Introduction

Intermetallic compounds provide extensive opportunities to investigate the relationships between composition, structure, and chemical bonding. [1][2][3][4][5][6][7] Among the various classes of intermetallic phases, polar intermetallics stand out as particularly suitable for such studies as they feature great structural diversity. [8,9] Polar intermetallics typically consist of less electronegative elements like alkali, alkaline-earth, and rare-earth metals, combined with more electronegative elements from the late transition metals groups and early post-transition metals, such as Al, Si, and Ge. [10] As such, many polar intermetallics are close relatives to the Zintl phases, where the polarization of the bonding is even more pronounced and covalent-like bonding characteristics are easily discernable. [11][12][13] As noted in prior contributions, including some authored by Prof. G. J. Miller, [10] the relatively high electronegativity difference between the constituent elements leads to three distinct bonding characteristics: i) the bonding within the electronegative (poly) anionic network is optimized at the Fermi level, creating a clear separation between filled bonding states and unoccupied antibonding states. ii) Although there is no distinct energy gap between the valence and conduction bands, the density of states (DOS) at the Fermi level often exhibits a minimum, commonly referred to as a pseudogap. iii) Less electronegative metals may not contribute all of their valence electrons to the network of electronegative polyanions. [14] In this regard, polar intermetallics can be viewed as bridging the gap between the traditional Zintl phases and the Hume-Rothery (electronic) and Laves (geometric) phases. [9,15,16] The crystal growth of intermetallics is greatly facilitated by the metal flux technique, which provides a robust process toward the synthesis of highly crystalline materials. [17,18] In the past, our group utilized the latter and studied a large number of new compounds, germanides of alkaline-earth and rare-earth metals in particular, [19][20][21][22][23][24][25] which were readily obtained from molten metal fluxes. In many instances, incorporation of the flux metal leading to ternary and quaternary compounds was serendipitously identified. Consequently, complex structures with unusual chemical bonding and "coloring" of the metal sites can be observed. [26] Of specific relevance to the compound described in this article are the indium germanides: i) A 2 InGe 2 ("2À1À2" phase), [21] ii) A 3 In 2 Ge 3 ("3À2À3" phase), [19] iii) A 3 In 2 Ge 4 ("3À2À4" phase), [20] iv) A 5 In 3 Ge 6 ("5À3À6" phase), [20] and v) A 4 In 3 Ge 4 ("4À3À4" phase) [19] where A denotes rare-earth and alkaline-earth metals, often times not crystallographically ordered. The common structural feature of those families is the [InGe 4 ] tetrahedron, which by either edge-or corner-sharing yields this wide variety of structures.

Since the focus of this article is on a new member of the "4À3À4" family, it is appropriate to provide a brief overview of the structural diversity within it. The parent structure is actually that of the binary phase Mg 5 Si 6 (Pearson symbol mS22), [27] and until not too long ago, there were only few known isotypic phases, all of which were investigated in the early 2000's.

Among them are the quaternary phases RE 4 Ni 2 InGe 4 (RE = Dy, Ho, Er, and Tm) [28] where Ni atoms take one of the Si sites and the In atoms take the Mg site with the special position at the origin (Figure 1).

More quaternary RE 4 M 2 InGe 4 , RE 4 M 2 CdGe 4 , and RE 4 M 2 AgGe 4 analogs (M = transition metal) [29,30] have since been discovered, however, their structures are not devoid of disorder. In 2010, we reported on the structure of (Eu 1Àx Ca x ) 4 In 3 Ge 4 (0.35(1) ≤ x ≤ 0.70(1)), [19] a phase where rare-earth metal cations are partially substituted by alkaline-earth metal cations; the In and Ge sites are fully occupied although one may notice that In atoms occupy sites that in the archetype Mg 5 Si 6 structure are both cationic and anionic (Figure 1). Although we made an effort, ternary Eu 4 In 3 Ge 4 or Ca 4 In 3 Ge 4 phases could not be synthesized, leaving an open question as to what is the exact role of the mixed cations with regards to the crystal chemistry and chemical bonding.

