Introduction

Intermetallic phases that combine electropositive group 1-3 elements with main group or late transition metal elements have a wealth of fascinating chemistry and many exotic physical properties. These properties include catalysis in BaGa 2 and CaGaGe, [1] topological phenomena and magnetism in EuSn 2 As 2 and EuIn 2 P 2 , [2] superconductivity in SrPtAs, [3] or structural phase transitions such as those observed in Sr 1-x Ca x PdAs alloys. [4] Phases such as Yb 14 MgSb 11 and Mg 3 Bi 2 , have been also extensively studied for applications in thermoelectrics. [5] The bonding of these phases is often dictated by Zintl-Klemm counting rules in which the electropositive elements donate electrons to the main group elements, which themselves form covalently bonded networks to achieve a full octet. Further work has emphasized how the structures of these phases can vary based on the changes in the cation and anion sizes, such as in A 21 Cd 4 Pn 18 (A=Eu, Sr, Ba; Pn=Sb, Bi). [6] Discovering new materials in this family has also led to new structural motifs such as the bell-like [Ga 5 ] polyanions in Sr 3 Li 5 Ga 5 . [7] Recently, we discovered that transition metal-free layered Zintl-Klemm compounds with electronic structures that are Lewis acidic such as BaGa 2 , YGa 2 , and a new 13-layer trigonal polytype of CaGaGe (13T-CaGaGe), exhibit extraordinary catalytic activities in the partial and full hydrogenation of phenylacetylene to styrene and ethylbenzene. [1] These structures consist of honeycomb networks of main-group elements separated by the electropositive group 1-3 element/lanthanide. The Lewis acidity stems from the elements in the main group framework having either formally 7 valence electrons or weak intralayer π-π bonding. We hypothesized that the presence of 7 valence electrons would make these phases acidic, thereby promoting the adsorption of both H 2 and alkynes. By far, 13T-CaGaGe was the most catalytically active and oxidation-resistant catalyst, maintaining appreciable conversion after exposure to air for five months. Surprisingly, despite the presence of nine known binary CaÀGa and five known binary CaÀGe phases, [8] the only two reported ternary CaGaGe phases are 13T-CaGaGe and the 4-layer hexagonal CaGaGe polytype. In contrast, many other ternary (Ae/Ln)-GaÀGe phases exist (Ae = divalent alkaline earth, Ln = divalent lanthanide Eu 2 + , Yb 2 + ), such as Eu 4 Ga 8 Ge 16 and Sr 8 Ga 16 Ge 30 clathrate, [9] as well as Yb 2 Ga 4 Ge 6 , and Yb 3 Ga 4 Ge 6 (Table 1). [10] Thus, we set out to explore whether other ternary CaÀGaÀGe phases exist. Herein, we report two new phases in the CaÀGaÀGe ternary system Ca 2 Ga 4 Ge 6 and Ca 3 Ga 4 Ge 6 . These compounds are isostructural and isoelectronic analogs to the previously reported Yb 2 Ga 4 Ge 6 and Eu 3 Ga 4 Ge 6 structure types. [10] In both structures, each Ga and Ge atom in the framework would formally feature 8 valence electrons considering electron donation from the Ca. These phases show negligible activity in the hydrogenation of phenylacetylene, in agreement with the expected lack of Lewis acidity. A combination of DFT calculations and electrical transport measurements show both compounds are metallic, similar to the Yb analogues.

