Crystal Structure, Chemical Bonding and Magnetism Studies for Three Quinary Polar Intermetallic Compounds in the (Eu1−xCax)9In8(Ge1−ySny)8 (x = 0.66, y = 0.03) and the (Eu1−xCax)3In(Ge3−ySn1+y) (x = 0.66, 0.68; y = 0.13, 0.27) Phases

Three quinary polar intermetallic compounds in the (Eu1−xCax)9In8(Ge1−ySny)8 (x = 0.66, y = 0.03) and the (Eu1−xCax)3In(Ge3-ySn1+y) (x = 0.66, 0.68; y = 0.13, 0.27) phases have been synthesized using the molten In-metal flux method, and the crystal structures are characterized by powder and single-crystal X-ray diffractions. Two orthorhombic structural types can be viewed as an assembly of polyanionic frameworks consisting of the In(Ge/Sn)4 tetrahedral chains, the bridging Ge2 dimers, either the annulene-like “12-membered rings” for the (Eu1−xCax)9In8(Ge1−ySny)8 series or the cis-trans Ge/Sn-chains for the (Eu1−xCax)3In(Ge3−ySn1+y) series, and several Eu/Ca-mixed cations. The most noticeable difference between two structural types is the amount and the location of the Sn-substitution for Ge: only a partial substitution (11%) occurs at the In(Ge/Sn)4 tetrahedron in the (Eu1−xCax)9In8(Ge1−ySny)8 series, whereas both a complete and a partial substitution (up to 27%) are observed, respectively, at the cis-trans Ge/Sn-chain and at the In(Ge/Sn)4 tetrahedron in the (Eu1−xCax)3In(Ge3−ySn1+y) series. A series of tight-binding linear muffin-tin orbital calculations is conducted to understand overall electronic structures and chemical bonding among components. Magnetic susceptibility measurement indicates a ferromagnetic ordering of Eu atoms below 5 K for Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13.


Introduction
Polar intermetallic and Zintl phase compounds have been one of the most interesting research topics for solid-state chemists to investigate the co-relationship among composition-structure-property and to apply the obtained knowledge to various energy-related materials, such as thermoelectrics, magnetocalorics and magnetoresistance materials [1][2][3][4][5][6]. Among these compounds, the rare-earth metal containing compounds are worth exploring due to their intriguing chemical and physical characteristics derived by electrons in the 4f orbitals [7][8][9][10][11]. In particular, some polar intermetallics containing europium with the half-filled 4f orbitals are known to show anomalous magnetic properties [12][13][14].
In this article, we report crystal structures of two title phases in terms of the amount and the location of the Sn-substitution and provide the rationale for these phenomena using the atomic size-factor perspective and comprehensive theoretical analyses. Tight-binding linear muffin-tin orbital (TB-LMTO) calculations [21][22][23][24][25] were conducted using two structural models with idealized compositions. Density of states (DOS) and crystal orbital Hamilton population (COHP) curves [26] were thoroughly studied to understand orbital contributions for particular energy regions and chemical bonding from interatomic interactions. Physical and chemical analyses including energy-dispersive X-ray spectroscopy (EDS), scanning electron microscope (SEM), differential scanning calorimeter (DSC), and magnetization were also performed. Eu3.04(4)Ca5.96In8Ge7.77(2)Sn0.23 is the first quinary derivative of the recently reported (Eu1−xCax)9In8Ge8 [14] series having a partial Sn-substitution for Ge. The title compound adopted its parental Eu2.94 (2)Ca6.06In8Ge8-type structure and crystallized in the orthorhombic Pmmn space group (Z = 2, Pearson code oP50) with 14 crystallographically independent sites in the asymmetric unit ( Table 1). The overall crystal structure is illustrated in Figure 1, and a SEM image of a needle-/bar-shaped single-crystal is also shown in Figure 2a. (b) The edge-sharing In(Ge/Sn)4 tetrahedra; (c) The "12-membered rings"; (d) The 1D zig-zag In-chain; and (e) The 1D cis-trans Ge/In-chain are also illustrated. Unit cell is outlined in black. Color codes are as follows: M(Eu/Ca-mixed site), gray; Ge, magenta; Ge1/Sn-mixed site, purple; and In, yellow.  