Crystal Structure and Oxide-Ion Diffusion of Nanocrystalline

Dec 14, 2012 - *E-mail: [email protected]. ... at 1023 K. The diffusion path is not straight but curved and forms a three-dimensional network. ...
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Crystal Structure and Oxide-Ion Diffusion of Nanocrystalline, Compositionally Homogeneous Ceria−Zirconia Ce0.5Zr0.5O2 up to 1176 K Masatomo Yashima,*,† Tomohiro Sekikawa,‡ Daisuke Sato,‡ Hiromi Nakano,§ and Kazuki Omoto‡ †

Department of Chemistry and Materials Science and ‡Department of Materials Science and Engineering, Tokyo Institute of Technology, 2-12-1-W4-17, O-okayama, Meguro-ku, Tokyo, 152-8551, Japan § Cooperative Research Facility Center, Toyohashi University of Technology, Hibarigaoka 1-1, Tempaku, Toyohashi-shi, 441-8580, Japan S Supporting Information *

ABSTRACT: The crystal structure, phase stability, and oxideion diffusion of nanocrystalline ceria−zirconia materials are unresolved important issues, in particular at high temperatures, where the ceria−zirconia catalysts work efficiently. Here, we report a high-temperature neutron diffraction study of nanocrystalline [10.1(7) nm], compositionally homogeneous, tetragonal Ce0.5Zr0.5O2. Contrary to the previous work, we have observed no tetragonal-to-cubic phase transition in the nanocrystalline Ce0.5Zr0.5O2 up to 1176 K. The axial ratio c/aF and oxygen displacement along the c-axis from the fluorite regular 8c 1/4,1/4,1/4 position of the nanocrystalline Ce0.5Zr0.5O2 are almost independent of temperature. It was found that the c/aF ratio and oxygen displacement in nanocrystalline Ce0.5Zr0.5O2 are smaller than those of the bulk sample. It was shown that the refined atomic displacement parameter and spatial (maximum entropy method nuclear density) distribution of oxygen atom in nanocrystalline Ce0.5Zr0.5O2 are larger than those in nanocrystalline CeO2, which are factors of the high bulk oxygen diffusivity and catalytic activity in nanocrystalline Ce0.5Zr0.5O2. Possible diffusion pathways of oxide ions along the fluorite ⟨100⟩ and ⟨110⟩ directions were visualized in the spatial distribution of bond valence sums calculated using the present refined crystal structure of nanocrystalline Ce0.5Zr0.5O2 at 1023 K. The diffusion path is not straight but curved and forms a three-dimensional network.

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INTRODUCTION Nanocrystalline ceria−zirconia (CeO2−ZrO2) materials are widely utilized as components of (1) automotive exhaust catalysts for the removal of noxious compounds and (2) catalysts for reforming ethanol and CH4 to produce hydrogen in fuel cells.1−10 The material properties of the nanocrystalline and bulk ceria−zirconia are strongly dependent on the existing phase and crystal structure; yet, the form of these compounds remains poorly understood, in particular, at high temperatures, at which most function most efficiently. In the case of the CexZr1−xO2 solid solutions, there have been strong interests in the compositionally homogeneous, nonequilibrium, or metastable forms of the tetragonal phase, because these materials are used extensively as promoters in three-way catalysts for automotive exhaust. It is considered that the nonequilibrium tetragonal forms are important also in the ceria−zirconia catalysts for reforming ethanol and CH4 at high temperatures to produce hydrogen for fuel cells. The existing phase and crystal structure of compositionally homogeneous, nonequilibrium, or metastable CexZr1−xO2 solid solutions have been investigated by many researchers.11−35 There exist three forms, t, t′, and t″, in the tetragonal phase.15,19,24,25,29 All three forms have the distorted fluorite-type structure with the tetragonal P42/nmc © 2012 American Chemical Society

space group (Figure 1). The t-form is stable in the equilibrium state at high temperatures, and the solubility limit of CeO2 in tZrO2 is x = 0.18 in CexZr1−xO2.14 The t′-form is nonequilibrium or metastable and has an axial ratio c/aF larger than unity (c/aF > 1), where aF is the unit-cell parameter of the pseudo fluorite lattice and is equal to (2)1/2atet (Figure 1).12,15,19,25 Here, atet is the unit-cell parameter a of the tetragonal phase. The t′-form diffusionally transforms into a stable (t-form + cubic phase) two-phase mixture at high temperatures.12 The t″-form is a tetragonal form with the c/aF ratio of unity (c/aF = 1).15,19,29 Both of the t″-cubic phase boundaries of bulk15,19,29 and nanocrystalline24 CexZr1−xO2 are located at around x = 0.85−0.9. The t′−t″ phase boundary of bulk CexZr1−xO2 ranges from 0.55 to 0.65, depending on the synthesis method and grain size.12,15,19,29 The determination of the t′−t″ boundary of nanocrystalline samples is very difficult due to the broadening of Bragg peaks from small crystallites. The crystal structure, phase stability, and oxide-ion diffusion of bulk and nanocrystalline ceria−zirconia materials are Received: October 18, 2012 Revised: December 12, 2012 Published: December 14, 2012 829

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Figure 2. Flowchart of the polymerized complex route for the synthesis of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solid-solution sample.