Results and Discussion

Single crystals of Ca 3 Ga 4 Ge 6 were prepared by first arc melting together Ca : Ga:Ge in a 3 : 6 : 6 stoichiometry, followed by a crystal growth step in a Ga flux. The resulting Ca 3 Ga 4 Ge 6 product crystallized as needles with typical dimensions of 150-250 μm in diameter and 0.8-2 mm in length. From the single crystal diffraction data, a base-centered monoclinic Bravais lattice was established, and the analysis of the systematic extinctions led to 3 space groups (C2, Cm, and C2/m). Single crystal diffraction analysis confirmed that this phase was a C2/m space group. The fully solved single crystal structure of Ca 3 Ga 4 Ge 6 is shown in Figure 1, S1, Table 2, and Table 3. The solved crystal structure and the lattice constants closely resemble the previously established Yb 3 Ga 4 Ge 6 phase. The a, b, and c lattice constants of Ca 3 Ga 4 Ge 6 were within 0.06-0.12 Å of Yb 3 Ga 4 Ge 6 . Considering the Shannon ionic radii of Ca 2 + and Yb 2 + are within 0.02 Å of each other, it is unsurprising that these changes are subtle. [10,14] Compared to the lattice parame- 3. Atomic coordinates and equivalent isotropic displacement parameters (Å 2 ) for Ca 3 Ga 4 Ge 6 . U(eq) is defined as one third of the trace of the orthogonalized U ij tensor.

x y z U(eq) Ge(1) 0.39517(2) 0 0.63375(3) 0.0142(1) Ge(2) 0.29161(2) 0 0.64436(3) 0.0128(1) Ge(3) 0.44890(2) 1/2 0.96462(4) 0.0160(1) Ge(4) 0.27456(2) 1/2 0.97437 (3) 0.0130(1) Ge(5) 0.34770(2) 0 0.23628(3) 0.0123(1) Ge(6) 0.47697(2) 1/2 0.39761(4) 0.0139(1) Ga(1) 0.25891(2) 1/2 0.74453(4) 0.0135(1) Ga(2) 0.36359(2) 1/2 0.11459(4) 0.0137(1) Ga(3) 0.42065(2) 0 0.41322(3) 0.0111(1) Ga(4) 0.56450(2) 1/2 0.27013(4) 0.0130(1) Ca(1) 0.35541(3) 0 0.89321(7) 0.0149(2) Ca(2) 0.47565(3) 0 0.16846(7) 0.0144(1) Ca(3) 0.32264(3) 1/2 0.45448(7) 0.0175(2)

ters of the Yb phase, Ca 3 Ga 4 Ge 6 is slightly smaller even though the Shannon ionic radius is larger. [14] The size differences do, however, agree with the reported Eu 3 Ga 4 Ge 6 . [10] Additional data collected via single crystal XRD describing the bonding anisotropy are enumerated in Tables S1-2. In this material, the Ca atoms can be thought of as donating electrons into the [Ga 4 Ge 6 ] 6À framework, consistent with the Zintl-Klemm concept. The local coordination of each of the Ca, Ga, and Ge atoms is depicted in Figure S2. The Ca 3 Ga 4 Ge 6 structure contains ten-, seven-, six-and five-membered rings (Figure 1). The ten-membered rings contain 2 Ca 2 + ions between which spans a distance of 4.1987(12) Å. Ca(1) and Ca(2) reside within two different seven-membered ring tunnels.

The anionic [Ga 4 Ge 6 ] 6À framework contains four unique Ga sites which are exclusively coordinated by Ge in distorted tetrahedra and can be assigned a charge of À1, according to the Zintl-Klemm formalism. There are also six distinct Ge sites; four sites are four-coordinate distorted tetrahedra and two sites are three-coordinate. The electron donation by Ca partially reduces two of the 6 Ge atoms (Ge(3) and Ge( 2)), breaking a GeÀGe bond in the framework and leading to a Ge atom in trigonal pyramidal and trigonal planar geometry. There is not a charge assigned to the four-coordinate Ge atoms and the Ge sites that are three-coordinate are assigned a charge of À1. This results in an overall 6-charge on the [Ga 4 Ge 6 ] 6À framework, which is counterbalanced by 3 Ca 2 + atoms.

Figure S2 displays the local coordination of each atomic site within the structure. Each of the Ga sites has a distorted tetrahedral geometry; Ga(1) has angles ranging from 92.421 (17)-113.82(2)°. Ga(2) has 100.354(15)-117.17 (12)°between its bond angles. Ga(3) has bond angles ranging from 102.182( 14)-123.14(2)°and Ga(4) contains bond angles from 94.836 (14)-117.43(2)°. The nearest neighbor GaÀGe bond distances range from 2.5057(3)-2.6630(6) Å with an average of 2.548(45) Å.