The overall crystal structure can be viewed as an assembly of the three-dimensional (3D) polyanionic framework consisting of three types of anions and five mixed-cationic sites embedded within the framework. Furthermore, the 3D framework can be understood as a combination of (1) the one-dimensional (1D) In(Ge/Sn)4 tetrahedral chains extending along the b-axis direction and (2) the distorted annulene-like "12-membered rings", which stacked on top of each other along the b-axis direction and eventually resulted in forming three edge-sharing pentagonal-prisms (See the right side of Figure 1). This anionic 12-membered ring can alternately be viewed as a combination of the 1D zig-zag In-chains ( Figure 1d) and the 1D cis-trans Ge/In-chains (Figure 1e) propagating, respectively, along the b-axis and the c-axis as illustrated in the left side of Figure 1. According to this alternative perspective, the structure type of the (Eu1−xCax)9In8(Ge1−ySny)8 phase can more easily be comparable to the other title phase, the (Eu1−xCax)3In(Ge3−ySn1+y) series, which will be discussed in a subsequent section. In addition, the In(Ge/Sn)4 chains and the 12-membered rings are further connected via the Ge2 dimers along the a-axis direction. Interestingly, the newly introduced Sn partially substituted for Ge (11%) only at the Ge1 site in the In(Ge/Sn)4 tetrahedron among total nine anionic sites. The rest of Ge and In sites showed no sign of the Sn-substitution. The limited Sn-substitution at the Ge1 site is clearly distinctive from the Sn-substitution occurred in the (Eu1−xCax)3In(Ge3−ySn1+y) series. We will further discuss about the different Sn-substitutions in the subsequent section.

Crystal Structure Descriptions
The overall crystal structure can be viewed as an assembly of the three-dimensional (3D) polyanionic framework consisting of three types of anions and five mixed-cationic sites embedded within the framework. Furthermore, the 3D framework can be understood as a combination of (1) the one-dimensional (1D) In(Ge/Sn)4 tetrahedral chains extending along the b-axis direction and (2) the distorted annulene-like "12-membered rings", which stacked on top of each other along the b-axis direction and eventually resulted in forming three edge-sharing pentagonal-prisms (See the right side of Figure 1). This anionic 12-membered ring can alternately be viewed as a combination of the 1D zig-zag In-chains ( Figure 1d) and the 1D cis-trans Ge/In-chains ( Figure 1e) propagating, respectively, along the b-axis and the c-axis as illustrated in the left side of Figure 1. According to this alternative perspective, the structure type of the (Eu1−xCax)9In8(Ge1−ySny)8 phase can more easily be comparable to the other title phase, the (Eu1−xCax)3In(Ge3−ySn1+y) series, which will be discussed in a subsequent section. In addition, the In(Ge/Sn)4 chains and the 12-membered rings are further connected via the Ge2 dimers along the a-axis direction. Interestingly, the newly introduced Sn partially substituted for Ge (11%) only at the Ge1 site in the In(Ge/Sn)4 tetrahedron among total nine anionic sites. The rest of Ge and In sites showed no sign of the Sn-substitution. The limited Sn-substitution at the Ge1 site is clearly distinctive from the Sn-substitution occurred in the (Eu1−xCax)3In(Ge3−ySn1+y) series. We will further discuss about the different Sn-substitutions in the subsequent section.