Over the years, we tried a different approach, namely, using a single cation-either Ca or Eu-and substituting indium with an electron-poorer or richer element. With this contribution, we report a detailed synthesis and structural analysis of Ca 4 CdIn 2 Ge 4 , a new member of the "4À3À4" family with different cation ordering.

Experimental Section

Synthesis

Single crystals of Ca 4 CdIn 2 Ge 4 were synthesized by using molten In as a flux. The elements Ca, Cd, In, and Ge were purchased from Sigma-Aldrich and Alfa Aesar with a purity ≥99.9% wt. Briefly, all synthetic and postsynthetic manipulations were performed in an argon gas-filled glove box with O 2 /H 2 O levels below 1 ppm, or under vacuum. Ca: Cd: Ge: In were weighed in ratio 2:1:3:30 inside an argon-filled glovebox. The elemental mixtures were loaded into alumina crucibles, which were placed inside fused silica tubes. The alumina crucibles were covered with a plug made of quartz wool on top. After that, the tubes were evacuated and flame-sealed.

The heat treatment took place in programmable muffle furnaces with the following optimized procedure: 1) sample was heated to 973 K (heating rate 200 K h À1 ); 2) equilibrated for 20 h; and 3) cooled down to 673 K at a rate of 10 K h À1 followed by cooled down to 373 K at a rate of 25 K h À1 . Then the mixture was heated again to 573 K to melt the excess indium. At this stage, the reaction vessel was taken out from the furnace, and the In-flux was quickly removed by a centrifuge. Then, the tubes were brought back in the glove box and cut open inside there.

The crystals of Ca 4 CdIn 2 Ge 4 have needle-like habit and exhibit silver metallic luster. In polycrystalline form, the material is stable in the ambient atmosphere for at least 24 h, as confirmed by X-Ray diffraction work.

Structural Characterization

Powder X-Ray diffraction measurements were carried out at room temperature on a Rigaku Miniflex diffractometer (Ni-filtered Cu Kα radiation, λ = 1.5418 Å). A few of the obtained single crystals were selected and ground into powder using an agate mortar and pestle (in the protective atmosphere of the glove box). The polycrystalline material was then laid flat on a glass slide (Figure S1, Supporting Information). The diffraction pattern was collected between 5°and 75°in 2θ with a step size of 0.02°and 1 s per step counting time.

Suitable single crystals were selected and were cut under Paratone-N oil to appropriate dimensions (≤0.10 mm). After that, crystals were scooped by MiTeGen plastic loops and transferred to the goniometer of a Bruker APEX diffractometer, equipped with monochromatized Mo Kα radiation, λ = 0.71073 Å. During the data collection, the crystal was under a stream of cold [27] b) RE 4 Ni 2 InGe 4 (RE = Dy, Ho, Er, and Tm), [28] and c) (Eu 1Àx Ca x ) 4 In 3 Ge 4 (for simplicity, Ca and Eu atoms are considered as ordered, i.e., the shown structure has the chemical formula Ca 2 Eu 2 In 3 Ge 4 ). [19] The respective Wyckoff positions of each crystallographically independent atom are given in parentheses.

nitrogen (200(2) K). The data were collected and processed with SAINT and SADABS software packages. Structure solution (intrinsic phasing method using SHELXT) and refinement (fullmatrix least-squares methods on F 2 with SHELXL) were carried out under the OLEX2 interface. [31][32][33] Atomic coordinates were standardized using the STRUCTURE TIDY program, [34] and atomic labels were set to be consistent with previous studies. [19] Refinements yielded flat difference Fourier map and low conventional residual factors, with all atoms treated anisotropically and showing no anomalous displacement parameters (Figure S2, Supporting Information). Selected details of the data collection and relevant crystallographic parameters of the sample are given in Table 1. The full crystallographic data (CIF) are deposited in the Cambridge Crystallographic Data Centre (CCDC) with a deposition number 2417195.

