Introduction

Minerals with the pyrochlore structure which are complex oxides with formula (Na,Ca)(Nb,Ta)O6F·nH2O, are a well-known source of the rare elements, such as tantalum and niobium, with some ancient specimens (with an estimated age of 1.4 billion years) also containing thorium or uranium. Owing to their resistance to corrosion and chemical alteration the synthetic counterparts of pyrochlores have been proposed as host materials for nuclear waste disposal, and several investigations have been performed in that regard (Ewing et al. 2004). Recent studies performed by ionic bombardment on zirconate pyrochlores of general formula Ln2Zr2O7 where Ln = lanthanide have shown a good resistance against radiation damage when compared with equivalent titanates (Lian et al. 2002). Experiments conducted with transuranium elements (249Cf, 241Am) have also confirmed the excellent crystallinity retention of zirconate compounds (Sykora et al. 2005; Belin et al. 2008). Because pyrochlore oxides Ln2Zr2O7 (where Ln = La to Gd) have low thermal conductivity and good physical/chemical resistance under thermal stress, they are also very attractive for high temperature applications such as thermal coating on metallic parts of turbines (Cao et al. 2004). In addition, they exhibit other interesting physical properties, such as ionic conductivity, and have been proposed as a candidate for high temperature solid oxide fuel cells (Wuensch et al. 2000). Structural features, synthesis procedures and practical applications of pyrochlores are described in a comprehensive, although not recent review (Subramanian et al. 1983). Under extreme conditions (high temperature, high pressure, high radiation dose), several varieties of phase transition occur in the pyrochlore structure including order–disorder transformations, amorphisation or a structural transition leading to a monoclinic phase.

Previous studies on the high pressure structural stability have been reported (Zhang et al. 2007, 2008; Kumar et al. 2008), which show a marked dependence of the phase transformations on the ratio of cationic radii r Ln3+/r Zr4+. The aim of this work is to study the structural stability under high pressure of three zirconate pyrochlores Ln2Zr2O7 (Ln = Ce, Nd and Gd). We report on the observation of a pressure-induced cubic to monoclinic phase transformation, and the determination of the compressibility parameters from high pressure X-ray diffraction data.

Structure of pyrochlore oxides

Cubic pyrochlores of general formula A2B2O7 are isometric (Fd-3m, Z = 8, a = 9–12 Å) and their structure can be described in a variety of ways. Most commonly, cubic pyrochlores are considered as having a fluorite-type structure with a double unit cell and an ordered deficiency of 1/8 of the oxygen atoms. The A-site, generally occupied by large trivalent cations (e.g. La–Gd, Pu–Cf) (Haire et al. 2002) is eightfold coordinated and located within a distorted cubic coordination polyhedron. The B-site is occupied by smaller tetravalent cations (e.g. Zr, Hf) and surrounded by six oxygen atoms in a distorted octahedron. If the origin of the unit cell is placed at the B-site, the structure is centrosymmetric and the A cations are located on the 16d Wyckoff position (1/2, 1/2, 1/2) and the B cations on the 16c site (0, 0, 0). Six of the seven O atoms are located on the 48f position (x, 1/8, 1/8), while the remaining oxygen is on an 8b site (3/8, 3/8, 3/8). The unoccupied site is on 8a (1/8, 1/8, 1/8) (oxygen vacancy). As all of the atoms, except the 48f site oxygen, are fixed by symmetry, the pyrochlore structure can be fully described as having a cubic lattice parameter, a, and the oxygen positional parameter, x of the 48f position. This latter site characterizes the distortion on the oxygen polyhedra around the two cations and defines the deviation from the ideal fluorite structure (where x = 0.375). The exact shape of the BO6 and AO8 polyhedra depend on this parameter. When x = 0.3125, the BO6 arrangement is a perfect octahedron while the AO8 polyhedra forms a distorted cube. Conversely, when x = 0.375, the BO6 octahedra are distorted and AO8 polyhedra form perfect cubes. For all, the synthetic pyrochlores reported so far, x lies between values of 0.355 and 0.309. In Fig. 1, the orange cell represents one-eighth of the pyrochlore unit cell and can be described like a defect fluorite.

Fig. 1
figure 1

Structure of the pyrochlore A2Zr2O7 (A3+= Gd3+ as an example). The black line draws the cell of the defect fluorite structure

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Experimental

Sample preparation

The compounds with Ln = Nd and Gd were both synthesized by the same aqueous route. First nitrate solutions of lanthanide Ln(NO3)3 (Alfa Aesar 99.99%) and zirconyl-oxinitrate ZrO(NO3)2·nH2O (Fluka) have been prepared and their concentration determined by gravimetry. Then, appropriate volumes of these solutions were mixed and slowly dried. The residue was calcinated in air at 1,673 K in alumina crucibles for 72 h, then reground and recalcined for 96 h at 1,173 K.

