High-Pressure Synthesis and Chemical Bonding of Barium Trisilicide BaSi3

BaSi3 is obtained at pressures between 12(2) and 15(2) GPa and temperatures from 800(80) and 1050(105) K applied for one to five hours before quenching. The new trisilicide crystallizes in the space group I4¯2m (no. 121) and adopts a unique atomic arrangement which is a distorted variant of the CaGe3 type. At ambient pressure and 570(5) K, the compound decomposes in an exothermal reaction into (hP3)BaSi2 and two amorphous silicon-rich phases. Chemical bonding analysis reveals covalent bonding in the silicon partial structure and polar multicenter interactions between the silicon layers and the barium atoms. The temperature dependence of electrical resistivity and magnetic susceptibility measurements indicate metallic behavior.


Introduction
The Zintl-Klemm concept [1,2] constitutes a powerful framework for understanding the interdependence of chemical bonding and electron count of a rich variety of binary phases formed by element semiconductors such as silicon or germanium with electropositive partners of the alkaline-, alkaline earth-and rare-earth metal groups. Counting rules for compounds such as Ba 2 Si [3], Ba 3 Si 4 [4] and BaSi 2 [5] work successfully when a complete charge transfer from the electropositive metal to the tetrel atoms is assumed. The formation of covalent two-center two-electron interactions in the resulting polyanionic partial structures yields an electron-precise electron balance. Phases violating the classical electron count because of unusual coordination environments in the covalent partial structure of the p-block element exhibit more exotic bonding properties, often in combination with metal-type electrical conductivity [6,7]. Quite a few of these so-called covalent metals are accessible by high-pressure high-temperature synthesis.
Electronic structure calculations and chemical bonding analysis were carried out with the experimentally determined lattice parameters and the refined atomic coordinates of an idealized crystal structure model without disorder. First, band structure calculations were performed with the TB-LMTO-ASA (TB: tight-binding, LMTO: linear muffin tin orbitals, ASA: atomic sphere approximation) program package [31]. In these computations, the Barth-Hedin exchange potential [32] was used. The following radii of the atomic spheres were applied for the calculations: r(Ba1) = 2.375 Å, r(Ba2) = 2.419 Å, r(Si1) = 1.430 Å, r(Si2) = 1.415 Å, r(Si3) = 1.418 Å. Due to the calculations already including corrections for the neglect of interstitial regions and partial waves of higher order [33], insertion of additional so-called empty spheres was not necessary. A basis set of Ba(6s,5d) and Si(3s,3p) orbitals was employed for self-consistent calculations with Ba(6p,5d) and Si(3d) functions being downfolded. To obtain the partial waves, the radial scalar-relativistic Dirac equation was solved. After convergence, the electronic density of states (DOS) was calculated using a mesh of 32 × 32 × 32 k-points.
For the analysis of the chemical bonding in direct space the electron density and the electron localizability indicator ELI-D was calculated [34,35] with a module implemented in the program package. The computed spatial arrangement of ELI-D and electron density was analyzed with the program DGrid [36]. For this purpose, the electron density was integrated within so-called basins, i.e., space regions confined by zero-flux surfaces of the gradient field. This technique follows the procedure proposed in the Quantum Theory of Atoms In Molecules (QTAIM [37]) and provides electron counts for the basins of atoms (QTAIM populations of the atoms) and bonds (bond populations). The combined analysis of electron density and ELI-D constitutes a basis for the description of chemical bonding [38,39], especially in intermetallic compounds [40,41].
Electrical resistivity ρ was measured using a cuboid (1.00 mm × 1.80 mm × 0.90 mm) cut from a polycrystalline sample of cylindrical shape by a direct-current four-probe method carried out on a PPMS (Quantum Design International, San Diego, USA) AC transport option, 0.11 to 2.0 K and 2.0 to 305 K). The inaccuracy of ρ was estimated to be ±20%, because of the intricate contact geometry. The measurement of magnetic susceptibility χ was conducted using a polycrystalline sample of cylindrical shape (diameter 1.0 mm, length 1.0 mm) and a SQUID magnetometer (MPMS XL-7, Quantum Design).
