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Germanium Dumbbells in a New Superconducting Modification of BaGe3 Rodrigo Castillo, Alexey I. Baranov, Ulrich Burkhardt, Raul Cardoso-Gil,† Walter Schnelle, Matej Bobnar, and Ulrich Schwarz* Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Straße 40, 01187 Dresden, Germany S Supporting Information *

ABSTRACT: We report the high-pressure high-temperature synthesis (P = 15 GPa, T = 1300 K) of BaGe3(tI32) adopting a CaGe3-type crystal structure. Bonding analysis reveals layers of covalently bonded germanium dumbbells being involved in multicenter Ba−Ge interactions. Physical measurements evidence metal-type electrical conductivity and a transition to a superconducting state at 6.5 K. Chemical bonding and physical properties of the new modification are discussed in comparison to the earlier described hexagonal form BaGe3(hP8) with a columnar arrangement of Ge3 triangles.

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and 8(1)−15(2) GPa. The previously described modification of BaGe3(hP8) is reported to form between 5 and 13 GPa and 770 and 1470 K.7 The new phase BaGe3(tI32) forms at 15 GPa and 1300 K. X-ray Diffraction Data Collection and Processing. Phase identification was realized by X-ray powder diffraction experiments with a Huber Image Plate Guinier camera G670, employing Cu Kα1 radiation, λ = 1.540 562 Å. High-temperature experiments were realized in a STOE-STADIP-MP equipped with a Ge-monochromator, in Debye−Scherrer geometry using a heating rate of 10 K/min and a holding time for data acquisition of 150 min. For Rietveld refinement, high-resolution synchrotron X-ray diffraction data were collected with powder samples at the beamline ID22 of the ESRF, with an incident wavelength of λ = 0.400 66 Å. Crystal structure solution and refinement were performed by means of the WinCSD software packages,8 and estimated standard deviations for the full-profile refinements were calculated using the Berar−Lelann algorithm taking into account local correlations.9 Thermal Analysis. Differential scanning calorimetry (DSC) experiments were performed on sample material in closed alumina crucibles operated under an argon atmosphere and using a Netzsch DSC 404C apparatus. The heating and cooling rates were set to 10 K/ min. Energy-Dispersive X-ray Analysis. For the metallographic analysis, the samples were polished by using discs of micrometersized diamond powders (6, 3, 0.25 μm) in paraffin and investigated with a Philips XL 30 scanning electron microscope (LaB6 cathode). Energy-dispersive X-ray spectroscopy (EDXS) was performed with an attached EDAX Si(Li) detector. The composition was determined by wavelength-dispersive X-ray spectroscopy (WDXS, Cameca SX 100). For that purpose, Ba6Ge25 and Ge(cF8) were used as standards for Ba and Ge, respectively. The WDXS measurements were performed at 10

INTRODUCTION In a property-guided approach to basic materials and energy science, the electronic organization of the solid is the essential quality that predetermines the functionality of the material. The determining factors for the valence electron distribution are chemical composition and atomic organization, and highpressure synthesis has proven successful as a tool to expand and modify the spectrum of accessible structure patterns.1−4 Most suited objects of investigation are covalent framework ensembles constituted by main-group elements since electron balance and network topology are interconnected by established counting rules.5 Here, we report the synthesis of the recently and independently predicted new high-pressure modification BaGe3(tI32)6 and discuss its chemical bonding and superconducting properties in comparison to the earlier described modification BaGe3(hP8) with a columnar Ge substructure.7

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EXPERIMENTAL SECTION

Synthesis. Preparation and sample handling were realized in argon-filled gloveboxes (MBraun; p(H2O) ≤ 0.1 ppm and p(O2) ≤ 0.1 ppm). Precursor samples with nominal composition BaGe3 were prepared by arc melting of elemental Ba (Alfa Aesar 99.98%) and Ge (Chempur 99.9999%). In order to account for evaporation losses during the melting process, a mass excess of 1% of the alkaline-earthmetal barium was added. The resulting ingots were ground and loaded in the BN crucibles, which are enclosed in graphite sleeves for resistive heating. High-pressure generation was realized with a Walker-type module using MgO octahedra of 14 mm edge length. Pressure and temperature calibration were performed prior to the experiments by in situ monitoring of the resistance changes of bismuth and by runs using a thermocouple, respectively. Several conditions for temperature and pressure have been applied in the ranges 1100(110)−1500(150) K © XXXX American Chemical Society