Elemental Microanalysis

Metallographic analyses and elemental mapping were conducted on several crystals of Ca 4 CdIn 2 Ge 4 from different batches to confirm their elemental compositions and uniform distribution of the elements. The crystals were mounted on a carbon tape glued to an aluminum holder. The analyses were performed on Auriga 60 cross-beam scanning electron microscope (SEM) equipped with Oxford Synergy X-MAX80 and EBSD (electron back-scattering diffraction) X-Ray energy-dispersive (EDX) spectrometer. The beam current was 10 μA at 20 kV accelerating potential. Data were collected over several spot and the observed elemental proportions were consistent from sample to sample and are in agreement with the single-crystal X-Ray diffraction work. The EDX result from a selected spot, the respective SEM image, and elemental mappings are shown in Figure 2.

Electronic Structure Calculations

To calculate the electronic band structure of Ca 4 CdIn 2 Ge 4 , we used the Stuttgart TB-LMTO-ASA code [35,36] with the local density approximation. Experimental unit cell parameters and atomic coordinates of Ca 4 CdIn 2 Ge 4 were used as the input parameters in our calculation. To satisfy the atomic sphere approximation (ASA), we introduced empty spheres into the calculation. The von Barth-Hedin functional (LDA) was employed, [37] and 8 Â 8 Â 8 k-point grid was used for Brillouin zone (BZ) integrations. Chemical bonding was examined by plotting crystal orbital Hamilton population (COHP) curves, [38] using the dedicated module of LMTO software.

Results and Discussion

Synthesis and Structure

The In-flux method has been very successful for the synthesis of many "4À3À4" phases. [19] As noted already, in our own work, we were successful in obtaining (Eu 1Àx Ca x ) 4 In 3 Ge 4 (0.35(1) ≤ x ≤ 0.70(1)), but the trials syntheses of ternary Eu 4 In 3 Ge 4 or Ca 4 In 3 Ge 4 phases were unsuccessful. We also tried experiments aimed at (Yb 1Àx Ca x ) 4 In 3 Ge 4 (keeping in mind the close radii of Yb 2þ (1.00 Å) and Ca 2þ (1.02 Å) [39] ), but those reaction failed to yield the desired phases. Yet, isostructural compounds with smaller RE 3þ ions are known in the literature. [28] These results indicate that for their existence, the A 4 In 3 Ge 4 phases require both optimization of atom packing (geometric principle) and number of valence electrons (electronic principle).

Following that notion, we attempted the growth of Ca 4 Cd 3 Ge 4 and Yb 4 Cd 3 Ge 4 crystals from In flux. The experiments with Yb afforded orthorhombic Yb 5 Ge 4 [40] as the main product, while experiments with Ca produced small needle-like crystals with a previously unknown structure. Structure solution from single-crystal X-Ray diffraction (SCXRD) data confirmed that the monoclinic structure of the new phase belongs to the "4À3À4" family, but it was unclear if the synthesized material is Ca 4 Cd 3 Ge 4 or Ca 4 (In 1Àx Cd x ) 3 Ge 4 (the other end member Ca 4 In 3 Ge 4 , based on prior work can be deemed improbable). The reason for the ambiguity is trivial-SCXRD cannot distinguish Cd and In atoms (with just one electron difference), therefore, new set of experiments was carried out, this time without indium and using excess Cd as a self-flux. These trials did not result in Ca 4 Cd 3 Ge 4 , instead, the rhombohedral CaGe 2 [41] phase was identified as a main product. The inability to access the target phase from a mixture of Ca, Cd, and Ge can serve as an indirect proof that In must be present in the crystal structure, i.e., the chemical formula Ca 4 (In 1Àx Cd x ) 3 Ge 4 is the most reasonable. The complimentary EDX spectroscopy results corroborate the presence of both cadmium and indium (Figure 2). The elemental mapping analysis also confirmed that all the elements are well-dispersed and distributed homogeneously. Since the ratio In:Cd was found to be almost exactly 2:1, in the structure refinements, Cd atom was placed in the special position 2a while In atom was placed at position 4i (vide infra). This results in a structure with full atomic ordering and a composition Ca 4 CdIn 2 Ge 4 . We note that refining both positions as occupied by In (Z = 49) produces very good fit to the data with freely refined occupancies of 99.3(4)% (4i) and 98.6(4)% (2a)

