Fingerprint of local disorder in long range ordered isometric pyrochlores

The detailed characterization of local order and disorder in isometric A2B2O7 crystalline pyrochlores is of significant importance in view of their wide range and sensitive technological applications. Nevertheless, much remains to be understood concerning their atomic scale structures. Here we specifically pinpoint local order and disorder in four stoichiometric Ln2Zr2O7 (Ln = La, Nd, Sm and Eu) pyrochlores using a combination of three standard easily available laboratory techniques: XRD, 17O solid-state MAS NMR and Raman spectroscopy. The evolution of the oxygen sub-lattice identifies specific features (extra 17O NMR signals and Raman bands) which undoubtedly reveal local oxygen order and disorder in these stoichiometric long range ordered crystalline pyrochlores. These results complete the understanding of the atomic scale in these stoichiometric pyrochlores necessitating the need for new microscopic structural models.

fluorite structure at the large scale 27 . Unfortunately, due to their high neutron absorption cross sections, this technique cannot be applied to the Ln 2 Zr 2 O 7 with Ln = Sm, Eu and Gd 35 . Though other techniques have been used to probe the local order and disorder in this Ln 2 Zr 2 O 7 pyrochlore series at different length scales, they have suffered by virtue of their indirect approach and disorder was unveiled by detecting an anomaly in the trend of the resulting parameters over the full series of pyrochlores. Thus, Zr-XANES yields a variation of the Zr-coordination number 35 and Raman spectroscopy a broadening of the bands 31 . In the present communication, the structural complexity has been unravelled by XRD, to probe the long range order, and 17 O MAS NMR and Raman spectroscopy to elucidate changes in the oxygen local environment of these four stoichiometric rare earth pyrochlores. Thereby, it was possible to detect directly this important subtle order-to-disorder variation by probing the local O-atom environment. The observations reported here are of acute importance as they form the basis for the complete understanding of what is essentially "an ordered pyrochlore structure".

Results
The XRD patterns of the four well crystallized pyrochlores are presented in Fig. 1 confirming their purity (a small non-characterized impurity was identified in the pattern of La 2 Zr 2 O 7 ). The patterns possess the characteristic superstructure peaks of cubic pyrochlore, Fd-3m and the lattice parameters of 10.8019(1), 10.6911(1), 10.5753(1) and 10.5533(1) Å were obtained for respectively La 2 Zr 2 O 7 , Nd 2 Zr 2 O 7 , Sm 2 Zr 2 O 7 and Eu 2 Zr 2 O 7 . These values are in general agreement with the one previously published 26,34,[36][37][38][39][40][41][42][43][44] and, especially with stoichiometric pyrochlores. As expected, there is an increase of the lattice parameter as a function of the ionic radii (Supplementary Figure 2 Figure 3) for peak B (C Q = 121 kHz, η Q = 0.7) and D (C Q = 635 kHz, η Q = 0.8) are detected. This characteristic pattern of spinning sidebands is linked to local distortions around the O site as described elsewhere 45,46 . Therefore Peaks B and D can be both attributed to the (O2, 48f) site and consequently, peaks A and C to the (O1, 8b) site. For La 2 Zr 2 O 7 , this attribution is confirmed by the relative intensity between peaks B and A which is 6:1 as expected from its crystal structure. Even 3 (H) ppm with relative intensities of 13, 61, 12 and 14%. Due to its 17 O NMR shift, peak H can be attributed to oxygen atoms in the (O1, 8b) site (See Supplementary note 1) while peak F can only be attributed to (O2, 48f) due to its high relative intensity and important spinning sideband pattern. Taking the most obvious features in the Eu 2 Zr 2 O 7 spectrum, three main peaks can be identified at −196 (I), −767.5 (J) and −3033.3 (K) ppm. This sample exhibits important spectral broadening due in part to the paramagnetic effect as observed in other Eu-based materials [51][52][53] . Considering its 17 O NMR shift, peak K can be attributed to O atoms at the (O1, 8b) site (See Supplementary note 1). Even if the current spectrum is qualitative, peaks I and J are derived from local disorder with one of them emanating from the (O2, 48 f) sites. For both samples, spinning sidebands are detected for all the peaks: peak E (C Q = 1412 kHz, η Q = 0.7), peak F (C Q = 756 kHz, η Q = 0.5), peak G (C Q = 1067 kHz, η Q = 0.6), peak H(C Q = 1067 kHz, η Q = 0.6), peak I (C Q = 874 kHz, η Q = 1), peak J (C Q = 1237.57 kHz, η Q = 1) and peak K (C Q = 528 kHz, η Q = 0.8).
The Raman spectrum of Sm 2 Zr 2 O 7 seems very similar to that of the La and Nd counterparts, but, an additional band must be introduced at 191 cm −1 (A*) to reproduce the low frequency tail of the spectrum. The remaining five bands at 296, 336, 392, 523 and 588 cm −1 are designated as B*, C*, D*, G* and H*. For Eu 2 Zr 2 O 7 , six bands at 198, 296, 332, 390, 533 and 594 cm −1 attributed to A*, B*, C*, D*, G* and H* were also identified, albeit with a substantial increase of the line broadening. The fitted Raman band parameters have been plotted in Fig. 4.

