In situ observation of the tetragonal–cubic phase transition in the CeZrO₄ solid solution – a high-temperature neutron diffraction study

The crystal structure of the compositionally homogeneous ceria–zirconia solid solution CeZrO₄ is refined by Rietveld analysis of neutron diffraction data measured in situ over the temperature range 296–1831 K. The CeZrO₄ exhibits a tetragonal structure with the space group P4₂/nmc at temperatures from 296 to 1542 K (Z = 1), and a cubic fluorite-type form with the space group at 1831 K (Z = 2). The isotropic atomic displacement parameters of Ce and Zr atoms B(Ce,Zr) and O atoms B(O) are found to increase with temperature, with B(O) being larger than B(Ce,Zr), suggesting the higher diffusivity of oxygen ions. The ratio of the c axial length to the a length of the pseudo-fluorite lattice (c/a_F axial ratio) for the tetragonal CeZrO₄ phase increased from 296 to 1034 K and decreased from 1291 to 1542 K, reaching unity between 1542 and 1831 K. The displacement of O atoms along the c axis in the tetragonal CeZrO₄ phase increased from 296 to 1034 K and decreased from 1291 to 1542 K, reaching 0.0 Å between 1542 and 1831 K. These results indicate that the cubic-to-tetragonal phase transition between 1542 and 1831 K is accompanied by oxygen displacement along the c axis and the increase of the c/a_F axial ratio from unity.

1. Introduction

Materials containing ceria and zirconia have become the focus of intense study in recent years as a result of several applications in the field of high-temperature materials for technologies such as fuel cells, oxygen gas sensors (Inaba & Tagawa, 1996) and structural ceramics (Tsukuma & Shimada, 1985), and as components of automotive exhaust catalysts for the removal of noxious compounds (Yao & Yao, 1984; Ozawa et al., 1993; Murota et al., 1993; Trovarelli, 1996). The material properties of these compounds are strongly dependent on the crystal structure and phase, yet the form of these compounds at high temperature, at which most function most efficiently, remains poorly understood. In the case of the Ce_1 − xZr_xO₂ solid solutions, there is strong interest in the compositionally homogeneous metastable forms of the tetragonal phase, since these materials are used extensively as promoters in three-way catalysts for automotive exhausts. The compositional dependence of the phase and crystal structure of compositionally homogeneous metastable Ce_1 − xZr_xO₂ solid solutions have been investigated by many researchers (Meriani, 1985; Yashima et al., 1993a,b; Yashima, Arashi, Kakihana & Yoshimura, 1994; Yashima, Takashina, Kakihana & Yoshimura, 1994; Yashima, Ohtake, Kakihana, Arashi & Yoshimura, 1996; Yashima et al., 1998; Omata et al., 1999; Kaspar & Fornasiero, 2003; Enzo et al., 2000; Lamas et al., 2005; Zhang et al., 2006). As the compositionally homogeneous CeZrO₄ solid solution also exhibits high catalytic performance in the Ce_1 − xZr_xO₂ (Trovarelli et al., 1997; Suda et al., 2001), it is therefore important to investigate the crystal structure and phase transition in the CeZrO₄ solid solution at high temperatures.

The crystal structure of the compositionally homogeneous Ce_1 − xZr_xO₂ solid solutions has been studied by Yashima et al. (1993a,b), Yashima, Arashi, Kakihana & Yoshimura (1994), Yashima, Takashina, Kakihana & Yoshimura (1994) and Yashima et al. (1998), who have reported three forms of the tetragonal phase (t, t′, t′′), all belonging to the space group P4₂/nmc. The stable form of the tetragonal phase is called the t form and is restricted to the solubility limit in the equilibrium phase diagram (Yashima et al., 1993a,b; Yashima, Arashi, Kakihana & Yoshimura, 1994; Yashima, Takashina, Kakihana & Yoshimura, 1994). The t′ form is metastable and unstable compared with the coexistence of the t form and cubic (c) phase. The t′ form has an axial ratio larger than unity, that is, c_t′/(2^1/2a_t′) > 1, where c_t′ and a_t′ are the unit-cell parameters c and a of the t′ form (Fig. 1). The t′′ form is another metastable tetragonal phase with an axial ratio of unity [c_t′/(2^1/2a_t′)  =  1]. The t′′ form is designated as a tetragonal symmetry owing to the displacement of O atoms along the c axis from the regular position in the cubic phase (Fig. 1).