The geometries of Ge are tetrahedral in the four-coordinate sites and either trigonal planar or trigonal pyramidal in the three-coordinate sites. The four Ge sites' bond angles are approximately tetrahedral with Ge(1) with 108.208(19)-111.99(2)°, Ge(4) with 99.520(19)-115.63(3)°, Ge(5) with 101.962( 14)-126.640(19)°, and Ge( 6) with 98.06(2)-119.422( 12)°. Ge( 2) is in a trigonal pyramidal environment with angles ranging from 110.179( 14)-113.82(2)°with three Ga atoms forming the base. Ge( 3) is in a distorted trigonal planar environment with bond angles between 113.39(2)-124.17(2)°w hich is relatively close to the 120°of a perfect trigonal planar molecule. Germanium is coordinated to both Ge and Ga and the average GeÀGe bond distances are 2.500(31) Å.

The local coordination environments of the three Ca atoms of Ca 3 Ga 4 Ge 6 are shown in Figure S2. Within a radius of 3.6 Å, Ca (1) is surrounded by 13 atoms including both Ga and Ge atoms in its environment, while Ca (2) and Ca (3) are surrounded by only twelve. The range of CaÀGe bond distances is from 2.9306(9)-3.4811(8) Å and the average CaÀGe bond distance is 3.17( 13) Å. As for CaÀGa bonds, the range of distances is 3.0246(8)-3.5806(7) Å, with an average distance of 3.376 Å. The simulated and calculated diffraction patterns for Ca 3 Ga 4 Ge 6 are available in Figure S3.

Because of the similar X-ray scattering factors and anisotropic displacement parameters of Ga and Ge, it was difficult to conclusively determine the site occupancies of the Ga and Ge. To determine the Ga and Ge positions, we utilized a similar strategy to that which was reported for the initial determination of the structure of Yb 3 Ga 4 Ge 6 . [10] First, careful X-ray Fluorescence (XRF) analysis of the Ca 3 Ga 4 Ge 6 crystals was performed using a calibration curve, and indicated a Ga: Ge ratio of 3.94:6.0, confirming the stoichiometry of these neighboring elements (Figure 2). Second, since the covalent radius of Ge is slightly but still measurably smaller than that of Ga, we initially assigned the longer Ca-metal distances to CaÀGa and the shorter ones to CaÀGe. This resulted in an assignment of Ga and Ge positions as occurs in Yb 3 Ga 4 Ge 6 . To confirm that this assignment was correct, Density Functional Theory (DFT) calculations were performed on four different structures in which certain Ga and Ge assignments were swapped. These alternate structures were chosen in an attempt to keep the longer Ca-metal distances to Ga, maximize the presence of GaÀGe bonds, and minimize the presence of GaÀGa bonds as the presence of homoatomic bonds of the minority component in four-bonded networks in clathrates are exceptionally rare. The original structure was found to be the most stable phase by À1 eV/unit cell (Table S3). Thus, these calculations strongly support the single crystal structure assignment. In addition, Ca has a Bader charge of 1.3, indicating an overall + 2 oxidation state, and an anionic [Ga 4 Ge 6 ] 6-framework. [15] Future neutron diffraction studies could determine whether Ga and Ge site mixing occurs.

We also established a route to synthesize the orthorhombic phase Ca 2 Ga 4 Ge 6 . Single crystals of this new ternary phase were also isolated from and found to be the majority product in a Ga flux reaction, in this case having a 1:15:3 stoichiometry of Ca: Ga: Ge. Minor impurity phases include Ca 3 Ga 4 Ge 6 , and Ge. 4, and Table 5 show the crystal structure that was elucidated from single crystal refinements, and it closely resembles the reported structure of Yb 2 Ga 4 Ge 6 . It crystallizes into a polar orthorhombic space group Cmc2 1 , and is constructed from a [Ga 4 Ge 6 ] 4À framework. In this compound, each Ga site is 4-coordinate with a distorted tetrahedral coordination with neighboring Ge atoms (Figure S4). A myriad of tunnels are formed in this [Ga 4 Ge 6 ] 4À framework, featuring GaÀGe three-, five-, six-, seven-, and nine-membered rings. The Ca (1) and Ca (2) atoms reside within the holes of the sevenand nine-membered rings, respectively. Additional data collected via single crystal XRD fully detailing the bonding anisotropy are enumerated in Tables S4-S5.