The Ce2Zr2O7 compound was obtained by solid-state reaction using high purity amounts of CeO2 and ZrN as starting materials (Popa et al. 2008; Raison et al. 2010). The mixture was ground in a Retsch zirconia ball mill (10 min at 20 Hz) and then heated in air at 1,173 K for 5 h. The resulting powder was ground again and pressed into pellets (7 mm diameter and 7–10 mm-thick disk). These were then heated in an alumina crucible under a reducing atmosphere (Ar 95% + H2 5%) at 1,873 K for 48 h in a metallic furnace. To assure a crystallographically pure Ce2Zr2O7 product, the grinding/pressing/firing cycle was repeated four times. It is worthwhile to mention that given the potential for partial oxidation of Ce3+ in air even at room temperature, the preparation and manipulation of this material must be performed under strict reductive/inert conditions as any trace of oxygen will immediately oxidize the compound.

Diffraction setup and characterization

Each compound was first characterized under normal conditions by X-ray diffraction using a high-resolution Bruker D8 X-ray diffractometer mounted in a Bragg–Brentano configuration with a curved Ge monochromator (111), a ceramic Cu X-ray tube (40 kV, 40 mA), and a Vantec position sensitive detector. A complete structural analysis was performed for each sample by the Rietveld method with the Fullprof2k suite (Rodriguez-Carvajal 1993) giving results in excellent accord with the literature values (Thomson et al. 1996; van Dijk et al. 1984; Mandal et al. 2007). The main structural data are summarized in Table 2.

The high pressure studies were performed at room temperature using a modified Bruker D8 diffractometer with focusing mirror optics, installed on a molybdenum rotating anode source at the Institute for Transuranium Elements (ITU) in Karlsruhe. X-ray wavelength and spot size at the sample position were 0.70926 Å (Mo Kα1) and 100 × 100 µm2. Diffraction images were recorded with a Bruker SMART Apex II charge-coupled device (CCD), with 1,024 × 1,024 pixel of dimensions 61 × 61 µm2. The finely ground crystalline powders were loaded into Diacell- and Betsa-type membrane diamond anvil cells (MDAC) with 300–500 µm culets.

Pre-indented steel or Inconel gaskets with 150–250 µm diameter holes were used for each sample with a ruby chip included for pressure determination by the fluorescence method (Mao and Bell 1978). Silicone oil was used as the pressure transmitting medium. Owing to its instability under air, the Ce2Zr2O7 sample was loaded under argon atmosphere into the MDAC, while no special precautions were necessary for the Nd or Gd pyrochlore compounds. Diffraction images were integrated using the ESRF FIT2D software (Hammersley et al. 1996), which generates files suitable for Rietveld refinement.

Results and discussion

Rietveld refinements of the diffraction patterns measured at each pressure have been performed for the three investigated compounds. The quality of the data was assessed by calculating weighted reliability factors (R wp) and Bragg factors (R B), R wp = {Σw i [y i (obs) − y i (calc)]2/Σy i (obs)}1/2 and R B = Σ[I hkl(obs) − I hkl(calc)]/ΣI hkl(obs). From the refinement of the profiles recorded with the D8 X-ray diffractometer, we obtained R wp < 3.10 and R B < 4.49, suggesting a good quality of the samples. Satisfactory values of R wp (R wp < 5) were also obtained from the fit of the profiles recorded at higher pressure, whereas the value of R B was found to increase with pressure from about 2–22. This shortcoming can be attributed to the small quantity of sample loaded in the pressure cell (~20 µg) and to the limited number of measurable diffraction peaks accessible through the relatively small opening angle, 2θmax, of the MDAC.

As an example, we show in Fig. 2, the diffraction profiles recorded for Nd2Zr2O7, with the two instruments, together with the corresponding calculated and difference profiles.

Fig. 2
figure 2

Rietveld plot for Nd2Zr2O7 at ambient pressure, using data collected with the D8 diffractometer (Cu anode). The difference between calculated (solid line) and experimental profiles (open circle) is given by the lowest solid line. The positions of the Bragg peaks are indicated by vertical tags. The inset shows the refinement of the data collected for the sample mounted inside an MDAC and using the ITU high pressure diffractometer (Mo anode). In this case, the diffraction profile was obtained by integrating the Debye–Scherrer rings appearing in the 2D diffraction image

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The high pressure behavior of each of the pyrochlore samples was studied up to a maximum pressure of between 30 and 50 GPa using around 20–30 increments of increasing pressure per sample. The experiments show clearly that the three compounds undergo a pressure-induced structural transition from the pyrochlore structure to a monoclinic structure (distorted fluorite-type structure) as already observed for other pyrochlore compounds (Zhang and Saxena 2005; Kumar et al. 2008). The high pressure phase is identified by some characteristic peaks, namely the Bragg reflection near 14° together with some reflections present in the range 2θ = 18°–23°, as shown in Fig. 3. After releasing pressure, all the samples became amorphous.