As briefly mentioned earlier, there exist five asymmetric Eu/Ca mixed-sites, which are surrounded by Ge and In. In particular, the M1 site having ca. 30% of Eu occupation has a total coordination number of 9 and shows the distorted square-pyramidal coordination environment. The rest of four cationic sites having a total coordination number of 10 are surrounded by the pentagonal-prismatic environments: the M2 and the M3 sites are coordinated by six Ge (or Ge/Sn) and four In atoms, whereas the M4 and the M5 sites are coordinated by six In and four Ge atoms ( Figure 1 and Table 2).   27 in the (Eu1−xCax)3In(Ge3−ySn1+y) phase have been serendipitously produced when the reaction condition satisfied two following criteria: (1) the loaded Sn content increased up to equal to or slightly higher than the loaded Ge content and (2) the loaded ratio between Eu/Ca-and Ge/Sn-mixture was 1:1. Interestingly, according to a recent article about the (Eu1−xCax)4In3Ge4 and the (Eu1−xCax)3In2Ge3 series [12], either one of two phases could selectively be produced by controlling the loaded ratio between Eu and Ca. For instance, the (Eu1−xCax)4In3Ge4 phase was produced when the ratio varied between ca. 2:1 and 1:2, whereas the (Eu1−xCax)3In2Ge3 phase was obtained only when the loaded Ca content was at least three times larger than Eu, such as Eu:Ca = 1:3 or 1:9. However, in this study, we revealed that two quinary derivatives from the (Eu1−xCax)3In(Ge3−ySn1+y) phase could possibly be obtained even when the loaded Ca contents were much smaller than those claimed in the earlier report, such as Eu:Ca = 1:1.94 and 1:2.16. In addition, the overall atomic % of Eu in title compounds was different from those in the parental (Eu1−xCax)3In2Ge3 phase, which could not exceed 20% under any attempted reaction conditions. The rationale behind the limited Eu content was attributed to the fact that packing two different size cations in an ordered manner provided very little energy profit [12]. However, in the title phase, it increased up to 34 atomic % and could be explained by the atomic size-factor: the larger-size Sn atoms substituted the smaller-size Ge atoms not only at the vertex of the In(Ge/Sn)4 tetrahedron, but also on the 1D cis-trans chain. As a result, an overall size of the unit cell including the 3D anionic framework expanded large enough to accommodate extra amounts of Eu.
Two title compounds in the (Eu1−xCax)3In(Ge3−ySn1+y) phase adopted the orthorhombic space group Pnma (Z = 4, Pearson code oP32) and contained eight crystallographically independent atomic sites in the asymmetric unit as provided in Tables 1 and 2. The overall crystal structure can be viewed as an assembly of three structural moieties: (1) the 1D edge-sharing In(Ge/Sn)4 tetrahedral chains propagating along the b-axis direction; (2) the infinite cis-trans Ge/Sn-chains extending along the a-axis direction and (3) the Ge2 dimers bridging these two structural moieties as illustrated in Figure 3. SEM images of two needle-/bar-shaped single-crystals are also displayed in Figure 2b,c. The In(Ge/Sn)4 tetrahedral chain resembles the chain observed in Eu3.04(4)Ca5.96In8Ge7.77(2)Sn0.23 including a partial Sn substitution for Ge, and the In-Ge/Sn bond distances in the tetrahedron (2.779 and 2.914 Å) are well comparable to those in Eu3.04(4)Ca5.96In8Ge7.77(2)Sn0.23 as well as in some compounds discussed earlier. In particular, the infinite cis-trans Ge/Sn-chains, in which Ge and Sn atoms were alternately arranged in the cis-and trans-conformation, showed the relatively longer Ge-Sn bond distances (2.859 and 2.861 Å) than the sum of covalent radii of Ge and Sn (2.62 Å = 1.22 Å(rGe) + 1.40 Å(rSn)) [27]. Lastly, the Ge-Ge distances of the Ge2 dimer in two title compounds were nearly