Figure 1 Crystal structure of metastable tetragonal (t′) CeZrO4 solid solution and relationship between tetragonal cell and pseudo-cubic fluorite (F) cell. Filled and shaded circles denote cations and anions, respectively. Arrows denote the displacement of O atoms along the c axis. Thick dashed lines denote the primitive cell after Teufer (1962), and thin solid lines delineate two pseudo-fluorite cells.

Yashima et al. (1993b) investigated the temperature dependence of the c_t′/(2^1/2a_t′) ratio in the CeZrO₄ solid solution by ex situ X-ray diffraction measurements of quenched samples at room temperature. In the present work the temperature dependence of the unit-cell parameters and axial ratio of the CeZrO₄ solid solution are investigated by in situ neutron diffraction measurements at high temperatures. Yashima and co-workers (Yashima, Arashi, Kakihana & Yoshimura, 1994; Yashima, Takashina, Kakihana & Yoshimura, 1994; Yashima et al., 1998) suggested that the cubic-to-tetragonal phase transition is induced by the displacement of O atoms (Fig. 1) on the basis of the high-temperature Raman spectra of Ce_0.8Zr_0.2O₂ and ex situ neutron and synchrotron powder diffraction data for Ce_1 − xZr_xO₂ (x  =  0.1, 0.2, 0.3, 0.35, 0.4 and 0.5) obtained at room temperature. As no high-temperature in situ studies of the crystal structure or cubic–tetragonal phase transition have been conducted for the CeZrO₄ solid solution, the temperature dependence of the oxygen displacement and atomic displacement parameters remains an unresolved issue. Through the investigation of the temperature dependence of the unit-cell parameters, the axial ratio c_t′/(2^1/2a_t′), positional and atomic displacement parameters, and oxygen displacement of the CeZrO₄ solid solution, it is demonstrated in this study for the first time that the c–t′ transition between 1542 and 1831 K is accompanied by oxygen displacement along the c axis and an increase in the c/a_F axial ratio from unity.

2. Experiments and data analysis

Fig. 2 shows the synthesis procedure of CeZrO₄ powders and pellets. Ce(NO₃)₃ (99.9% purity) and ZrO(NO₃)₂ (99.9% purity) aqueous solutions were supplied from Daiichi Kigenso Kagaku Kogyo Co. Ltd. These solutions were mixed at an atomic ratio of Zr:Ce  =  1:1 and added to a 5 mass % ammonia aqueous solution, resulting in the formation of hydroxides containing Ce and Zr species. The resultant precipitates were washed after filtration and then calcined at 1073 K for 3 h. The CeZrO₄ powders thus obtained were pressed uniaxially at 17 MPa, and then pressed isostatically into pellets at 98 MPa. The pellets were sintered at 1973 K for 5 h in air and then annealed at 1073 K for 24 h in air to afford a cylindrical product of 19 mm in diameter and 76 mm in height. The CeZrO_4 − δ solid solution thus obtained was pale yellow, indicating the stoichiometry to be δ  =  0, where δ denotes the proportion of oxygen vacancies. Chemical analysis by inductively coupled plasma optical-emission spectroscopy (ICP-OES) indicated a small amount of hafnium, corresponding to an average chemical composition of Ce_0.4943 (3)(Zr_0.993 (2)Hf_0.007 (2))_0.5057 (3)O₂, where the values in parentheses denote the error bar in the last digit.

Figure 2 Synthesis procedure for CeZrO4 pellets.

