(CaxNd11-x)Ru4O24 (x = 4.175)

Single crystals of the title compound, calcium neodymium ruthenate, (CaxNd11-x)Ru4O24 (x = 4.175), have been grown by the flux method. The structure consists of two crystallographically independent RuO6 octahedra, which are isolated from each other and embedded in a matrix composed of the Ca and Nd atoms. There are seven M sites which accommodate the Ca and Nd atoms with different populations. Four M sites at general positions are enriched with Nd, whereas the remaining three M sites on twofold rotation axes are enriched with Ca. The coordination numbers of O atoms to the M sites range from 6 to 9. The mean oxidation state of Ru was estimated at +4.79 from the composition analysis. The title compound is non-centrosymmetric and potentially multiferroic.


Comment
The structure of (Ca x Nd 11-x )Ru 4 O 24 (x=4.175) consists of two crystallographically independent RuO 6 octahedra which are isolated from each other and embedded in a matrix composed of the Ca and Nd atoms, as shown in Fig. 1. The Ru1O 6 octahedron is slightly distorted with a larger octahedral volume of 10.26 Å 3 compared with Ru2O 6 of 9.92 Å 3 . The composition analysis indicated that the mean oxidation state of Ru was +4.79, assuming formal charges for Ca, Nd and O.
If we assume that the oxidation state of Ru is 5+, the bond valence sums (BVSs) become 4.80 valence unit (vu) for Ru1 and 5.00 vu for Ru2 (Brown, 1992;Adams, 2001). If we assume that the oxidation state of Ru is 4+, BVSs become 4.05 vu for Ru1 and 4.21 vu for Ru2. Geometrical features of the Ru1O 6 and Ru2O 6 octahedra indicated that Ru 4+ should enrich at Ru1. If we assume that the Ru1 site is occupied by Ru 4+ and Ru 5+ , and that the Ru2 site is exclusively occupied by Ru 5+ , then the ratio of Ru 4+ :Ru 5+ becomes 40:60 for Ru1 in the compound with x=4.175. The 40:60 ratio then leads BVS to 4.50 vu for the Ru1 site. This value is quite reasonable, suggesting that the crystal exhibits a partial charge disproportionation, i.e., Ru1 is occupied by Ru 4+ and Ru 5+ in almost even probabilities, whereas Ru2 is exclusively occupied by Ru 5+ . If Ru1 is occupied by Ru 4+ and Ru 5+ exactly in the equal proportion, then the mean oxidation state of Ru in the compound becomes +4.75, providing a commensurate composition Ca 4 Nd 7 Ru 4 O 24 (i.e., x=4). The present crystal is very close to this ideal one.
There are seven M sites which accommodate the Ca and Nd atoms with different populations. The M1-M4 sites are located at the Wyckoff notation, 8b of I4 1 , whereas the M5-M7 sites are at 4a. The M1-M4 sites are enriched with Nd in contrast with the Ca-rich M5-M6 sites. The M7 site is almost exclusively occupied by Ca. Coordination numbers of O around the M site are 9 for M1 and M2, 8 for M3, M4, M6 and M7, and 6 for M5. The BVSs of Nd and Ca at all M sites were 3.0±0.2 and 2.0±0.2 vu, respectively, except for M6 where BVS of Nd was 2.55 vu, a slightly lower value than usual. Since the anisotropic ADP ellipsoid of M6 was relatively large and prolate, a possible small displacement of Nd from Ca could resolve the BVS problem.
The global instability indices, defined as the root mean square of the BVS deviation for all the atoms present in the asymmetric unit (Brown, 1992), were 0.14 and 0.17 vu for the oxidation states of 5+ and 4+ for Ru, respectively. These values lay within a modest deviation of ±0.2, suggesting the legitimacy of the present structure.
The present compound is isostructural with Ca 11 Re 4 O 24 (I4 1 ) (Jeitschko et al., 1998) (Bramnik et al., 2000) and Ba 11 Os 4 O 24 (Wakeshima & Hinatsu, 2005) are based on the I4 1 /a non-split-atom model containing 4 crystallographically independent M sites (Fig. 2a). This model was quite poor for the present crystal because one M site (coloured in yellow in Fig. 2a) at 4b in I4 1 /a showed an extraordinary prolate ADP ellipsoid along the c axis, as mentioned in the refinement section in detail.
The I4 1 /a split-atom model, assuming 8e (blue in Fig. 2b) instead of 4b, was better than the I4 1 /a non-split-atom model, but still did not explain the observed weak reflections breaking the glide symmetries in I4 1 /a. The deviation of the M7 atom site (black in Fig. 2c) at 4a in I4 1 from the corresponding one (yellow in Fig. 2a) in I4 1 /a is clear. Since M7 is virtually composed of Ca in the present crystal, its small ionic radius compared with Sr or Ba could be ascribed to the symmetry breaking into the noncentrosymmetric and polar structure. The presence of I4 1 /a structure in other compounds, however, may suggest a possible order-disorder transition of the present compound at elevated temperatures.