identical, 2.534 and 2.536 Å, and these values were also comparable to those in Eu3.04(4)Ca5.96In8Ge7.77(2)Sn0.23 and in the parental (Eu1−xCax)3In2Ge3 series [12]. As briefly mentioned earlier, the crystal structure of the (Eu1−xCax)3In(Ge3−ySn1+y) phase can be compared with that of the (Eu1−xCax)9In8(Ge1−ySny)8 phase. Firstly, both phases contain the common structural moieties including the edge-sharing In(Ge/Sn)4 tetrahedra and the cis-trans Ge/In-or Ge/Sn-chains. However, the (Eu1−xCax)9In8(Ge1−ySny)8 phase exclusively includes the additional 1D zig-zag In-chains propagating along the b-axis and perpendicular to the cis-trans In/Ge-chains. In addition, the crystal structure contains two crystallographic mirror planes, respectively, along the (1/4 0 0) and (3/4 0 0) planes containing those zig-zag In-chains. Furthermore, the (Eu1−xCax)3In(Ge3−ySn1+y)-type structure is very closely related to the previously reported the (Eu1−xCax)4In3Ge4 phase [12], in which the isotypic InTt4 (Tt = Tetrels) tetrahedra with the Ge2 dimers (previously-called "dumbbells") were connected directly to each other along the a-axis and via In atoms along the c-axis. Therefore, all these three phases can also be regarded as an intergrowth series with slightly different structural moieties.
It is noteworthy to mentioned that the most noticeable difference between the (Eu1−xCax)9In8(Ge1−ySny)8 and the (Eu1−xCax)3In(Ge3−ySn1+y) phases was the amount and the location of Sn-substitution: in the (Eu1−xCax)9In8(Ge1−ySny)8 phase, the 11% of Sn-substitution was successfully demonstrated only at one vertex of In(Ge/Sn)4 tetrahedron; whereas, in the (Eu1−xCax)3In(Ge3−ySn1+y) phase, not only the partial Sn-substitution (ca. 13% or 27%) occurred at one vertex of the tetrahedron, but also the complete substitution happened at one Ge site on the cis-trans chain. Therefore, if the Zintl-Klemm concept is applied to this phase, the chemical formula can be re-written as where a slightly charge-unbalanced formula should be expected. In addition, this chemical formula can explain the metallic property of the (Eu1−xCax)3In(Ge3−ySn1+y) phase represented by the following DOS curves shown in Figure 4b.

Electronic Structure Calculations
A series of theoretical investigations have been systematically conducted using TB-LMTO method [24] to understand overall electronic structures of two title phases and chemical bonding among components [28][29][30]. Given the practical reason, a mixed-occupation of two atoms at one atomic site cannot be applied to computational calculations. Therefore, two structural models with idealized compositions of "Eu3Ca6In8-7Sn" and "EuCa2InGe3Sn", respectively, representing the (Eu1−xCax)9In8(Ge1−ySny)8 and the (Eu1−xCax)3In(Ge3−ySn1+y) phases were designed and exploited for our theoretical studies.

Eu3Ca6In8Ge7Sn
To build a model with an idealized composition of Eu3Ca6In8Ge7Sn, firstly the experimentally obtained space group Pmmn was replaced by Pmm2 to divide one Ge1/Sn mixed-site (Wyckoff 4f) into two individual sites (Wyckoff 2e and 2f), and then Ge and Sn atoms were allocated to each site accordingly. In addition, two mixed-cationic sites having the larger Eu contents than other sites (M2 and M5) were solely assigned for Eu, whereas the rest of three mixed-cationic sites (M1, M3 and M4) were assigned for Ca. TB-LMTO calculations were executed using this structural model, and the resultant DOS and COHP curves are displayed in Figure 4a. Total and partial DOS curves show an overall valence orbital mixing of five components throughout the entire energy window. The local DOS minimum (so-called pseudogap) is observed at the Fermi level (EF) implying a semi-metallic property of this phase, just like its parental (Eu1−xCax)9In8Ge8 phase.