Received: February 3, 2016

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DOI: 10.1021/acs.inorgchem.6b00299 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry different spots on the polished surface of a bulk piece and reveal the composition Ba0.9(1)Ge3.1(1). Physical Properties Measurements. Magnetization measurements (temperatures 1.8−400 K, magnetic fields μ0H = 0.002−7 T) were performed in a SQUID magnetometer (MPMS XL-7, Quantum Design). High-field susceptibility data were corrected for tiny ferromagnetic contributions. The heat capacity was measured by a relaxation-type method (PPMS, Quantum Design) between 1.9 and 100 K in fields up to 1 T. Electrical resistivity (ρ) measurements were performed between 2 and 320 K by a standard four-probe technique (ac transport option, PPMS). Due to the irregular shape of the sample and uncertainties of the contact geometry, the estimated inaccuracy of ρ is ±40%. Electronic Structure Calculations. Electronic structure calculations for the BaGe3 polymorphs were carried out using the FPLAPW+lo method as implemented in the Elk code10 within the local density approximation.11 For the calculations, the experimentally determined structural parameters were employed. The muffin-tin radii were set to 1.17 and 1.06 Å (2.2 and 2.0 bohr) for Ba and Ge, respectively; the plane wave cutoff factor RMT × kmax = 9.0 was used, and the number of irreducible k-points for the Brillouin zone integration was 128. The chemical bonding was analyzed in the framework of the QTAIM method12 and with the electron localizability approach, ELI.13,14 In both complementary methods, the program DGrid15 was used for the computation of the electron density and all the topological properties.16 The integration of the electron density and ELI was performed numerically on the grid with a step size of 0.026 Å (0.05 bohr).

temperature XRD measurements (Figure S2 in the SI) reveal additional peaks already at 573 K is attributed to the longer holding times of the diffraction experiments in conjunction with the kinetic control of the decomposition. Annealing experiments with the tetragonal modification (Figure S3 in the SI) in the region near the two overlapping exothermic effects in the DSC evidence the disintegration of BaGe3(tI32) into BaGe2 and germanium. In accordance with the phase diagram,18 this mixture partially transforms into Ba6Ge25 at slightly higher temperatures with the consequence that Ba6Ge25 and BaGe2 are co-resident. The hP8 modification of BaGe3 decomposes at slightly higher temperature than its tI32 counterpart, transforming directly into a mixture of Ba6Ge25 and BaGe2 (Figure S4 in the SI). The crystal structure of the tI32 modification of BaGe3 was refined by means of the Rietveld method (Figure S5 in the SI) using high-resolution X-ray synchrotron diffraction data. The larger displacement parameter of Ge2 is in line with the findings for the isotypic calcium compound as well as with recent single-crystal X-ray diffraction refinements of the isotypic strontium compound.3 The atomic arrangement of BaGe3(hP8) was refined on the basis of conventional (sealed-tube) X-ray diffraction data (Figure S6 in the SI). Parameters of data collection and refinement as well as crystallographic data are listed in Tables 1−4, and selected interatomic distances in the Supporting Information (Tables S1 and S2).

RESULTS AND DISCUSSION Synthesis and Thermal Stability. BaGe3 forms the earlier described hP8 modification (Mg3Cd type)17 at moderately high pressures between 5 and 13 GPa.7 The tetragonal form of BaGe3 (CaGe3-type structure, tI32)3 forms at 15(2) GPa and 1300(130) K, and the required synthesis pressure is in almost perfect agreement with a recent theoretical prediction.6 The metallographic microstructure of as-cast samples evidences a majority phase with composition BaGe3 (Figure S1 in the SI) together with a minority phase BaGe5 occupying less than 3% of the complete sample volume. At ambient pressure, the tI32 modification of BaGe3 decomposes exothermically at 602 K and the hP8 phase at 619 K (Figure 1). The sequence of decomposition temperatures is inversely proportional to the synthesis pressures (9 and 15 GPa, respectively). The finding that in situ high-

