(Ca, Eu, Yb)₂₃Cu₇Mg₄ as a Step towards the Structural Generalization of Rare Earth-Rich Intermetallics

1. Introduction

The components interaction in R-T-X intermetallic systems (R = rare earth metal; T = transition metal; X = other metal) results in many ternary compounds with recurrent stoichiometries in different concentration ranges. These compounds have been widely studied both for their applicative and fundamental properties [1,2,3,4,5,6,7,8,9,10], and they represent an ever growing database for studying structural relationships aiming simplified descriptions and rational generalizations.

Families of rare earth-rich R-T-X representatives are highly populated, especially for R₄TX and R₂₃T₇X₄ stoichiometries, each characterized by two different crystal structures (see Figure 1).

In the framework of a recent investigation on the R₄TX family, the new {Ca,Eu,Yb}₄CuMg compounds (hR144) were discovered and structurally elucidated in terms of intergrowth concept [11].

As a logical evolution of this research, our attention focused on the R₂₃T₇X₄ family, mostly showing the hP68-Pr₂₃Ir₇Mg₄ structure; an overview of chemical compositions of the known so far members is presented in Figure 2. This periodic table map shows that the components of these phases are light trivalent rare earth metals (R with Z < 65), late transition elements from 8 to 10 group (T) and Mg, Zn, Cd or In (X). As derives from the expanded table in Figure2b, the Mg and Cd containing groups are the most abundant, Zn and In having only one representative each, in combination with Ce and Ru.

The hP68-Yb₂₃Cu₇Mg₄ structure is only represented by the prototype [12], thus it was decided to perform some explorative syntheses on divalent R analogues (R = Ca, Eu) with the aim to enrich this family and looking for meaningful structural and chemical generalization criteria.

2. Experimental Section

Samples of nominal composition Ca_67.6Cu_20.6Mg_11.8 (total mass = 0.5 g) and Eu_66.7Cu_20.3Mg₁₃ (total mass = 0.8 g) were prepared from pure (>99.9 mass %) components. The starting metals were weighted in stoichiometric amounts and placed in tantalum crucibles, arc-sealing their cap to prevent Mg evaporation. These operations were done in a glove box filled with Ar, to minimize side reactions with oxygen and water. The Ta crucibles were put in a quartz glass tube sealed under an inert atmosphere, then placed in a resistance furnace where the following thermal cycle was applied: 20 °C → (5 °C/min) → 850 °C (10 min) → (-0.1 °C/min) → 400 °C (5 min) → (-0.2 °C/min) → 100 °C (furnace switched off).

For microscopic characterization, some pieces of each sample were selected and embedded in a conductive phenolic resin, polymerized in a hot mounting press machine Opal 410 (ATM GmbH, Germany). Surfaces were smoothed by SiC abrasive papers with no lubricant and polished with the aid of diamond pastes with particle size decreasing from 6 to 1 μm, using petroleum ether as lubricant. An automatic polishing machine Saphir 520 (ATM GmbH, Germany) was applied for this purpose.

Microstructure observation together with qualitative and quantitative analyses were conducted on a Zeiss Evo 40 Scanning Electron Microscope (SEM) equipped with a Dispersive X-ray Spectroscopy (EDXS) system (INCA X-ACT) managed by the INCA Energy software (Oxford Instruments, Analytical Ltd., Bucks, U.K.). Both samples showed a good yield of the compound of interest, of average composition ~ 67 at.% R, 20 at.% Cu, 13 at.% Mg (see Figure 3), and were therefore subjected to X-ray diffraction studies. X-ray Powder Diffraction (XRPD) patterns were recorded on a Philips X'Pert MPD diffractometer (Cu K_α radiation, step mode of scanning) and indexed by Powder Cell [13] software.

Good quality single crystals were selected with the help of a light microscope from mechanically crushed alloys covered with mineral oil. Crystals, embedded in an excess of grease to prevent oxidation, were then glued to pins and remained stable for several days.

The X-ray diffraction data were collected on a three-circle Bruker D8 QUEST diffractometer equipped by a PHOTON III 14 photon counting detector, using the graphite monochromatized Mo Kα radiation. Data collection strategies, consisting of both ω- and ϕ-scans, were decided using the APEX4 software [14] to obtain good data completeness, redundancy, and resolution limit. Data were collected over the reciprocal space up to ~ 31° in θ (resolution of ca. 0.7 Å) with exposures of 30-40 s per frame. The software SAINT [15] and XPREP [16] were used for data reduction. Lorentz, polarization, and absorption effects were corrected by SADABS [17]; the crystal structure was solved and refined with the aid of SHELXTL [18].