Figure 1. Crystal structure of the tetragonal ceria−zirconia solid solution CexZr1−xO2, which shows the relationship between the tetragonal and the pseudo cubic fluorite lattices. Thin solid black and thick dashed red lines stand for the pseudo cubic fluorite and tetragonal cells, respectively. The closed circle denotes the cation Zr4+,Ce4+, and the shaded circle with a green arrow stands for the anion O2−. The arrows schematically indicate the oxygen displacement along the c-axis from the regular fluorite position (8c 1/4,1/4,1/4 site in the cubic Fm3̅m space group).

citric acid (CA), and ethylene glycol (EG). The Ce(CH3COO)3·2.17H2O and ZrOCl2·8H2O were dissolved into distilled water. This mixture was put into a CA−EG mixed solution during heating at about 100 °C. This solution was stirred at this temperature until it became transparent in a beaker on a heater with a stirrer. The colorless clear solution thus obtained was heated with stirring up to about 140 °C to promote the ester reaction between the CA and the EG. The solution became concentrated and highly viscous, accompanied with a change in color from colorless to yellow or brown, which indicates the formation of a polymeric gel (Photo S1 in the Supporting Information A). The viscous polymeric product was heated at about 450 °C in a mantle heater to remove the organics. The precursor thus obtained was heated in air at 800 °C for 3 h in an electric furnace, resulting in nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solid solution. This nanocrystalline Ce0.5Zr0.5O2 sample was characterized by various techniques including neutron powder diffraction, synchrotron powder diffraction, X-ray powder diffraction, Raman scattering, and STEM equipped with EDS. Nanocrystalline ceria (CeO2) powders were prepared by a precipitation method. An aqueous solution of Ce(NO3)3 (99.9%, Daiichi-Kigenso-Kagaku-Kogyo Co.) was dropped into ammonia solution. The precipitation thus obtained was washed and dried and then calcined in air at 800 °C for 3 h. The crystal structure of this nanocrystalline ceria was investigated by neutron and synchrotron Xray powder diffraction. Characterization of the Nanocrystalline, Compositionally Homogeneous Ce0.5Zr 0.5O2 Solid-Solution Sample. X-ray powder diffraction data of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solid-solution sample were measured at 299 K by a laboratory-based Rigaku X-ray powder diffractometer (RINT-2000, Cu Kα, 2θ range from 15 to 85°, step interval of 0.02°, counting time = 1 s/step). Raman spectra of the nanocrystalline and bulk, compositionally homogeneous ceria−zirconia Ce0.5Zr0.5O2 were measured at 297 K by a micro-Raman system equipped with CCD detectors (JASCO, NRS-5100). The Raman spectra were excited by a 532.1 nm diode pumped solid state (DPSS) laser (Size of the laser = 1 μm in diameter at the sample, power of the laser = 2.2 and 1.1 mW at the nanocrystalline and bulk samples, respectively). The microstructure and chemical compositions of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 were investigated by a scanning transmission electron microscope equipped with an energy dispersive X-ray spectrometer (JEOL JEM-2100F STEM-EDS, 200 kV). The probe size for an EDS measurement was about 1 nm. We measured EDS data at nine points to investigate the distribution of the chemical composition, Zr/Ce atomic ratio. The chemical composition of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solidsolution sample was examined by the inductively coupled plasma optical emission spectrometry (ICP-OES). Reproducibility was checked three times by using different aqueous solutions. The chemical composition of the nanocrystalline Ce0.5Zr0.5O2 was

unresolved important issues, in particular at high temperatures, where the catalysts work efficiently. Yashima et al.13 investigated the annealing temperature dependence of the axial ratio c/aF of the bulk tetragonal Ce0.5Zr0.5O2 solid solution by ex situ X-ray diffraction measurements of quenched samples at room temperature. We also studied the temperature dependence of crystallographic parameters of bulk tetragonal Ce0.5Zr0.5O2 solid solution by in situ neutron diffraction measurements and found the t′-to-cubic phase transition occurs between 1543 and 1829 K.25 Acuna et al.27 reported that the nanocrystalline tetragonal Ce0.5Zr0.5O2 transforms to cubic symmetry between 1073 and 1123 K, through in situ synchrotron X-ray powder diffraction experiments. However, it is difficult to detect the t″-to-cubic phase transition induced by the oxygen dislpacements along the c-axis through the synchrotron X-ray powder diffraction due to the relatively small X-ray scattering power of oxygen. On the contrary, neutron powder diffraction is powerful to study the structure change of tetragonal Ce0.5Zr0.5O2, because the oxygen position is essentially important for the tetragonal structure (Figure 1). The purpose of this work is to investigate the crystal structure, phase stability, and oxide-ion diffusional pathway of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2, by in situ neutron powder diffraction, synchrotron powder diffraction, Raman scattering, scanning transmission electron microscopy (STEM), and energy dispersive X-ray spectrometry (EDS).