Every Ga and Ge atom is covalently bonded to 4 other atoms in this framework, [Ga 4 Ge 6 ] 4À , resulting in an octet for both atoms. In Ca 2 Ga 4 Ge 6 , Ge is coordinated to both Ge and Ga, Ga is exclusively coordinated to Ge. The 2 Ca atoms donate a total of 4 electrons to the 4 different Ga atoms, thereby forming an octet.

There is a four-coordinate, nearly tetrahedral geometry for all Ga and Ge atoms (Figure S2). Ge(3) and Ge( 4) have bond angles that are close to ideal tetrahedral geometries, ranging from 108.04(4)-113.70( 6)°and 103.55(4)-114.94( 6)°. Ge(2) and Ge( 5) are more distorted with Ge(1) bond angles ranging from 91.23(5)-117.89(3)°and 101.06(4)-125.60 (6)°for Ge(2). Ge( 1) and ( 6) have very distorted geometries with angles ranging from 61.24(5)-123.83(3)°and 58.88(4)-124.54(3)°, respectively. The average GeÀGe bond distance at 2.539(29) Å is very similar to that in elemental Ge, which has GeÀGe bond lengths of 2.449 Å. [16] The Ga atoms are also generally in a distorted tetrahedral coordination geometry where the 4 nearest neighbors are Ge atoms. Ga(1) has bond angles ranging from 106.89(4)-127.24(6)°, Ga(3) from 101.83(4)-119.96(5)°and Ga(4) from 103.44(4)-115.33(3)°. By far the most distorted Ga atom is Ga(2) which contains a nearly equilateral triangular bonding arrangement with Ge(1) and Ge (6), with bond lengths ranging from 2.5370( 16)-2.5981 (17) Å and bond angles ranging from 58.88(4)-61.24(5)°. The analogous Yb 2 Ga 4 Ge 6 structure shares this same unique, three-membered, triangular Ge 2 Ga rings, which are occasionally observed in other compounds featuring group 13 atoms. Previous reports of similar three membered rings include Sr 2 Au 6 Ga 3 and Eu 2 Au 6 Ga 3 , both of which contain Ga 3 triangular units. [17] While the triangular moiety is rare, the overall GaÀGe interactions are strong and have an average bond distance of 2.51(4) Å which agrees with the 2.51 Å GaÀGa bond distance reported by Kanatzidis et. al in Yb 2 Ga 4 Ge 6 . [10] Summing the average radius of Ga from its crystal structure (1.33 Å) and the covalent radius of Ge (1.22 Å) yields a distance of 2.55 Å, indicating strong covalent bonding between Ga and Ge in the rigid [Ga 4 Ge 6 ] 4À network.

