Exploratory Work in the Quaternary System of Ca–Eu–Cd–Sb: Synthesis, Crystal, and Electronic Structures of New Zintl Solid Solutions

Investigation of the quaternary system, Ca–Eu–Cd–Sb, led to a discovery of the new solid solutions, Ca1−xEuxCd2Sb2, with the CaAl2Si2 structure type (x ≈ 0.3–0.9, hP5, P3¯m1, a = 4.6632(5)–4.6934(3) Å, c = 7.630(1)–7.7062(7) Å), Ca2−xEuxCdSb2 with the Yb2CdSb2 type (x ≈ 0.6, oS20, Cmc21, a = 4.646(2) Å, b = 17.733(7) Å, c = 7.283(3) Å), and Eu11−xCaxCd6Sb12 with the Sr11Cd6Sb12 type (x ≈ 1, mS58, C2/m, a = 32.407(4) Å, b = 4.7248(5) Å, c = 12.377(1) Å, β = 109.96(1)°). Systematic crystallographic studies of the Ca1−xEuxCd2Sb2 series indicated expansion of the unit cell upon an increase in the Eu content, in accordance with a larger ionic radius of Eu2+ vs. Ca2+. The Ca2−xEuxCdSb2 composition with x ≈ 0.6 adopts the non-centrosymmetric space group, Cmc21, although the parent ternary phase, Ca2CdSb2, crystallizes in the centrosymmetric space group, Pnma. Two non-equivalent Ca sites in the layered crystal structure of Ca2−xEuxCdSb2 get unevenly occupied by Eu, with a preference for the interlayer position, which offers a larger available volume. Similar size-driven preferred occupation is observed in the Eu11−xCaxCd6Sb12 solid solution with x ≈ 1.


Introduction
Zintl phases constitute a unique family of intermetallic compounds with polar chemical bonding. Due to a significant electron transfer, formal charges can be assigned to parts of crystal structures in such compounds, considering that all elements in a given composition achieve a stable closed-shell (octet) electron configuration [1]. In Zintl phases, the idealized charges are balanced, which can be understood, yet within an oversimplified picture, as an optimal redistribution of electrons among the constituting elements, leading to fully occupied bonding states and empty antibonding levels. Different patterns of hetero-and homoatomic bonding can be realized in Zintl compounds. Consequently, their crystal structures frequently display a high degree of complexity. Many known intermetallic compounds, especially those with group 15 elements, represent electronically balanced phases crystallizing in structures with huge unit cells and large numbers of atoms per cell [2][3][4][5][6][7]. Group 15 elements are commonly referred to as pnictogens, and their compounds with metals are called pnictides, which is the terminology adopted in this paper.
The energetic separation of the bonding and antibonding states in Zintl phases typically result in semiconducting properties [1,8]. Since electronegativity differences for metals are not high in comparison to metal-nonmetal pairs, the magnitudes of the electronic bandgaps in Zintl compounds are

First-Principle Calculations
Electronic structure calculations were done on the scalar relativistic level for the idealized composition, CaEuCdSb 2 , (a hypothetical member of the Ca 2−x Eu x CdSb 2 solid solution with x = 1, space group Cmc2 1 ) using the SIESTA code [19]. The initial atomic coordinates and lattice parameters were taken from the refined Ca 2−x Eu x CdSb 2 structure with x ≈ 0.6. The AE1 and AE2 sites were treated as fully occupied by Eu and Ca, respectively (see the Results and Discussion for details of the crystal structure). The Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (GGA) functional was employed [20]. At first, suitable Troullier-Martins pseudopotentials were generated with the ATOM program and carefully tested on several known compounds to achieve good reproducibility of electronic structures and optimized lattice parameters [21]. After that, atomic coordinates and lattice constants of Ca 2−x Eu x CdSb 2 were relaxed down to residual forces of less than 10 −2 eV/Å. Double zeta polarized orbitals were employed as a basis set. The Brillouin zone was sampled by a 18 × 12 × 10 k-point grid and the mesh cut-off was set to 800 Ry after checking for convergence. Strong correlations of the Eu 4f orbitals considered by applying the GGA + U approach with U eff = 7 eV (rotationally invariant formulation [22]). For consistency with the previous theoretical work on d 10 metal antimonides [23,24], we also introduced U eff = 2 eV for the Cd 4d states. Spin polarization was treated in a simple ferromagnetic model. The forces were relaxed down to less than 10 −2 eV/Å. Chemical bonding investigation was performed using the Crystal Orbital Hamilton Population analysis [25] as implemented in SIESTA.