Neutron powder diffraction measurements were performed in air using a 150 detector HERMES system (Ohoyama et al., 1998) installed at the JRR-3M reactor of the Japan Atomic Energy Agency, Tokai, Japan. Neutrons with wavelength of 1.81430 (7) Å were obtained from the (311) reflection of a Ge monochromator. Diffraction data were collected in the 2θ range 5–155° at intervals of 0.1° over the temperature range 296–1831 K. A furnace equipped with MoSi₂ heaters (Yashima, 2002) was used for the high-temperature neutron diffraction measurements. Sample temperatures were maintained constant during data acquisition.

The crystal structures of the CeZrO₄ material were refined by the Rietveld method using the computer program RIETAN-2000 (Izumi & Ikeda, 2000). The peak shape was assumed to be a modified split-type pseudo-Voigt function and a cut-off value of 7.00 (Toraya, 1990). The background was approximated by a 12-parameter polynomial in 2θⁿ (n  =  0–11). The n parameters were refined simultaneously with the unit-cell, zero-point scale, profile-shape and crystal structural parameters.

3. Results

Figs. 3 and 4 show the neutron diffraction profiles of the CeZrO₄ solid solution measured at 296, 1542 and 1831 K. All reflections are indexed by a tetragonal cell (P4₂/nmc) between 296 and 1542 K. The peak splitting between the 004_t′ and 220_t′ reflections was clearly observed between 296 and 1542 K (Figs. 3a and b). Here hkl_t′ denotes the hkl reflection of the t′ form. The 102_t′ reflection was clearly detected in this temperature range (Fig. 4), allowing the CeZrO₄ solid solution to be identified as the single phase of the t′ form with an axial ratio c_t′/(2^1/2a_t′) larger than unity [c_t′/(2^1/2a_t′) > 1] at temperatures between 296 and 1542 K. All reflections in the neutron diffraction profile measured at 1831 K are indexed by a cubic fluorite-type cell (; Fig. 3c). The 400_c reflection exhibits a single feature without splitting between the 004_t′ and 220_t′ reflections. No 102_t′ reflection was detected at 1831 K (Fig. 4c). Thus, the CeZrO₄ solid solution at 1831 K is identified as having a cubic structure. No impurity phases were detected in the neutron diffraction profiles between 296 and 1831 K. Each peak did not exhibit anisotropic peak broadening. These results indicate that the CeO₂ composition in the sample is homogeneous in the whole temperature range. The t′ form is metastable and unstable compared with the stable t + c two-phase coexistence. The stable t and c phases did not form, because the heating rate (ca 10 K min⁻¹) was too high and the measurement time (ca 90 min) was too short for the phase separation to occur.

Figure 3 Rietveld fitting patterns for neutron diffraction data of CeZrO4 solid solution measured at (a) 296, (b) 1542 and (c) 1831 K. Crosses and lines denote observed and calculated intensities, respectively. Short vertical lines indicate the positions of possible Bragg reflections of (a), (b) tetragonal and (c) cubic CrZrO4 phases. Lines below the profiles denote the difference between observed and calculated intensities.

Figure 4 Neutron diffraction profiles around the 102t′ reflection of CeZrO4 solid solution measured at (a) 296, (b) 1542 and (c) 1831 K.

Rietveld analysis of the CeZrO₄ solid solution was carried out for the tetragonal structure with the P4₂/nmc space group (Z = 1) at 296–1542 K, where the cation (Ce⁴⁺ and Zr⁴⁺) and anion (O²⁻) were placed at the special positions of 2(a) 0,0,0 and 4(d) 0,1/2,z, respectively. Data at 1831 K were analyzed assuming the cubic fluorite-type structure with the space group (Z = 2), where the cation (Ce⁴⁺ and Zr⁴⁺) and anion (O²⁻) were placed at 4(a) 0,0,0 and 8(c) 1/4,1/4,1/4, respectively. In a preliminary analysis, the occupancy factor of the O atom g(O) was refined. The refined g(O) was unity within the error bar, thus we fixed the g(O) to be unity in the final refinement. The calculated profile is in good agreement with the observed data (Fig. 3). Table 1¹ lists the crystal parameters and reliability factors in the Rietveld analyses of the neutron diffraction data for the CeZrO₄ solid solution between 296 and 1831 K. The refined axial ratio c_t′/(2^1/2a_t′) at room temperature was 1.0088 (1), consistent with that reported previously (Yashima et al., 1998). The refined fractional coordinate z of oxygen atoms z(O) was 0.2189 (2) at room temperature, which is also consistent with the results of Yashima et al. (1998) and Lamas et al. (2005) within ±3 standard deviations (σ) of z(O).