The thermal stability of the high-pressure phase was studied by differential scanning calorimetry (DSC) experiments. A commercially available Netzsch DSC 404C apparatus was equipped with corundum crucibles and operated with an argon atmosphere. Both heating and cooling were realized at a rate of 10 K/min.

Results and Discussion
The new phase was obtained by high-pressure high-temperature treatment of pre-reacted Ba 25 Si 75 mixtures before quenching. The chemical composition of the hp-ht product as determined using energy dispersive X-ray spectroscopy amounted to Ba 22.4 Si 77.6 which corresponds to BaSi 3 within the estimated error. Differential scanning calorimetry (DSC) measurements at ambient pressure evidenced the decomposition of BaSi 3 ( Figure 1) at 570(5) K. The first exothermic anomaly upon heating (Figure 1, inset) corresponded to the onset of disintegration. Powder XRD and EDXS analyses of the obtained decomposition product after heating to 623 K evidenced the formation of (hP3)BaSi 2 [42] plus two amorphous phases with averaged composition Ba 24.3(5) Si 75.7(5) (≈BaSi 3 ) and Ba 14.5(5) Si 85.5(5) (≈BaSi 6 ), respectively. The following features at 725(5), 745(10) and 985(10) K represented different reaction steps of the decomposition products of BaSi 3, and XRD data evidenced the formation of (oP24)BaSi 2 (often labeled as Ba 2 Si 4 [43]) and (cF8)Si [44]. As the final effect at 1325 K correlated with a corresponding signal upon cooling, the signal is essentially assigned to the eutectic of BaSi 2 + Si in full accordance with phase diagram data [45]. As the cooling curve shows no further signal indicating the back transformation of BaSi 2 and Si into BaSi 3, the experimental data indicate that BaSi 3 is a high-pressure phase, which is metastable at ambient pressure. reaction steps of the decomposition products of BaSi3, and XRD data evidenced the formation of (oP24)BaSi2 (often labeled as Ba2Si4 [43]) and (cF8)Si [44]. As the final effect at 1325 K correlated with a corresponding signal upon cooling, the signal is essentially assigned to the eutectic of BaSi2 + Si in full accordance with phase diagram data [45]. As the cooling curve shows no further signal indicating the back transformation of BaSi2 and Si into BaSi3, the experimental data indicate that BaSi3 is a highpressure phase, which is metastable at ambient pressure. Characterization of the crystal structure was performed by X-ray powder diffraction experiments using synchrotron radiation. Indexing of peak positions yields a tetragonal unit cell for Characterization of the crystal structure was performed by X-ray powder diffraction experiments using synchrotron radiation. Indexing of peak positions yields a tetragonal unit cell for the new high-pressure phase BaSi 3 . The resulting diffraction symbol, as well as the axial ratio c/a, could be compatible with a CaGe 3 -type atomic arrangement as predicted by an earlier ab-initio study [46]. However, refinements of this structure pattern in space group I4/mmm (no. 139) do not produce satisfactory results with respect to reflection intensities (which is reflected in residuals R(P) = 0.215). Thus, structure models in maximal non-isomorphic subgroups were developed. The refinement of a structure model in space group I42m converged in a straightforward manner (R(P) = 0.073). However, unusually large displacement parameters motivated the introduction of split-positions for Ba1 and Si3 in the final refinements ( Figure 2 and Tables 1 and 2). As the profiles of some reflections show evidence for subtle shoulders, crystal structure solutions assuming further decrease of symmetry were attempted. With the available X-ray powder diffraction data, these tests remained unsuccessful.