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EXPERIMENTAL PROCEDURES

Synthesis of the Nanocrystalline, Compositionally Homogeneous Ce0.5Zr0.5O2 Solid-Solution and Nanocrystalline CeO2 Samples. A nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 sample was prepared by annealing the precursor obtained through the polymerized complex method16,36 based on the Pechini process37 at 800 °C for 3 h, following the process shown in Figure 2. The organic polymer precursor was synthesized by the polymerized complex method. Starting materials were Ce(CH3COO)3·2.17H2O (Daiichi-Kigenso-Kagaku-Kogyo Co. Ltd., Osaka of Japan), ZrOCl2·8H2O (Daiichi-Kigenso-Kagaku-Kogyo Co. Ltd.), anhydrous 830

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using a computer program PRIMA.45 In MEM analysis, any kind of complicated nuclear-density distribution is allowed as long as it satisfies the symmetry requirements. This method has successfully been applied to various nanocrystalline and bulk materials.28,29,42,45−48 The neutron diffraction data of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 pellets were measured at room temperature also by a high-resolution neutron powder diffractometer SuperHRPD installed at the Materials Life science Facility (MLF) of Japan Proton Acceralator Research Complex (J-PARC), Tokai of Japan.49

confirmed to be Ce0.5017(5)(Zr0.99389(90)Hf0.00611(5))0.4983(5)O2, where the values in parentheses denote standard deviations in the last digit. Synchrotron X-ray Diffraction Measurements of Nanocrystalline, Compositionally Homogeneous Ce0.5Zr0.5O2 and Nanocrystalline CeO2. Synchrotron X-ray powder diffraction measurements of the nanocrystalline Ce0.5Zr0.5O2 and CeO2 were performed at 303 K by the Debye−Scherrer camera with an imaging plate as a detector,38 installed at BL02B2 experimental station of the SPring-8, Hyogo of Japan. The powders were put into a glass capillary tube with a 0.2 mm inner diameter. The wavelength of incident X-ray beam was determined to be 0.39755 Å using standard reference material National Institute of Science and Technology (NIST) ceria powders. The crystal structures of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 were refined on the basis of the tetragonal P42/nmc t′-form by the Rietveld method using a computer program RIETAN-FP39 (Figure S1 in the Supporting Information B). The synchrotron X-ray powder diffraction data of the nanocrystalline Ce0.5Zr0.5O2 were also measured by the high angular resolution diffractometer40 and an electric furnace41,42 installed at the BL-4B2 beamline of the Photon Factory in air at 299 K and at high temperatures up to 1679 K. The wavelength of the synchrotron X-ray was 1.195754(4) Å. Neutron Diffraction Data Collection of the Nanocrystalline, Compositionally Homogeneous Ce0.5Zr0.5O2 Solid-Solution and Nanocrystalline CeO2 Samples and Data Processing. Nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solidsolution and nanocrystalline CeO2 powders were pressed uniaxially at 17 MPa and then pressed isostatically into pellets at 98 MPa. The size of the pellet thus obtained was 10 mm in diameter and about 40 mm in height. Neutron powder diffraction measurements of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 and CeO2 pellets were performed in air using a 150 detector HERMES system43 installed at the research reactor JRR-3 M reactor of the Japan Atomic Energy Agency (Tokai, Japan). Neutrons with a wavelength of 1.84760 Å were obtained from the 311 reflection of a Ge monochromator. The wavelength was determined by the Rietveld analysis of the neutron diffraction data of NIST Si standard. Neutron powder diffraction data of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 and CeO2 pellets were measured at 298.5(1) and 297.7 K, respectively. Diffraction data were collected in the 2θ range of 7−157° at intervals of 0.1°. In situ neutron powder diffraction measurments of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 pellets were perfomed in air up to 1701 K using the HERMES diffractometer43 and a homemade furnace.44 The sample temperature was accurately monitored with a calibrated thermocouple contacting the sample. To obtain accurate crystallographic parameters, we measured the neutron diffraction data keeping the sample temperature constant at 473.7(2), 672.4(1), 872.1(5), and 1022.9(2) K, where the number in parentheses is the standard deviation of the sample temperature during each data collection. To prevent the [t′ to (t + cubic)] phase separation as possible, we measured the neutron diffraction data heating the sample for a shorter time above 1023 K (heating rate = 10 K min−1). The reproducibility of the data was confirmed by carring out the high-temperature neutron diffraction measurements two times using different fresh nanocrystalline Ce0.5Zr0.5O2 pellets. The crystal structures of the nanocrystalline Ce0.5Zr0.5O2 and CeO2 pellets were refined by the Rietveld method using the computer program RIETAN-FP.39 The peak shape was assumed to be a modified split-type pseudo-Voigt function with asymmetry and a cutoff value of 7.00. The background profile was approximated by a 12 parameters Legendre polynomial. The unit-cell, background, profile shape, and crystal structural parameters were refined simultaneously. We have corrected the absorption effect in the Rietveld refinement using the measured density of the pellets. To investigate the spatial distribution of oxygen atom in the nanocrystalline Ce0.5Zr0.5O2 and CeO2, their nuclear-density distributions were analyzed by the maximum entropy method (MEM) of neutron diffraction data taken at room temperature. The MEM analysis was performed with 64 × 64 × 91 and 64 × 64 × 64 pixels