Results and Discussion
3.1. Crystal Structure of the Ca 1-x Eu x Cd 2 Sb 2 Solid Solution The Ca 1−x Eu x Cd 2 Sb 2 solid solution crystallizes in the space group, P3m1, and adopts the CaAl 2 Si 2 structure type (Pearson code hP5), which can be also viewed as a ternary derivative of the La 2 O 3 type ( Figure 1a). Atomic coordinates and equivalent displacement parameters for Ca 1−x Eu x Cd 2 Sb 2 with x = 0.29(1) are presented in Table 2. Crystallographic data for the other studied compositions are given in the Supporting Information. The Ca/Eu, Cd, and Sb atoms are shown in green, red, and blue, respectively; (b) variation of the lattice parameters and unit cell volume of Ca1−xEuxCd2Sb2 as a function of the Eu content. The lattice parameters of the end members, i.e., the ternary phases CaCd2Sb2 and EuCd2Sb2, are included in the plot, but comparing the metrics, it must be born in mind that the literature data for CaCd2Sb2 (marked with asterisks) are from room temperature [26] and that the sample is prepared via a different synthetic route. The parameters for EuCd2Sb2 are from own data (CSD 1875197), whereby the crystal has been grown the same way as Ca1−xEuxCd2Sb2.
In line with the increasing average size of the AE 2+ cation in AECd2Sb2 (AE = Ca + Eu), the AE-Sb contacts become progressively longer upon increasing the level of Eu substitution (Table 3). At the same time, the Cd-Sb bonds remain virtually unaffected. Another noteworthy structural change occurring as the Eu concentration increases concerns the Sb-AE-Sb bond angles, and the trend is suggestive of adopting a more regular octahedral environment of the AE atoms.  and Sb atoms are shown in green, red, and blue, respectively; (b) variation of the lattice parameters and unit cell volume of Ca 1−x Eu x Cd 2 Sb 2 as a function of the Eu content. The lattice parameters of the end members, i.e., the ternary phases CaCd 2 Sb 2 and EuCd 2 Sb 2 , are included in the plot, but comparing the metrics, it must be born in mind that the literature data for CaCd 2 Sb 2 (marked with asterisks) are from room temperature [26] and that the sample is prepared via a different synthetic route. The parameters for EuCd 2 Sb 2 are from own data (CSD 1875197), whereby the crystal has been grown the same way as Ca 1−x Eu x Cd 2 Sb 2 .
The crystal structure accommodates two-dimensional slabs of corner-and edge-sharing CdSb 4 tetrahedra alternating with hexagonal layers of AE atoms, where AE = Ca + Eu. The AE atoms are six-fold coordinated by the adjacent Sb atoms, forming almost perfectly regular octahedra. Assignment of the formal charges to the atoms in the structure yields an electron-balanced composition according to the notation (AE 2+ )(Cd 2+ ) 2 (Sb 3− ) 2 . The end members of these series with x = 0 (CaCd 2 Sb 2 ) and x = 1 (EuCd 2 Sb 2 ) are also known and crystallize in the same structure [26]. In addition, various other pnictides with the AETM 2 Pn 2 composition (AE = alkaline-earth metal, Eu, or Yb; TM = transition metal; Pn = pnictogen) adopt this type [27][28][29]. Many of these phases have been studied as potential thermoelectric materials owing to their narrow-gap semiconducting properties [30][31][32][33][34][35][36]. In the Ca 1−x Eu x Cd 2 Sb 2 series, the lattice parameters and the unit cell volume gradually increase on going from the Eu-poorer to the Eu-richer compositions (Figure 1b), in accordance with a larger ionic size of Eu 2+ in comparison with Ca 2+ (for the same coordination number 6 for instance, r(Ca 2+ ) = 1.00 Å, r(Eu 2+ ) = 1.17 Å [37]). The Vegard's law is not strictly observed, i.e., the change of the unit cell dimensions is not linear, suggesting that local ordering may be taking place. Analysis of the single-crystal diffraction data gives no indication of superstructure reflections, thus confirming the preservation of the long-range CaAl 2 Si 2 structure.