1.11, À1.26

and a flat difference Fourier map. Conversely, refining both positions as occupied by Cd (Z = 48) also produced quite reasonable fit to the data with occupancies (freely refined) slightly exceeding unity. This, together with the small improvement of the anisotropic displacement parameters when In and Cd were refined on the 4i and 2a sites, respectively, (Figure S2, Supporting Information) was taken as an indication of it being the best structural model. Nevertheless, we caution the reader that the put forth refinement model is just one of many possibilities, since 2:1 ratio of In: Cd could be achieved by disordering the atoms on both positions. For example, full occupation of 2a by Cd and 50:50 admixture of Cd and In on 4i will yield the same elemental makeup. Unfortunately, this hypothesis cannot be tested experimentally neither with X-rays (too close scattering factors), nor neutrons (Cd is a very heavy neutron absorber). Whether the former or the latter model is closer to reality may not be known, yet, experimental evidence supports the composition remaining nearly constant, i.e., the homogeneity range in Ca 4 (In 1Àx Cd x 4) Å. [19] The larger unit cell volume for (Eu 1Àx Ca x ) 4 In 3 Ge 4 is of course expected since there is a significant difference in radii between Eu (1.98 Å) and Ca (1.76 Å). [42] The difference in radii between Cd (1.44 Å) and In (1.42 Å) [42] is not as pronounced though, and some degree of Cd-In disordering may remain unnoticed.

Having touched upon the crystal structure already, let us now take a more careful look at its important elements. There are six unique crystallographic positions in the structure-two are taken by Ca atoms, and two by Ge atoms (Table 2). Cd and In atoms occupy the other two, with Cd at Wyckoff site 2a and the In atom at 4i, as already stated. This atomic arrangement constitutes an ordered quaternary structure with a chemical formula Ca 4 CdIn 2 Ge 4 (Figure 3). The close relationship with other ubiquitous structure types has already been recognized, [19] and the overall atomic arrangement can be viewed as an intergrowth of CsCl-, AlB 2 -, and the TiNiSi-like fragments.

Comparing Ca 4 CdIn 2 Ge 4 to the archetype Mg 5 Si 6 structure (Pearson code mS22) [27] requires one of the Mg atoms to be assigned as Cd with the remaining two Mg sites given to Ca. Similarly, one of the three Si sites of Mg 5 Si 6 will be taken by the In atom, and the other two will be assigned to Ge (Figure 1a and 3). If a parallel is drawn to (Eu 1Àx Ca x ) 4 In 3 Ge 4 , (Figure 1c), then the only change is the assignment of the In at site 2a as Cd. Interestingly, for the other ordered quaternary structure, that of RE 4 Ni 2 InGe 4 (RE = Dy, Ho, Er, and Tm), [28] (Figure 1b) the assignment of the main group and transition element positions differhere, In is located at Wyckoff site 2a and the Ni atom is at 4i.

The main features of the crystal structure of Ca 4 CdIn 2 Ge 4 are the ribbons of fused [InGe 4 ] tetrahedra connected by Ge 2 dimers and bridged by Cd atoms in nearly square-planar environment. This description follows the consideration of the In─Ge and Cd─Ge interactions as mostly covalent, and the Ca─Ge or Ca─M (M = Cd, In) interactions as mostly ionic. Assuming the ordered structural model with Cd at Wyckoff site 2a and In atom at 4i (Table 2), one will see the formation of [InGe 4 ] tetrahedra (Figure 4a) and [CdGe 4 ] planar fragments (Figure 4b). The double chains of edge-shared and corner-shared tetrahedra run along the crystallographic b-axis and are conjoined via Ge─Ge bridges in the ac-plane, resulting in polyanionic [InGe 2 ] layers parallel to the ab-plane and stacked along the c-axis (Figure 3). Should there be only partial Cd and In ordering (vide supra), the ribbons ought to be a statistical mixture of edge-sharing [InGe 4 ] and [CdGe 4 ] tetrahedra. The Ca2 atoms are situated within the same layer in the ab-plane, while Ca1 atoms are located between adjacent layers (Figure 3).

