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

Abstract

The R₂₃Cu₇Mg₄ (R = Ca, Eu) intermetallics, studied by single-crystal X-ray diffraction, were found to be isostructural with the Yb₂₃Cu₇Mg₄ prototype (hP68, k⁴h²fca, space group P6₃/mmc), forming a small group inside the bigger 23:7:4 family, otherwise adopting the hP68-Pr₂₃Ir₇Mg₄ crystal structure. The observed structural peculiarity is connected with the divalent character of the R component and with a noticeable volume contraction, resulting in the clear clustering of title compounds inside the whole 23:7:4 family. The occurrence of fragments typical of similar compounds, particularly Cu-centered trigonal prisms and Mg-centered core–shell polyicosahedral clusters with R at vertices, induced the search of significant structural relationships. In this work, a description of the hexagonal crystal structure of the studied compounds is proposed as a linear intergrowth along the c-direction of the two types of slabs, R₁₀CuMg₃ (parent type: hP28-kh²ca, SG 194) and R₁₃Cu₆Mg (parent type: hR60-b⁶a², SG 160). The ratio of these slabs in the studied structure is 2:2 per unit cell, corresponding to the simple equation, 2 × R₁₀CuMg₃ + 2 × R₁₃Cu₆Mg = 2 × R₂₃Cu₇Mg₄. This description assimilates the studied compounds to the {Ca, Eu, Yb}₄CuMg ones, where the same slabs (of p3m1 layer symmetry) are stacked in a different way/ratio and constitutes a further step towards a structural generalization of R-rich ternary intermetallics.

1. Introduction

The component interaction in RTX 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 [1,2,3,4,5,6,7,8,9,10,11,12], and they represent an ever-growing database for studying structural relationships, aiming for simplified descriptions and rational generalizations.

The families of rare, earth-rich RTX representatives are highly populated, especially for R₄TX and R₂₃T₇X₄ stoichiometries, of which are 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 an intergrowth concept [13].

As a logical evolution of this research, our attention focused on the R₂₃T₇X₄ family, mostly showing the hP68-Pr₂₃Ir₇Mg₄ structure [14]; an overview of chemical compositions of the currently known 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 groups (T) and Mg, Zn, Cd or In (X). As derived from the expanded table in Figure 2b, 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 [15], thus it was decided to perform some explorative syntheses on divalent R analogues (R = Ca, Eu) with the aim to enrich this family and look for meaningful structural and chemical generalization criteria.

2. Experimental Section

Samples of the 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 performed 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 and polymerized in a hot mounting press machine Opal 410 (ATM GmbH, Blieskastel, Germany). The 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. The automatic polishing machine Saphir 520 (ATM GmbH, Blieskastel, Germany) was applied for this purpose.

Microstructure observations, 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 Suite software version 4.15 (Oxford Instruments, Analytical Ltd., Bucks, UK). Both samples showed a good yield of the compound of interest, with an average composition of ~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 X’Pert MPD diffractometer (Philips, Almelo, Netherlands) (Cu K_α radiation, step mode of scanning) and indexed using Powder Cell [16] software (version 2.4).

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 (version 2022.10-1) [17] 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 (version 8.30) [18] and XPREP [19] were used for data reduction. Lorentz, polarization, and absorption effects were corrected by SADABS [20]; the crystal structure was solved and refined with the aid of SHELXTL [21].

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 the 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 residuals. For the Eu representative, no need for the statistical mixture was evidenced, and the structural model turned 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 the structure refinement are summarized in

Table 1. Selected crystallographic data and structure refinement parameters for the single crystals studied in this work.

Formula	Ca22.93 (4)Cu7Mg4.07 (4)	Eu23Cu7Mg4
EDXS composition	Ca68.2Cu19.8Mg12.0	Eu66.2Cu19.2Mg14.6
Depositing CSD-code	2266948	2266951
Formula weight (g/mol)	1463.86	4037.10
Space group	P63/mmc (194)
Pearson symbol-protoype, Z	hP68-Yb23Cu7Mg4, 2
a, Å	10.236 (2)	10.659 (2)
c, Å	23.413 (5)	24.379 (5)
V, Å3	2124.5 (9)	2398.7 (10)
Calc. density (g·cm−3)	2.29	5.59
Absorption coefficient (μ, mm−1)	6.27	32.61
Theta range (°)	2.3 ≤ θ ≤ 33.2	2.8 ≤ θ ≤ 30.5
Index ranges h, k, l	−15 ≤ h ≤ 11 −15 ≤ k ≤ 14 −36 ≤ l ≤ 35	−15 ≤ h ≤ 15 −15 ≤ k ≤ 13 −34 ≤ l ≤ 34
Data/parameters	1592/41	1435/40
GOF	1.16	0.98
Rint/Rsym	0.1014/0.045	0.083/0.018
R1/wR2 (I > 2σ(I))	0.0403/0.0932	0.0259/0.0454
R1/wR2 (all data)	0.0864/0.1320	0.0445/0.0524
Max diff. peak and hole (e−/Å3)	1.19 and −1.40	2.59 and −1.36