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RESULTS AND DISCUSSION Formation of Nanocrystalline, Compositionally Homogeneous t′-Ce0.5Zr0.5O2. All of the reflections in X-ray powder diffraction data of nanocrystallilne Ce0.5Zr0.5O2 were indexed by the tetragonal phase (Figure 3). Rietveld analysis of

Figure 3. X-ray powder diffraction pattern of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solid-solution sample prepared by the polymerized complex method. All of the reflections are indexed by the tetragonal lattice.

neutron and synchrotron powder diffraction data taken at room temperature indicated a single phase of tetragonal Ce0.5Zr0.5O2 (Figure 3, Table 1, and Figure S1 in the Supporting Information B). The 102tet reflection in the neutron, X-ray, and synchrotron diffraction profiles and a Raman band characteristic of the tetragonal ceria−zirconia [band (3) in Figure 4c; see also Figure S2 in the Supporting Information C] are clearly observed, which indicates the tetragonal symmetry. Here, the 102tet denotes the 102 reflection index of the tetragonal phase, which is forbidden for the cubic fluorite-type structure. The splitting between 004 and 220 reflections in the synchrotron, X-ray, and neutron powder diffraction profiles of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 is not detected due to the peak broadening, which is ascribed to the small crystallites. The refined unit-cell parameters strongly suggest that the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 is t′-form, because the refined c [=5.2980(17) Å] is larger than (2)1/2atet [=5.2684(4) Å]. The particle size of Ce0.5Zr0.5O2 was determined to be 10.1(7) nm from the STEM photograph (Figure 4a), which agrees with the crystallite size 8.8(4) nm from the diffraction data and Scherrer’s equation. Here, the number in parentheses is the standard deviation. EDS measurements at nine points (probe size = 1 nm) confirmed that the chemical composition is homogeneous (molar fraction of Zr4+ in cations, 0.509 ± 0.006; molar fraction of Ce4+ in cations, 0.491 ± 0.004). The average molar fraction x = 0.491 ± 0.004 in CexZr1−xO2 from EDS measurements in the nanocrytalline Ce0.5Zr0.5O2 sample agrees well with the value (x = 0.5017 ± 0.0005) from the ICP-OES measurements of the same sample. 831

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Table 1. Refined Crystallographic Parameters and Reliability Factors of Rietveld Analysis of Nano-Crystalline, Compositionally Homogeneous Ce0.5Zr0.5O2 Solid Solution Measured at Different Temperaturesa temperature (K) space group unit-cell parameters Ce,Zr O

reliability factors in the Rietveld analysis

atet (Å) c (Å) B (Å2)b g(O) B (Å2)b z(O)c Rwp (%)d Rp (%)d GoFd RI (%)d RF (%)d

298.5(1) P42/nmc 3.7275(3) 5.2980(17) 0.76(4) 1.0 1.32(4) 0.2231(4) 2.64 1.83 1.62 0.42 0.17

473.7(2) P42/nmc 3.7337(4) 5.3142(11) 0.93(3) 1.0 1.65(3) 0.2239(3) 5.21 4.05 1.27 0.77 33

672.4(1) P42/nmc 3.7401(7) 5.3207(17) 1.05(6) 1.0 1.95(6) 0.2235(3) 5.36 4.13 1.23 0.70 0.34

872.1(5) P42/nmc 3.7481(8) 5.3299(20) 1.33(7) 1.0 2.38(7) 0.2230(3) 5.62 4.42 1.26 0.87 0.41

1022.9(2) P42/nmc 3.7555(7) 5.3432(18) 1.39(6) 1.0 2.55(6) 0.2217(3) 5.04 3.00 1.14 0.61 0.24

a

The number in parentheses for the sample temperature is the standard deviation in the last digit during each data collection. The number in parentheses for unit-cell, positional, and atomic displacement parameters is the estimated standard deviation in the last digit. bB, isotropic atomic displacement parameter. cz(O), fractional coordinate z of oxygen atoms. Fractional coordinates of (Ce,Zr) and O atoms are 0,0,0 and 0,1/2,z(O), respectively. dStandard Rietveld agreement index (Young, R. A.; Prince, E.; Sparks, R. A. J. Appl. Crystallogr. 1982, 15, 357−359).