Table 1. Details of Data Collection and Refinement for BaGe3(tI32)a

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composition Pearson symbol cryst syst, space group unit cell params unit cell volume formula units per cell calcd density sample preparation temperature measurement device radiation profile function measurement range no. of points/reflns no. of params cryst structure/profile structure refinement residuals and GoF

BaGe3 tI32 tetragonal, I4/mmm (no. 139) a = 7.8261(5) Å c = 12.7956(9) Å V = 783.7(2) Å3 Z=8 ρcalc = 6.02 g cm−3 glass capillary ϕ = 0.5 mm 293(2) K ESRF ID22, 9 detectors stage Debye−Scherrer setup synchrotron, λ = 0.40066 Å pseudo-Voigt 1° ≤ 2θ ≤ 32° 0 ≤ h < 10, 0 ≤ k ≤ 10, 0 ≤ l ≤ 17 15500/359 (step width: 0.002°) 9/20 full-profile method, WinCSD RP = 0.09, RF = 0.03, GoF = 1.51

a

The lattice parameters predicted for 18.7 GPa amount to a = 7.23 Å and c = 12.06 Å.6

Chemical Bonding and Electronic Structure. The topology of the electron density of BaGe3 was characterized by the QTAIM method.12 For BaGe3(tI32), the integration within the atomic basins yields the average charges Ba1.14+(Ge0.38−)3, indicating substantial charge transfer from the electropositive barium to the Ge atoms. For the hexagonal modification BaGe3(hP8), the atomic basins resemble almost regular polyhedra and the integrated electron density results in the species Ba1.2+ and Ge0.4−. Hence, the charge transfer remains basically unaffected by the structure change. The same

Figure 1. Differential thermal analysis of BaGe3 in the tetragonal (black curve) and in the hexagonal (blue curve) modification. B

DOI: 10.1021/acs.inorgchem.6b00299 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

holds for the volume of the atomic basins of barium, which amount to 27.9 and 27.3 Å3 for hP8 and tI32, respectively. However, the average volumes assigned to the germanium basins correspond to 24.4 Å3 for hP8 and only 23.4 Å3 for tI32 (Table S3 in the SI). The significant volume reduction of the germanium basins is in accordance with the higher formation pressure and, thus, stronger compression of the tetragonal modification at the synthesis conditions. In BaGe3(tI32), the volume of the atomic basin of Ge2 is larger than that of Ge1, which is compatible with the significantly larger displacement parameter determined by the X-ray diffraction data refinements (Table 2). Analysis of the calculated electron density in BaGe3(tI32) reveals five bond critical points on the Ge−Ge as well as on the Ba−Ge contacts, respectively (Figure 2 as well as Tables S4 and S5 in the SI). For the germanium dumbbells they are characteristic of covalent interactions, and the remaining ones exhibit the features for a delocalized bonding situation.19 Among the ring critical points present in BaGe3(tI32) (Table S4 in the SI, not indicated in Figure 2a), the one with the highest electron density is located within the triangle Ge2− Ge1−Ge2, thus supporting the idea of delocalization for the long Ge1−Ge2 contacts. Regarding the contacts between the Ba and Ge atoms, significant electron density and a positive Laplacian for the bond critical points located in the interconnection path of Ba and Ge atoms evidence substantial interactions by a charge transfer process. The bonding situation was also analyzed by means of the electron localizability indicator ELI-D.12,13 The penultimate shell of the barium atoms is structured; that is, it deviates from spherical symmetry, suggesting the participation of the outmost inner shell in the chemical bonding (Figure 3a). ELI-D sections around the Ge atoms (for simplicity, Ba atoms are not shown) show several regions of high values that are located in the vicinity of the Ge atoms (Figure 3b). Three attractors are located close to the short Ge−Ge distances (labeled as 1, 2, and 3 in Figure 3c). In the bonding region of the Ge1−Ge1 and Ge2−Ge2 dumbbells, populations close to two electrons essentially indicate conventional 2c2e bonds (Table S6 in the SI). The third basin located around the long Ge2−Ge2 contact