Total DOS curve can roughly be divided into three sectors below EF. The sector between −10.5 and −7 eV displays several large peaks, which represent Ge σs bonding-and σs* antibonding-states originated from the bridging Ge2 dimer. The sector between −7 and −4 eV includes strong contributions descended from In 5p and Ge 4p states consisting of the 12-membered ring. Lastly, the sector from −4 to 0 eV shows significant contributions from In 5p and Ge 4p states with small additions from Sn 4p states, respectively, consisting of the In(Ge/Sn)4 tetrahedron and the Ge2 dimer. In particular, the noticeably large contributions from Eu and Ca are also observed in this sector implying that some degrees of bonding interactions between cations and anions should exist. This is one of the typical features of polar intermetallic compounds, which is caused by an incomplete electron transfer from cations to anions. Six COHP curves are also displayed in the middle and the bottom of Figure 4a. The Ge-Ge COHP curve from the Ge2 dimer shows a strong anti-bonding character at EF, whereas the In-Ge and the In-Sn COHP curves from the In(Ge/Sn)4 tetrahedron are optimized at EF. Three In-Ge COHPs representing various interactions on the 12-membered ring indicate relatively weak, but nearly optimized, interactions at EF.

EuCa2InGe3Sn
For the structural model representing the (Eu1−xCax)3In(Ge3−ySn1+y) phase, the orthorhombic space group Pnma was exploited as obtained from the SXRD refinement. However, the M2 site showing the largest Eu content among three mixed-cationic sites was solely assigned for Eu, and two other cationic sites were assigned for Ca. In addition, the mixed-site occupied by Ge3 and Sn2 was fully allocated by Ge to fulfill the idealized composition. It is noteworthy to mention that the Eu partial occupations over three mixed-cationic sites in the title phase resembled the partial occupation trend observed in the parental (Eu1−xCax)3In2Ge3 phase, where the largest Eu content was found at the M2 site, then the next largest one at the M1 site. The M3 site showed the smallest amount of Eu. The rationales for this site-preference of Eu were thoroughly investigated using both the coloring-problem and the QVAL value criteria in the earlier article [14].
A series of calculations was performed using EuCa2InGe3Sn, and DOS and COHP curves are illustrated in Figure 4b. The overall DOS curves and the location of EF are similar to those obtained from Eu3Ca6In8Ge7Sn as compared in Figure 4. In addition, the total DOS curve below EF can roughly be divided into three sectors as well. However, the specific orbital contributions to these sectors were slightly different from those in Eu3Ca6In8Ge7Sn. In particular, the sector between −10.5 and −7.5 eV is mostly contributed by Ge 4s and Sn 5s orbitals originated, respectively, from bonding-and antibonding-states of the Ge2 dimers, and bonding-states of the 1D cis-trans Ge/Sn chains. The sector between −7 and −4.5 eV has contributions from Ge 4s, Sn 5s and In 5s orbitals from antibonding-states of the infinite cis-trans Ge/Sn-chain and bonding-/antibonding-states of the In(Ge/Sn)4 tetrahedron, respectively. Lastly, the sector between −4 and 0 eV displays a strong orbital mixing of Ge 4p, In 5p and Sn 5p states with some contributions from two cations. Two COHP curves of the Ge-Ge and the Ge-Sn bonding, respectively, from the Ge2 dimer and the cis-trans Ge/Sn chain display small antibonding characters at EF, whereas the In-Ge COHP from the In(Ge/Sn)4 tetrahedron is nearly optimized at EF. Three COHP curves representing interatomic interactions between cations and anions (Ca1-Ge2, Eu2-Ge1, and Ca3-Ge3) show relatively weak and small bonding characters (bottom of Figure 4b). These favorable bonding interactions can compensate several unfavorable antibonding characters descended from the Ge-Ge and the Ge-Sn bonding and eventually stabilize the overall crystal structure in the given chemical composition.