, together with selected crystal data; standardized atomic coordinates, site occupancy factors, and equivalent displacement parameters are listed in

Table 2. Standardized atomic coordinates and equivalent displacement parameters (U_eq) for the {Ca, Eu}₂₃Cu₇Mg₄ single crystals.

Atom	Site	Atomic Coordinates			Ueq [Å2]
		x/a	y/b	z/c
Ca22.93(4)Cu7Mg4.07(4)
Ca1	4f	1/3	2/3	0.61757 (8)	0.0180 (4)
Ca2	12k	0.20651 (6)	0.4130 (1)	0.03215 (5)	0.0209 (2)
Ca3	6h	0.12164 (9)	0.24328 (9)	1/4	0.0211 (3)
Ca4	12k	0.12389 (6)	0.2478 (1)	0.61877 (5)	0.0219 (2)
Ca5	12k	0.53951 (6)	0.07902 (6)	0.66824 (5)	0.0217 (2)
Cu1	12k	0.52555 (4)	0.05110 (4)	0.04959 (3)	0.0243 (2)
Cu2	2c	1/3	2/3	1/4	0.0277 (4)
Mg1 (Ca) SOF(Mg) = 0.93	2a	0	0	0	0.0234 (17)
Mg2	6h	0.7706 (1)	0.5412 (3)	1/4	0.0190 (5)
Eu23Cu7Mg4
Eu1	4f	1/3	2/3	0.61610 (3)	0.0221 (2)
Eu2	12k	0.20717 (3)	0.41434 (5)	0.03062 (2)	0.0244 (1)
Eu3	6h	0.12316 (4)	0.24632 (4)	1/4	0.0264 (1)
Eu4	12k	0.12549 (3)	0.25099 (5)	0.61768 (2)	0.0277 (1)
Eu5	12k	0.53839 (2)	0.07678 (2)	0.66768 (2)	0.0240 (1)
Cu1	12k	0.52492 (6)	0.04984 (4)	0.04907 (6)	0.0308 (3)
Cu2	2c	1/3	2/3	1/4	0.0311 (6)
Mg1	2a	0	0	0	0.0255 (6)
Mg2	6h	0.76850 (2)	0.53700 (5)	1/4	0.0254 (9)

. The corresponding CIF files, available as Supplementary Materials, 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 a crystal structure (hP68-Yb₂₃Cu₇Mg₄, Wyckoff sequence k⁴h²fca, see Table 2) different from all of the others (hP68-Pr₂₃Ir₇Mg₄, Wyckoff sequence c¹⁰b²a²); however, having in common with all of them is 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 [22]; 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 RTX 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 [13], 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 the Mg7@R32 composition. Recently, we proposed an elegant description of the R₄CuMg structure in terms of the linear intergrowth of slabs of R_9.5CuMg_3.5 and R₁₃Cu₆Mg composition [13]. Considering the cited similarities, an analogous description was attempted with success also for R₂₃Cu₇Mg₄ with the 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 [13]: the hexagonal hP28-kh²ca (SG 194) adopted by many R₉TX₄ and R₁₀TX₃ compounds and the rhombohedral hR60-b⁶a² (SG 160) only adopted by Lu₁₃Ni₆In [23]. 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 the slabs from the hexagonal parent type is R₁₀CuMg₃, and instead the composition of the 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 [13]. 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 ${∆V}_f\left(\%\right)=100\times \frac{V_{meas}-V_{calc}}{V_{calc}}$, 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 [24]) and V_meas is the experimentally determined volume [25]. The 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 noting 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} [2,26,27,28]. On the other hand, for T belonging to the 10th group (Ni, Pd, Pt) 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 investigating.

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 an Pr₂₃Ir₇Mg₄-type structure. The distribution in 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, R₂₃{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 the 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 [13,29];

(3)

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

The results of the 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.