Table 2. Wyckoff Site, Site Occupancy Factors (SOF), Atomic Coordinates (x, y, z), and Isotropic Displacement Parameters (Biso) for BaGe3(tI32)a atom

site

SOF

x

y

z

Biso

Ba1 Ba2 Ge1 Ge2

4e 4d 8i 16m

1 1 1 1

0 1/2 0.3396(6) 0.3185(3)

0 0 0 x

0.1740(3) 1/4 0 0.0982(3)

0.63(8) 0.50(7) 0.68(10) 1.03(7)

a

The atomic positions predicted for 18.7 GPa are Ba1 (0, 0, 0.1761); Ba2 (1/2, 0, 1/4); Ge1 (0.3307, 0, 0); Ge2 (0.3193, x, 0.1049).6

Table 3. Details of Data Collection and Refinement for BaGe3 in the hP8 Modification composition Pearson symbol cryst syst, space group unit cell params

BaGe3 hP8 hexagonal, P63/mmc (no. 194) a = 6.8288(3) Å c = 5.0303(3) Å V = 203.15(3) Å3 Z=2 ρcalc = 5.81 g cm−3 293(2) K Huber G670 Guinier camera Cu Kα1, λ = 1.540562 Å pseudo-Voigt 10° ≤ 2θ ≤ 90° 0 ≤ h < 6, 0 ≤ k ≤ 6, 0 ≤ l ≤ 4 16 000/46 (Step width: 0.005°) 4/11 full-profile method, WinCSD RP = 0.10, RF = 0.03, GoF = 1.33

unit cell volume formula units per cell calcd density temperature measurement device radiation profile function measurement range no. of points/reflns no. of params cryst struct/profile struct refinement residuals and GoF

Table 4. Wyckoff Site, Site Occupancy Factors (SOF), Atomic Coordinates (x, y, z), and Isotropic Displacement Parameters (Biso) for BaGe3 in the hP8 Modification atom

site

SOF

x

y

z

Biso

Ba Ge

2d 6h

1 1

1/3 0.1278(3)

2/3 2x

3/4 1/4

1.3(1) 1.4(1)

Figure 2. QTAIM12 atoms and bond critical points of (a) BaGe3(tI32) and (b) BaGe3(hP8); (c) ELI-D13,14 in selected planes of the crystal structure of BaGe3(hP8). C

DOI: 10.1021/acs.inorgchem.6b00299 Inorg. Chem. XXXX, XXX, XXX−XXX

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bonds are located on the four long Ge2−Ge2 contacts, and multicenter bonding with participation of the Ba atoms contributes to the Ge1−Ge2 bonds. For BaGe3(hP8), the ELI-D (Figure 2c) shows high values between the Ge atoms in the Ge3 units, indicating covalent bonding. Moreover, local maxima with a lone-pair shape are found at each corner of the Ge triangle. Thus, the ELI-D topology of the covalently bonded layer bears a striking similarity to that of the ordered model of EuGe3.20 Integration of the electron density within the ELI-D valence basins of BaGe3(hP8) results in populations of approximately 1.2 and 3.5 electrons for the bond and lone-pair basins, respectively (Table S7 in the SI). Intersecting these two ELI-D valence basins with those obtained by the QTAIM partitioning reveals that the Ge−Ge interaction involves only contributions of the respective Ge atoms. For the lone-pair attractor, a share of 0.9 is contributed by the Ge atoms and the remaining contribution of 0.1 involves Ba atoms. This participation shows in the structuring of the penultimate shell of barium, i.e., the involvement of semicore states of the metal atom. Like the tetragonal case, this finding is interpreted as a fingerprint of multicenter delocalized covalent bonding between the barium and germanium atoms, and the share of the barium atoms in the bonding interactions is similar to that found for the tetragonal modification. For an analysis of the bonding within the germanium substructure by means of the MO diagram, we refer to the earlier investigation.6 Physical Properties. The corrected magnetic susceptibilities χ(T) of the two modifications of BaGe3 (Figure S7 in the SI) are diamagnetic but clearly different. While BaGe3(hP8) shows a slow linear increase of χ(T) above 80 K, the tl32 modification displays a rise and then a saturation. Taking into account the Curie-like contributions to χ(T) caused by minor paramagnetic impurities, the values of χ0 at T = 0 are extrapolated as −76 × 10−6 and −98 × 10−6 emu mol−1 for tl32 and hP8, respectively. χ0 is a sum of diamagnetic closed-shell contributions (χdia) and of Pauli paramagnetism (χP) from conduction electrons. Assuming that the difference of χ0 of the two phases is solely due to this influence, we estimate within the free-electron model that the electronic density of states at