Stability of Nanocrystalline, Compositionally Homogeneous t′-Ce0.5Zr0.5O2: An In Situ Neutron Diffraction Study. Between 299 and 1176 K, only a single tetragonal phase was observed, and the 102tet reflection was clearly detected (Figure 5 and Figure S3 in the Supporting Information D).

Figure 5. Rietveld patterns of neutron diffraction data of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 measured in air and in situ at (a) 1023 and (b) 1176 K. Insets c and d are enlargements around the 102tet reflection in panels a and b, respectively, where the 102tet is the reflection index 102 of tetragonal phase.

Figure 4. (a) Transmission electron micrograph of the nanocrystalline, compositionally homogeneous Ce 0.5Zr0.5O2. Raman spectra of compositionally homogeneous, bulk t′-Ce0.5Zr0.5O2 (b, blue dotted line) and nanocrystalline Ce0.5Zr0.5O2 (c, red solid line). The peaks of (1) to (6) stand for the six Raman bands of tetragonal phase. The Raman spectrum of bulk t′-Ce0.5Zr0.5O2 is consistent with the literature.15 The bulk Ce0.5Zr0.5O2 was synthesized by annealing at 800 °C for 1 hour after heating the nano-crystalline sample at 1600 °C for 3 hours.

Above 1208 K, an anisotropic peak broadening in a Bragg reflection was detected, and the anisotropy was more significant at higher temperatures, which indicates the starting and progress of the phase separation from the t′ to stable two phases of ZrO2-rich t-form and CeO2-rich cubic phase. This phase separation is consistent with previous works.12,16,30 The present results clearly indicate no tetragonal-to-cubic phase 832

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transition in the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 between 299 and 1176 K in air. On the contrary, Acuna et al.27 reported the tetragonal-to-cubic phase transition of nanocrystalline Ce0.5Zr0.5O2 between 1073 and 1123 K. In the present work, we were able to detect clearly the 102tet reflection up to 1176 K with the help of a relatively higher neutron scattering power of oxygen as compared with the synchrotron X-ray (compare Figure 5 with Figure 3 and Figure S1 in the Supporting Information B). The Bragg peak width of the present Ce0.5Zr0.5O2 is almost unchanged between 299 and 1176 K, which indicates that the crystallite size (ca. 10 nm) was constant in this temperature range. This means that we are able to study the crytal structure of not bulk but nanocrystalline (ca. 10 nm), compositionally homogeneous Ce0.5Zr0.5O2 between 299 and 1176 K in this work. Crystal Structure of Nanocrystalline, Compositionally Homogeneous t′-Ce0.5Zr0.5O2 between 299 and 1176 K. Rietveld analysis of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 was carried out by the tetragonal P42/nmc structure between 299 and 1176 K (Figure 1 and Table 1). The Ce4+,Zr4+ cation and O2− anion were put at the special positions 2a 0,0,0 and 4d 0,1/2,z(O), respectively, in the tetragonal P42/nmc lattice. Here, the z(O) is the atomic coordinate z of oxygen atom of tetragonal P4 2 /nmc Ce0.5Zr0.5O2. In preliminary analyses, the occupancy factor of oxygen atom g(O) was refined in the whole temperature range from 299 to 1176 K. The refined g(O) agreed with 1.000 within three times of the estimated standard deviation. Therefore, the g(O) was fixed to be 1.000 in the final refinements. Calculated intensities agreed well with observed ones (Figure 5 and Table 1). For example, the weighted reliability factor Rwp, goodness of fit GoF, the reliability factors based on Bragg intensity RI and structure factor RF in the Rietveld analysis for the neutron diffraction data of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 measured at 1023 K were Rwp = 5.04%, GoF = 1.14, RI = 0.61%, and RF = 0.24%, respectively (Figure 5a and Table 1). Figure 1 shows the refined crystal structure of the nanocrystalline t′-Ce0.5Zr0.5O2. Nanocrystalline t′-Ce0.5Zr0.5O2 has a distorted fluorite-type structure where the oxygen atoms are alternatively displaced along the c-axis from the regular fluorite position (arrows in Figure 1) between 299 and 1176 K. The structure of the present nanocrystalline t′-Ce0.5Zr0.5O2 is similar with that of bulk t′-Ce0.5Zr0.5O2.19,28,29 The refined crystallographic parameters of Ce0.5Zr0.5O2 from neutron data at room temperature agreed well with those from synchrotron data at room temperature, which indicates the accuracy of the refined crystallographic parameters. The unit-cell parameters aF = (2)1/2atet and c, and unit-cell volume of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 increase with an increase of temperature (Figure 6a,c). In the whole temperature range between 299 and 1176 K, the c parameter is larger than aF (Figure 6a); thus, the axial ratio c/aF is larger than unity (Figure 6b), which indicates the t′-form. The c/aF ratio is almost independent of temperature [average value of c/aF = 1.0057(5) between 299 and 1176 K, where the number in the parentheses is the standard deviation in the last digit, Figure 6b]. The atomic coordinate z of oxygen atom z(O) is also almost independent of temperature [average value of z(O) = 0.2232(8) between 299 and 1176 K, where the number in parentheses is the standard deviation in the last digit, Table 1 and Figure S4 in the Supporting Information E]. The oxygen displacement d(O) along the c-axis from the fluorite