Table 1
Crystal parameters and reliability factors of Rietveld analysis of CeZrO₄ solid solution measured at different temperatures

M_r = 295.40, θ_min = 25°, θ_max = 150°.

Temperature (K)		296	507	772	1034	1291	1542	1831
Space group		P42/nmc	P42/nmc	P42/nmc	P42/nmc	P42/nmc	P42/nmc
Unit-cell parameters	a (Å)	3.7191 (2)	3.7286 (2)	3.7386 (3)	3.7503 (3)	3.7640 (3)	3.7781 (4)	5.3848 (6)
	c (Å)	5.3057 (4)	5.3215 (4)	5.3381 (4)	5.3564 (5)	5.3745 (5)	5.3833 (7)
Ce, Zr	B (Å^2)†	0.62 (4)	0.90 (4)	1.15 (4)	1.58 (5)	2.07 (5)	2.61 (7)	2.49 (6)
O	g (O)	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	B (Å^2)†	1.18 (3)	1.59 (4)	2.01 (4)	2.63 (5)	3.49 (6)	4.64 (7)	6.05 (8)
	z (O)‡	0.2190 (2)	0.2184 (2)	0.2179 (2)	0.2170 (2)	0.2170 (2)	0.2199 (3)	0.25
Reliability factors in the Rietveld analysis	Rwp§	0.0879	0.0787	0.0834	0.0749	0.0685	0.0720	0.0821
	Rp§	0.0628	0.0573	0.0618	0.0563	0.0514	0.0551	0.0605
	GoF§	4.91	4.40	4.70	4.74	4.88	5.69	6.40
	RI§	0.0483	0.0512	0.0587	0.0553	0.0562	0.0582	0.0797
	RF§	0.0325	0.0350	0.0394	0.0353	0.0343	0.0378	0.0441
V (Å^3)		73.39 (1)	73.98 (1)	74.61 (1)	75.34 (1)	76.14 (1)	76.84 (2)	156.13 (3)
Z		1	1	1	1	1	1	2
No. of parameters		32	32	32	32	32	32	27

†B: isotropic atomic displacement parameter.
‡z(O): fractional coordinate z of O atoms.
§Standard Rietveld agreement index (Young et al., 1982).

The unit-cell parameters a and c of the CeZrO₄ solid solution increased with temperature, coinciding between 1542 and 1831 K because of the t′–c transformation (Fig. 5). The axial ratio c_t′/(2^1/2a_t′) of the metastable t′-CeZrO₄ increased slightly from 296 to 1034 K, and decreased from 1291 to 1542 K (Fig. 6). The axial ratio became unity between 1542 and 1831 K, corresponding to the t′–c phase transition. The fractional coordinate z(O) of CeZrO₄ decreased from 296 to 1034 K, and increased from 1291 K, reaching 1/4 between 1542 and 1831 K (Fig. 7). The oxygen displacement d(O) from the regular 8(c) position of the cubic fluorite-type structure can be estimated by the equation d(O)  =  c[0.25 − z(O)]. The d(O) value of CeZrO₄ increased slightly from 296 to 1034 K, and then decreased to 0.0 Å between 1542 and 1831 K (Fig. 8), corresponding to the t′–c phase transition. The isotropic atomic displacement parameters of Ce and Zr atoms B(Ce,Zr) and O atoms B(O) increased with temperature (Fig. 9). B(O) was larger than B(Ce,Zr), suggesting the higher diffusivity of oxygen ions. This is consistent with the relation of B(Ce,Zr) < B(O) in Ce_1 − xZr_xO₂ at room temperature (Lamas et al., 2005) and the diffusivity experiments in the literature (Yashima et al., 1993a; Yashima, Kakihara & Yoshimura, 1996).

