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Acta Crystallogr Sect E Struct Rep Online. 2010 December 1; 66(Pt 12): i80.
Published online 2010 November 17. doi:  10.1107/S1600536810046593
PMCID: PMC3011423

(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.

Related literature

For related compounds, see: non-centrosymmetric I41 structure of Ca11Re4O24 (Jeitschko et al., 1998 [triangle]); centrosymmetric I41/a structures of Sr11Re4O24 (Bramnik et al., 2000 [triangle]) and Ba11Os4O24 (Wakeshima & Hinatsu, 2005 [triangle]); centrosymmetric I2/a structure of Sr11Os4O24 (Tomaszewska & Müller-Buschbaum, 1993 [triangle]). For bond-valence sums, see: Adams (2001 [triangle]); Brown (1992 [triangle]).


Crystal data

  • Ca4.175Nd6.825Ru4O24
  • M r = 1940.16
  • Tetragonal, An external file that holds a picture, illustration, etc.
Object name is e-66-00i80-efi1.jpg
  • a = 11.2426 (2) Å
  • c = 16.1043 (3) Å
  • V = 2035.52 (6) Å3
  • Z = 4
  • Mo Kα radiation
  • μ = 21.11 mm−1
  • T = 296 K
  • 0.03 × 0.03 × 0.02 mm

Data collection

  • Bruker APEXII CCD diffractometer
  • Absorption correction: numerical (SAINT; Bruker, 2008 [triangle]) T min = 0.507, T max = 0.863
  • 17423 measured reflections
  • 5779 independent reflections
  • 5453 reflections with I > 2σ(I)
  • R int = 0.019


  • R[F 2 > 2σ(F 2)] = 0.021
  • wR(F 2) = 0.047
  • S = 1.08
  • 5779 reflections
  • 125 parameters
  • Δρmax = 3.05 e Å−3
  • Δρmin = −1.86 e Å−3
  • Absolute structure: Flack (1983 [triangle]), 2535 Friedel pairs
  • Flack parameter: 0.44 (2)

Data collection: APEX2 (Bruker, 2008 [triangle]); cell refinement: SAINT (Bruker, 2008 [triangle]); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 [triangle]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008 [triangle]); molecular graphics: ORTEPII (Johnson, 1976 [triangle]); software used to prepare material for publication: publCIF (Westrip, 2010 [triangle]) and PLATON (Spek, 2009 [triangle]).

Supplementary Material

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536810046593/br2148sup1.cif

Structure factors: contains datablocks I. DOI: 10.1107/S1600536810046593/br2148Isup2.hkl

Additional supplementary materials: crystallographic information; 3D view; checkCIF report


This work was supported by the Grant-in-Aids for Scientific Research Nos. 18206071 and 22360272 from the Japan Society for the Promotion of Science. TS and JW appreciate research assistant scholarships from the Institute of Ceramics Research and Education, Nagoya Institute of Technology.

supplementary crystallographic information


The structure of (CaxNd11-x)Ru4O24 (x=4.175) 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, as shown in Fig. 1. The Ru1O6 octahedron is slightly distorted with a larger octahedral volume of 10.26 Å3 compared with Ru2O6 of 9.92 Å3. 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 Ru1O6 and Ru2O6 octahedra indicated that Ru4+ should enrich at Ru1. If we assume that the Ru1 site is occupied by Ru4+ and Ru5+, and that the Ru2 site is exclusively occupied by Ru5+, then the ratio of Ru4+:Ru5+ 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 Ru4+ and Ru5+ in almost even probabilities, whereas Ru2 is exclusively occupied by Ru5+. If Ru1 is occupied by Ru4+ and Ru5+ exactly in the equal proportion, then the mean oxidation state of Ru in the compound becomes +4.75, providing a commensurate composition Ca4Nd7Ru4O24 (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 I41, 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 Ca11Re4O24 (I41) (Jeitschko et al., 1998) in which the mean oxidation state of Re is +6.5. In contrast with the present crystal, a complete charge disproportionation into +6 and +7 presumably occurs in Ca11Re4O24 over two crystallographically independent two Re sites from the geometrical consideration. On the other hand, several centrosymmetric structures were reported for Sr11Re4O24 (I41/a) (Bramnik et al., 2000), Ba11Os4O24 (I41/a) (Wakeshima & Hinatsu, 2005) and Sr11Os4O24 (I2/a) (Tomaszewska & Müller-Buschbaum, 1993).