The coordination environments of the two unique Ca atoms are shown in Figure S5. Ca(1) has 14 atoms in its coordination sphere, 8 are germanium and 6 are gallium. The CaÀGe distances range from 3.039(2)-3.666(3) Å with an average distance in the coordination sphere of 3.28( 23) Å. Ca(2) has a coordination number of 13 consisting of 7 germanium and 5 gallium atoms. The CaÀGa distances fall between 3.081(2)-3.5059(19) Å with the average distance in the coordination sphere of 3.26(15) Å. The lattice constants and bond distances are also similar to that of Yb 2 Ga 4 Ge 6 . [10] Again, the Shannon crystal radius of Ca 2 + is only 0.02 Å larger than Yb 2 + for the 6, 7, and 8 coordination numbers that are enumerated. [14] XRF analysis of the isolated Ca 2 Ga 4 Ge 6 crystals indicated a Ga:Ge ratio of ~3.96:6, again confirming the stoichiometry of these neighboring elements (Figure 2). To elucidate the Ga and Ge positions in the unit cell, we utilized a similar strategy that was described above for Ca 3 Ga 4 Ge 6 . DFT energies of four different structures in which specific Ga and Ge assignments were swapped indicated that this structure was the most stable phase by À1 eV/unit cell (Table S6). These DFT calculations strongly support the assignment of Ga and Ge at specific Wyckoff positions in the single crystal structure determination. Finally, Ca is again calculated to have a Bader charge of 1.3, which indicates an overall + 2 oxidation state and an anionic [Ga 4 Ge 6 ] 4-framework. [15] DFT calculations were also carried out to determine the electronic structure of both Ca 2 Ga 4 Ge 6 and Ca 3 Ga 4 Ge 6 (Figure 4). The band structures of Ca 2 Ga 4 Ge 6 and Ca 3 Ga 4 Ge 6 are available in Figure 4 a, c. Both materials are metallic with multiple bands crossing the Fermi level (E F ). Figure 4 b, d also shows the atomresolved density of states (DOS) plots of these two materials at energies close to E F . In both materials, E F lies in a pseudogap. Additionally, at E F in both compounds, the density of states increases with lower energies, which would suggest holes as the dominant carrier type. [18] Measurements of the electronic properties of sintered pellets of Ca 3 Ga 4 Ge 6 also indicate metallic behavior. Exceptional care was taken to ensure that no residual Ga flux was incorporated into the sintered pellet, as this would provide an electrical short that would convolute the transport data. The presence of residual Ga flux was noticeable in the powder XRD (Figure S6) and would lead to a metallic coating on an agate mortar and pestle upon grinding. To remove this trace Ga flux, we ground the powder in a warm mortar and pestle, cleaned away the Ga coating with HCl, and repeated this procedure multiple times until no further Ga coating was apparent on the mortar and pestle, and no Ga peaks were apparent in the powder XRD spectrum. Unfortunately, growing and separating a sufficiently large quantity of pure material of Ca 2 Ga 4 Ge 6 for electronic transport measurements proved challenging. The powder X-ray diffraction of the majority Ca 2 Ga 4 Ge 6 phase separated from the flux indicated the presence of residual Ca 3 Ga 4 Ge 6 , Ge, and Ga impurities (Figure S7).

Figure 5 shows the electrical resistivity, thermopower, and thermal conductivity of Ca 3 Ga 4 Ge 6 . The room temperature Journal of Inorganic and General Chemistry Zeitschrift für anorganische und allgemeine Chemie RESEARCH ARTICLE 5a), albeit a poor metal. The room temperature resistivity of Ca 3 Ga 4 Ge 6 is two orders of magnitude higher than previous measurements on single crystals of Yb 3 Ga 4 Ge 6 (1.4 μΩ m). [10] The much larger resistivity of this sintered Ca 3 Ga 4 Ge 6 pellet is likely a consequence of the multitude of grain boundaries. Althugh extraordinary care was taken to completely remove any detectable traces of Ga via Xray diffraction, it is possible that the observed metallic behavor was due to the presence of metallic material such as Ga coating the grains. Still, the observed metallic conductivity is strongly supported by band structure calculations. The thermopower ranges from 9-18 μV K À1 from 80-400 K (Figure 5a). The small value is consistent with the metallic nature of the compound and the positive values confirm holes to be the dominant carrier type. The thermal conductivity of the sintered pellet is also quite small and ranges from 3.5 to 2 W m À1 K À1 (Figure 5b). The thermal conductivity is dominated by the lattice component as the electronic portion of the thermal conductivity estimated using the Wiedemann-Franz law (assuming a Lorenz number of 2.44 × 10 À8 W Ω K À2 ) is only ~0.04 W m À1 K À1 at 300 K (Figure 5c). The low lattice thermal conductivity value is expected due to the multitude of grain boundaries in the sintered pellet, along with the relatively large and complex unit cell of the material.