Figure 5 Temperature dependence of the unit-cell parameters of CeZrO4 solid solution. Open circles and squares denote the unit-cell parameters 2^1/2at′ and ct′ of the metastable tetragonal t′ form, respectively. The filled circle denotes the unit-cell parameter ac of the cubic phase. Error bars of standard uncertainties in the Rietveld analysis are smaller than the datum symbols. The solid line is the least-squares fit (quadratic polynomial) and the dashed line is a guide to the eye.

Figure 6 Relationship between temperature and axial ratio ct′/aF for CeZrO4 solid solution. Open and filled circles denote the ct′/aF ratios of the t′ and c phases, respectively. The solid line is a least-squares fit (polynomial) and the dashed line is a guide to the eye.

Figure 7 Temperature dependence of the fractional coordinate z of O atoms in CeZrO4 solid solution. Open circles denote t′-CeZrO4 and the solid circle denotes c-CeZrO4. Error bars denote the standard uncertainties in the Rietveld analysis. The solid line is a least-squares fit (polynomial) and the dashed line is a guide to the eye.

Figure 8 Temperature dependence of the oxygen displacement of CeZrO4 solid solution. Open circles denote t′-CeZrO4 and the solid circle denotes c-CeZrO4. Error bars were estimated from the standard uncertainties of c and z obtained in the Rietveld analysis. The solid line is a least-squares fit (polynomial) and the dashed line is a guide to the eye.

Figure 9 Temperature dependence of isotropic atomic displacement parameters of Ce and Zr atoms [B(Ce, Zr)] and O atoms [B(O)] in CeZrO4 solid solution. Open circles denote B(Ce,Zr) and triangles denote B(O) for t′-CeZrO4. Filled symbols denote c-CeZrO4. The solid line is a least-squares fit (quadratic polynomial) and the dashed line is a guide to the eye.

4. Discussion

The present work based on in situ experiments has demonstrated that the c–t′ phase transition of the CeZrO₄ solid solution occurs between 1542 and 1831 K (Figs. 3–8). The c–t′ transition temperature between 1542 and 1831 K is consistent with the previous ex situ study (Yashima et al., 1993b). The c_t′/(2^1/2a_t′) value is 1.0 for the cubic phase and increases with decreasing temperature below the c–t′ phase transition temperature. This indicates that the c–t′ phase transition is accompanied by the increase of c/a_F ratio from unity. The present in situ experiments also revealed the temperature dependence of the atomic coordinate z(O) and oxygen displacement d(O) for the first time (Figs. 7 and 8). The d(O) value is 0.0 Å for the cubic phase and increases with decreasing temperature below the c–t′ phase-transition temperature. This indicates that the c–t′ phase transition is accompanied by oxygen displacement. Yashima et al. suggested oxygen-induced structural change as a mechanism for the c–t′ transformation in ZrO₂–CeO₂ systems (Yashima et al., 1993a,b; Yashima, Arashi, Kakihana & Yoshimura, 1994; Yashima, Takashina, Kakihana & Yoshimura, 1994; Yashima et al., 1998) and ZrO₂–RO_1.5 (R  =  Y, Nd, Sm, Er, Yb) systems (Yashima, Ohtake, Kakihana, Arashi & Yoshimura, 1996) on the basis of data acquired at room temperature. Yashima, Arashi, Kakihana & Yoshimura (1994) also suggested such oxygen-induced behavior in the ZrO₂–CeO₂ system through in situ Raman studies. The present work has provided direct evidence of the temperature dependence of oxygen displacement d(O) as an oxygen-induced structural change responsible for the c–t′ transition.

