Table 1. The list of the RE₅T₄X₁₀ (RE = Rare earth, T = Co, Rh, Ir, Os and Ni; X = Si, Ge and Sn) compounds reported.

^*This work.

The following reagents were used as purchased without further purification: Yb (in the form of metal pieces cut from metal chunk, 99.99% Alfa Aesar), Co (powder 99.99% Alfa Aesar), Ge (pieces, 99.999% Alfa Aesar) and In (shots, 99.99% Alfa-Aesar). High quality single crystals of Yb₅Co₄Ge₁₀ were obtained by combining ytterbium metal (0.3 g), cobalt powder (0.1 g), germanium (0.3) and indium shots (2 g) in an alumina crucible. The crucible was placed in a 13 mm fused silica tube which was flame sealed under a vacuum of 10^–5 torr, to prevent oxidation during heating. The reactants were then heated to 1173 K over 8 h, and maintained at that temperature for 2 h to allow proper homogenization, then cooled down to 1073 K in 2 h and kept at this temperature for 72 h. Finally, the sample was allowed to cool slowly to 303 K over 48 hrs. No reactions with the alumina crucible material could be detected. The reaction product was isolated from the excess indium flux by heating at 673 K and subsequently centrifuging through a coarse frit. Any remaining flux was removed by immersion and sonication in glacial acetic acid for 24 h. The final crystalline product was rinsed with water and dried with acetone. A few small gray rod-shaped crystals of Yb₅Co₄Ge₁₀ carefully selected for the elemental analysis and single crystal XRD data collection. Yb₅Co₄Ge₁₀ is stable in air and no decomposition was observed even after several months.

Semi-quantitative microanalyses were performed on the single crystals obtained from the flux techniques using a scanning Leica 220i electron microscope (SEM) equipped with Bruker 129 eV energy dispersive X-ray analyzer (EDS). Data were acquired with an accelerating voltage of 20 kV and in 60 s accumulation time. The EDS analysis performed on visibly clean surfaces of the single crystals obtained from the flux method indicated that the atomic composition was close to 5:4:10 in good agreement with the composition obtained from the single crystal data refinement. A typical SEM image of rod-like crystals of Yb₅Co₄Ge₁₀ grown from the flux synthesis is shown in Figure 1.

Single crystal structural data of Yb₅Co₄Ge₁₀ was collected at room temperature on rod shaped single crystals using a Bruker Smart-CCD diffractometer equipped with

a normal focus, 2.4 kW sealed tube X-ray source with graphite monochromatic Mo-Kα radiation (λ = 0.71073 Å) operating at 50 kV and 30 mA, with ω scan mode. A crystal of suitable size (0.5 × 0.05 × 0.05 mm) was cut from a small rod shape crystal and mounted on a thin glass (~0.1 mm) fiber with commercially available super glue. A full sphere of 60 frames was acquired up to 57.87˚ in 2θ. The individual frames were measured with w steps of 0.50˚ and an exposure time of 20 s per frame. The programme SAINT [40] was used for integration of diffraction profiles and absorption correction was made with SADABS programme [41]. The systematic absences were leading to the centrosymmetric space group P4/mbm. However, the Platon program within WinGx system, ver. 1.80.05 [42] was used to check the additional symmetry, and this was not suggesting any additional symmetry. The structure was solved by SHELXS 97 [43] and refined by a full matrix least-squares method using SHELXL [44] with anisotropic atomic displacement parameters for all atoms. Packing diagrams were generated with Diamond [45]. In order to check for the correct composition, the occupancy parameters were refined in a separate series of least-squares cycles. All bond lengths are within the acceptable range compared to the theoretical values. Details of the crystallographic data are given in Tables 2 to 5.

Table 2. Crystal data and structure refinement for Yb₅Co₄Ge₁₀.

^aR = Σ||F_o| − |F_c||/Σ|F_o|, wR = {Σ[w(|F_o|² − |F_c|²)²]/Σ[w(|F_o|⁴)]^1/2 and calc w = 1/[σ²(Fo²) + (0.0318P)² + 111.1197P] where P = (Fo² + 2Fc²)/3.

Table 3. Atomic coordinates (×10⁴) and equivalent isotropic displacement parameters (Ų × 10³) for Yb₅Co₄Ge₁₀ at 296(2) K with estimated standard deviations in parentheses.

^*U_eq is defined as one third of the trace of the orthogonalized U_ij tensor.

Table 4. Anisotropic displacement parameters (Ų × 10³) for Yb₅Co₄Ge₁₀ with estimated standard deviations in parentheses.

The anisotropic displacement factor exponent takes the form: −2π²[h²a*²U₁₁ + ∙∙∙ + 2hka*b*U₁₂].

Table 5. Selected bond lengths [Å] for Yb₅Co₄Ge₁₀ at 296(2) K with estimated standard deviations in parentheses.