In line with the increasing average size of the AE 2+ cation in AECd 2 Sb 2 (AE = Ca + Eu), the AE-Sb contacts become progressively longer upon increasing the level of Eu substitution (Table 3). At the same time, the Cd-Sb bonds remain virtually unaffected. Another noteworthy structural change occurring as the Eu concentration increases concerns the Sb-AE-Sb bond angles, and the trend is suggestive of adopting a more regular octahedral environment of the AE atoms.  A crystal of the new solid solution with the composition, Ca 2−x Eu x CdSb 2 (x ≈ 0.6), was discovered as a by-product in the sample containing Ca 1−x Eu x Cd 2 Sb 2 as the main phase. The crystal structure of Ca 2−x Eu x CdSb 2 belongs to the Yb 2 CdSb 2 type (Pearson code oS20, space group Cmc2 1 ), in contrast to the parent ternary phase, Ca 2 CdSb 2 , crystallizing in its own type (Pearson code oP20, space group Pnma) [38]. The two prototypic structures possess no homoatomic Sb-Sb bonds and can therefore be rationalized within the Zintl concept as (AE 2+ ) 2 (Cd 2+ )(Sb 3− ) 2 , where AE stands for Yb or Ca. The main difference between the two types stems from non-identical stacking of the layers built up of corner-sharing CdSb 4 tetrahedra. Whereas in the non-centrosymmetric Yb 2 CdSb 2 , the adjacent Cd-Sb layers are related only by translation, in Ca 2 CdSb 2 , similar layers alternate along the stacking direction with their crystallographically inverted counterparts.
From another point of view, the structures of Yb 2 CdSb 2 and Ca 2 CdSb 2 can be understood as two different ways of occupying tetrahedral voids in otherwise isostructural Yb-Sb or Ca-Sb substructures [38]. As local atomic environments in both types appear to be almost identical, subtle electronic or size differences must be responsible for stabilization of one or another structure. As a matter of fact, several pnictides with the "2-1-2" composition have been found to crystallize in the Yb 2 CdSb 2 structure [39,40], whereas Ca 2 CdSb 2 remains the only representative of its type. In this regard, it is important to mention that the Zn-variants with the same composition are totally different (defect ZrBeSi-type structure) [41], and the Mn-based "2-1-2" analogs adopt their own structure [42,43]. Within this context, it also is instructive to recall that a ternary compound, "Eu 2 CdSb 2 ", with either a Ca 2 CdSb 2 or Yb 2 CdSb 2 structure type, is not known to exist (to date). Apparently, the Ca 2 CdSb 2 structure becomes destabilized upon isovalent substitution of Ca with Eu, yielding a solid solution with the non-centrosymmetric Yb 2 CdSb 2 atomic arrangement (Figure 2a). Further optimization of the synthetic procedure will be required to systematically study the structural evolution of the "2-1-2" phase in a wider compositional range and to find the critical Eu content necessary to disrupt the original Ca 2 CdSb 2 structure.   In the crystal structure of Ca2−xEuxCdSb2 (x ≈ 0.6), two nonequivalent AE sites (AE = Ca + Eu) are located between the Cd-Sb layers (AE1) and within the layers (AE2), respectively. The former site adopts a distorted octahedral coordination by the Sb atoms, while the latter position displays a square-pyramidal coordination (Figure 2b). Due to the substantially different volumes of these two coordination polyhedra, pronounced preferred occupation is observed. The AE1 site, offering a larger available volume, accumulates most of the Eu in the structure, whereas the smaller AE2 site shows a minute Eu occupancy of about 2%, in line with a larger ionic radius of Eu 2+ versus Ca 2+ . A similar trend was previously observed for the Yb2CdSb2-type solid solutions, Sr2−xAxCdSb2 (A = Ca, Yb), Ba2−xAxCdSb2 (A = Ca, Sr, Eu, Yb) [39], and Yb2−xEuxCdSb2 [24,39]. In the crystal structure of Ca 2−x Eu x CdSb 2 (x ≈ 0.6), two nonequivalent AE sites (AE = Ca + Eu) are located between the Cd-Sb layers (AE1) and within the layers (AE2), respectively. The former site adopts a distorted octahedral coordination by the Sb atoms, while the latter position displays a square-pyramidal coordination (Figure 2b). Due to the substantially different volumes of these two coordination polyhedra, pronounced preferred occupation is observed. The AE1 site, offering a larger Materials 2018, 11, 2146 7 of 13 available volume, accumulates most of the Eu in the structure, whereas the smaller AE2 site shows a minute Eu occupancy of about 2%, in line with a larger ionic radius of Eu 2+ versus Ca 2+ . A similar trend was previously observed for the Yb 2 CdSb 2 -type solid solutions, Sr 2−x A x CdSb 2 (A = Ca, Yb), Ba 2−x A x CdSb 2 (A = Ca, Sr, Eu, Yb) [39], and Yb 2−x Eu x CdSb 2 [24,39]. Electronic structure calculations were performed within the GGA+U scheme for the idealized CaEuCdSb 2 composition after optimizing the lattice parameters and atomic coordinates. The electronic density of states (DOS) is shown in Figure 3a. In accordance with the simple electron counting in the frame of the Zintl concept, CaEuCdSb 2 displays an electronic bandgap of about 0.5 eV. This value is larger than the 0.1 eV bandgap calculated for the isostructural YbEuCdSb 2 [24]. This is likely is an electronic effect due to electronegativity differences between Yb and Ca, suggesting lower iconicity of the bonding in the latter compound. The states just below the Fermi level (E F ) mainly show the Sb(5p) character, indicating a significant electron transfer onto the Sb atoms. A strong hybridization of these states with Cd(5s) and Cd(5p) occurs in the energy window, −5.5 eV < E-E F < 0. The s, p, and d states of Ca and Eu also demonstrate a sizeable contribution in this energy region. A high peak of the Eu(4f) character is localized around E-E F = −3.7 eV. The converged magnetic moment on the Eu atom is 7.0 µ B , in accordance with the 4f 7 ground term of the Eu 2+ ion. Similar to the case of YbEuCdSb 2 , the Eu f orbitals cannot be considered completely inert in this case, since an apparent hybridization with the Sb(5p) states takes place around the peak position. In addition, a "tail" of the 4f peak extends up to the top of the valence band, hybridizing further with the Sb states. Well below the Fermi level, the DOS is dominated by the Sb(5s) states, corresponding to the Sb lone pairs, and by the occupied Cd(4d) states.
