Crystal structure of Dy₁₁Ge_4.33In_5.67 and Tm₁₁Ge₄In₆ from X-ray single-crystal and powder data

2.1 Synthesis

The samples with the initial compositions RE₅₅Ge₂₀In₂₅ (RE = Dy and Tm) were prepared by arc-melting [30] of high purity starting materials (rare earths – 99.8 wt%; germanium and indium – 99.99 wt%; total sample weight 1.5 g) under an argon atmosphere of ca. 800 mbar. The argon was purified using titanium sponge (T = 900 K), silica gel, and molecular sieves. The arc-melted buttons were sealed in evacuated silica tubes and annealed at 870 K for one month.

After the melting and annealing routines only polycrystalline samples were obtained. Therefore, a special heat treatment procedure was used to grow small single crystals for diffraction studies of the dysprosium compound. The obtained ingot was placed in a tantalum tube, sealed in a quartz ampule (as an oxidation protection) and then placed in an electrical furnace with automatic temperature control. The ampule was (i) heated up to 1275 K and kept at this temperature for 5 h, (ii) gradually cooled to 1000 K, (iii) then to 700 K and (iv) finally to room temperature over a period of 10 h. The RE₅₅Ge₂₀In₂₅ samples are stable in air.

2.2 X-ray diffraction

The polycrystalline Dy₅₅Ge₂₀In₂₅ sample was first studied by powder X-ray diffraction using the Guinier technique (Enraf-Nonius FR552 camera, imaging plate detector, Fujifilm BAS-1800) with CuKα₁ radiation and α-quartz (a = 491.30, c = 540.46 pm) as an internal standard. Powder data of the Dy₅₅Ge₂₀In₂₅ and Tm₅₅Ge₂₀In₂₅ samples was then measured at room temperature using a PANalytical X’Pert PRO diffractometer (CuKα radiation, Bragg-Brentano geometry, measured angle interval 2θ = 10–90°, step scan mode, step size in 2θ = 0.03°, 30 s per step).

The FullProf [31] program package was used for X-ray phase analysis and Rietveld refinement of the collected data. The results obtained from the powder data, are presented in Figure 1 and they are in good agreement with those calculated from the single crystal data (Table 1), i.e. the refined parameters are a = 11.493(2) and c = 16.184(3) Å, R_Bragg = 3.51%, 62(3) wt% Dy₁₁Ge₄In₆ in the Dy₅₅Ge₂₀In₂₅ sample and a = 11.262(2), c = 15.979(3) Å, R_Bragg = 3.53%, 64(2) wt% Tm₁₁Ge₄In₆ in the Tm₅₅Ge₂₀In₂₅ sample. Phase analysis for both samples revealed the following by-products: Dy₅Ge₃ (Mn₅Si₃ type, 33(1) wt%) and metallic indium (4.8(3) wt%) in the Dy₅₅Ge₂₀In₂₅ sample and Tm₅Ge₃ (Mn₅Si₃ type, 23.3(5) wt%), metallic indium (9.2(3) wt%) and a minor amount of Tm₂O₃ ((Mn_0.5Fe_0.5)₂O₃ type, 3.6(4) wt%) in the Tm₅₅Ge₂₀In₂₅ sample. Metallic indium and Tm₂O₃ might result from slow decomposition of the samples in moist air.

Figure 1:

Rietveld refinements (line) of the XRD patterns (dots) and difference curves (bottom lines) for the (a) Dy₅₅Ge₂₀In₂₅ and (b) Tm₅₅Ge₂₀In₂₅ samples, both containing a ternary RE₁₁Ge₄In₆ phase with Sm₁₁Ge₄In₆-type structure. The vertical bars indicate the positions of Bragg reflections (from top to bottom) from the phases: a) Dy₁₁Ge₄In₆, Dy₅Ge₃ and In; b) Tm₁₁Ge₄In₆, Tm₅Ge₃, In and Tm₂O₃.

Irregularly shaped single crystals for X-ray diffraction studies were selected from the Dy₅₅Ge₂₀In₂₅ sample. The sample was carefully crushed and small crystals were glued to thin quartz fibers with beeswax. Their quality was checked through Laue photographs on a Buerger precession camera (white MoKα radiation) prior to the intensity data collection with a STOE IPDS II single crystal diffractometer (graphite-monochromatized MoKα radiation; oscillation mode). A numerical absorption correction was applied to the data set. All crystallographic parameters and details about the structure refinement are listed in Table 2.