5. Conclusions

The crystal structure of the compositionally homogenous CeZrO₄ solid solution was investigated by in situ neutron powder diffraction analysis and Rietveld refinement over a temperature range of 296 to 1831 K. The CeZrO₄ solid solution was found to transform from the tetragonal t′ phase to the cubic phase between 1542 and 1831 K, accompanied by an increase in the isotropic atomic displacement parameters B(Ce,Zr) and B(O) with increasing temperature. B(O) was found to be larger than B(Ce,Zr), suggesting a higher diffusivity of oxygen ions. The axial ratio c/a_F of the tetragonal CeZrO₄ phase increased from 296 to 1034 K and decreased from 1291 to 1542 K, reaching unity between 1542 and 1831 K. The displacement of O atoms along the c axis in the tetragonal CeZrO₄ phase increased from 296 to 1034 K and decreased from 1291 to 1542 K, reaching 0.00 between 1542 and 1831 K. These results indicate that the tetragonal-to-cubic phase transition is accompanied by oxygen displacement along the c axis and the increase of the c/a_F axial ratio from unity.

Supporting information

Computing details

For all compounds, cell refinement: RIETAN-2000 (Izumi and Ikeda, 2000); program(s) used to solve structure: RIETAN-2000; program(s) used to refine structure: RIETAN-2000; software used to prepare material for publication: VICS (Izumi and Dilanian, 2002).

Figures

(296K) cerium zirconiuim oxide

Crystal data

Ce0.4943Hf0.0035O2Zr0.5022	Dx = 6.684 Mg m^−3
Mr = 147.70	Neutron radiation, λ = 1.81430 (7) Å
Tetragonal, P42/nmc	T = 296 K
a = 3.7191 (2) Å	yellow
c = 5.3057 (4) Å	cylinder, 76 × 19 mm
V = 73.39 (1) Å^3	Specimen preparation: Prepared at 1973 K and 100 kPa
Z = 2

Data collection

150 detector system HERMES diffractometer	Data collection mode: transmission
Radiation source: neutron	Scan method: step
None monochromator	2θmin = 5°, 2θmax = 155°, 2θstep = 0.1°
Specimen mounting: Polycrystalline pellets without container

Refinement

Rp = ?	Profile function: pseudo-Voigt
Rwp = 0.088	32 parameters
Rexp = 0.02
χ^2 = NOT FOUND	Background function: 12-parameter polynomial
1500 data points	Preferred orientation correction: no
Excluded region(s): 5-25, 150-155

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ce	0	0	0	0.0079 (5)*	0.4943
Zr	0	0	0	0.0079 (5)*	0.5022
Hf	0	0	0	0.0079 (5)*	0.0035
O	0	0.50000	0.2190 (2)	0.0150 (4)*

Geometric parameters (Å, º)

Ce—O	2.1928 (6)	Zr—O	2.1928 (6)
Ce—O—Zr	115.99 (9)

(507K) cerium zirconiuim oxide

Crystal data

Ce0.4943Hf0.0035O2Zr0.5022	Dx = 6.630 Mg m^−3
Mr = 147.70	Neutron radiation, λ = 1.81430 (7) Å
Tetragonal, P42/nmc	T = 507 K
a = 3.7286 (2) Å	yellow
c = 5.3215 (4) Å	cylinder, 76 × 19 mm
V = 73.98 (1) Å^3	Specimen preparation: Prepared at 1973 K and 100 kPa
Z = 2

Data collection

150 detector system HERMES diffractometer	Data collection mode: transmission
Radiation source: neutron	Scan method: step
None monochromator	2θmin = 5°, 2θmax = 155°, 2θstep = 0.1°
Specimen mounting: Polycrystalline pellets without container

Refinement

Rp = ?	Profile function: pseudo-Voigt
Rwp = 0.079	32 parameters
Rexp = 0.02
χ^2 = NOT FOUND	Background function: 12-parameter polynomial
1500 data points	Preferred orientation correction: no
Excluded region(s): 5-25, 150-155