Both crystals possess hexagonal symmetry, and their diffraction patterns show systematic absences due to the presence of a c-type glide plane. Reconstructed intensity profiles of selected zones are shown in Figure 4 for the Eu-compound diffraction pattern.

The best structural model was found using the intrinsic phasing method in the P6₃/mmc space group (N. 194), corresponding to the hP68-Yb₂₃Cu₇Mg₄ prototype. The unit cell, containing 2 formula units of R₂₃Cu₇Mg₄ composition, accounts for 68 atoms, distributed among 5 Wyckoff sites of R, 2 sites of Cu and 2 of Mg. In the case of Ca₂₃Cu₇Mg₄, the first refinement resulted in somewhat high isotropic displacement parameters for Mg atoms in the 2a position. A Mg/Ca statistical mixture was refined for this site, resulting in 0.93/0.07 ratio and significantly improving the structural model. For the Eu representative, no need of statistical mixture was evidenced, and the structural model turns out to be perfectly stoichiometric. The final anisotropic full-matrix least-squares refinements converged to good residuals for both compounds. Details of data collection and structure refinement are summarized in Table 1 together with selected crystal data; standardized atomic coordinates, site occupancy factors and equivalent displacement parameters are listed in Table 1. The corresponding CIF files, available as supplementary material, were deposited at the Cambridge Database.

3. Results and Discussion

The studied {Ca,Eu}₂₃Cu₇Mg₄ compounds, together with the Yb-containing prototype, form a small sub-family of R₂₃T₇X₄ with crystal structure (hP68-Yb₂₃Cu₇Mg₄, Wyckoff sequence k⁴h²fca, see Table 2) different from all the others (hP68-Pr₂₃Ir₇Mg₄, Wyckoff sequence c¹⁰b²a²), however having in common with them the hexagonal symmetry and the number of atoms in the unit cell.

A first glance to the crystal structures of interest in terms of interatomic distances shows that the R–Mg (3.52 ÷ 3.74 Å for Ca, 3.69 ÷ 3.90 Å for Eu), Cu–Cu (2.49 for Ca, 2.56 for Eu) and Mg–Mg (3.19 for Ca, 3.26 for Eu) contacts are compatible with the metallic radii sums [19], instead Mg and Cu are well apart and do not interact. Also, the first coordination spheres of the different species are geometrically similar to those in other R-T-X compounds rich in R. These polyhedra are: capped Cu-centered trigonal prisms, either isolated (Cu@R(6+3)) or sharing a rectangular face (Cu@CuR(6+2)), isolated Mg-centered icosahedra (Mg@R12) and polyicosahedral Mg3@R20 core-shell clusters (see Figure 5).

The same coordination polyhedra were observed in R₄CuMg (R=Ca, Eu, Yb) compounds [11], with a difference in the Mg-centered polyicosahedral units: in the 23:7:4 these are formed by three fused icosahedra, instead in the 4:1:1 six fused icosahedra form core-shell clusters of Mg7@R32 composition. Recently, we proposed an elegant description of the R₄CuMg structure in terms of linear intergrowth of slabs of R_9.5CuMg_3.5 and R₁₃Cu₆Mg composition [11]. Considering the cited similarities, an analogous description was attempted with success also for R₂₃Cu₇Mg₄ with divalent R.

In fact, the structure of title compounds can be interpreted as a stacking of slabs from the same parent structures, that have been extensively described in [11]: the hexagonal hP28-kh²ca (SG 194) adopted by many R₉TX₄ and R₁₀TX₃ compounds and the rhombohedral hR60-b⁶a² (SG 160) only adopted by Lu₁₃Ni₆In [20]. Slabs of each parent type are alternatively stacked along the c-direction, fulfilling the crystal space with no gaps neither need of “gluing” atoms (see Figure 6a). Slabs, possessing the same p3m1 layer symmetry, are joined by a common corrugated layer composed exclusively by R atoms, showing two types of nodes represented by (3⁶)¹;(3²434)⁶ Schläfli notation (see Figure 6b).

As a consequence of this, the composition of slabs from the hexagonal parent type is R₁₀CuMg₃, instead the composition of other slabs is exactly R₁₃Cu₆Mg. Therefore, the 23:7:4 unit cell content can be easily described by properly considering the composition and number of stacked slabs: 2×R₁₀CuMg₃ + 2×R₁₃Cu₆Mg = 2×R₂₃Cu₇Mg₄.