Figure 3. ELI-D in the unit cell of BaGe3(tI32) with (a) and without (b) the Ba atoms. (c) ELI-D isosurfaces of the germanium layer. Numbers 1−3 indicate attractors close to short Ge−Ge distances; 4 and 5 designate lone-pair-like features.

holds a population of half an electron. Additional lone-pair-like attractors (4 and 5 in Figure 3c) are situated in the immediate vicinity of Ge1 and Ge2 with populations close to four and approximately three electrons, respectively. Intersection of these lone-pair-like ELI-D basins with the atomic basins yields the contributions of the surrounding atoms to the valence attractor. The resulting contributions for the lone-pair-like basin close to Ge1 corresponds to 0.82 from Ge1 and 0.1 of Ge2, and the basin near Ge2 involves a share of 0.88 from Ge2. In both cases, the remaining amount is provided by Ba atoms, indicating their participation in the bonding interaction. Thus, strong 2c2e bonds hold the dumbbells, weak covalent 4c2e

Figure 4. Magnetic susceptibility (at μ0H = 2 mT, left) and normalized electrical resistance (right) of BaGe3 in the tI32 and hP8 modification, respectively. D

DOI: 10.1021/acs.inorgchem.6b00299 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry EF (DOS) of BaGe3(tI32) is higher by ∼0.7 state eV−1 f.u.−1 than that of BaGe3(hP8). This finding is in good agreement with our band structure results (Figure S8 in the SI). The rise of χ(T) for BaGe3(tl32) hints at a sharp structure of the DOS a few meV above EF. The first evidence for superconductivity in the BaGe3 polymorphs was the strong diamagnetism in the magnetic low-field susceptibility data (Figure 4). The onset critical temperatures (Tc,on) are 6.5 and 4.0 K for the tI32 and the hP8 modification, respectively. The shielded volume fractions (uncorrected for demagnetization factors) amount to values above 1.0, suggesting bulk superconductivity. However, the Meissner effect measured during cooling in field is much less, indicating that the superconductivity in both phases is type II. Specific heat measurements at low temperatures (Figure 5) disclose sizable anomalies confirming the bulk character of the

the specific heat at low temperatures yields critical fields μ0Hc2 of 340(100) and 290(40) mT for the tI32 and the hP8 modification, respectively. The observed sequence of Debye temperatures (266 K for the tI32 and 205 K for the hP8 modification) is in line with the succession of decomposition temperatures (see Figure 1) and inverse with respect to the progression of the required synthesis pressures. The higher Tc of BaGe3(tI32) in comparison to BaGe3(hP8) corresponds to a larger Pauli susceptibility and a larger DOS at EF (1.32 and 1.85 states eV−1 f.u.−1 for hP8 and tI32, respectively; see Figure S8 and Table S8 in the SI) in conjunction with an increased strength of the electron−phonon interaction (λep derived from McMillan’s equation corresponds to 0.71 and 0.74 for hP8 and tI32, respectively). In line with the findings of an earlier analysis of the interrelation of band structure properties and superconductivity in the tI32 modification,6 the measurements evidence a significant electron−phonon coupling. Further, the computations reveal that the DOS in the vicinity of EF is dominated by germanium p contributions (shares of 0.67 and 0.72 for the tI32 and hP8 modification, respectively) with a significant admixture of Ba d states (ratios of 0.13 and 0.04 for tI32 and hP8, respectively). Both modifications are characterized by a similar charge transfer from Ba to Ge. In conclusion, we have synthesized the theoretically predicted6 CaGe3-type modification BaGe3(tI32), which is metastable at ambient conditions. The significantly higher temperature of the superconducting transition temperature in BaGe3(tI32) in comparison to BaGe3(hP8) is in line with the increased density of states at the Fermi level in conjunction with increased strength of the electron−phonon interaction as revealed by λep derived from McMillan’s equation. In both phases, the density of states in the vicinity of EF is essentially shaped by Ge p and Ba d states so that the prominent changes of the superconducting properties are traced back to the different topology of the covalent frameworks in conjunction with substantially differing barium d contributions.