The atomic parameters of Sc₅Co₄Si₁₀ [1] were taken as starting parameters and the structure was refined using SHELXL-97 (full-matrix least-squares on F²) [43] with anisotropic atomic displacement parameters for all atoms. As a check for the correct composition, the occupancy parameters were refined in a separate series of leastsquares cycles. Our data confirms the previous X-ray powder data [5], but the atomic positions have been refined with higher precision. Single crystals of Yb₅Co₄Ge₁₀ from different synthesis batches were used for the data collection. In the first step of refinement on the single crystal data collected shows that Yb₅Co₄Ge₁₀ crystallizes in a primitive tetragonal lattice (P4/mbm) within the Sc₅Co₄Si₁₀ type structure and lattice constants are a = b = 12.6369 (18) Å and c = 4.1378 (8) Å. This refinement resulted in seven crystallographical positions (three Yb, one Co and three Ge) in the Yb₅Co₄Ge₁₀ structure. The data collection and structure refinement for Yb₅Co₄Ge₁₀ are listed in Table 2.

The standard atomic positions and isotropic atomic displacement parameters of this compound are collected in Table 3. The anisotropic displacement parameters and important bond lengths are listed in Tables 4 and 5, respectively. Further information on the structure refinements is available from: Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen (Germany), by quoting the Registry Nos. CSD-425832.

The crystal structure of Yb₅Co₄Ge₁₀ along c-axis is shown in Figure 2.

Yb₅Co₄Ge₁₀ crystallizes in the primitive tetragonal Sc₅Co₄Si₁₀ type structure (space group P4/mbm). Crystal structure of Yb₅Co₄Ge₁₀ is composed of a complex [Co₄Ge₁₂] polyanion network with three types of one dimensional channels, showed along the c-axis (Figure 2), in which Yb atoms are embedded. The cages are shared through the corners of Co and Ge form pentagonal and hexagonal rings and resulted in a three dimensional network. The pentagonal and hexagonal rings are occupied with Yb2 and Yb3 atoms, respectively. These rings are connected through Co and Ge in ab plane and resulted in another large 8-membered ring, which is occupied by large Yb1 atoms. A detailed crystal structure description of the compounds crystallizing in the Sc₅Co₄Si₁₀ was reported as an example of the Yb₅Ni₄Ge₁₀ compound [2].

Crystallographically there are three different Yb-atoms are present in Yb₅Co₄Ge₁₀. All three Yb-coordination environments are significantly different. The Yb1 atom is located at the center of a cage consisting of 12 Ge and 4 Co atoms forming a cage as Yb[Ge₁₂Co₄], Yb2 atoms are surrounded by eight Ge and four Co forming as Yb [Ge₈Co₄] and Yb3 atoms are surrounded by fourteen atoms, Yb[Ge₁₀Co₄]. The Yb-Ge and Yb-Co bond lengths in Yb₅Co₄Ge₁₀ are in the wide range (2.8218 (9) Å to 3.2138 (10) Å for Yb-Ge and 2.9815 (11) Å to 3.2488 (12) Å for Yb-Co) due to the different size of Yb coordination environments. The average distance obtained for Yb3-Co, 3.2488 (12) Å, is longer than the corresponding distance for Yb1-Co and Yb2-Co with 3.1167 (16) and 2.9815 (11) Å, respectively. Similarly, the average bond distance for the Yb3-Ge is 3.1754 Å, is also longer than the corresponding distance for Yb1-Ge and Yb2-Ge with 3.0175 and 2.9343 Å, respectively. Similar kinds of bonding behavior were observed in the mixed valent Yb₅Ni₄Ge₁₀ as well [2]. Since Katoh et al. observed the mixed valent Yb in Yb₅Co₄Ge₁₀ based on the magnetic susceptibility measurements [22], our crystallographic data suggests the Yb1 and Yb2 atoms are mostly in the trivalent state and Yb3 in the divalent state. Considering the fact that divalent Yb is larger in size (1.86 Å) [46,47] compared to trivalent Yb (1.66 Å) [46,47], Yb3 prefer to be in large cage and others (Yb1 and Yb2) are in the smaller cages.

We also compared the covalent radii and the unit cell volume four Yb based compounds reported in this family, as shown in Figure 3. The cell volume of the compounds increases as the covalent radii of the transition metals except in case of Co where there is drop in the cell volume. The drop in the cell volume for Co analogue is due to the major contribution of small size trivalent Yb atoms which was already confirmed in the magnetic susceptibility of two compounds where Yb₅Ni₄Ge₁₀ has only 78% Yb³⁺ and Yb₅Co₄Ge₁₀ has 94% Yb³⁺.

The comparison of covalent radii in Figure 3 also suggests that the metals like Fe, Ru, Os, Pt and Pd are

suitable candidates for the formation Yb₅T₄Ge₁₀ compounds because the covalent radii of these metals are within the range of the reported compounds. This assumption can also be supported by the fact that Yb has the ability to show mixed valent compounds to stabilize the compounds.