Finally, considering the similar atomic composition to the highly active alkyne hydrogenation catalyst 13T-CaGaGe, [1a,b] Ca 2 Ga 4 Ga 6 and Ca 3 Ga 4 Ge 6 were explored for their ability to hydrogenate phenylacetylene to styrene and/or ethylbenzene. Under 51 bar H 2 , 8 mol% catalyst, 90 °C, and 24 h, 0.91 mmol phenylacetylene, in 2.4 mL n-butanol solvent, 13T-CaGaGe completely converts phenylacetylene to styrene and ethyl-benzene. Using these same conditions Ca 2 Ga 4 Ge 6 , Ca 3 Ga 4 Ge 6 , and a control experiment with no catalyst typically led to < 7 % conversion. Thus, Ca 2 Ga 4 Ge 6 and Ca 3 Ga 4 Ge 6 show negligible activity. As the Ga and Ge atoms in these frameworks have formal octets according to the Zintl-Klemm formalism, the lack of catalytic activity with these compounds is due to the absence of Lewis acidity on the framework. [1a]

Conclusions

Two new compounds, Ca 3 Ga 4 Ge 6 and Ca 2 Ga 4 Ge 6 , have been synthesized as single crystals from gallium flux. These compounds are built from [Ga 4 Ge 6 ] nÀ frameworks that are counterbalanced with Ca 2 + ions. Calculations and measurements indicate that both are metallic. Consistent with our previously established design principles for Zintl-Klemm phase catalysts, these materials are not catalytically active. Considering the complexity of the binary CaÀGa and CaÀGe phase diagrams as well as other ternary phases containing Ga and Ge, it is likely that many more ternary CaÀGaÀGe phases exist that feature exotic properties.

Experimental Section

Synthesis of Ca 2 Ga 4 Ge 6 and Ca 3 Ga 4 Ge 6 : Single crystals of both Ca 2 Ga 4 Ge 6 and Ca 3 Ga 4 Ge 6 were synthesized using a gallium flux method. Ca 2 Ga 4 Ge 6 crystals were prepared by weighing out amounts of Ca granules (Strem, 99.5 % purity), Ga (Acros, 99.99 %) and Ge (Alfa, Aesar, 99.999 % purity) in 1 : 15 : 3 ratio (Ca 2.52 mmol, Ga 37.7 mmol, Ge 7.55 mmol) The mixture was heated to 800 °C over 10 hours, held at 800 °C for 36 hours, and cooled to 200 °C over 18 hours. The resultant flux was centrifuged to reveal single crystals, with an overall yield of 94 %. Ca 3 Ga 4 Ge 6 crystals were prepared by weighing out amounts of Ca, Ga, and Ge in 1 : 2 : 2 ratio (Ca 2.48 mmol, Ga 4.93 mmol, Ge 4.92 mmol) and arc melted under positive pressure of argon via a thoriated tungsten electrode. The resulting button was ground in a Diamonite mortar and pestle (mass of powder 0.4518 g) and transferred into a quartz ampule. Excess gallium (19.6 mmol) was added as flux. The tube was evacuated and sealed. It was then placed in a vertical furnace. It was heated to 800 °C over 4 hours, held for 24 hours, and then cooled to 25 °C over 4 hours. The resulting ingot was warmed with a heat gun to melt the gallium and transferred into a centrifuge tube with quartz wool and centrifuged for 90 seconds at 3000 rpm. Yield was 99 %.

Powder X-ray diffraction: PXRD patterns were collected from the flux-grown crystals that were ground into a powder and collected using Johansson geometry. A Bruker D8 Advance Powder XRD with a monochromated Cu K �1 source was used at a wavelength of 1.5406 Å.

Microscope Images: Images were collected by Olympus EX41 Optical microscope equipped with OptixCam Summit Series for capturing images.

X-ray Fluorescence: X-ray fluorescence was used to elucidate the Ga: Ge ratio of the final compounds. A calibration curve was prepared by weighing out Ge and Ga 2 O 3 powders with Ga: Ge molar ratios ranging from 2 : 6-6 : 6. Data was collected via Thermo Scientific ARL QUANT'X EDXRF Analyzer using a palladium medium filter (Mid Zb).