Figure 5. Specific heat at low temperatures of BaGe3 in the tI32 and hP8 modification. Data in the superconducting state were collected without external field; measurements in the normal state were performed in overcritical fields.

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superconductivity. The anomalies are broadespecially that of BaGe3(tl32)indicating inhomogeneity or severe strain within the samples. Annealing of the samples at 473 K for 12 h does not reduce the strain significantly according to powder X-ray diffraction data (Figure S9 in the SI), but the thermal treatment lowers the superconducting transition temperature down to 3.5 K. Thus, as-cast samples were employed for measuring the heights ΔCP and midpoints Tc,mid of the step-like anomalies by using the entropy-conserving construction method. The obtained Tc,mid are 5.4 and 3.7 K for BaGe3(tI32) and BaGe3(hP8), respectively. The value for the tI32 modification is in good agreement with the transition temperature predicted on the basis of recent independent computations.6 The specific heat in the normal state at μ0H = 1.0 T is welldescribed by CP(T) = γT + βT3 + δT5. Here, γT is the Sommerfeld electronic specific heat in the normal state and βT3 + δT5 corresponds to the first terms in the harmonic lattice approximation of the phonon contribution (Table S8 in the SI). From the fit we obtain γ = 6.3 mJ mol−1 K−2. The finding that the ratio ΔCP/γTc amounts to ∼1.3 for BaGe3(tI32) is rather attributed to the fair sample quality than indicating significant deviation from the value of 1.43 predicted by the BCS theory for weak electron−phonon coupling in a single-band scenario. According to WHH extrapolations,21 the field dependence of

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b00299. Phase analysis, Rietveld refinements, and additional crystallographic information, bonding analysis data, and calculated density of state for BaGe 3 (tI32) and BaGe3(hP8) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

R. Cardoso-Gil: Departamento de Ingenieriá Metalúrgica y de Materiales, Universidad Técnica Federico Santa Maria,́ Avenida ́ Chile. España 1680, Valparaiso, †

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. E

DOI: 10.1021/acs.inorgchem.6b00299 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Funding

Steglich, F.; Grin, Yu. J. Am. Chem. Soc. 2010, 132, 10984−10985. (c) Okamoto, H. J. Phase Equilib. Diffus. 2009, 30, 114. (19) Covalent interactions are characterized by high absolute values of the electron density ρ(r) and a negative Laplacian of the electron density ∇2ρ(r). (20) Castillo, R.; Baranov, A. I.; Burkhardt, U.; Grin, Yu.; Schwarz, U. Z. Anorg. Allg. Chem. 2015, 641, 355−361. (21) Werthamer, N. R.; Helfand, E.; Hohenberg, P. C. Phys. Rev. 1966, 147, 295.

R.C. gratefully acknowledges the Becas Chile program for a doctoral grant. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Susann Leipe for high-pressure syntheses, Dr. Andy Fitch (ID22 at the ESRF, Grenoble) and Cevriye Koz for supporting synchrotron X-ray powder diffraction experiments, Marcus Schmidt and Vicky Süß for DTA characterization, Monika Eckert and Sylvia Kostmann for help with the metallographic investigations, and Ralf Koban for physical measurements.