Physical Property Measurements
The temperature-dependent dc magnetization was measured on a polycrystalline sample of Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13 to study the magnetic interactions between Eu atoms. Since the magnetization study for the parental (Eu1−xCax)3In2Ge3 phase was unsuccessful due to the presence of a secondary phase in products, the current magnetic property for its quinary derivative is the first report for its kind. Figure 5 illustrates the magnetization as a function of temperature between 5 and 300 K under zero-field cooled (ZFC) and field cooled (FC) conditions using the dc magnetic field of 10 kOe. The inverse susceptibility is also shown as a function of temperature in inset.
Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13 followed the Curie-Weiss law with the corresponding paramagnetic behavior, and there was no indication of magnetic ordering down to 5 K. The effective magnetic moment of 7.34 μB per Eu 2+ ion was calculated from a linear fit of the inverse magnetic susceptibility versus temperature, and this value was relatively lower than the theoretically expected effective moment of 7.94 μB for a free Eu 2+ ion. This kind of discrepancy between the experimental and the theoretical values was previously reported in our recent article about Eu3.13(2)Ca5.87In8Ge8, which was also synthesized by the molten In-metal flux method. The reason for this discrepancy was attributed to small amounts of remaining In metals even after the centrifugation conducted at the last stage of the flux reaction. The inclusion of In metals in our product was verified by powder X-ray diffraction (PXRD) (Figure 6), DSC ( Figure 7) and SEM images analyses. The extrapolation of the linear fitting for the magnetic susceptibility curve in the paramagnetic region resulted in θP = +3.32 K, which indicated a weak and relatively low temperature ferromagnetic (FM) ordering of Eu atoms.  7 displays a DSC curve plotting the heat flow as a function of temperature change between 300 and 770 K. No exothermic or endothermic peak was observed except a peak at 420 K originated from In metal. This implies that there exists no impurity phase in a product and no possibility of structural transformation or decomposition of the product in the measured temperature range.

Synthesis
All manipulations during the synthesis were carried out in an argon-filled glove-box with O2 and H2O contents of <0.1 ppm or under vacuum. The starting materials were used as purchased from Alfa, and the list of materials is as follows: Eu-ingot, 99.9%; Ca-shot, 99.5%; In-tear drop, 99.99%; Ge-pieces, 99.999%; and Sn-shot, 99.99%. Tanned surface of the Eu ingot was scrapped off using a scalpel before loaded in a reaction container. The molten In-metal flux reaction, in which excess amounts of In metals were used as a reactive flux, was carried out in an alumina crucible (ca.  1.0-1.2), respectively, for derivatives of the (Eu1−xCax)9In8(Ge1−ySny)8 and the (Eu1−xCax)3In(Ge3−ySn1+y) phases. After each elemental mixture was loaded in a reaction container, it was subsequently enclosed in a fused-silica ampoule by flame-sealing under vacuum. Then, the fused-silica ampoule was heated up to 960 °C at the rate of 200 °C/h by a box-type furnace, held there for 20 h, then cooled down to 500 °C at the rate of 5 °C/h. The extra amounts of molten In metals were removed by the instantaneous centrifugation at 500 °C. Large amounts of well-grown bundles of bar-/needle-shaped single-crystals with a silver luster were obtained from all three products. Eu3.04(4)Ca5.96In8Ge7.77(2)Sn0.23 was air-/moisture-sensitive and started to decompose after one day, whereas two compounds in the (Eu1−xCax)3In(Ge3−ySn1+y) phase remained intact at least for one week.

