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The new ternary intermetallic title compounds, namely trilanthanum undeca(zinc/magnesium), La3(Zn0.874Mg0.126)11, (I), and tricerium undeca(zinc/magnesium), Ce3(Zn0.863Mg0.137)11, (II), are isostructural and crystallize in the orthorhombic La3Al11 structure type. These three phases belong to the same structural family, the representative members of which may be derived from the tetragonal BaAl4 structure type by a combination of internal deformation and multiple substitution. Compared to the structure of La3Al11, in (I), a significant decrease of 11.9% in the unit-cell b axis and an increase in the other two directions, of 3.6% along a and 5.2% along c, are observed. Such an atypical deformation is caused by the closer packing of atoms in the unit cell due to atom shifts that reflect strengthening of metallic-type bonding. This structural change is also manifested in a significant difference in the coordination around the smaller atoms at the 8l Wyckoff position (site symmetry m). The Al atom in La3Al11 is in a tricapped trigonal prismatic environment (coordination number 9), while the Zn atoms in (I) and (II) are situated in a tetragonal antiprism with two added atoms (coordination number 10).
Recently, intermetallic compounds containing rare earths, transition metals and magnesium have been of particular interest to researchers in relation to their useful properties as modern lightweight alloys and hydrogen-storage materials. The crystal structures, physical properties and hydrogenation behaviour of these materials have been reviewed by Rodewald et al. (2007 ). Until now, the most heavily studied intermetallic compounds in this class have been those with transition metals such as Ni and Cu. Only one ternary compound, i.e. La2Mg3Zn3 (cubic, a = 7.145 Å), was investigated from the La–Mg–Zn ternary system (Melnik, Kinzhibalo et al., 1978 ). The Ce–Mg–Zn ternary system was first reported by Melnik, Kostina et al. (1978 ), and the isothermal section of the phase diagram was constructed partially up to 60 at.% of Zn and 50 at.% of Ce at 573 K. Four new ternary compounds with preliminary compositions ~CeMg7Zn12, ~Ce(Mg0.5–0.85Zn0.5–0.15)9, ~CeMg3Zn5 and ~Ce2Mg3Zn3 were reported in this region. The last compound was found to crystallize with a cubic unit cell (a = 7.064 Å), whereas the crystal structures of the first three compounds remain unknown. We decided to explore the rest of the phase diagram starting from the Zn-rich region. During the investigation of the Ce–Mg–Zn phase diagram in the Zn-rich concentration range, several ternary phases were found. In our previous papers, the crystal structures of CeMgZn2 (Pavlyuk et al., 2007 ) and Ce20Mg19Zn81 (Pavlyuk et al., 2008 ) were reported, and it was found that the CeMgZn2 ternary phase [MnCu2Al structure type, cubic, cF16, a = 7.0358 (4) Å] belongs to a numerous family of Heusler-type structures, which are an ordered variant of the BiF3 cubic structure type, while the ternary compound Ce20Mg19Zn81 crystallizes with a large cubic unit cell [space group F 3m, a = 21.1979 (8) Å] and represents a new type of structure. The results of crystallographic studies of two further intermetallic compounds, i.e. La3(Zn0.874Mg0.126)11, (I), and Ce3(Zn0.863Mg0.137)11, (II), are presented here.
The title compounds crystallize with the orthorhombic La3Al11 structure type (space group Immm), with 28 atoms per unit cell. The formation of compounds with this structure type is typical for the R 3Al11 (Buschow & Van Vucht, 1967 ) and R 3Zn11 (Bruzzone et al., 1970 ) binary intermetallics (R = rare earth), and for the ternary compounds in the following systems: R–Ag–Al, R–Cu–Al (Stel’makhovych et al., 2000 ), R–T–Ga (T = Cu, Ag, Au, Pd, Pt, Rh, Ir; Grin et al., 1993 ) and Yb–Zn–Al (Fornasini et al., 2005 ). The shortest interatomic distances in (I) and (II) are in the ranges typical for intermetallic compounds containing La (or Ce), Mg and Zn, and indicate metallic-type bonding. The projection of the unit cell and coordination polyhedra of the atoms are shown in Fig. 1 . The number of neighbour atoms correlates well with the dimensions of the central atoms. The largest La or Ce atoms are enclosed in 17- and 18-vertex polyhedra that can be treated as distorted pseudo-Frank–Kasper polyhedra. The statistical mixture of (Zn/Mg)6 is characterized by the monocapped cuboctahedron polyhedra having the coordination number (CN) of 13. The statistical mixture of (Zn/Mg)5 and the Zn3 atom are surrounded by 12 neighbours in the form of distorted cuboctahedra (CN = 12), while the atomic environment of the Zn4 atom is a bicapped tetragonal antiprism (CN 8 + 2).
