Redetermination of the crystal structures of rare-earth trirhodium diboride RERh3B2 (RE = Pr, Nd and Sm) from single-crystal X-ray data

The short RE⋯RE interatomic distance is a common structural feature of rare-earth trirhodium diborides RERh3B2 (Pr, Nd, and Sm). The crystal-structure redeterminations using single-crystal X-ray data revealed that the displacement ellipsoids of Rh and RE atoms elongated along the c axis are attributed to the unusually short RE⋯RE interatomic distances. Moreover, the anisotropic ellipsoids of Rh and RE could be associated with the appearance of disordered La1–x Rh3B2-type and/or Nd1–x Rh x Rh3B2-type structures.


Chemical context
CeCo 3 B 2 -type RERh 3 B 2 (RE = rare-earth element) compounds exhibit anomalous ferromagnetic properties (Malik et al., 1983;Yamada et al., 2004), and the unit-cell parameters of these compounds have been reported using powder X-ray diffraction (XRD) data (Ku et al., 1980;Ku & Meisner, 1981). Higashi et al. (1987) analyzed the crystal structure of CeRh 3 B 2 by using single-crystal XRD data and discussed the characteristics of the anisotropic atomic displacement parameters (ADP) of atoms in CeRh 3 B 2 in relation to the structure. We report here the results of structural refinements using single crystals of RERh 3 B 2 (RE = Pr, Nd, and Sm) grown by the arc-melting method.

Structural commentary
The crystal structures of hexagonal RERh 3 B 2 (RE; La-Gd) compounds are isotypic with CeCo 3 B 2 and crystallize in spacegroup type P6/mmm (Kuz'ma et al., 1969). The CeCo 3 B 2 type of structure is ordered and can be derived from the CaCu 5 type of structure, whereby two distinct atoms (Rh and B) occupy the corresponding Cu sites. Each B atom is surrounded by six Rh atoms, forming a trigonal prism. Such [BRh 6 ] ISSN 2056-9890 trigonal prisms constitute a honeycomb structure and RE atoms are accommodated at the centers of the twelve [RERh 12 ] hexagonal prisms, as shown in Fig. 1. The RERh 3 B 2 type of structure can also be described as being built up of kagomé layers of Rh atoms stacked along the c axis with an stacking sequence and with B and RE atoms at the centers of the Rh triangular and hexagonal prisms, respectively.
The unit-cell parameters a and c and the unit-cell volume V of RERh 3 B 2 (RE = La-Sm) compounds are shown in Fig. 2. The decrease in unit-cell volume results from the lanthanide contraction. The lattice parameters a and c decrease and increase, respectively. These anisotropic changes in the unitcell parameters are consistent with those of a previous report using powder XRD analysis (Malik et al., 1983).
The anisotropic change in the unit-cell parameters can be explained by the change in interatomic distances due to the lanthanide contraction. The ranges of B-Rh and RE-Rh distances are 2.2129 (1)-2.2151 (1) Å and 3.1370 (1)-3.1447 (1) Å (Table 1), respectively, which are close to the values of the sums of the atomic radii (r Rh = 1.35 Å , r B = 0.85 Å , r Pr = 1.84 Å , r Nd = 1.83 Å , and r Sm = 1.81 Å ; Daane et al., 1954;Spedding et al., 1956;Zachariasen, 1973). The RE-Rh interatomic distances decrease due to the effect of the lanthanoid contraction. Rh-Rh interatomic distances in the ab plane also decrease with a decrease in RE-Rh distances. By contrast, the Rh-Rh interatomic distances along the c axis increase. This causes the [RERh 12 ] hexagonal and [BRh 6 ] trigonal prisms to shrink horizontally and stretch vertically, resulting in decreases of the volumes of the hexagonal and trigonal prisms. Therefore, the unit-cells of RERh 3 B 2 compounds change anisotropically, suggesting that the unitcell changes elastically in response to the substitution of elements of different sizes at the RE site.
The obtained ADPs for each atom are summarized in Table 2. The displacement ellipsoid of the Rh atom shows a larger anisotropy than those of the B and RE atoms, as shown in Fig. 3    Unit-cell parameters a (circles), c (squares) and unit-cell volume (triangles) of RERh 3 B 2 compounds. Closed and open marks refer to this study and previous work (Malik et al., 1983), respectively. larger than U 11 , which means that the displacement ellipsoids of Rh atoms are elongated along the c axis. The displacement ellipsoids of Rh atoms with large anisotropy correspond to the anisotropic electric resistivity of RERh 3 B 2 compounds (Yamada et al., 2004;Obiraki et al., 2006). The ADPs of RE atoms are described as displacement ellipsoids suppressed in the c axis (U 11 < U 33 ). The feature of displacement ellipsoids of Rh and RE atoms is attributed to the unusually short RE-RE interatomic distances of 3.1084 (1)-3.1190 (1) Å , which are much shorter (15%) than the distance in the metal Pr, Nd, and Sm with hexagonal close-packed structures, (i.e., 3.67, 3.66, and 3.62 Å , respectively). The short RE-RE interatomic distance is a common feature of the CeCo 3 B 2 type of structure. Anisotropy of electric or thermal conductivity is also expected to be observed in CeRh 3 B 2 compounds. The obtained anisotropic ADPs of each atom in the structures of RERh 3 B 2 compounds can be discussed in terms of the nucleation of interstitial atoms or layers in PrRh 4.8 B 2 (Higashi et al., 1988). Higashi et al. (1988) discovered a new layered structure, namely, PrRh 4.8 B 2 , which is regarded as a stacking variant of a modified PrRh 3 B 2 structure. The interstitial single Rh layer is positioned between the Rh kagomé layers of the modified PrRh 3 B 2 blocks. The displacement ellipsoid in the stacking direction of the Rh atom in the PrRh 3 B 2 structure implies that the Rh kagomé layer in PrRh 3 B 2 could be a base for the nucleation of interstitial atoms or layers. The appearance of disordered La 1-x Rh 3 B 2 type and/or Nd 1-x Rh x Rh 3 B 2 type of structures Vlasse et al., 1983;Ku et al., 1985) might be associated with the anisotropic ADPs of Rh and RE atoms.