Figure 6. Temperature dependence of (a) unit-cell parameters, (b) axial ratio c/aF, and (c) unit-cell volume of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solid solution. The error bar for each data is the estimated standard deviation in the Rietveld analysis. The red solid lines were obtained by the least-squares means fit with a quadratic polynomial.

regular position [8c 1/4,1/4,1/4 site in Fm3̅m; 0,1/2,1/4 site (z(O) = 1/4) in P42/nmc] was calculated by the equation19,29 d(O) = c[1/4 − z(O)]

As shown in Figure 7a, the d(O) does not change largely with temperature [average value of d(O) = 0.143(5) Å between 299 and 1176 K, where the number in parentheses is the standard deviation in the last digit]. The d(O) values [=0.143(5) Å] larger than 0 Å are also evidence for the tetragonal phase of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 between 299 and 1176 K. The d(O) of nanocrystalline Ce0.5Zr0.5O2 increases a little with temperature between 474 and 1023 K (Figure 7a). A similar temperature dependence of the unit-cell and positional parameters was reported also in bulk Ce0.5Zr0.5O225 (Figures 8−10). Comparison of the Crystal Structures between the Nanocrystalline and Bulk t′-Ce0.5Zr0.5O2. The present unitcell parameter aF of nanocrystalline, compositionally homoge833

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Figure 9. Temperature dependence of the unit-cell volume of the nanocrystalline (red circles and lines) and bulk (black squares and lines) compositionally homogeneous Ce0.5Zr0.5O2 solid solutions. The error bar for each data is the estimated standard deviation in the Rietveld analysis. The solid line was obtained by the least-squares means fit by a polynomial.

Figure 7. Temperature dependence of (a) oxygen displacement from the regular fluorite position and (b) atomic displacement parameters of the nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 solid solution. The error bar for each data is the estimated standard deviation in the Rietveld analysis. The solid lines were obtained by the least-squares means fit with a quadratic polynomial.

Figure 10. Temperature dependence of the oxygen displacement along the c-axis from the regular fluorite position in the nanocrystalline (red circles and lines) and bulk (black squares and lines) compositionally homogeneous Ce0.5Zr0.5O2 solid solutions. The error bar for each data is the estimated standard deviation in the Rietveld analysis. The solid line was obtained by the least-squares means fit by a polynomial. The inset is a part of the refined crystal structure of nanocrystalline Ce0.5Zr0.5O2 [(Ce,Zr)O8 cube] where the arrows schematically indicate the oxygen displacements.

homogeneous Ce0.5Zr0.5O2 is higher than that of bulk Ce0.5Zr0.5O2,25 while they agree with each other above 700 K (Figure 9). Consequently, the thermal expansion of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 is lower than that of bulk sample below 700 K. The present oxygen displacement along the c-axis from the regular cubic fluorite position d(O) of nanocrystalline Ce0.5Zr0.5O2 is lower than that of bulk sample (Figure 10).25 The normalized Raman intensity of the third band in nanocrystalline Ce0.5Zr0.5O2 [I3/I4 = 0.17 (Figure S2 in the Supporting Information C and Figure 4c)] is also lower than that in bulk Ce0.5Zr0.5O2 [I3/I4 = 0.32 (Figure 4b)], which is consistent with the lower oxygen displacement d(O) of nanocrystalline Ce0.5Zr0.5O2. These differences between the nanocrystalline and the bulk samples are attributable to (1) the kinetics12,50,51 and/or (2) size effects46 of the nanocrystalline sample. In bulk Ce0.5Zr0.5O2 and Zr0.88Er0.12O1.94, the axial ratio c/aF increases, while the z(O)

Figure 8. Temperature dependence of the unit-cell parameters in the nanocrystalline (red circles and lines) and bulk (black squares and lines) compositionally homogeneous Ce0.5Zr0.5O2 solid solutions. The error bar for each data is the estimated standard deviation in the Rietveld analysis. The solid line was obtained by the least-squares means fit by a polynomial.

neous Ce0.5Zr0.5O2 is higher than that of bulk Ce0.5Zr0.5O2,25 while the present c parameter of nanocrystalline Ce0.5Zr0.5O2 is lower than that of bulk Ce0.5Zr0.5O225 (Figure 8). Thermal expansions along the a- and c-axes of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 are a little lower than those of bulk sample, respectively. Below 700 K, the present unit-cell volume of nanocrystalline, compositionally 834