A difference in the tetragonal I41 and I41/a structures can be clearly seen in the substructure composed of M atoms, as shown in Fig. 2. The centrosymmetric tetragonal structures reported for Sr11Re4O24 (Bramnik et al., 2000) and Ba11Os4O24 (Wakeshima & Hinatsu, 2005) are based on the I41/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 I41/a showed an extraordinary prolate ADP ellipsoid along the c axis, as mentioned in the refinement section in detail. The I41/a split-atom model, assuming 8e (blue in Fig. 2b) instead of 4b, was better than the I41/a non-split-atom model, but still did not explain the observed weak reflections breaking the glide symmetries in I41/a. The deviation of the M7 atom site (black in Fig. 2c) at 4a in I41 from the corresponding one (yellow in Fig. 2a) in I41/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 I41/a structure in other compounds, however, may suggest a possible order-disorder transition of the present compound at elevated temperatures.


Powders of Nd2O3 (3 N, Wako chemical), RuO2 (3 N, Kojundo Chemical Laboratory Co. Ltd.) and CaCl2 (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.


A small monoclinic distortion of the body-centred tetragonal cell was reported on Sr11Os4O24 (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 I41/a was reported for similar structures in the literature, the distinction between I41 and I41/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 I41/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 residual electrons, 32 e Å-3 at 0.66 Å from M4 and -42 e Å-3 at 0.0 Å from M4, also indicated that M4 should be split. The refinement assuming a split atom model for M4 in I41/a with 68 parameters resulted in R1=0.034, which still seemed significantly worse than 0.021 for the final I41 model. The I41/a model was thus discarded in the course of refinements. Because of significantly large displacements of M7 from the ideal position in the I41/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 I41 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.

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 M11Ru4O24 (M=Ca, Nd), showing the atom labelling and with displacement ellipsoids drawn at 95% probability level.
Fig. 2.
The M atom substructures in the I41/a non-split-atom model (a), the I41/a split-atom model (b) and the I41 model (c), projected along the a axis. The fully-occupied M atom site (yellow) in (a) becomes the split-atom site (blue) in (b), and turns into ...

Crystal data

Ca4.175Nd6.825Ru4O24Dx = 6.331 Mg m3
Mr = 1940.16Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I41Cell parameters from 7875 reflections
Hall symbol: I 4bwθ = 2.2–40.0°
a = 11.2426 (2) ŵ = 21.11 mm1
c = 16.1043 (3) ÅT = 296 K
V = 2035.52 (6) Å3Block, black
Z = 40.03 × 0.03 × 0.02 mm
F(000) = 3444

Data collection

Bruker APEXII CCD diffractometer5779 independent reflections
Radiation source: fine-focus sealed tube5453 reflections with I > 2σ(I)
graphiteRint = 0.019
[var phi] and ω scansθmax = 40.0°, θmin = 2.2°
Absorption correction: numerical (SAINT; Bruker, 2008)h = −19→20
Tmin = 0.507, Tmax = 0.863k = −20→19
17423 measured reflectionsl = −29→27


Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullw = 1/[σ2(Fo2) + (0.0127P)2 + 23.2349P] where P = (Fo2 + 2Fc2)/3
R[F2 > 2σ(F2)] = 0.021(Δ/σ)max = 0.002
wR(F2) = 0.047Δρmax = 3.05 e Å3
S = 1.08Δρmin = −1.85 e Å3
5779 reflectionsExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
125 parametersExtinction coefficient: 0.000440 (12)
0 restraintsAbsolute structure: Flack (1983), 2535 Friedel pairs
Primary atom site location: structure-invariant direct methodsFlack parameter: 0.44 (2)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'s involving l.s. planes.
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > 2σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2)