2.3 EDX data

The studied single crystal was additionally analyzed by EDX using a Leica 420і scanning electron microscope; dysprosium trifluoride, Ge, and InAs were used as standards. The averaged value of three point analyses (54 ± 1 at% Dy:20 ± 1 at% Ge:26 ± 1 at% In) is close to the starting composition and the composition refined from the X-ray data (52.4:20.6:27.0). No impurity elements heavier than sodium (detection limit of the instrument) were observed.

3.1 Structure refinement

The data set of the dysprosium compound showed a body-centered tetragonal lattice with high Laue symmetry and no additional systematic extinctions, leading to space group I4/mmm, in agreement with our previous studies on Sm₁₁Ge₄In₆ [9] and Ce₁₁Ge_4.74In_5.26 [10]. The atomic parameters of Sm₁₁Ge₄In₆ [9] were taken as starting values and the structure was refined on F² with the Shelx-97 [32] software package with anisotropic displacement parameters for all sites. Since many of the previous structure refinements of related phases (Table 1) revealed small homogeneity ranges, we refined the occupancy parameters in separate least-squares cycles in order to test for deviations from the ideal composition. The 16m and 4e sites revealed Ge/In mixing with the occupancies listed in Table 3. These mixed occupancies were refined as least-squares variables in the final cycles, while all other sites were assumed to be fully occupied. The refinement then smoothly converged to the residuals listed in Table 2 and the composition of the studied single crystal was Dy₁₁Ge_4.33In_5.67. The final difference Fourier synthesis revealed no significant residual peaks. The refined atomic positions, the displacement parameters and the interatomic distances are summarized in Tables 3–5.

CCDC 2130278 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

3.2 Crystal chemistry

Dy₁₁Ge_4.33In_5.67 and Tm₁₁Ge₄In₆ are further members of the Sm₁₁Ge₄In₆-type structure [9], a ternary ordered variant (see Table 1) of the Ho₁₁Ge₁₀ type [3]. The rare earth atoms (dysprosium and thulium) occupy the holmium sites, while the germanium positions show either ordered or mixed occupancy by germanium and indium. The course of the cell volumes of the wholes series of RE₁₁Ge₄In₆ phases is presented in Figure 2. The cell volumes decrease from the lanthanum to the thulium compound (the member with the smallest rare earth element); however, not in the monotonic manner expected for the lanthanide contraction. This is a direct consequence of the germanium-indium disorder and the small homogeneity ranges RE₁₁Ge_4+xIn_6–x, which are also expressed by the small differences observed between the volumes of the powders and the single crystals. The cell volume of the yttrium compound is close to the one of the terbium compound, similar to the pair Y₁₁Ge₁₀ [33] and Tb₁₁Ge₁₀ [34].

Figure 2:

Course of the cell volumes in the series of RE₁₁Ge₄In₆ compounds. Data was taken from refs. [4, 9, 10, 22].

The germanium-indium substitution has been observed for two coloring variants (Ge with 32 and In with 49 electrons can safely be distinguished in the diffraction experiments). In the RE₁₁Ge₈In₂ phases [21], only the 8h site (one of the four crystallographically independent germanium sites) is occupied by indium. This has been substantiated through single crystal X-ray diffraction data for Gd₁₁Ge₈In₂ [21]. The RE₁₁Ge₈In₂ phases can be considered as examples of the indium-poor coloring variant, while the RE₁₁Ge₄In₆ phases are at the indium-rich border. The increasing germanium-indium substitution has a pronounced effect on the course of the lattice parameters, since the covalent radii [35] of germanium (1.22 Å) and indium (1.50 Å) differ significantly. As an example we compare the lattice parameters of Gd₁₁Ge₁₀ [34], Gd₁₁Ge₈In₂ [21] and Gd₁₁Ge₄In₆ [22] in Table 6. The cell volume increases with increasing indium content (9% for Gd₁₁Ge₄In₆); however, with an anisotropy in the course of the lattice parameters, i. e. increasing a and decreasing c lattice parameters, thus a decrease in the c/a ratio. We draw back to this anisotropy below.