Discussion
The main finding of this research is the specific identification of local disorder in each of these pyrochlores, whose derivation presented in Supplementary note 2 has been achieved on collective examination of the entire series, as commonly done. We can now start our discussion with 17 O MAS NMR as it is a proven powerful tool to probe local order and disorder in crystalline pyrochlore 54 . The fully ordered stoichiometric pyrochlore structure possesses only two distinct crystallographic O sites; the presence of more than two O signals on the 17 O MAS NMR spectrum immediately signifies a local disorder at the atomic scale. This is clearly observed for Sm 2 Zr 2 O 7 and Eu 2 Zr 2 O 7 for which no impurities were detected by XRD. As the 17 O MAS NMR spectrum of Sm 2 Zr 2 O 7 was acquired under quantitative conditions we give it more attention. The intensity ratio of peaks (E, F, and G): peak H is 6:1, i.e. exactly the ratio expected between the two different crystallographic sites (O1, 8b) and (O2, 48f). The intensities of peak E, G and H are very similar, but cannot be simply ascribed to a depopulation of the (O2, 48f) sites into the vacant (V O , 8a) sites, as this would imply full occupancy of the vacancies. Therefore, the mechanism underlying the disordering seems to be more complex than expected for a simple depopulation of the (O2, 48f) sites. This NMR observation could have been due to the presence of a cationic disorder in our samples, but, the fitting of the XRD patterns considering this type of disorder did not improve the Rietveld refinement (not shown). The increase of disorder is also seen when comparing the 17 O MAS NMR spectra of the two ordered pyrochlores with those of the two disordered pyrochlores, one can notice the apparition of spinning sidebands for peak H and K (contrary to peaks A and C) which correspond to the oxygen at the (O1, 8b) sites. This reveals an increase of the local distortion around the O atoms (See Supplementary note 3) 55 . As the cation size decreases through the series, a steric effect cannot be at the origin of these bond distortions, but in contrast, it can be linked to an  increasing disorder in the second coordination shell. A first glance of answer can nevertheless be given to understand this anionic disorder based on the previous Zr-XANES results which showed a change of coordination number through the Ln 2 Zr 2 O 7 series associated to a growing disorder through the series 35 .
Accordingly, the second and most convincing proof is found in the Raman vibrational mode assignment, a key pointer in the understanding of the competition between order and disorder. Alarmingly, many discrepancies exist in published assignments thereof [56][57][58] . The most common method to interpret the Raman data relies on the spectral comparison with each other and between different pyrochlore families [42][43][44] . Here, we take an alternative approach and attribute the different modes by comparing the spectra through this Ln 2 Zr 2 O 7 series. The five characteristic Raman bands detected for the ordered La 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 have similar frequencies as those previously published supporting the presence of local order and their good stoichiometry 28,59 . Importantly, the energy of all modes seems to be independent of the lanthanide cation except for the E* mode for which a clear upshift is observed when substituting La with Nd (see Fig. 4 and Supplementary Figure 4). This is in good agreement with the atomic displacement analysis 58 for these modes and supports their attribution to pure oxygen motions, except for the E* mode where a small contribution from Ln 3+ might be present. Armed with a characterization of the Raman spectrum of these two ordered pyrochlores, we analysed those of the disordered pyrochlores. We want to stress that as the main topic of this paper is to show the presence of local disorder at the atomic scale, we did not attempt a full characterization of the Raman modes. We therefore focus our discussion on modes A*, E*, F*, G* and H* which differ between ordered and disordered pyrochlore spectra. As mode A* appears in the spectrum of Sm 2 Zr 2 O 7 and Eu 2 Zr 2 O 7 (its absence is also confirmed in their equivalent 16 O Raman spectra reported in literature 28,43,44 ) it is unlikely that neither involves (O1, 8b) nor (O2, 48f) oxygens, since both sites are fully occupied in the ideal pyrochlore. To better understand the mode A*, we have to pursue our discussion of the other Raman bands. Our main observation is that G* and H* modes correspond to E* and F* modes, but shifted to higher Raman frequencies. Though, the shift from E* to G* can be explained by the decrease of the lanthanide ionic radii (or increase of the force-constant) the 70 cm −1 upshift of F* to H* is unlikely to be caused by the same effect. When considering the Raman data for La 2 Zr 2 O 7 to Nd 2 Zr 2 O 7 , there is the previously discussed upshift of mode E* to slightly higher frequency which continues for Sm 2 Zr 2 O 7 (Supplementary Figure 4). But, in the case of mode F*, there is no variation of the Raman band energy from La 2 Zr 2 O 7 to Nd 2 Zr 2 O 7 which should, according to the same logic, lead to an upshift of mode F* of at least 10 cm −1 . To support this statement, we took account of the previously published force constant change which confirms that the predicted splitting should not exceed 10 to 20 cm −1 60 . The difference in frequencies observed here between F* and H* is therefore far too high. Finally, ab initio calculations also seem to predict a mode at 617 cm −1 but, unfortunately, for the optically inactive F 1g symmetry instead of the F 2g symmetry expected for mode F* 61 . Based on all these evidences, we can safely propose that the two well resolved modes E* and F* in Nd 2 Zr 2 O 7 and La 2 Zr 2 O 7 actually merge to form the broad band G* for Sm 2 Zr 2 O 7 and this "merging" is caused by the apparition of the anionic disorder. While mode G* belongs to the ideal pyrochlore structure, it is definitely not the case for mode H* whose observation might be a result of symmetry breaking due to an inherent disorder in the O sites. Therefore, this band is derived from the Zr-O stretching motion modified due to interstitials in the Zr-environment. With this in mind, we can come back on the low frequency mode A* which can be attributed to the vibration of oxygen atoms at the centre of Zr 4 O tetrahedral due to interstitial O atoms.
The important redefinition of both these additional vibrational Raman bands inaccurately assigned in the literature, in addition to the 17 O MAS NMR analysis, specifically describe the inherent O local order in stoichiometric La 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 and disorder in stoichiometric Sm 2 Zr 2 O 7 and Eu 2 Zr 2 O 7 . It is worth mentioning that considering the previously calculated disorder enthalpy formation (both cationic and anionic) 19,30 , both Sm 2 Zr 2 O 7 and Eu 2 Zr 2 O 7 belong to the same range of defect energy formation. Even more interesting for this same family, the Raman spectrum 31 of Gd 2 Zr 2 O 7 , which also belongs to this range of energy, possesses the specific bands that we presently clarified through the text and characteristic of disordered pyrochlore. These observations might underline the range of energy delimiting ordered from disordered stoichiometric pyrochlore. Finally, our present study can easily be extended to any pyrochlore system but also, implemented to solid-solution or to their modelisation using computational methods. We can safely state that it will help assisting in the construction of a complete understanding of these complex and of high technological importance systems.  33,62 . These pure lanthanide zirconates with pyrochlore structure were further enriched in 17 O as it is the only active nucleus for NMR and possesses a low natural abundance (0.04%) 63 . To do so, the materials were enriched by the gas exchanged (O 2 enriched at 70% mixed with Ar) technique by putting the powders during 24 h at 800 °C in a furnace. These samples were used for analysis by XRD, Raman and 17 O MAS NMR in order to avoid the uncertainties led by analysing different samples.