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ce	0	0	0	0.0114 (5)*	0.4943
Zr	0	0	0	0.0114 (5)*	0.5022
Hf	0	0	0	0.0114 (5)*	0.0035
O	0	0.50000	0.2184 (2)	0.0201 (5)*

Geometric parameters (Å, º)

Ce—O	2.1970 (6)	Zr—O	2.1970 (6)
Ce—O—Zr	116.11 (9)

(772K) cerium zirconiuim oxide

Crystal data

Ce0.4943Hf0.0035O2Zr0.5022	Dx = 6.574 Mg m^−3
Mr = 147.70	Neutron radiation, λ = 1.81430 (7) Å
Tetragonal, P42/nmc	T = 772 K
a = 3.7386 (3) Å	yellow
c = 5.3381 (4) Å	cylinder, 76 × 19 mm
V = 74.61 (1) Å^3	Specimen preparation: Prepared at 1973 K and 100 kPa
Z = 2

Data collection

150 detector system HERMES diffractometer	Data collection mode: transmission
Radiation source: neutron	Scan method: step
None monochromator	2θmin = 5°, 2θmax = 155°, 2θstep = 0.1°
Specimen mounting: Polycrystalline pellets without container

Refinement

Rp = ?	Profile function: pseudo-Voigt
Rwp = 0.083	32 parameters
Rexp = 0.02
χ^2 = NOT FOUND	Background function: 12-parameter polynomial
1500 data points	Preferred orientation correction: no
Excluded region(s): 5-25, 150-155

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ce	0	0	0	0.0146 (6)*	0.4943
Zr	0	0	0	0.0146 (6)*	0.5022
Hf	0	0	0	0.0146 (6)*	0.0035
O	0	0.50000	0.2179 (2)	0.0254 (6)*

Geometric parameters (Å, º)

Ce—O	2.2018 (7)	Zr—O	2.2018 (7)
Ce—O—Zr	116.21 (9)

(1034K) cerium zirconiuim oxide

Crystal data

Ce0.4943Hf0.0035O2Zr0.5022	Dx = 6.511 Mg m^−3
Mr = 147.70	Neutron radiation, λ = 1.81430 (7) Å
Tetragonal, P42/nmc	T = 1034 K
a = 3.7503 (3) Å	yellow
c = 5.3564 (5) Å	cylinder, 76 × 19 mm
V = 75.34 (1) Å^3	Specimen preparation: Prepared at 1973 K and 100 kPa
Z = 2

Data collection

150 detector system HERMES diffractometer	Data collection mode: transmission
Radiation source: neutron	Scan method: step
None monochromator	2θmin = 5°, 2θmax = 155°, 2θstep = 0.1°
Specimen mounting: Polycrystalline pellets without container

Refinement

Rp = ?	Profile function: pseudo-Voigt
Rwp = 0.075	32 parameters
Rexp = 0.02
χ^2 = NOT FOUND	Background function: 12-parameter polynomial
1500 data points	Preferred orientation correction: no
Excluded region(s): 5-25, 150-155

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ce	0	0	0	0.0200 (6)*	0.4943
Zr	0	0	0	0.0200 (6)*	0.5022
Hf	0	0	0	0.0200 (6)*	0.0035
O	0	0.50000	0.2170 (2)	0.0333 (6)*

Geometric parameters (Å, º)

Ce—O	2.2063 (8)	Zr—O	2.2063 (8)
Ce—O—Zr	116.40 (10)

(1291K) cerium zirconiuim oxide

Crystal data

Ce0.4943Hf0.0035O2Zr0.5022	Dx = 6.442 Mg m^−3
Mr = 147.70	Neutron radiation, λ = 1.81430 (7) Å
Tetragonal, P42/nmc	T = 1291 K
a = 3.7640 (3) Å	yellow
c = 5.3745 (5) Å	cylinder, 76 × 19 mm
V = 76.14 (1) Å^3	Specimen preparation: Prepared at 1973 K and 100 kPa
Z = 2