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Figure 11. Yellow isosurfaces of the nuclear density at 0.1 fm Å−3 of (a) tetragonal Ce0.5Zr0.5O2 (299 K) and (b) cubic CeO2 (298 K). Nucleardensity distributions on the (a) (100) plane of tetragonal Ce0.5Zr0.5O2 and (b) (110) plane of cubic CeO2 are also plotted. This figure was drawn with the VESTA3 program.55

present work, we have demonstrated this correlation for nanocrystalline CexZr1−xO2. A high B(O) value and large spatial distribution of oxygen atoms indicates the high dynamic thermal vibration and/or high static positional disorder, which enhances the movement of oxygen ions across the unit cell. The high B(O) and larger spatial distribution of oxygen atoms are regarded as structural origins of high oxide-ion diffusivity and high catalytic activity of nanocrystalline Ce0.5Zr0.5O2. Diffusional Pathway of Oxide Ions of Nanocrystalline, Compositionally Homogeneous Ce0.5Zr0.5O2. Geometric information of the oxide-ion diffusion is important for the mechanism of the oxide-ion diffusion in solid materials and for the design of the ionic and mixed conductors. Here, we present the oxide-ion diffusional pathways in nanocrystalline Ce0.5Zr0.5O2, which are investigated using the spatial distributions of bond valence sums (BVS). The BVS maps were calculated by the 3DBVSMAPPER program54 with a spatial resolution of 0.1 Å for the present refined crystallographic parameters of tetragonal Ce0.5Zr0.5O2 (1023 K) and depicted with the VESTA3 program.55 As shown in Figure 12, the oxide ions shift to the opposite directions against the Ce,Zr cations in the ⟨111⟩F directions near the stable positions. For example, the Oa oxygen atom exhibits smaller distributions in the directions to Ma and Mb cations in Figure 12. This anisotropic distribution of oxygen atom in tetragonal Ce0.5Zr0.5O2 is similar with the anisotropic probability-density distributions of mobile ions in other fluorite-structured materials reported in the literature.56−60 A striking feature is the visualization of possible diffusional pathways of oxide ions in the ⟨100⟩F, ⟨001⟩, ⟨110⟩F, and ⟨101⟩F directions, which leads to the formation of a threedimensional network of diffusional pathways [lines with arrows in Figures 12 and 13; Oa−Ob and Oc−Od paths along the ⟨001⟩ direction and Oa−Oc and Ob−Od paths along the ⟨110⟩F direction (Figure 12); O1−O2 path along the ⟨100⟩F direction, O1−O3 path along the ⟨100⟩F direction, and O2−O3 path along the ⟨110⟩F direction (Figure 13a); O4−O5 and O5−O6 paths along the ⟨001⟩ direction, and the O5−O7 and O6−O8 paths along the ⟨101⟩F direction (Figure 13b)]. It should be noted that the diffusion path is not straight but curved (Figures 12 and 13). If the path is straight, the distance between the cation and the anion is quite short at around the center of the path, leading to unstable state. The anion migrates, keeping the cation−anion distance constant to some degree. For example, the Oa−Oc path along the ⟨110⟩F direction is curved, keeping

decreases with an increase of annealing time. This type of kinetics can explain the difference of unit-cell and positional parameters between the nanocrystalline and the bulk Ce0.5Zr0.5O2. A similar size effect was reported for the nanosized BaTiO3.46 The axial ratio c/a of nanosized BaTiO3 decreases with a decrease of particle size. Atomic Displacement Parameter, Nuclear-Density Distribution, Oxygen Diffusivity, and Catalytic Activity of Nanocrystalline, Compositionally Homogeneous Ce0.5Zr0.5O2. Figure 7b shows the temperature dependence of atomic displacement parameters of cation B(Ce,Zr) and anion B(O) of nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2. Both B(Ce,Zr) and B(O) of nanocrystalline Ce0.5Zr0.5O2 increase with an increase of temperature as well as those of bulk Ce0.5Zr0.5O2.25 The atomic displacement parameter of anions B(O) is higher than that of cations B(Ce,Zr) [B(O) > B(Ce,Zr)], which suggests higher diffusivity of anions as compared with the cations. This nature is important for the oxygen storage/release capacity of nanocrystalline Ce0.5Zr0.5O2, because the bulk oxygen diffusion is one of the steps of the oxygen storage/release process.52 The atomic displacement parameter of anions in nanocrystalline, compositionally homogeneous Ce0.5Zr0.5O2 [B(O) = 1.32(4) Å2 from neutron data, see Table 1, B(O) = 1.58(11) Å2 from synchrotron data] is higher than that in nanocrystalline CeO2 [B(O) = 0.502(17) Å2 from neutron data, B(O) = 0.542(16) Å2 from synchrotron data] at room temperature, which is consistent with the previous works of bulk samples at room temperature,29 at 900 K,34 and at 1832 K.28 The nucleardensity distributions of nanocrystalline Ce0.5Zr0.5O2 and CeO2 were obtained by the MEM analysis using neutron diffraction data (Figure 11). Figure 11 indicates that the spatial distribution of oxygen atoms in Ce0.5Zr0.5O2 is larger than that of CeO2, which is consistent with the higher B(O) of Ce0.5Zr0.5O2. The present higher B(O) and larger spatial distribution of oxygen atoms in nanocrystalline Ce0.5Zr0.5O2 as compared with nanocrystalline CeO2 correspond to the higher oxygen diffusivity of Ce0.5Zr0.5O2 as compared with CeO2.53 These results suggest that the oxygen diffusion coefficient increases with an increase of atomic displacement parameter of oxygen atom in nanocrystalline CexZr1−xO2 as well as in bulk samples. The previous works28,29,34 showed the correlation between the oxygen diffusivity and the B(O) for bulk CexZr1−xO2. In the 835