Although the isostructural compounds (I) and (II) are very similar to the La3Al11 structure type in terms of having the same space group, the same Wyckoff positions and similar lattice parameters, these two compounds cannot be treated as being isostructural with it. Comparing the structure of (I) with that of La3Al11 (Gomes de Mesquita & Buschow, 1967 ) we observe a significant decrease in the unit-cell dimension along the b axis of 11.9% [b = 10.132 (7) Å for La3Al11 and b = 9.0514 (8) Å for (I)], while the dimensions of the other two directions increase by 3.6% [a = 4.431 (5) Å for La3Al11 and a = 4.5992 (4) Å for (I)] and 5.2% [c = 13.142 (10) Å for La3Al11 and c = 13.8635 (11) Å for (I)]. This atypical deformation of the unit cell at the transition from the structure type La3Al11 to (I) cannot be associated only with the geometric factor of the difference in atomic radius of Al (r = 1.43 Å) and Zn (r = 1.38 Å) (Slater, 1964 ). The relative reduction of the radius in this case is only 3.5%. Rather, the reason for this atypical deformation is closer packing of atoms in the unit cell of (I) caused by shifts in atomic positions resulting from the strengthening of metallic-type bonding. The last assertion is based on the fact that Zn and Mg are still common metal atoms (d- and s-block elements, respectively), while Al has electronic nature as a p-block element, though with metal properties. Thus, bonding between the d electrons of the La atom and d electrons of the Zn atom (or bonding between the d electrons of the La atom and s electrons of the Mg atom) in structure (I) is stronger than bonding between the d electrons of the La atom and p electrons of the Al atom in the La3Al11 structure type.
A detailed crystal chemical analysis shows that, in the case of the La3Al11 structure, the Al2 atom has a trigonal prismatic coordination polyhedron with three additional capping atoms (CN = 9), while in structures (I) and (II) the Zn4 atom (which occupies the same 8l Wyckoff position as Al2 in La3Al11) has a tetragonal antiprismatic coordination polyhedron with two added atoms (CN = 10) (Fig. 2 ). Significant deformation in the direction of the b-cell axis and shifts of atoms in the same direction cause the observed changes in the coordination polyhedra. In fact, there is a close relationship between the tetragonal antiprism (CN = 8), in the ideal case, and the trigonal prism with two additional atoms (CN = 6 + 2) (Fig. 2 a). Transformation of the tetragonal antiprism to a trigonal prism with two additional capping atoms is due only to the shifts of two atoms of a square face, which is bent forming two triangular faces. The same method of transformation of the 8l coordination polyhedron occurs at the transition between (I) (Fig. 2 b) and La3Al11 (Fig. 2 c). The Al2—La2 distance in the La3Al11 structure is large (3.7382 Å), and thus the La2 atom does not belong to the Al2 polyhedron. By contrast, in the structure of (I) [and also in the Ce analogue, (II)], the distance between the corresponding atoms, i.e. betwen Zn4 and La2, is much smaller [3.3198 (10) Å] causing atom La2 to belong to the Zn4 polyhedron. As a result of these differences the title compounds and La3Al11 belong to different structural classes in the classification scheme of Krypyakevich (1977 ). (I) and (II) belong to class 9 (tetragonal antiprism as a coordination polyhedron), while La3Al11 belongs to class 10 (trigonal prism as a coordination polyhedron).
If we compare the known Al-containing compounds from systems R–Ag–Al and R–Cu–Al (Stel’makhovych et al., 2000 ) with the structure of La3Al11, we do not observe this atypical deformation. For these ternary compounds, it is observed that the decrease in the unit-cell dimension along the b axis is in the range 1.19–3.21% for R 3(CuAl)11 and 0.51–1.58% for R 3(AgAl)11 depending on the rare earth element (R). By contrast, in the binary compounds R 3Zn11 (Bruzzone et al., 1970 ), the decrease in the unit-cell dimension along the b axis is in the range 11.61–12.90% depending on R. Solid evidence that this anomaly is characteristic only for compounds containing Zn is obtained by comparing our results with data for compounds that contain Ga instead of Al (i.e. from systems R–T–Ga where T = Cu, Ag, Au, Pd, Pt, Rh, Ir; Grin et al., 1993 ). The atomic radius of Ga (r = 1.35 Å) (Slater, 1964 ) is very close to the radius of Zn (r = 1.38 Å), but the b axis in the Ga-containing compounds is larger than that in the Zn-containing compounds by an average of 5%. This is entirely inconsistent with the geometric factor (radius) and supports our assumption that the structural deformation is driven by closer packing in the Zn-containing structure caused by strengthening of metallic-type bonding as a consequence of changes in the electronic nature of the element.