xyzUiso*/UeqOcc. (<1)
Nd10.79795 (4)0.73064 (4)0.25967 (6)0.00757 (9)0.901 (3)
Nd20.20206 (4)0.76978 (4)−0.00960 (6)0.00713 (8)0.878 (3)
Nd30.29027 (5)0.97654 (5)0.16314 (7)0.00811 (11)0.599 (3)
Nd40.29060 (5)0.47661 (5)0.08656 (7)0.00821 (11)0.611 (3)
Nd50.00000.50000.00714 (9)0.0188 (3)0.422 (4)
Nd60.50001.0000−0.00729 (9)0.0158 (3)0.379 (4)
Nd70.00000.50000.21035 (9)0.0092 (2)0.047 (3)
Ca10.79795 (4)0.73064 (4)0.25967 (6)0.00757 (9)0.099 (3)
Ca20.20206 (4)0.76978 (4)−0.00960 (6)0.00713 (8)0.122 (3)
Ca30.29027 (5)0.97654 (5)0.16314 (7)0.00811 (11)0.401 (3)
Ca40.29060 (5)0.47661 (5)0.08656 (7)0.00821 (11)0.389 (3)
Ca50.00000.50000.00714 (9)0.0188 (3)0.578 (4)
Ca60.50001.0000−0.00729 (9)0.0158 (3)0.621 (4)
Ca70.00000.50000.21035 (9)0.0092 (2)0.953 (3)
Ru1−0.00013 (6)0.74968 (6)0.12491 (7)0.00535 (4)
Ru20.49979 (6)0.74990 (6)0.12500.00552 (4)
O10.1079 (4)0.6131 (4)0.0978 (3)0.0138 (7)*
O2−0.0089 (4)0.7999 (4)0.0077 (3)0.0065 (7)*
O3−0.1224 (3)0.8782 (3)0.1532 (2)0.0079 (6)*
O4−0.1468 (4)0.6608 (4)0.1179 (3)0.0121 (8)*
O50.0110 (4)0.7089 (4)0.2448 (3)0.0093 (8)*
O60.1409 (4)0.8488 (4)0.1334 (3)0.0106 (7)*
O70.3972 (4)0.6126 (4)0.1538 (3)0.0099 (7)*
O80.4113 (4)0.8283 (4)0.2162 (3)0.0086 (7)*
O90.6105 (3)0.8799 (3)0.0988 (3)0.0066 (6)*
O100.3897 (3)0.8277 (3)0.0502 (3)0.0079 (6)*
O110.6052 (4)0.6778 (4)0.2061 (3)0.0123 (8)*
O120.5873 (4)0.6714 (4)0.0346 (4)0.0094 (7)*

Atomic displacement parameters (Å2)

Nd10.00648 (15)0.00682 (15)0.00943 (15)−0.00027 (12)0.00102 (12)−0.00061 (12)
Nd20.00608 (15)0.00676 (15)0.00855 (15)−0.00038 (12)0.00078 (12)−0.00054 (12)
Nd30.0085 (2)0.00601 (19)0.0098 (2)−0.00132 (15)−0.00053 (17)0.00009 (14)
Nd40.00755 (19)0.00627 (19)0.0108 (2)−0.00106 (14)0.00007 (16)−0.00121 (14)
Nd50.0125 (5)0.0231 (6)0.0207 (5)−0.0049 (4)0.0000.000
Nd60.0196 (5)0.0088 (4)0.0189 (5)0.0093 (4)0.0000.000
Nd70.0074 (3)0.0067 (3)0.0136 (4)−0.0004 (3)0.0000.000
Ca10.00648 (15)0.00682 (15)0.00943 (15)−0.00027 (12)0.00102 (12)−0.00061 (12)
Ca20.00608 (15)0.00676 (15)0.00855 (15)−0.00038 (12)0.00078 (12)−0.00054 (12)
Ca30.0085 (2)0.00601 (19)0.0098 (2)−0.00132 (15)−0.00053 (17)0.00009 (14)
Ca40.00755 (19)0.00627 (19)0.0108 (2)−0.00106 (14)0.00007 (16)−0.00121 (14)
Ca50.0125 (5)0.0231 (6)0.0207 (5)−0.0049 (4)0.0000.000
Ca60.0196 (5)0.0088 (4)0.0189 (5)0.0093 (4)0.0000.000
Ca70.0074 (3)0.0067 (3)0.0136 (4)−0.0004 (3)0.0000.000
Ru10.00461 (7)0.00620 (7)0.00523 (7)−0.00037 (5)−0.00005 (5)0.00051 (5)
Ru20.00537 (7)0.00597 (7)0.00521 (7)0.00064 (5)−0.00009 (5)0.00053 (5)

Geometric parameters (Å, °)