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path due to a longer distance from cations, leading to the extremely low BVS (Figure 12). These features of oxygen diffusional pathway in tetragonal distorted fluorite-type Ce0.5Zr0.5O2 are similar with those reported in cubic fluoritestructured materials obtained by the MEM nuclear- and electron-density analyses.56−60

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ASSOCIATED CONTENT

S Supporting Information *

Photo of the formation of polymeric gel, additional neutron and synchrotron powder diffraction data, and temperature dependence of atomic coordinate z of oxygen atom. 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]. Figure 12. Difference bond valence sum (DBVS) map for an oxide ion (difference between the observed BVS and the valence of an oxide ion) in two unit cells of nanocrystalline Ce0.5Zr0.5O2 at 1023 K. Spatial distribution of the DBVS on the bc plane at x = 0. Contour lines from −0.2 to +0.2 valence unit (v.u.) and the step interval of 0.05 v.u. Black solid and black dotted lines stand for the contour lines with constant plus and minus values, respectively. Possible diffusion paths along the ⟨110⟩F direction (btet-axis) and the ⟨001⟩ direction (ctet-axis) are observed. The path along the ⟨111⟩F direction is not allowed as shown by the low DBVS. The arrows with Oa, Ob, Oc and Od denote the stable positions of oxide ions. The purple circle denotes the Ce,Zr cation (Ma and Mb). The anisotropic DBVS distribution near the stable position and the curve feature of the diffusional pathway are attributable to the existence of the Ce,Zr cation.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. K. Ohoyama, Prof. T. Ida, Prof. T. Kamiyama, Dr. S. Torii, Dr. J. Kim, M. Ohkawara, and facility staff for their arrangements and support on the neutron and synchrotron diffraction experiments. We thank Dr. K. Fujii for useful discussions. We express our thanks to Dr. M. Avdeev for the permission of our use of the 3DBVSMAPPER program. We thank Dr. M. Tada of the Center for Materials Analysis at Ookayama of Tokyo Institute of Technology and T. Soejima of JASCO Co. for the Raman measurements. We also acknowledge Dr. T. Wakita for the arrangement of ICP-OES measurements and supplying the starting materials. A part of this work was financially supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan,

the oxygen−Mb distance constant to some extent (Figure 12). The direct path along the ⟨111⟩F direction is not allowed, because the oxide ions are not stable around the center of the

Figure 13. DBVS maps for an oxide ion (difference between the observed BVS and the valence of an oxide ion) in nanocrystalline Ce0.5Zr0.5O2 at 1023 K. Yellow isosurfaces of the DBVS at ±0.1 (v.u.) on (a) (004) and (b) (110) planes. Regions of (a) (0 ≤ xF ≤ 2, 0 ≤ yF ≤ 2, and 0.65 ≤ z ≤ 0.85) and (b) (−1/4 ≤ x ≤ 1/4, −0.49 ≤ y ≤ 0.99, and 0 ≤ z ≤ 2) where the subscript F denotes the pseudo fluorite lattice. (a) Possible diffusional pathways of oxide ions along the ⟨100⟩F and ⟨110⟩F directions. (b) Possible diffusional pathways of oxide ions along the ⟨001⟩ direction (c -axis) and ⟨101⟩F direction. Red spheres denote the oxygen atoms. A green/yellow sphere stands for a Ce,Zr cation. Thick black dashed and thin red solid lines denote the tetragonal and pseudo cubic fluorite cells, respectively. 836

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through a Grant-in-Aid for Scientific Research (A) No. 24246107 and Challenging Exploratory Research No. 23655190. The neutron diffraction measurements were carried out as projects approved by the Neutron Science Laboratory, Institute for Solid State Physics, University of Tokyo (Proposal Nos. 10767, 9724, and 8766) and by the Japan Proton Accelerator Research Complex (J-PARC) and Institute of Materials Structure Science of KEK (Proposal Nos. 2010A0037 and 2010A0030). The synchrotron experiments were performed as projects approved by the Photon Factory of KEK (Proposal No. 2008G084) and by the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal Nos. 2010B1788, 2011B1995, 2012A1415, and 2011A1442).

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