-pair correlation functions gij(r) at both of the studied temperatures. Apart from a small thermal shift, there is little obvious difference between the two sets of plots. Two approaches were adopted in order to examine the coordination environments for each type of cation. In the first approach, the first minimum in the gM−O(r) (M = Bi or Yb) function was taken as the upper limit for the M−O bond length and the function integrated below this point to give the overall coordination number. The maximum in the function was taken as the modal bond length. This approach essentially gives the site coordination, but is less suitable for bismuth, which often shows stereochemically distorted coordination environments, with several short covalent interactions and some longer essentially nonbonding interactions completing the geometrical environment. In these cases, a better picture of the true coordination environment is to use the sum of the ionic radii as the maximum bond length and to take a mean of all contacts below this distance as the average bond length. The results of these two approaches are summarized in Table 3. It can be seen that the ionic radii

av. BL (Å) (a) 20 °C Bi−O 2.277 Yb−O (b) 800 °C Bi−O 2.295 Yb−O

Ionic Radii Approach

First Minimum in the g(r) Approach

CN

av. BL (Å)

CN

av. BL (Å)

max distance (Å)

4.18 3.91

2.245 2.137

5.93 5.87

2.245 2.175

3.376 3.350

3.90 3.49

2.232 2.118

5.56 5.28

2.172 2.159

3.298 3.166

approach gives a reasonable value for the bismuth coordination number, but tends to underestimate the Yb coordination number, whereas the minimum in gM−O(r) approach gives reasonable values for the site coordinations for both cations. The RMC-derived model was analyzed to establish the vacancy distribution in Bi4YbO7.5. Previously, as in the case of Bi3YO6,24 O−M−O angular distribution functions (ADFs) were analyzed to yield indirect information on vacancy distributions. Although this method is effective, it does rely on fitting the ADFs, which can be a source of error. A morereliable method is to identify individual vacancies in the RMC333



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characterized by three vacancy−vacancy distances as summarized in Figure 15. A completely random distribution of vacancy

derived configuration and examine the distribution of vacancy− vacancy distances directly. In order to achieve this, coordinates corresponding to the 8c site in the ideal fluorite structure were generated for the 10 × 10 × 10 configuration box, yielding 8000 sets of coordinates. Contact distances between these ideal sites and the O atoms in the RMC-derived model were calculated. The intersite contact distances (Table S2 in the Supporting Information) from the conventional Rietveld analysis were 0.531(6) Å and 0.552(14) Å for O(1)−O(2) and 1.478(4) Å and 1.530(4) Å for O(1)−O(3) at room temperature and 800 °C, respectively. Therefore, any ideal site with a contact distance to O of ≤1 Å, was taken to be occupied, with the remaining sites considered to be vacancies. Finally, contact distances between these vacant sites were calculated, in order to determine their distribution. The approach used is consistent with the view that O atoms corresponding to those on O(1) and O(2) sites in the crystallographic model lie within the tetrahedral site, while those corresponding to O(3) are essentially Frenkel interstitials. The approach also assumes that the location of the ideal tetrahedral sites are unchanged in the RMC-derived model, i.e., that the displacement of cations from their ideal site is minimal. This is confirmed in the M−M (M = Bi and Yb) pair distribution functions (Figure 14), which show relatively narrow distributions. As a first approximation, if it is assumed that the vacancy concentration in Bi4YbO7.5 is the same as that in δ-Bi2O3, then, on average, there would be two vacancies per unit cell, which could be located in ⟨100⟩, ⟨110⟩, or ⟨111⟩ orientations, with respect to the fluorite unit cell. These orientations are

Figure 15. Vacancy pair configurations around metal atoms in the ideal fluorite structure showing characteristic, vacancy−vacancy distances for (a) ⟨100⟩, (b) ⟨110⟩, and (c) ⟨111⟩ pairs. M and O atoms are indicated by large and small circles, respectively, and vacancies by open cubes.