Synthesis and crystallization
RERh 3 B 2 (RE = Pr, Nd, and Sm) single crystals were grown using the arc-melting method. The starting materials used were RE elements (99.9%), along with Rh (99.95%), and B (99.5%). They were weighed at an atomic ratio of (RE+3Rh+2B), and the mixtures of the starting materials were placed in an argon-arc melting furnace (ACM-01, Diavac). Each product was remelted three times to improve homogeneity. The grown crystals were composed of homogeneous RERh 3 B 2 , and the atomic ratio Rh/RE was confirmed to be 3.00 by energy dispersive X-ray spectroscopy.

Refinement details
Crystal data, data collection and structure refinement details are summarized in Table 3. A reciprocal space plot using all reflection data was in good agreement with the hexagonal lattice (a ' 5 Å and c ' 3 Å ), and there was no evidence of superstructure reflections. The refinement was conducted under the assumption that the space group type was P6/mmm, as reported by Ku et al. (1980). Based on structural reports of La 1-x Rh 3 B 2 and Nd 1-x Rh x Rh 3 B 2 , we determined whether Rh substitution and vacancies at the RE site were possible; however, the results were negative. Therefore, we concluded that the RE sites were completely occupied by RE elements. A correction for isotropic extinction was applied during the least-squares refinements. The final refinements were performed by applying anisotropic ADPs to each atom. The remaining electron densities located 0.7-0.6 Å around rhodium and RE heavy elements are censoring effects caused by the finite Fourier series. Displacement ellipsoids of each atom in NdRh 3 B 2 , with displacement ellipsoids drawn at the 99% probability level. Table 2 Atomic displacement parameters of RE, Rh, and B atoms in RERh 3 B 2 (RE = Pr, Nd, and Sm).   software used to prepare material for publication: publCIF (Westrip, 2010).

Special details
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Crystal data
NdRh 3  Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å 2 ) x y z U iso */U eq Nd1 0.000000 0.000000 0.000000 0.00818 (9)   Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.