[InGe 4 ] tetrahedra are not the rare, and are present in the structures of many ternary and quaternary germanides, including the isotypic (Eu 1Àx Ca x ) 4 In 3 Ge 4 . They are also known in the structurally related phases (Eu 1Àx Ca x ) 3 In 2 Ge 3 , [19] A 3 In 2 Ge 4 , [20] and A 5 In 3 Ge 6 , [20] among others. The range of In─Ge distances is somewhat wide, from 2.76(1) to 2.88(1) Å (Figure 4a and Table 3) with the average value being somewhat longer than the sum of the covalent radii (r In = 1.42 Å; r Ge = 1.20 Å). [42] The observed d In─Ge range is very close to what is found in the isotypic (Eu 1Àx Ca x ) 4 In 3 Ge 4 (d In─Ge = 2.75À2.89 Å). [19] Similar d In─Ge values are also reported for the structures of the ternary EuInGe (d In─Ge = 2.751 Å) [43] as well as quaternary A 2 LiInGe 2 (A = Ca, Sr) (d In─Ge = 2.806À2.904 Å) [44] and ALi 2 In 2 Ge 2 (A = Sr, Ba, Eu) (d In─Ge = 2.719À2.748 Å) [45] phases.

The Ge─Ge distances in Ca 4 CdIn 2 Ge 4 (2.53 Å) are similar to the distances in (Eu 1Àx Ca x ) 4 In 3 Ge 4 (d Ge─Ge = 2.54 Å), [19] (Sr 1-x Ca x ) 5 In 3 Ge 6 (d Ge─Ge = 2.52À2.55 Å), and (Sr 1-x Ca x ) 3 In 2 Ge 4 (d Ge─Ge = 2.53À2.62 Å), [20] which feature identical/similar structural motifs. Ge─Ge distance of 2.53 Å is also comparable to the reported a) U eq is defined as 1/3 of the trace of the orthogonalized U ij tensor. b) Another model that will result in a composition in line with the elemental analysis result is to place indium atoms at site 2a and disorder of In/Cd (with the ratio of 50/50) in site 4i. There is, however, no statistically significant improvement in residuals and/or U eq values that would indicate which model is more accurate. bond lengths for some binary germanides with typical 2center two-electron bonds: d Ge─Ge = 2.551 Å in EuGe 2 , [46] d Ge─Ge = 2.541 Å in CaGe 2 , [47] and d Ge─Ge = 2.575 Å in Ca 5 Ge 3 , [48] to name a few. We should also note that the distance within the Ge─Ge dimers in the title compound is substantially longer than the doubly-bonded Ge 2 unit (d Ge─Ge = 2.39 Å) in Li 3 NaGe 2 , [49] and slightly longer than d Ge─Ge = 2.48À2.50 Å in binary Li 5Àx Ge 2 , [50] and d GeÀGe = 2.50 Å in the ternary Ba 2 Li 1Àx Ge 3þx , [51] where the Ge─Ge dimers are considered as species being intermediate between singly-and doubly-bonded. Therefore, in Ca 4 CdIn 2 Ge 4 , the Ge─Ge bond should be of bond order 1. The bonding characteristic of the dimer will be further discussed in the context of the electronic structure calculation results in the next section.