Experimental
Powders of Nd 2 O 3 (3 N, Wako chemical), RuO 2 (3 N, Kojundo Chemical Laboratory Co. Ltd.) and CaCl 2 (95.0%, Wako chemical) were mixed together with a mole fraction of 2:1:9 with a total weight of 4.97 g and put into an alumina crucible. The crucible was then placed on alumina powder in a larger alumina crucible. The double crucible was heated in air to 1373 K at the rate of 100 K/h, held for 10 h at 1373 K, cooled at the rate of 4 K/h to 973 K, and then furnace-cooled by turning off the power. The flux component was washed away by distilled water. Crystals were found in a block shape of 30-50 µm in diameter. Energy dispersive spectroscopy indicated that the Ca:Nd ratio was 4.1:6.9 with estimated uncertainty of ±0.3, which agreed with the ratio 4.175:6.825 obtained from the structure refinement.

Refinement
A small monoclinic distortion of the body-centred tetragonal cell was reported on Sr 11 Os 4 O 24 (Tomaszewska & Müller-Buschbaum, 1993). The unconstrained refinement of the unit-cell parameters in the integration procedure by SAINT (Bruker, 2008) on the present crystal, however, gave no significant deviation from the right angle.
Since the centrosymmetric space group I4 1 /a was reported for similar structures in the literature, the distinction between I4 1 and I4 1 /a was examined on the present crystal. Systematic absence exceptions for the glide plane perpendicular to the tetragonal c axis amounted to 211 reflections in number, with the mean I/σ(I) being 2.5. The refinement assuming I4 1 /a with 65 parameters resulted in R1=0.066 for 3072 reflections with an extraordinarily prolate ADP ellipsoid along c for M4 at 4b.
The refinement assuming a split atom model for M4 in I4 1 /a with 68 parameters resulted in R1=0.034, which still seemed significantly worse than 0.021 for the final I4 1 model. The I4 1 /a model was thus discarded in the course of refinements.
Because of significantly large displacements of M7 from the ideal position in the I4 1 /a non-split-atom model, PLATON (Spek, 2009) detected any additional symmetry neither for the M atom substructure nor for the full unit cell structure.
The refinement assuming the I4 1 single domain structure resulted in R1=0.0212, S=1.077 and the Flack parameter x=0.44 (2). Another refinement assuming its enantiomer, which can be obtained by inverting the structure at the origin and subsequent shifting by b/2, resulted in R1=0.0214, S=1.082 and the Flack parameter x=0.47 (2). These results indicated that the crystal was composed of the two enantiomers with almost equal volumes.

supplementary materials sup-3
Populations of Ca and Nd at seven M sites were refined with constraints to have no vacancies. The positional and atomic displacement parameters of Ca and Nd at each site were constrained to have the same values. The fractional coordinate z of Ru2 was fixed at 0.125 to define the origin along the c axis. The highest remaining peak was 1.33 Å from M7 and the deepest hole was 0.64 Å from M5. Fig. 1. The asymmetric unit of M 11 Ru 4 O 24 (M=Ca, Nd), showing the atom labelling and with displacement ellipsoids drawn at 95% probability level. Refinement. Refinement of F 2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > 2σ(F 2 ) is used only for calculating Rfactors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.