Data collection

150 detector system HERMES diffractometer	Data collection mode: transmission
Radiation source: neutron	Scan method: step
None monochromator	2θmin = 5°, 2θmax = 155°, 2θstep = 0.1°
Specimen mounting: Polycrystalline pellets without container

Refinement

Rp = ?	Profile function: pseudo-Voigt
Rwp = 0.069	32 parameters
Rexp = 0.02
χ^2 = NOT FOUND	Background function: 12-parameter polynomial
1500 data points	Preferred orientation correction: no
Excluded region(s): 5-25, 150-155

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ce	0	0	0	0.0262 (7)*	0.4943
Zr	0	0	0	0.0262 (7)*	0.5022
Hf	0	0	0	0.0262 (7)*	0.0035
O	0	0.50000	0.2170 (2)	0.0442 (7)*

Geometric parameters (Å, º)

Ce—O	2.2142 (8)	Zr—O	2.2142 (8)
Ce—O—Zr	116.41 (10)

(1542K) cerium zirconiuim oxide

Crystal data

Ce0.4943Hf0.0035O2Zr0.5022	Dx = 6.383 Mg m^−3
Mr = 147.70	Neutron radiation, λ = 1.81430 (7) Å
Tetragonal, P42/nmc	T = 1542 K
a = 3.7781 (4) Å	yellow
c = 5.3833 (7) Å	cylinder, 76 × 19 mm
V = 76.84 (2) Å^3	Specimen preparation: Prepared at 1973 K and 100 kPa
Z = 2

Data collection

150 detector system HERMES diffractometer	Data collection mode: transmission
Radiation source: neutron	Scan method: step
None monochromator	2θmin = 5°, 2θmax = 155°, 2θstep = 0.1°
Specimen mounting: Polycrystalline pellets without container

Refinement

Rp = ?	Profile function: pseudo-Voigt
Rwp = 0.072	32 parameters
Rexp = 0.02
χ^2 = NOT FOUND	Background function: 12-parameter polynomial
1500 data points	Preferred orientation correction: no
Excluded region(s): 5-25, 150-155

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ce	0	0	0	0.0330 (9)*	0.4943
Zr	0	0	0	0.0330 (9)*	0.5022
Hf	0	0	0	0.0330 (9)*	0.0035
O	0	0.50000	0.2199 (3)	0.0587 (10)*

Geometric parameters (Å, º)

Ce—O	2.2296 (11)	Zr—O	2.2296 (11)
Ce—O—Zr	115.83 (12)

(1831K) cerium zirconiuim oxide

Crystal data

Ce0.4943Hf0.0035O2Zr0.5022	Dx = 6.283 Mg m^−3
Mr = 147.70	Neutron radiation, λ = 1.81430 (7) Å
Cubic, Fm3m	T = 1831 K
a = 5.3848 (7) Å	yellow
V = 156.13 (3) Å^3	cylinder, 76 × 19 mm
Z = 4	Specimen preparation: Prepared at 1973 K and 100 kPa

Data collection

150 detector system HERMES diffractometer	Data collection mode: transmission
Radiation source: neutron	Scan method: step
None monochromator	2θmin = 5°, 2θmax = 155°, 2θstep = 0.1°
Specimen mounting: Polycrystalline pellets without container

Refinement

Rp = ?	Profile function: pseudo-Voigt
Rwp = 0.082	27 parameters
Rexp = 0.02
χ^2 = NOT FOUND	Background function: 12-parameter polynomial
1500 data points	Preferred orientation correction: no
Excluded region(s): 5-25, 150-155

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ce	0	0	0	0.0315 (7)*	0.4943
Zr	0	0	0	0.0315 (7)*	0.5022
Hf	0	0	0	0.0315 (7)*	0.0035
O	0.25	0.25	0.25	0.0766 (11)*

Geometric parameters (Å, º)

Ce—O	2.3317 (2)	Zr—O	2.3317 (2)
Ce—O—Zr	109.4712 (1)

 

Footnotes

¹Supplementary data for this paper are available from the IUCr electronic archives (Reference: OG5020 ). Services for accessing these data are described at the back of the journal.