The Cd atoms are in CdGe 4 square-planar geometry (Figure 3 and 4b), bonded to two Ge1 and two Ge2 atoms. The Cd─Ge1 and Cd─Ge2 distances fall in the range from 2.94 to 3.11 Å (Figure 4b and Table 3) and are much longer than the sum of the respective covalent radii (r Cd = 1.44 Å; r Ge = 1.20 Å), [42] indicating weaker interactions comparing to the already discussed In─Ge bonds in the InGe 4 tetrahedra. One should notice that the Cd─Ge distances are longer compared to those in RE 2 CdGe 2 (RE = Pr, Nd, Sm, Gd─Yb; Y) [52] where the Cd atoms are also situated in square-planar arrangement of Ge (d Cd─Ge = 2.84À2.97 Å). In the structures of other cadmium germanides, such as A 3 Cd 8 Ge 4 (A = Sr, Eu) for example, the Cd atoms are in tetrahedral environment of Ge atoms and the range of Cd─Ge distances is much shorter (2.60À2.80 Å). [53] This is another indicator that in planar fourfold coordination, the Cd─Ge bonding character is not conventional. The latter can be expected to pose problems applying the valence principles for partitioning of the available electrons (vide infra).

The environments of the two crystallographically distinct Ca atoms are very different from each other (Figure 4c,d). As shown in the Figure, Ca1 atoms are found in the coordination of a total of ten atoms (five Ge atoms, three In atoms, and two Cd atoms). Ca1-Ge distances are relatively short, ranging between 3.06 Å to 3.17 Å (Figure 4c and Table 3). Three In atoms and two Cd atoms are located about 3.5 Å away, capping the edges of the {Ca1}Ge 5 polyhedron that resembles a square pyramid (Figure 4c). The Ca2 atom is surrounded by six nearest Ge atoms (Ge1 Â 4 and Ge2 Â 2) with distances ranging between 3.09 and 3.26 Å (Figure 4d and Table 3). Two In atoms (at distance of 3.37 Å) and two Cd atoms (3.44 Å away) make the Ca2 coordination polyhedron resemble the ferrocene molecule in its eclipsed form (pentagonal prism, as depicted in Figure 4d). Similar atomic environment of the Ca atoms are known in the "5-3-6" and "3-2-4" germanides, with similar structural motifs. [20] In both Ca polyhedra, Ca─In and Ca─Cd distances are much longer than the sum of the respective covalent radii; Ca─Ge distances are also longer than the sum of the covalent radii, although d Ca1─Ge1 = 3.06 Å and d Ca1─Ge2 = 3.08 Å are approaching the value expected for covalency (r Ca = 1.76 Å; r Ge = 1.20 Å). [42] Based on the above, one might reason that the Ca-interactions exhibit the traits of both ionic and weakly covalent bonding, as narrated next in the theoretical calculations section.

Electronic Structure

Prior to this work, electronic structure calculations for the "4-3-4" phase were only performed for an idealized Eu 2 Ca 2 In 3 Ge 4 model structure by taking the approximation that Eu and Ca atoms are ordered on the two cationic positions. [19] Here, we present the calculation for the Ca

4 CdIn 2 Ge 4 structure, as discussed in the previous section, without further constraints. The total DOS and partial DOS for each element are presented in Figure 5a. There is no band gap opening and the Fermi level (E F ) cuts through a region of relatively low DOS. This clearly indicates metallic characteristics, indirectly supporting the failure of the valence rules and the Zintl concept to arrive at an electron-balanced formulation. That is, neither the covalent [Ca 2þ ] 4 [4b-Cd 0 ][4b-In 1À ] 2 [3b-Ge 1À ] 2 [4b-Ge 0 ] 2 (a formal charge of zero is assigned to Cd following the considerations put forth by Köhler et al. regarding La 2 InGe 2 ,

where the In atoms are square-planar as well [54] ), nor the fully ionic approximation [Ca 2þ ] 4 [Cd 2þ ][In 3þ ] 2 [Ge 3À ] 2 [Ge 4À ] 2 (Ge atoms are in two different oxidation states to account for the formation of homoatomic Ge─Ge bonds) produce sensible results. In part, this shortcoming of the classic rules might be due to the participation of Ca 2þ "cations" in covalent interactions (vide infra), which could be the actual contributing factor for not opening of a gap in the electronic band structure. Another likely contributing factor is the ambiguous assignment of charge for the Cd atom in a planar 4-coordinate environment (Figure 4b); calculating the corresponding charges of the neighboring Ge atoms also contributes to this conundrum. Specifically, as discussed earlier, some Cd─Ge interatomic distances are greater than 3.10 Å, longer than some of the Ca─Ge ones, which could indicate the absence of appreciable Cd─Ge covalency. Accordingly, Ge2 atom may be said to have only three covalent bonds to In atoms and a formal charge of 1À; following the same reasoning, the Ge1 atom will have only two bonds-one to In atom and another one to a symmetryequivalent Ge1 atom, with a formal charge of 2-. Thus, the Zintl concept could be applied to arrive at the electron-balanced formulation