Analysis of the chemical bonding with the aid of the Crystal Orbital Hamilton Population curves (COHP) revealed optimized bonding interactions for the Ca-Sb and Eu-Sb pairs (Figure 3c,d). Most importantly, orbital-resolved COHP analysis showed a small, yet non-negligible contribution of the Eu(4f)-Sb orbital mixing to the overall Eu-Sb bonding. The hybridization of the Eu(4f) and Sb(5p) states around the center of the Eu(4f) peak results in a localized set of bonding states, whereas the hybridization just under E F gives rise to a broad domain of antibonding character. This finding suggests that the typically core-level 4f orbitals may play a role in the crystal structure formation/selection. The involvement of the 4f states in chemical bonding can be important, alongside atomic size factors, for understanding the stability of compounds that are known to form only with certain rare-earth elements, such as the binary RE 3 Bi 7 phases with RE = Nd and Sm [44]. The Cd-Sb contacts display predominantly bonding interactions below E F , with a small domain of antibonding states in the near vicinity of the Fermi level (Figure 3d). A similar bonding pattern was observed for the Cd-Sb interactions in the prototypic Yb 2 CdSb 2 structure [38]. magnetic moment on the Eu atom is 7.0 µB, in accordance with the 4f 7 ground term of the Eu 2+ ion. Similar to the case of YbEuCdSb2, the Eu f orbitals cannot be considered completely inert in this case, since an apparent hybridization with the Sb(5p) states takes place around the peak position. In addition, a "tail" of the 4f peak extends up to the top of the valence band, hybridizing further with the Sb states. Well below the Fermi level, the DOS is dominated by the Sb(5s) states, corresponding to the Sb lone pairs, and by the occupied Cd(4d) states.   Table 6. The inset in (c) shows the orbital resolved Eu(4f)-Sb interaction.
3.3. Crystal Structure of the Eu 11−x Ca x Cd 6 Sb 12 Solid Solution (x ≈ 1) Eu 11−x Ca x Cd 6 Sb 12 crystallizes isotypically to the parent Eu 11 Cd 6 Sb 12 compound (Sr 11 Cd 6 Sb 12 type, Pearson code mS58, space group C2/m (No. 12), Figure 4a) [45,46]. The refined x ≈ 1 in the studied crystal must be close to the upper limit of the Ca substitution for Eu, since the starting mixture contained a large surplus of Ca (recall that the nominal Eu: Ca ratio was 1:1). The crystal structure likely becomes unstable at higher Ca contents due to geometric/size factors. Accordingly, the pure ternary Ca phase has not been reported. This result is in line with the study on the isostructural solid solution, Eu 11−x Yb x Cd 6 Sb 12 , where the Sr 11 Cd 6 Sb 12 type is retained only up to x ≈ 2 [47]. The similarity between the two quaternary systems is likely related to the close ionic radii of Ca 2+ and Yb 2+ : r(Ca 2+ ) = 1.00 Å, r(Yb 2+ ) = 1.02 Å for coordination number 6 [37].