Synthesis.
Scientific RepoRts | 7: 12269 | DOI:10.1038/s41598-017-12544-8 XRD. The patterns of the three 17 O-enriched well crystallized samples (Fig. 1.) were obtained at room temperature on 20 mg of a powdered sample. A Bruker D8 Advance diffractometer (Cu Kα radiation, 40 kV, and 40 mA) with a Bragg−Brentano θ/2θ configuration were used for the analysis. This diffractometer is equipped with a curved Ge monochromator (111) and a Lynxeye linear position-sensitive. The powder patterns were recorded using a step size of 0.0197° across the angular range 10 ° ≤ 2θ ≤ 120 °. Structural analyses were performed by the Rietveld method using Jana2006 software 64 . Peak profile fitting was achieved musing Pseudo-Voigt functions.
17 O MAS NMR. The spectra were acquired on a Bruker 9.4 T at the Larmor frequency of 54.25 MHz. To obtain quantitative results for La 2 Zr 2 O 7 and Sm 2 Zr 2 O 7 , the spectra were acquired using a one pulse experiment with a very short length of 1 μs 65 . For Eu 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 , a Hahn echo was used with pulse durations of 3 μs (π/2) and 6 μs (π) with an echo delay of 16.3 μs (1 rotor period). In addition, two offsets were needed to acquire the full spectrum (to be sure that all the peaks were detected, we performed the experiments with several other offsets but here, we only show at the resonating frequency of the two relevant peaks). Because a Hahn echo experiment was used and the spectra acquired at two offsets, the data are only qualitative. All spectra were externally referenced to 17 O enriched H 2 O set at 0 ppm. They were fitted with the DMfit software 66 using the quad first model and the quadrupolar coupling constant, C Q , and the quadrupolar asymmetry parameter, η Q , were extracted from the 1D MAS NMR spectra.
Raman spectroscopy. The experiments were performed at room temperature with a Horiba Jobin-Yvon T64000 spectrometer equipped with 1800 gr/mm grating. A 100× objective was used to focus the incident laser operating at 647 nm and collect the backscattered light. Extreme care was taken to avoid sample damage or laser induced heating. Measurements were performed at ~1 mW incident power. No significant change in the spectra was observed in this power range. It must be pointed out that as the samples are enriched in 17 O, the isotopic shifts for all bands is about −1 to −2% which is in very good agreement with the calculated shift for one-phonon excitation and partial substitution (20 to 30% 17  where ω i is the phonon frequency.
Data availability statement. The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.