It should be noted that the P6₃/mmc space group of title compounds is the only centrosymmetric one among the three hexagonal space groups compatible with the p3m1 layer symmetry of the stacked slabs [11]. Lattice parameters of representatives with the same slabs stacked along c should be related to those of the parent structures, with a and b being similar or integer multiples and c correlated to the total number of slabs in the unit cell: this is true for 23:7:4 and 4:1:1 compounds, having a = b ≈ 10 Å and c ≈ 24 Å and 51 Å, respectively.

The compositions of the two families of divalent R-rich compounds can be plotted on a Gibbs triangle highlighting the relation with compositions of parent types (see Figure 7) and helping to develop the structural/compositional generalization idea: in fact, hypothetic new compounds with similar intergrowth architectures should show stoichiometries laying along the dotted tie-lines.

At this point, it is interesting to compare the two structural sub-families of R₂₃T₇X₄ intermetallics in terms of their component nature. A similar analysis was applied to R₄TMg using the volume contraction as a criterion. This is defined as $\Delta V_f\left(\%\right)=100\times \frac{V_{meas}-V_{calc}}{V_{calc}}$, where $V_{calc}={\sum }_i{N}_i\times V_i$, (N_i = number of i-type atoms in the unit cell, V_i = atomic volume of the i-type species taken from [21]) and V_meas is the experimentally determined volume [22]. Values of ΔV_f (%) for R₂₃T₇X₄ are plotted in Figure 8, as a function of the T group and of the R trivalent/divalent nature.

A major part of ΔV_f (%) are negative, except for compounds with T = Pt, for which values lay in the range between 0 and +2.4%. No separation is observed as a function of X nature.

Instead, the title compounds, the only representatives known for divalent R, form a clearly clustered group, showing the most prominent volume contractions, extending down to -10% and indicating strong chemical interactions.

It is worth to note that both R and T nature are determinant for the formation and structure of these R-rich compounds; for example, the existence of R₂₃T₇Mg₄ has been excluded for several combinations of trivalent R with {Cu, Ag, Au}[4,23,24,25]. On the other hand, for T belonging to the 10^th group no representatives were found with divalent R so far: considering the similar trend observed for the structurally related 4:1:1, these combinations are indeed worth to be investigated.

4. Conclusions

In this work, the crystal structures of the {Ca,Eu}₂₃Cu₇Mg₄ compounds were solved by single crystal X-ray measurements, being the second and third representatives of the Yb₂₃Cu₇Mg₄ prototype, and forming a small structural sub-family of 23:7:4 with a divalent R constituent. These few compounds are characterized by pronounced volume contractions if compared with the highly populated R₂₃T₇X₄ family with trivalent R having Pr₂₃Ir₇Mg₄-type structure. The distribution of members of both groups discovered so far as a function of the nature of components suggests combinations for new exploratory syntheses aiming to enrich the Yb₂₃Cu₇Mg₄-type representatives, for example R₂₃{Ag,Au}₇Mg₄, R ₂₃{Ni,Pd,Pt}₇Mg₄ and R₂₃Cu₇{Zn,Cd,Al,In}₄ with R= Ca, Eu, Yb.

The crystal structure of the title compounds was interpreted in terms of linear intergrowth of slabs R₁₀CuMg₃ (parent type: hP28-kh²ca, SG 194) and R₁₃Cu₆Mg (parent type: hR60-b⁶a², SG 160), alternating along c-axis in the 1:1 ratio. This description brings together {Ca,Eu,Yb}₂₃Cu₇Mg₄ and {Ca,Eu,Yb}₄CuMg compounds, the latter being formed by the same type of slabs in a 2:1 ratio. An evolution of this idea pushes towards the recognition/discovery of new structural families based on different intergrowths of the same slabs. To this purpose, the following conditions should be fulfilled:

(1)

Composition restraint – stoichiometries laying along the lines joining the end-members

(2)

Symmetry restraint – rhombohedral, hexagonal and cubic space groups including the p3m1 among possible sd linear orbits [11,26]

(3)

Metric restraint – for hexagonal and rhombohedral representatives a=b≈10÷11 Å or their multiples

The results of structural/chemical analysis illustrated here constitute a further step towards a planned wider generalization aimed to a simple and chemically significant representation in terms of few common building blocks of complex R-rich ternary intermetallics.