pairs would yield a 1:2:1.33 ratio of these distances. As vacancies are introduced into the structure, any nonrandom distribution results in a change in this ratio. Table 4 summarizes the vacancy distributions observed in the RMC-derived models for Bi4YbO7.5 at the two studied temperatures. It is immediately evident that the total number of vacancies per cell exceeds that in δ-Bi2O3 and is consistent with a second approximation where additional vacancies are introduced through Frenkel defects. The numbers of tetrahedral vacancies per fluorite cell are slightly higher than those derived from the crystallographic model of 2.672 and 2.896 tetrahedral vacancies per cell at room temperature and 800 °C, respectively. This discrepancy is probably associated with an averaging effect caused by tying the oxide ion thermal parameters to a single value in the Rietveld refinement. The increasing trend in vacancy concentration with temperature is the same in both models. The observed ratios clearly show a higher frequency of ⟨100⟩-aligned vacancies than predicted in a random distribution. However, overall there is a predominance of ⟨110⟩-aligned vacancies, as in the random distribution. There is a significant increase in vacancy concentration with temperature, but little change in the distribution ratio. This suggests that there is no significant change in vacancy ordering with temperature, but there is a significant change in vacancy concentration caused by the creation of more Frenkel defects. In explaining the high frequency of ⟨110⟩ vacancy pairs, one cannot ignore the high vacancy concentration, which leads to different likelihoods for the vacancy pair distributions. To examine this, it is helpful to consider the case of a single vacancy located in a tetrahedral site (Figure 16a). To maintain an exclusive type of vacancy pair ordering, there are a limited number of locations for additional vacancies. Thus, exclusive ⟨100⟩ (Figure 16b) or ⟨111⟩ (Figure 16d) vacancy ordering is limited to a maximum of two vacancies per cell, while exclusive ⟨110⟩ (Figure 16c) ordering offers the possibility of up to four vacancies per unit cell. This means that, in systems with high vacancy concentrations, even a random distribution would lead to predominance of ⟨110⟩ vacancy pairs. In the present case, where the total number of tetrahedral vacancies exceeds two per unit cell, exclusive ⟨100⟩ or ⟨111⟩ vacancy pairing is impossible and the likelihood is that ⟨110⟩ pairs will predominate, as is observed. The increase in the frequency of ⟨100⟩ vacancy pairs, with respect to that in the random distribution, suggests that this pairing is energetically favorable. Indeed, density functional theory and molecular dynamics studies on the parent compound δ-Bi2O3 predict ⟨100⟩

Figure 14. M−M pair correlation functions gM−M(r) for Bi4YbO7.5 at (a) 20 °C and (b) 800 °C. 334



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Table 4. Vacancy Pair Distributions from RMC Models of Bi4YbO7.5 temperature (°C)

vacancies per configuration cell

vacancies per fluorite cell

no. of ⟨100⟩ contacts per configuration cell



ratio

20 800

2884 2975

2.884 2.975

3480 3603

6338 6669

4076 4308

1:1.82:1.17 1:1.85:1.20

Figure 17. Very low-angle neutron diffraction pattern for Bi4YbO7.5 at 20 °C.

Figure 16. Schematic representation of vacancy pair ordering schemes in the ideal fluorite structure, showing maximum number of exclusive vacancy alignments per unit cell. For clarity, cells shown are origin shifted by (1/4, 1/4, 1/4) compared to the ideal fluorite crystallographic cell. (a) Single vacancy, (b) ⟨100⟩ vacancy ordering, (c) ⟨110⟩ vacancy ordering, and (d) ⟨111⟩ vacancy ordering. Large and small circles represent M and O atoms, respectively, with open cubes representing vacancies.

ordering as the most stable configuration42,43 and our own studies using atomistic simulation and molecular dynamics show little difference in energy between ⟨100⟩ and ⟨110⟩ vacancy pair alignments in the related system Bi3YO6.24,44 It is useful to compare the results from the present study with those of Battle et al.,23 who studied several compositions of the type (Bi2O3)1−x(Yb2O3)x. They found evidence of possible cation ordering in diffuse neutron scattering for the x = 0.2 composition (Bi4YbO7.5), with maxima in the diffuse neutron scattering at Q ≈ 0.7, 1.15, and 1.55 Å−1. For higher x-value compositions, only the maximum at Q ≈ 0.7 Å−1 was evident in this range, which was associated predominantly with oxide ion/ vacancy ordering. In the present study, only the data from the very low angle bank fall within this range. Figure 17 shows the diffraction pattern obtained from this bank at 20 °C and clearly shows only the Q ≈ 0.7 Å−1 maximum in this range. Therefore, the present data seem to be in closer agreement with the data obtained by Battle et al. for higher x-value compositions. Although we cannot completely preclude cation ordering, our RMC analysis of the data revealed no evidence of this. Based on the data in Table 4, it is evident that there are 2−3 tetrahedral vacancies per fluorite cell. Figure 18 shows a proposed configuration for a model involving an average of 3 vacancies per cell. In this example, the ratio of ⟨100⟩:⟨110⟩:⟨111⟩ vacancy−vacancy contacts is 1:1.7:1.3, which is close to the observed ratio. It is interesting to note that, in their detailed analysis of δ-Bi2O3, using a combination of molecular dynamics, electronic structure calculations and

Figure 18. Proposed model for vacancy distribution in Bi4YbO7.5, with three vacancies per fluorite cell. For clarity, the cell is origin shifted by (1/4, 1/4, 1/4) compared to the ideal fluorite crystallographic cell. Large and small circles represent M and O atoms, respectively, with open cubes representing vacancies.

crystallographic analysis, Aidhy et al. proposed a model for vacancy ordering involving clusters of ⟨110⟩ and ⟨111⟩ vacancy pairs and they predicted that, for poorly polarizable dopants, such as Yb, vacancy ordering was favorable.42