Crystal Structure Determinations
Crystal structures of three title compounds have been characterized by both powder and single-crystal X-ray diffractions (SXRD). Powder X-ray diffraction (PXRD) patterns were obtained using Bruker D8 diffractometer (monochromatic Cu Kα1 radiation, λ = 1.54059 Å) with a step size of 0.05° in the range of 15° ≤ 2θ ≤ 85° and a total exposure time of 1 h. Primarily, a phase purity of each product was briefly checked, and lattice parameters of each unit cell were obtained using program Rietica [31]. Several peaks originated from remaining In metals were also indexed. SXRD data were collected using Bruker SMART APEX2 CCD-based diffractometer (Bruker, Billerica, MA, USA) equipped with Mo Kα1 radiation (λ = 0.71073 Å) at room temperature. Firstly, several silvery lustrous bar-/needle-shaped single-crystals were isolated and selected from bundles or aggregates of each product. After then, the qualities of selected crystals were briefly checked by a rapid scan, and the best crystal was chosen for the further data collection. Full data collection was processed using the Bruker APEX2 software [32]. Data reduction, integration, and unit-cell refinements were carried out using SAINT program [33], and semi-empirical absorption correction based on equivalents was conducted using the SADABS program [34]. The program XPREP in the SHELXTL software package was exploited to sort and merge the structure factors [35]. Refined parameters included the scale factor, atomic positions with anisotropic displacement parameters, extinction coefficients, and occupation factors of five Eu/Ca mixed-sites and one Ge/Sn mixed-site for Eu3.04(4)Ca5.96In8Ge7.77(2)Sn0.23, and three Eu/Ca mixed-sites and one Ge/Sn mixed-site for Eu0.95(1)Ca2.05InGe2.73(1)Sn1.27 and Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13, respectively.
During the structure refinement for two compounds in the (Eu1−xCax)3In(Ge3−ySn1+y) series, we found that the atomic displacement parameters (ADP) for the Sn1 sites were slightly higher than those of Ge and In sites. These Sn1 sites were crystallographically the identical sites to the In2 sites of the parental (Eu/Ca)3In2Ge3 phase [12], and the ADP for the In2 sites in the parental phase were also slightly higher than those of other In-and Ge-sites. Therefore, the larger ADP at the given site should be regarded as a structural characteristic of this type of structure. However, in order to clarify any possibility of a partial occupation or a Ge-mixed occupation for the Sn1-sites, we attempted to refine the crystal structures by allowing free occupations at the given site. However, as the occupations of the Sn1-sites were set free, the values became 99.7(2)% and 100.3(3)%, respectively, for Eu1.02Ca1.98InGe2.87Sn1.13 and Eu0.95Ca2.05InGe2.73Sn1.27, and the ADP were kept nearly constant. Thus, we concluded that there was no further reason to consider either a partial or a mixed-occupation for the Sn1 sites.
In the last refinement cycle, atomic positions were standardized using STRUCTURE TIDY [36]. Important crystallographic data, atomic positions, thermal displacement parameters, and selected interatomic distances are listed in Tables 1-3

Electronic Structure Calculations
Theoretical investigations have been carried out using two structural models with idealized compositions of "Eu3Ca6In8Ge7Sn" and "EuCa2InGe3Sn" representing for the (Eu1−xCax)9In8(Ge1−ySny)8 and the (Eu1−xCax)3In(Ge3−ySn1+y) phases, respectively. The Stuttgart TB-LMTO47 program with the atomic sphere approximation (ASA) [25] was exploited, and exchange and correlation were treated by the local density approximation (LDA) [22]. All relativistic effects except spin-orbit coupling were taken into account by using a scalar relativistic approximation. In the ASA method, space is filled with overlapping Wigner-Seitz (WS) atomic spheres [25], and the symmetry of the potential is considered spherical inside each WS sphere. A combined correction is used to take into account the overlapping part [37]. The radii of WS spheres were determined by an automatic procedure and by requiring the overlapping potential be the best possible approximation to the full potential [37]. This overlap should not be too large because the error in kinetic energy introduced by the combined correction is proportional to the fourth power of the relative sphere overlap. No empty sphere [25] [25]. The 4f wave functions of Eu were treated as core functions. The k-space integrations were conducted by the tetrahedron method [38], and the self-consistent charge density was obtained using 360 and 216 irreducible k-points in the Brillouin zone, respectively, for Eu3Ca6In8Ge7Sn and EuCa2InGe3Sn.