Fig. 3
figure 3

X-ray diffraction patterns of Ln2Zr2O7 (Ln = Ce, Nd, Gd) at different pressure values. Black curves correspond to the cubic phase. The blue curves show the appearance of a monoclinic phase as the pressure increases above a value P t1 that depends on the Ln cation. Red curves correspond to the single high pressure phase. The monoclinic phase occupies a volume that progressively increases with the pressure, until the transformation is completed at a pressure P t2. Peaks labeled by “G” are due to the gasket

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For each step of pressure, a Lebail profile matching was performed with Fullprof2k from which we deduced the lattice parameters, and the relative volumes V/V 0 (Fig. 4). The pressure data were analyzed in two different ways. In the first one, the pressure variation of the individual lattice parameters g i (for the cubic structure g i  = a) is fitted to a polynomial quadratic in P.

Fig. 4
figure 4

a Pressure dependence of the crystallographic parameter a in the cubic phase. Solid lines are a fit to a quadratic polynomial as described in the text; b pressure dependence of the normalized (to the Ce compound) unit cell volume for the cubic phase of Ln2Zr2O7 (Ln = Ce, Nd and Gd). The symbols indicate the experimental points, while the full lines represent a fit of the Birch/Murnaghan EOS

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$$ g_{i} (P) = g_{i} (0) - k_{i} g_{i} (0)P + k_{i}^{'} g_{i} (0)P^{2} $$
(1)

where k i and k′ i represents the linear compressibility along the lattice direction i.

In the second method, the relative volume V(P)/V 0 is fitted to the Birch Murnaghan equations of state (Murnaghan 1937; Birch 1947) to obtain directly the bulk modulus B 0(1/B 0 = −∂lnV/∂P) and its pressure derivative B′0 (2), (3). The results obtained by the two methods can be easily compared, as the bulk modulus B 0 is equal to 1/k v, where k v is the volume compressibility given by k v = 3 k a. To compare the results with values available in the literature, the data range for the above analysis was restricted up to 18 GPa.

$$ {\text{BIRCH}}\;P = \frac{3}{2}B_{0} \left[ {\left( {{\frac{V}{{V_{0} }}}} \right)^{{ - {\raise0.7ex\hbox{$7$} \!\mathord{\left/ {\vphantom {7 3}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$3$}}}} - \left( {{\frac{V}{{V_{0} }}}} \right)^{{ - {\raise0.7ex\hbox{$5$} \!\mathord{\left/ {\vphantom {5 3}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$3$}}}} } \right]\;\left[ {1 + \frac{3}{4}\left( {B_{0}^{'} - 4} \right)\left\{ {\left( {{\frac{V}{{V_{0} }}}} \right)^{{{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 3}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$3$}}}} - 1} \right\}} \right] $$
(2)
$$ {\text{MURNAGHAN}}\;P = {\frac{{B_{0} }}{{B_{0}^{'} }}}\left[ {\left( {{\frac{V}{{V_{0} }}}} \right)^{{ - B_{0}^{'} }} - 1} \right]$$
(3)

The experimentally determined pressure–volume behavior is shown in Fig. 4b. The two different methods of data evaluation provide values of B 0 in good agreement, as reported in Table 1. The average values of the bulk modulus (B 0 = 253, 143 and 155 GPa for the Ce, Nd and Gd compounds, respectively) indicate that all of these pyrochlores are fairly incompressible. The fit for the Gd2Zr2O7 sample is comparable to the result reported by (Kumar et al. 2008) who found (B 0 = 161.5 ± 2.2 GPa and B′0 = 9 ± 0.8). Although not fully understood, the bulk modulus of crystallized materials is in essence related to the crystallographic structure and the strength of the atomic bonds in the material. It is, therefore, somehow surprising to obtain across the series values with no general trend, linear or polynomial, because in the zirconate pyrochlore series the Ln–O bond strength follows the sequence: Gd < Sm < Nd < Ce < La.

Table 1 Overview of linear compressibility’s k a, isothermal bulk modulus (B 0), and its pressure derivative (B′0)
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In Table 2, we report the pressure at which the monoclinic phase first appears, Pt1, and also the pressure where the high pressure phase occupies the whole volume of the sample, Pt2. The transition is sluggish and both structures co-exist over a large pressure range. As shown in Fig. 5, the evolution of Pt1 and Pt2 depends on the ratio of the cation radii r Ln/r Zr, with Pt1 appearing constant with r Ln/r Zr, whereas Pt2 decreases when the radii r Ln decreases. According to the general trend observed in Fig. 5, one can reasonably expect that for the La2Zr2O7 compound, the end member of the series, the P–M transition would begin around 19 ± 2 GPa as with the other compounds and be complete by 43 ± 2 GPa.