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REFERENCES

(1) (a) Fukuoka, H.; Yamanaka, S. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 094501. (b) Meier, K.; Cardoso-Gil, R.; Schnelle, W.; Rosner, H.; Burkhardt, U.; Schwarz, U. Z. Anorg. Allg. Chem. 2010, 636, 1466−1473. (2) (a) Yamanaka, S.; Enishi, E.; Fukuoka, H.; Yasukawa, M. Inorg. Chem. 2000, 39, 56−58. (b) Fukuoka, H.; Kiyoto, J.; Yamanaka, S. Inorg. Chem. 2003, 42, 2933−2937. (c) Rachi, T.; Yoshino, H.; Kumashiro, R.; Kitajima, M.; Kobayashi, K.; Yokogawa, K.; Murata, K.; Kimura, N.; Aoki, H.; Fukuoka, H.; Yamanaka, S.; Shimotani, H.; Takenobu, T.; Iwasa, Y.; Sasaki, T.; Kobayashi, N.; Miyazaki, Y.; Saito, K.; Guo, F. Z.; Kobayashi, K.; Osaka, K.; Kato, K.; Takata, M.; Tanigaki, K. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 144504. (d) San Miguel, A.; Toulemonde, P. High Pressure Res. 2005, 25, 159−185. (e) Toulemonde, P.; San Miguel, A.; Merlen, A.; Viennois, R.; Le Floch, S.; Adessi, Ch.; Blase, X.; Tholence, J. L. J. Phys. Chem. Solids 2006, 67, 1117−1121. (f) Tang, J.; Xu, J.; Heguri, S.; Fukuoka, H.; Yamanaka, S.; Akai, K.; Tanigaki, K. Phys. Rev. Lett. 2010, 105, 176402. (3) (a) Schnelle, W.; Ormeci, A.; Wosylus, A.; Meier, K.; Grin, Yu.; Schwarz, U. Inorg. Chem. 2012, 51, 5509−5511. (b) Nishikawa, T.; Fukuoka, H.; Inumaru, K. Inorg. Chem. 2015, 54, 7433−7437. (4) Schwarz, U.; Wosylus, A.; Rosner, H.; Schnelle, W.; Ormeci, A.; Meier, K.; Baranov, A.; Nicklas, M.; Leipe, S.; Müller, C. J.; Grin, Yu. J. Am. Chem. Soc. 2012, 134, 13558−13561. (5) Baitinger, M.; Böhme, B.; Ormeci, A.; Grin, Yu. Solid state chemistry of clathrate phases: crystal structure, chemical bonding and preparation routes. In Clathrates; Nolas, G. S., Ed.; Springer, 2014. (6) Zurek, E.; Yao, Y. Inorg. Chem. 2015, 54, 2875−2884. (7) Fukuoka, H.; Tomomitsu, Y.; Inumaru, K. Inorg. Chem. 2011, 50, 6372−6377. (8) Akselrud, L.; Grin, Yu. J. Appl. Crystallogr. 2014, 47, 803−805. (9) Berar, J.-F.; Lelann, P. J. Appl. Crystallogr. 1991, 24, 1−5. (10) http://elk.sourceforge.net. (11) Perdew, J. P.; Wang, Y. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13244−13249. (12) Bader, R. F. W. Atoms in Molecules, A Quantum Theory; Clarendon Press and Oxford University Press Inc.: New York, 1994. (13) Kohout, M. Int. J. Quantum Chem. 2004, 97, 651−658. (14) Kohout, M. Faraday Discuss. 2007, 135, 43−54. (15) Kohout, M. DGrid, version 4.6e; Radebeul, Germany, 2011. (16) Baranov, A. I.; Kohout, M. J. Phys. Chem. Solids 2010, 71, 1350− 1356. (17) (a) Edwards, D. A.; Wallace, W. E.; Craig, R. S. J. Am. Chem. Soc. 1952, 74, 5256−5261. (b) Watanabe, Y. J. Phys. Soc. Jpn. 1975, 38, 141−149. (c) Shastry, C. R.; Bhan, S. Z. Metallkd. 1975, 66, 56−58. (d) Faessler, T. F.; Kronseder, C. Angew. Chem., Int. Ed. Engl. 1997, 36, 2683−2686. (18) (a) Carrillo-Cabrera, W.; Budnyk, S.; Prots, Yu.; Grin, Yu. Z. Anorg. Allg. Chem. 2004, 630, 2267−2276. (b) Aydemir, U.; Akselrud, L.; Carillo-Cabrera, W.; Candolfi, C.; Oeschler, N.; Baitinger, M.; F

DOI: 10.1021/acs.inorgchem.6b00299 Inorg. Chem. XXXX, XXX, XXX−XXX