EDS and SEM Images Analyses
Elemental analysis via EDS and product images of single-crystals were taken by ULTRA Plus field-emission SEM system (Zeiss, Oberkochen, Germany) with an acceleration voltage of 30 kV. Several bar-/needle-shaped single-crystals were selected from each product batch, and those crystals were carefully mounted on the circumference of an aluminum puck with double-sided conducting carbon tapes inside an argon-filled glove-box. EDS results are as follows: Eu3.27 (9)

DSC Measurement
Thermal characteristic of Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13 was investigated by DSC using the TA instruments DSC2910 (TA Instruments, New Castle, DE, USA). The sample was enclosed in an aluminum container and heated from 300 up to 773 K at 10 K/min, then cooled down to 300 K at 10 K/min under N2 atmosphere.

Magnetic Property Measurements
Magnetization of Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13 was measured by MPMS-7 using a polycrystalline sample weighing ca. 60 mg. To investigate the dc magnetization, the measurement was initially performed on heating the sample from 25 to 300 K under zero-field-cooled condition (ZFC). The measurement was repeated upon cooling from 300 to 5 K with a magnetic field of 10 kOe under field-cooled condition (FC).

Conclusions
Three Sn-substituted quinary polar intermetallic compounds in the (Eu1−xCax)9In8(Ge1−ySny)8 and the (Eu1−xCax)3In(Ge3−ySn1+y) series have been synthesized using the molten In-metal flux method and characterized by both powder and single-crystal X-ray diffractions. Eu3.04(4)Ca5.96In8Ge7.77(2)Sn0.23 adopted its parental Eu2.94(2)Ca6.06In8Ge8-type structure, and the overall crystal structure was viewed as an assembly of the 3D polyanionic framework consisting of the 1D In(Ge/Sn)4 tetrahedral chain, the annulene-like 12-membered rings and the bridging Ge2 dimers, and the space filling mixed-Eu/Ca cations. The 12-membered ring can alternately be viewed as a combination of two different types of 1D anionic chain, the zig-zag and the cis-trans, propagating orthogonal directions to each other. Since the partial Sn-substitution for Ge was confined at the Ge1 site in the In(Ge/Sn)4 tetrahedron, the overall size of a unit cell as well as various interatomic distances were not much enlarged. Five mixed-cationic sites were locally surrounded by either 9 or 10 anions, respectively, forming a distorted pyramid or pentagonal-prisms. On the other hand, two derivatives in the (Eu1−xCax)3In(Ge3−ySn1+y) phase were obtained as the loaded Sn content increased up to equal to or slightly higher than that of Ge. Unlike the parental phase, two derivatives were successfully crystallized in the given structure type even when the loaded Eu:Ca ratio was nearly 1:2. In addition, the overall atomic % of Eu included in compounds also increased up to 34 atomic %, which exceeded the previously claimed maximum limit of 20 atomic %. The rationale for this phenomenon should be attributed to the atomic size-factor: the Sn-substitution for Ge both in the In(Ge/Sn)4 tetrahedron and the 1D cis-trans chain caused polyanionic frameworks to expand resulting in accommodating extra amounts of larger-size Eu in compounds.
A series of theoretical investigations was conducted using two structural models of Eu3Ca6In8Ge7Sn and EuCa2InGe3Sn. The resultant DOS and COHP analyses indicated overall significant valence orbital mixings of all five components throughout the entire energy window and implied semi-metallic characters for both title phases. The temperature-dependent magnetization measurement for Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13 proved the effective magnetic moment of 7.34 μB per Eu 2+ ion and a low temperature FM ordering of Eu with θP = +3.32 K. The relatively low value of an effective magnetic moment was attributed to the presence of remaining In metals in a product. The DSC measurement also confirmed that there existed no secondary phase in Eu1.02(1)Ca1.98InGe2.87(1)Sn1.13 and no structural transformation or decomposition within the measured temperature range.