A projection of the Dy₁₁Ge_4.33In_5.67 structure onto the xz plane and the coordination polyhedra of the atoms are presented in Figure 3. The coordination polyhedra of the dysprosium atoms are distorted, penta-capped pentagonal prisms (CN = 15) and penta-capped pentagonal prisms with additional centering on the pentagonal faces (CN = 17). The germanium atoms have distorted trigonal prismatic coordination with two additional, capping atoms (CN = 8). The coordination polyhedra for the indium atoms and the mixed occupied sites (M1 and M2) are derivatives of distorted icosahedra, which are formed by subtracting one (CN = 11 for In), two (CN = 10 for M1) or three atoms (CN = 9 for M2).

Figure 3:

Projection of the structure of Dy₁₁Ge_4.33In_5.6 onto the xz plane (left) and coordination polyhedra of the atoms (right). The site symmetries are indicated.

In Figure 4 we compare the structures of Dy₁₁Ge₁₀ [34], Dy₁₁Ge₂In₈ [21] and Dy₁₁Ge_4.33In_5.67. In the left-hand part of the drawing, we present the condensed coordination polyhedra of the Ge1 atoms, which are similar in all three structures. The striking differences concern the p element substructure that is affected by the germanium-indium ordering. The binary Dy₁₁Ge₁₀ structure contains 16 isolated Ge atoms (sites 4d, 4e and 8i), 8 Ge₂ dumb-bells (site 16m) and 2 Ge₄ squares (site 8h) per unit cell (Z = 4). In the first substitution step (Dy₁₁Ge₂In₈), only the 8h site is filled with indium. Since the In₄ squares lie in the xy plane, one can easily understand the increase of the a lattice parameter. With higher indium concentration, the 16m and 4e sites are partially filled with indium in Dy₁₁Ge_4.33In_5.67. The different p element substructures are shown at the right-hand sides of Figure 4 along with relevant interatomic distances. An interesting feature concerns the interatomic distances. The decrease of the c parameter with increasing indium content results from a decrease of the In–M1 distances (3.260 in Dy₁₁Ge₁₀ → 3.041 Å in Dy₁₁Ge_4.33In_5.67) between the squares and the dumb-bells. For further crystal chemical details we refer to previous work [9, 10, 25].

Figure 4:

The Ge or In–Ge substructures in the structures of Dy₁₁Ge₁₀ (top), Dy₁₁Ge₂In₈ (middle), and Dy₁₁Ge_4.33In_5.67 (bottom). Indium and germanium atoms are drawn as green and blue filled circles, respectively, and the mixed-occupied sites are emphasized by segments.

Finally we turn to a description of the structures with an ionic formula splitting following the Zintl concept. The description is electron-precise in the case of the pnictides with the divalent alkaline earth elements, e. g. Ca₁₁Sb₁₀ [5]:

4 Ca₁₁Sb₁₀ ≍ 44 Ca²⁺ + 16 Sb^3– + 8 Sb₂⁴⁻ + 2 Sb₄^4–

The tetrelides with the trivalent rare earth elements show a small deficit of 4 electrons (132 from the rare earth atoms and only 128 accommodated in the Zintl anions) for an electron precise description:

4 Dy₁₁Ge₁₀ ≍ 44 Dy³⁺ + 16 Ge⁴⁻ + 8 Ge₂⁶⁻ + 2 Ge₄⁸⁻ + 4 e^–

The stepwise substitution of germanium by indium then leads to a reduction of the electron count. Extended Hückel electronic structure calculations were performed for the ordered In₆ substructure (dumb-bells + squares; see Figure 4) of La₁₁Ge₄In₆ [25].

4 La₁₁Ge₄In₆ ≍ 44 La³⁺ + 16 Ge⁴⁻ + (8 In₂ + 2 In₄)^68–

The Zintl precise formulation requires (8 In₂ + 2 In₄)⁵⁶⁻ [25] leaving a surplus of 12 electrons per unit cell. La₁₁Ge₄In₆ and the other RE₁₁Ge₄In₆ phases can thus be classified as metallic Zintl phases. This is of course only a crude approximation, since the single crystal data of Ce₁₁Ge_4.74In_5.26 [10], Pr₁₁Ge_5.21In_4.79 [26] and Dy₁₁Ge_4.33In_5.67 showed different degrees of Ge/In mixing, thus pointing to homogeneity ranges and again, nicely underlining the electronic flexibility of the Ho₁₁Ge₁₀ type.