The crystal structure of Eu 11 Cd 6 Sb 12 and isostructural compositions has been described in detail previously [45][46][47][48][49]. The anionic substructure contains infinite fragments of corner sharing CdSb 4 tetrahedra propagating along the monoclinic b axis (Figure 4a). Homoatomic Sb-Sb bonding develops within these fragments, resulting in Sb 2 dumbbells shared between adjacent Cd atoms. In Eu 11−x Ca x Cd 6 Sb 12 , the AE atoms (AE = Eu + Ca), except AE5, are six-fold coordinated by Sb. AE5 resides in a five-fold coordination environment with an average AE-Sb bond length of 3.35 Å. A six-fold coordination of AE5 can be completed by including an Sb atom located at a much longer distance of 3.98 Å. Similarly, the six-fold coordination of the AE1 site (<d(AE-Sb)> = 3.43 Å) can be regarded as a highly distorted square antiprism (coordination number 8) with two additional Sb atoms at 4.02 Å and 4.03 Å from AE1. Although such long distances can hardly be considered bonding interactions, when considered, they provide an estimate of the available volume offered by the Sb coordination environment around each AE position. In fact, the occupancy of the AE sites by Eu correlates well with the volume of such "extended" polyhedra ( Figure 4b). The largest AE1 site is occupied mainly by Eu, whereas the highest Ca occupancy is found for the most spatially confined AE2 position. pattern was observed for the Cd-Sb interactions in the prototypic Yb2CdSb2 structure [38].

Crystal Structure of the Eu11−xCaxCd6Sb12 Solid Solution (x ≈ 1)
Eu11−xCaxCd6Sb12 crystallizes isotypically to the parent Eu11Cd6Sb12 compound (Sr11Cd6Sb12 type, Pearson code mS58, space group C2/m (No. 12), Figure 4a) [45,46]. The refined x ≈ 1 in the studied crystal must be close to the upper limit of the Ca substitution for Eu, since the starting mixture contained a large surplus of Ca (recall that the nominal Eu: Ca ratio was 1:1). The crystal structure likely becomes unstable at higher Ca contents due to geometric/size factors. Accordingly, the pure ternary Ca phase has not been reported. This result is in line with the study on the isostructural solid solution, Eu11−xYbxCd6Sb12, where the Sr11Cd6Sb12 type is retained only up to x ≈ 2 [47]. The similarity between the two quaternary systems is likely related to the close ionic radii of Ca 2+ and Yb 2+ : r(Ca 2+ ) = 1.00 Å, r(Yb 2+ ) = 1.02 Å for coordination number 6 [37]. The crystal structure of Eu11Cd6Sb12 and isostructural compositions has been described in detail previously [45][46][47][48][49]. The anionic substructure contains infinite fragments of corner sharing CdSb4 tetrahedra propagating along the monoclinic b axis (Figure 4a). Homoatomic Sb-Sb bonding develops within these fragments, resulting in Sb2 dumbbells shared between adjacent Cd atoms. In Eu11−xCaxCd6Sb12, the AE atoms (AE = Eu + Ca), except AE5, are six-fold coordinated by Sb. AE5 resides in a five-fold coordination environment with an average AE-Sb bond length of 3.35 Å. A six-fold coordination of AE5 can be completed by including an Sb atom located at a much longer

Conclusions
In summary, using a Pb flux synthesis, we have discovered three new series of solid solutions in the Ca-Eu-Cd-Sb system. The Ca 1−x Eu x Cd 2 Sb 2 series extend the field of quaternary compositions crystallizing in the CaAl 2 Si 2 type. In contrast to these mixed crystals, where the ternary end members adopt the same crystal structure as their solid solution, Ca 2−x Eu x CdSb 2 with x ≈ 0.6 crystallizes in the Yb 2 CdSb 2 structure type, whereas Ca 2 CdSb 2 represents its own type and the hypothetical end member "Eu 2 CdSb 2 " has not been reported. The disruption of the parent Ca 2 CdSb 2 structure upon Eu doping may be a result of size and electronic factors. Interestingly, our first-principle calculations on the idealized CaEuCdSb 2 structure indicate that the Eu(4f) states may be relevant for chemical bonding in this phase. Finally, the Eu 11−x Ca x Cd 6 Sb 12 solid solution adopts the same structure as the parent Eu 11 Cd 6 Sb 12 compound (Sr 11 Cd 6 Sb 12 type). The distribution of Eu over the non-equivalent AE sites (AE = Eu + Ca) correlates well with the available volume offered by these positions. Although the pure calcium counterpart does not exist, the Eu 11−x Ca x Cd 6 Sb 12 appears to extend up to x ≈ 1. In the realm of Zintl chemistry, formation of mixed crystals has been widely employed as a tool for electronic property optimization. Results of the present study demonstrate that, in addition to this capability, solid solutions may provide a way of stabilizing crystal structures not observed for the end members of the corresponding series.