, in line with the calculated pseudo-gap at the Fermi level (Figure 5). From Figure 5a, four main regions of DOS can be differentiated: i) the region between À7.4 and À10.8 eV, which is dominated by core Cd states following by Ge states with minimum contributions from Ca and In states; ii) the region between À4.9 and À6.3 eV is mostly contributed by In and Ge states followed by Cd states. The overlapping between In and Ge states indicates covalent bonding characteristics; iii) the region between À4.5 and 0 eV, where Ge and Ca states are the dominant, and iv) the region above the E F , which is dominated by Ca states.

We also note that Ca 4 CdIn 2 Ge 4 and the previously considered Eu 2 Ca 2 In 3 Ge 4 are isostructural, but are not isoelectronic. The total DOS for Ca 4 CdIn 2 Ge 4 shows a minimum at the Fermi level (corresponding to 32 valence electrons per formula unit). For comparison, the reported DOS for Eu 2 Ca 2 In 3 Ge 4 has the Fermi level (33 valence electrons per f.u.) located between two "local minima" within AE0.35 eV from E F , corresponding to 32 and 34 valence electrons, respectively. [19] To evaluate more scenarios of Fermi level locations and local minima, we performed calculations for two additional imaginary models, Ca 4 In 3 Ge 4 (close analog of the already mentioned model compound Eu 2 Ca 2 In 3 Ge 4 ) and Ca 4 Cd 2 InGe 4 , considering the unit cell parameters from Table 1, and atomic coordinates given in Table 2. þ0.70 eV, respectively (Figure S3 and S4, Supporting Information), relative to E F from the integration with 32 valance electrons.

The COHP curves for selected interactions are shown in Figure 5b. The plots indicate that all interactions that were considered are not fully optimized at the Fermi level. The In─Ge, Cd─Ge, and Ge─Ge interactions show antibonding characteristics at the Fermi level, which are "compensated' by the slightly bonding characteristics of the Ca─Ge interactions. The Ge1-Ge1 shows a distinctive antibonding character at À7.8 eV (Figure 5b), which is expected for the typical single-bonded Ge─Ge dimers. [19,50] Not surprisingly, the integrated value per Ge─Ge bond at the Fermi level (-ICOHP) shows the highest value, affirming the notion that Ge─Ge covalent interactions are the strongest in general. Analogously, the -ICOHP values for the Ca─Ge interactions are smaller than the others indicating the weakest covalent characteristic of Ca─Ge bonding, as also indicated in the previous section. The -ICOHP value for Cd─Ge interaction at the Fermi level is lower than that of In─Ge interaction, clearly indicating that the bonds in square-planar geometry are less covalent in character comparing the In─Ge bonds in tetrahedral geometry.

Conclusion

In this work, we dealt with the synthesis and the structural characterization of the new quaternary germanide Ca 4 CdIn 2 Ge 4 . The structure was established by SCXRD methods and the refined chemical formula was complemented by analysis. The model used for the structure refinements based on SCXRD data uses fullrange atomic ordering with indium and cadmium atoms situated on sites with tetrahedral and square-planar coordination, respectively. However, there also is a possibility that indium and cadmium atoms are partially disordered. With the deference of only one electron between In and Cd atoms, it is impossible to differentiate the two scenarios based on X-Ray diffraction methods alone. Possible experimental validation could come from studying Ca 4 CdGa 2 Ge 4 or Ca 4 ZnIn 2 Ge 4 , if such phases can be synthesized. Such further studies on new "4-3-4" phases can shed more light on the outstanding issues.