4. CONCLUSIONS Bi4YbO7.5 possesses a defect fluorite structure closely related to δ-Bi2O3. Upon heating, Bi4YbO7.5 exhibits a second-order transition at ∼600 °C, which is associated with an increase in disorder in the oxide ion sublattice. Above this transition, there is an oxide ion redistribution, with an increase in oxide Frenkel defects, which results in an increase in the tetrahedral site vacancy concentration. This phase transition is reflected in a larger-than-expected unit-cell volume at high temperatures and a jump in ionic conductivity to a highly conducting region. In the RMC configurations, ⟨100⟩ vacancy pairs are found to be favored, although, because of the large concentration of vacancies, ⟨110⟩ vacancy pairs predominate, since these have the maximum likelihood. 335



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(24) Abrahams, I.; Liu, X.; Hull, S.; Norberg, S. T.; Krok, F.; Kozanecka-Szmigiel, A.; Islam, M. S.; Stokes, S. J. Chem. Mater. 2010, 22, 4435. (25) Liu, X.; Abrahams, I.; Hull, S.; Norberg, S. T.; Holdynski, M.; Krok, F. Solid State Ionics 2011, 192, 176. (26) International Tables for Crystallography, Vol. C: Mathematical, Physical and Chemical Tables, 3rd Edition; Prince, E., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2004. (27) Larson, A. C.; Von Dreele, R. B. General Structure Analysis System; Los Alamos National Laboratory Report LAUR 8-748; Los Alamos National Laboratory: Los Alamos, NM, 1986. (28) Abrahams, I.; Kozanecka-Szmigiel, A.; Krok, F.; Wrobel, W.; Chan, S. C. M.; Dygas, J. R. Solid State Ionics 2006, 177, 1761. (29) Drache, M.; Roussel, P.; Conflant, P.; Wignacourt, J.-P. Solid State Sci. 2005, 7, 269. (30) Antao, S. M.; Hassan, I.; Wang, J.; Lee, L. P.; Toby, B. H. Can. Mineral. 2008, 46, 1501. (31) Keen, D. A. J. Appl. Crystallogr. 2001, 34, 172. (32) Soper, A. K. Unpublished software. (33) Tucker, M. G.; Keen, D. A.; Dove, M. T.; Goodwin, A. L.; Hui, Q. J. Phys.: Condens. Matter 2007, 19, 335218. (34) Norberg, S. T.; Tucker, M. G.; Hull, S. J. Appl. Crystallogr. 2009, 42, 179. (35) Dygas, J. R.; Kurek, P.; Breiter, M. W. Electrochim. Acta 1995, 40, 1545. (36) Malys, M.; Dygas, J. R.; Holdynski, M.; Borowska-Centkowska, A.; Wrobel, W.; Marzantowicz, M. Solid State Ionics 2012, 225, 493. (37) Shannon, R. D. Acta Crystallogr., Sect. A: Cryst. Phys. Diffr., Theor. Gen. Crystallogr. 1976, A32, 751. (38) Abrahams, I.; Krok, F.; Chan, S. C. M.; Wrobel, W.; KozaneckaSzmigiel, A.; Luma, A.; Dygas, J. R. J. Solid State Electrochem. 2006, 10, 569. (39) Abrahams, I.; Krok, F.; Struzik, M.; Dygas, J. R. Solid State Ionics 2008, 179, 1013. (40) Krok, F.; Abrahams, I.; Kario, A.; Malys, M.; Dygas, J. R. Solid State Ionics 2008, 179, 172. (41) Ling, C. D. J. Solid State Chem. 1999, 148, 380. (42) Aidhy, D. S.; Nino, J. C.; Sinnot, S. B.; Wachsman, E. D.; Phillpot, S. R. J. Am. Ceram. Soc. 2008, 91, 2349. (43) Walsh, A.; Watson, G. W. Phys. Rev. B 2006, 73, 235104. (44) Krynski, M.; Wrobel, W.; Dygas, J. R.; Wrobel, J.; Malys, M.; ́ Spiewak, P.; Kurzydlowski, K. J.; Krok, F.; Abrahams, I. Submitted to Solid State Ionics.

ASSOCIATED CONTENT

S Supporting Information *

Supporting Information includes supplementary tables and figures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +44 207 882 3235 (I.A.), +48 22 234 8463 (F.K.). Emails: [email protected] (I.A.), [email protected] (F.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the ISIS facility at the Rutherford Appleton Laboratory for neutron beam time. Part of this work was supported by the Polish Ministry of Science and Higher Education (under Grant No. 2783/B/T02/2009/36). We gratefully acknowledge the Science and Technology Facilities Council (STFC) for a CMPC studentship grant to X.L. and for neutron beam time at ISIS. S.T.N. wishes to thank Vetenskapsrådet (the Swedish Research Council) for financial support.

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Thermal Variation of Structure and Electrical Conductivity in Bi4YbO7

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