DFT calculations:

For the DFT calculations, we used the VASP code [19] with PAW PBE potential, [20] a Γ-centered k-point mesh for Brillouin zone integration with a k-spacing of 0.1 Å À1 , and a kineticenergy cutoff for plane-wave expansion of 217 eV. For the band structure, the experimental lattice constants were held fixed, while the atomic positions were allowed to relax. The primitive files and k-space paths for band structure calculations were generated with the SeeK-path online tool. [21] For determining the Ga and Ge assignment, the energy of the different structures was calculated by fixing the experimental lattice constants and relaxing the atomic positions, as well as relaxing both the lattice constants and atomic positions which yielded very similar results.

Single crystal refinements: Ca 2 Ga 4 Ge 6 : The single crystal X-ray diffraction studies were carried out on a Nonius Kappa diffractometer equipped with a Bruker APEX-II CCD and Mo K α radiation (λ = 0.71073 Å). A 0.327 × 0.154 × 0.069 mm 3 piece of a metallic silver block was mounted on a Cryoloop with clear enamel. Data were collected at ambient condition using ϕ and ˆscans. Crystal-todetector distance was 40 mm and exposure time was 10 seconds per frame using a scan width of 1.0°. Data collection was 99.8 % complete to 25.00°in θ. A total of 17751 reflections were collected covering the indices, À5 � h � 5, À32 � k � 32, À15 � l � 15. 1784 reflections were found to be symmetry independent, with an R int of 0.0559. Indexing and unit cell refinement indicated a C-centered, orthorhombic lattice. The space group was found to be Cmc2 1 . The data were integrated using the Bruker SAINT software program and scaled using the SADABS software program. Solution by direct methods (SHELXT) produced a complete model for the phase problem for refinement. [22] All atoms were refined anisotropically by full-matrix least-squares (SHELXL-2014). [23] The absolute stereochemistry of the material was established by anomalous dispersion using the Parson's method with a Flack parameter of 0.006 (22). Ca 3 Ga 4 Ge 6 : The single crystal X-ray diffraction studies were carried out on a Nonius Kappa diffractometer equipped with a Bruker APEX-II CCD and Mo K α radiation (λ = 0.71073 Å). A 0.102 × 0.044 × 0.038 mm 3 piece of a metallic silver block was mounted on a Cryoloop with clear enamel. Data were collected at ambient condition using ϕ and ˆscans. Crystal-to-detector distance was 40 mm and exposure time was 10 seconds per frame using a scan width of 1.0°. Data collection was 100 % complete to 25.00°in θ. A total of 16233 reflections were collected covering the indices, À32 � h � 34, À5 � k � 6, À15 � l � 15. 1883 reflections were found to be symmetry independent, with an R int of 0.0388. Indexing and unit cell refinement indicated a C-centered, monoclinic lattice. The space group was found to be C2/m. The data were integrated using the Bruker SAINT software program and scaled using the SADABS software program. Solution by direct methods (SHELXT) produced a complete model for the phase problem for refinement. All atoms were refined anisotropically by full-matrix least-squares (SHELXL-2014).

Electronic and thermal transport measurements:

The Seebeck coefficients, resistivities, and thermal conductivities of sintered Ca 3 Ga 4 Ge 6 pellets were measured from 80 K to 400 K in a Janis liquid nitrogen vacuum cryostat. A four-probe measurement geometry was used to measure sample resistance. For thermal conductivity and thermopower measurements, current was passed through a 120 Ω Omega strain gauge to apply heat to one end of the sample while two type T thermocouples measured the resulting temperature gradient and Seebeck voltage. The thermocouples, resistive heater, and current wires were attached to the sample using Epo-Tek H2OE silver epoxy cured at 135 °C.

The errors of thermopower and resistivities were propagated based on the value of ΔL T /L T , or the diameter of silver epoxy used to affix copper (voltage) wires to the sample divided by the length between the wires. Care was taken to use as little silver epoxy paste as possible to minimize heat dissipation from the sample through the electrical contacts. Sample cross-sectional areas were measured both manually with calipers and digitally with image processing software to confirm the dimensions.