Table 2 Overview of the high pressure structural stability of Ln2Zr2O7 pyrochlores
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Fig. 5
figure 5

Transition pressure at ambient temperature as a function of the ratio of ionic radius for the Ln2Zr2O7 compounds (Ln = Ce, Nd, Gd this work; Ln = Sm taken from reference). Black squares represent the experimental pressure of the last observed single phase pyrochlore pattern. The di-phasic region (pyrochlore + monoclinic) occurs between the two red diamonds and the pressure at which the first single phase monoclinic pattern is observed is represented by blue circles. The two solid lines are a guide to the eye showing the limits of the different regions

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In a recent paper (Zhang et al. 2008), the authors studied the phase stability of Gd2(Ti1−x Zr x )2O7 compounds with x varying from 1 to 0. The authors found that the so-called critical transition pressure, which is defined as the lowest pressure before the phase transition occurs, increases with Ti content. This critical transition pressure increases with a parabolic curvature with the rGd/r(Ti + Zr) ratio (when Ti content increases). If one reports the cationic radii ratio r Ln3+(VIII)/r Zr4+(VI) for the Ce, Nd, Sm and Gd pyrochlores on their plot, the critical transition pressure would be expected to vary from 17 ± 2 GPa for the gadolinium to 18 ± 2 GPa for the cerium. This is perfectly in accordance with our experimental results where we found Pt1 to be constant in this range, within the limits of our experimental conditions.

For the pure Gd2Zr2O7 compounds, the authors also found a domain where the two phases coexist in a pressure range of 10–15 GPa. The high pressure phase is reported to occur already at 17.6 GPa in agreement with our data, and a pure high pressure phase is observed at 37.2 GPa which is higher than our experimental value, but in the same order of magnitude (33.65 GPa). A possible explanation for this could be that the Gd/Zr ratio between the two samples is slightly different. If this ratio is not equal to 1, the transition pressure Pt2 could be affected, as one can deduce from Fig. 5. However, there is unfortunately no indication given in Zhang’s 2008 paper concerning the initial characterization of their compound. In our Rietveld refinement, attempts to refine the occupancy factors of gadolinium and zirconium did not indicate any deviation from full occupancy which means that the Gd/Zr ratio is close to one.

Two different high pressure structures are mentioned in the literature concerning the pyrochlore family. For Sm2Zr2O7 and Gd2Zr2O7 (Zhang and Saxena 2005; Zhang et al. 2007, 2008) the structure is proposed to be similar to that of the monoclinic phase (distorted related-fluorite-type) of ZrO2, while Kumar et al. (2008) reported that the high pressure structure of Gd2Zr2O7 is a double layered (La2Ti2O7 type) perovskite structure. Both of these structure types were tried in our analysis, but the best refinements were obtained using the ZrO2 structure indexed with a monoclinic cell (P21/c). Owing to the experimental limitations of using a laboratory X-ray source to determine a monoclinic structure at high pressure, a future synchrotron radiation experiment would be beneficial for an unambiguous determination of the exact structure.

The volume of the monoclinic cell observed at high pressures and the volume of the elementary cell volume at lower pressures are plotted in Fig. 6 for Gd2Zr2O7 and Nd2Zr2O7. Unfortunately, the cell volume for the cerium compound could not be determined with sufficient accuracy due to broadening of the diffraction peaks. A volume decrease of 18–19% was observed across the P–M phase transition for the Nd2Zr2O7 and Gd2Zr2O7 compounds, close to the values reported for Sm2Zr2O7 (Zhang et al. 2007, 2008).

Fig. 6
figure 6

Pressure dependence of the unit cell volume for Nd2Zr2O7 (triangle) and Gd2Zr2O7 (square). The volumes corresponding to the pyrochlore structure are represented with full symbols, while the empty symbols stand for the monoclinic phase

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Conclusion

The high pressure behavior of three zirconate pyrochlore compounds has been comprehensively examined by X-ray diffraction up to 50 GPa. Structural transitions leading to a monoclinic phase at high pressure were observed in all samples with the transition pressure dependant on the cationic radii ratio. The compressibility of the low pressure cubic phase was determined, revealing no general trend in bulk moduli across the members of the series investigated. For future studies, the determination of precise atomic positional parameters for the high pressure monoclinic phase of these pyrochlores would require the use of a synchrotron source, which in addition would allow verification of whether a low pressure order–disorder transition occurs, as in the case of the pyrochlore titanates.