Nd1—O112.406 (5)Nd5—O12.285 (4)
Nd1—O5i2.419 (5)Nd5—O1viii2.285 (4)
Nd1—O9ii2.470 (4)Nd5—O7x2.389 (4)
Nd1—O4i2.493 (5)Nd5—O7iv2.389 (4)
Nd1—O2iii2.494 (4)Nd5—O11iv2.464 (4)
Nd1—O4iii2.510 (5)Nd5—O11x2.464 (4)
Nd1—O12ii2.525 (5)Nd6—O3iv2.418 (4)
Nd1—O3i2.548 (4)Nd6—O3xi2.418 (4)
Nd1—O3iii2.764 (4)Nd6—O10v2.479 (4)
Nd2—O102.408 (4)Nd6—O102.479 (4)
Nd2—O22.412 (4)Nd6—O9v2.507 (4)
Nd2—O5iv2.467 (5)Nd6—O92.507 (4)
Nd2—O8iv2.512 (5)Nd6—O6iv2.915 (4)
Nd2—O7iv2.546 (4)Nd6—O6xi2.915 (4)
Nd2—O62.562 (5)Nd7—O2vi2.377 (4)
Nd2—O6iv2.589 (4)Nd7—O2xii2.377 (4)
Nd2—O12.686 (4)Nd7—O5viii2.416 (4)
Nd2—O1iv2.857 (4)Nd7—O52.416 (4)
Nd3—O9v2.219 (4)Nd7—O12.524 (4)
Nd3—O62.262 (4)Nd7—O1viii2.524 (4)
Nd3—O82.316 (5)Nd7—O42.865 (5)
Nd3—O12vi2.358 (5)Nd7—O4viii2.865 (5)
Nd3—O3vii2.501 (4)Ru1—O41.931 (5)
Nd3—O102.713 (4)Ru1—O61.942 (4)
Nd3—O10vi2.753 (4)Ru1—O21.973 (4)
Nd3—O5iv2.864 (4)Ru1—O51.989 (4)
Nd4—O72.225 (4)Ru1—O12.005 (4)
Nd4—O4viii2.292 (5)Ru1—O32.046 (4)
Nd4—O12ix2.314 (5)Ru2—O101.936 (4)
Nd4—O8iv2.350 (5)Ru2—O111.942 (5)
Nd4—O12.571 (4)Ru2—O121.966 (5)
Nd4—O11iv2.620 (4)Ru2—O91.965 (4)
Nd4—O11ix2.845 (4)Ru2—O71.981 (4)
Nd4—O2vi2.943 (4)Ru2—O81.981 (5)
O4—Ru1—O6176.1 (2)O10—Ru2—O11176.1 (2)
O4—Ru1—O292.84 (19)O10—Ru2—O1293.5 (2)
O6—Ru1—O286.75 (18)O11—Ru2—O1290.3 (2)
O4—Ru1—O589.49 (19)O10—Ru2—O986.29 (16)
O6—Ru1—O590.74 (19)O11—Ru2—O993.92 (18)
O2—Ru1—O5176.6 (2)O12—Ru2—O981.85 (19)
O4—Ru1—O196.22 (18)O10—Ru2—O797.22 (17)
O6—Ru1—O187.72 (17)O11—Ru2—O782.67 (18)
O2—Ru1—O192.38 (18)O12—Ru2—O796.60 (19)
O5—Ru1—O189.79 (18)O9—Ru2—O7176.3 (2)
O4—Ru1—O378.74 (16)O10—Ru2—O886.56 (19)
O6—Ru1—O397.33 (16)O11—Ru2—O889.6 (2)
O2—Ru1—O388.71 (16)O12—Ru2—O8179.7 (3)
O5—Ru1—O389.35 (17)O9—Ru2—O898.42 (18)
O1—Ru1—O3174.89 (18)O7—Ru2—O883.13 (19)

Symmetry codes: (i) x+1, y, z; (ii) y, −x+3/2, z+1/4; (iii) y, −x+1/2, z+1/4; (iv) y−1/2, −x+1, z−1/4; (v) −x+1, −y+2, z; (vi) −y+1, x+1/2, z+1/4; (vii) −x, −y+2, z; (viii) −x, −y+1, z; (ix) −x+1, −y+1, z; (x) −y+1/2, x, z−1/4; (xi) −y+3/2, x+1, z−1/4; (xii) y−1, −x+1/2, z+1/4.


Supplementary data and figures for this paper are available from the IUCr electronic archives (Reference: BR2148).


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