The crystal structures of the title compounds are also closely related to the tetragonal BaAl4 (space group I4/mmm; Andress & Alberti, 1935 ) and orthorhombic LaAl4 (space group Imm2; Zalutskii & Krypyakevych, 1967 ) structural types, i.e. types adopted by the binary rare earth compounds RAl4 (R = La, Ce, Pr, Nd). In these structures, the rare earth atoms are embedded in the three-dimensional networks, which are formed by the smaller metal atoms (Fig. 3 ). The primary fragment of such networks has the composition [RM 18]. For example, in the BaAl4 structure, each Ba atom is surrounded by 18 Al atoms. Further, the structural [RM 18] fragment is connected to six other identical fragments. The structures of (I) and (II) also contain the analogous [RM 18] fragments and each of them is connected to six fragments containing 16 smaller atoms [RM 16]. The [RM 16] fragment type can be derived from the [RM 18] fragment by internal deformation and multiple substitutions (Fig. 4 ).
La, Ce, Mg and Zn, all with a nominal purity greater than 99.9 wt%, were used as the starting elements. First, the powders of the pure metals with a stoichiometry La(or Ce):Mg:Zn = 2:1:7 were pressed into pellets, enclosed in an evacuated silica ampoule (internal pressure = 10−5–10−6 Pa) and placed in a resistance furnace with a thermocouple controller. The heating rate from room temperature to 670 K was 5 K min−1. The alloys were kept at this temperature over a period of 2 d and then the temperature was increased from 670 to 1073 K over a period of 6 d. The alloys were then annealed at this temperature for 4 h and cooled slowly to room temperature. In the second step, the pellets were remelted in an arc furnace under an argon atmosphere at least three times in order to ensure homogeneity. After the melting procedures, the total weight loss was less than 2%. The brittle samples were stable in air, showing a metallic lustre. Wavelength dispersive spectrometry and electron-probe microanalysis (CAMECA SX100 analyser) were used to control the number of phases and their content in the samples. Various point analyses on this phase were in good agreement with the ideal composition determined by the single-crystal X-ray data [an average result for the title compounds is 21.4 at.% La, 9.9 at.% Mg and 68.7 at.% Zn for (I), and 21.3 at.% Ce, 10.1 at.% Mg and 68.6 at.% Zn for (II)]. Tabular-shaped single crystals, exhibiting a metallic lustre, were isolated by mechanical fragmentation from the alloys.
A statistical test of the distribution of the E values using the program E-STATS from the WinGX system (Farrugia, 1999 ) suggested that the structure is centrosymmetric. The analysis of systematic extinctions yielded the space group Immm (No. 71), and this was confirmed by the following structure refinement. The structure was solved by direct methods. The rare earth atoms were located in the Wyckoff sites 2a and 4i. The Zn3 and Zn4 atoms were localized in the two 8l Wyckoff sites. The Zn5 and Zn6 atoms in the 4h and 2d Wyckoff sites, respectively, showed displacement parameters which differ considerably from those of the Zn atoms in the other sites. This suggested that, in addition to Zn, these positions are partially occupied by the Mg atoms. In (I), the 2d site is occupied by 0.393 (15) Mg and 0.607 (15) Zn, and the 4h site is occupied by 0.495 (10) Mg and 0.505 (10) Zn. In (II), the 2d site is occupied by 0.378 (13) Mg and 0.622 (13) Zn, and the 4h site is occupied by 0.484 (10) Mg and 0.516 (10) Zn. In the final refinement cycles, the isotropic displacement parameters for the (ZnMg) statistical mixtures in the 4h and 2d Wyckoff sites were refined. All other atoms were successfully refined with anisotropic displacement parameters. The positional and U iso parameters for the (ZnMg) statistical mixtures were equated using the EXYZ and EADP constraints. The atomic coordinates were standardized using the STRUCTURE_TIDY program (Gelato & Parthé, 1987 ).
For both compounds, data collection: CrysAlis CCD (Oxford Diffraction, 2008 ); cell refinement: CrysAlis RED (Oxford Diffraction, 2008 ); data reduction: CrysAlis RED; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008 ); molecular graphics: DIAMOND (Brandenburg, 2006 ); software used to prepare material for publication: SHELXL97.
Crystal structure: contains datablocks I, II, global. DOI: 10.1107/S0108270110002556/sq3225sup1.cif
Structure factors: contains datablocks I. DOI: 10.1107/S0108270110002556/sq3225Isup2.hkl
Financial support from the Polish Ministry of Science and Higher Education is gratefully acknowledged (project No. N507 378035).
Supplementary data for this paper are available from the IUCr electronic archives (Reference: SQ3225). Services for accessing these data are described at the back of the journal.