The crystal structure of BaSi 3 ( Figure 3) may be described as comprising silicon layers which are stacked along the c axis and separated by barium atoms. Ba1 and Ba2 are surrounded by 13 and 12 silicon atoms, respectively. The barium-silicon distances in the irregular polyhedrons of Ba1 and Ba2 cover the range from 3.325(8) to 3.79(1) Å and from 3.375(3) to 3.592(9) Å, respectively. For comparison, the binary silicon-rich barium compounds BaSi 6 and BaSi 2 exhibit Ba-Si distances in the range from 3.20(1) to 3.82 Å [47][48][49][50].
satisfactory results with respect to reflection intensities (which is reflected in residuals R(P) = 0.215). Thus, structure models in maximal non-isomorphic subgroups were developed. The refinement of a structure model in space group I4 2m converged in a straightforward manner (R(P) = 0.073). However, unusually large displacement parameters motivated the introduction of split-positions for Ba1 and Si3 in the final refinements ( Figure 2 and Tables 1 and 2). As the profiles of some reflections show evidence for subtle shoulders, crystal structure solutions assuming further decrease of symmetry were attempted. With the available X-ray powder diffraction data, these tests remained unsuccessful.     (2) The crystal structure of BaSi3 ( Figure 3) may be described as comprising silicon layers which are stacked along the c axis and separated by barium atoms. Ba1 and Ba2 are surrounded by 13 and 12 silicon atoms, respectively. The barium-silicon distances in the irregular polyhedrons of Ba1 and Ba2 cover the range from 3.325 (8)     The refined crystal structure model of BaSi 3 evidences that the new compound comprises silicon atoms in unusual connectivity situations. Assuming single-bonded silicon dumbbells would imply a rather non-realistic electron balance with huge electron demand: Considering the slightly longer distances of Si1 and Si3 as additional single bonds reduces the problem: 1+ . In agreement with this predicted electron demand, the calculated electronic density of states reveals that the Fermi level (calculated for the idealized structure model without disorder [51]) is located below the pseudogap (Figure 4). Nevertheless, a quantitative estimate of the electron count requires a more elaborate analysis of chemical bonding in real space [34,35]. The refined crystal structure model of BaSi3 evidences that the new compound comprises silicon atoms in unusual connectivity situations. Assuming single-bonded silicon dumbbells would imply a rather non-realistic electron balance with huge electron demand: (Ba 2+ )2{[(1b)Si−(1b)Si)] 6-}3 × 12p 1+ . Considering the slightly longer distances of Si1 and Si3 as additional single bonds reduces the problem: (Ba 2+ )2[(3b)Si1 1-]2[(1b)Si2 3-]2[(3b)Si3 1-]2 × 6p 1+ . In agreement with this predicted electron demand, the calculated electronic density of states reveals that the Fermi level (calculated for the idealized structure model without disorder [51]) is located below the pseudogap ( Figure 4). Nevertheless, a quantitative estimate of the electron count requires a more elaborate analysis of chemical bonding in real space [34,35]. The calculated electron density reveals Ba species with almost spherical shape indicating essentially ionic character. The shapes of the silicon species have a more polyhedral character, especially the contact faces between the two nearest silicon atoms appear rather flat, which is characteristic for non-polar covalent bonding. Integrating the electron density within the QTAIM shapes and subtracting the atomic number yields effective charges. The net charge transfer from barium to silicon ( Figure 5) is in accordance with the electronegativity difference of the constituents. The effective charges of the barium species (+1.30) fall into the range of +1.2 to 1.4 which is observed for barium-germanium clathrates [54] but are markedly smaller than those of calcium in CaSi3 (+1.44, +1.49 [8]   The calculated electron density reveals Ba species with almost spherical shape indicating essentially ionic character. The shapes of the silicon species have a more polyhedral character, especially the contact faces between the two nearest silicon atoms appear rather flat, which is characteristic for non-polar covalent bonding. Integrating the electron density within the QTAIM shapes and subtracting the atomic number yields effective charges. The net charge transfer from barium to silicon ( Figure 5) is in accordance with the electronegativity difference of the constituents. The effective charges of the barium species (+1.30) fall into the range of +1.2 to 1.4 which is observed for barium-germanium clathrates [54] but are markedly smaller than those of calcium in CaSi 3 (+1.44, +1.49 [8]). Moreover, the computed charges of silicon in BaSi 3 (−0.3 to −0.6) show a larger spread than those in CaSi 3 (−0.40 and −0.54). Both findings consistently indicate a slightly different organization of the bonding in BaSi 3 in comparison to the other trisilicides. Further analysis of the chemical bonding in BaSi3 was realized by applying the electron localizability approach. The ELI-D distribution in the penultimate shell of the barium atoms shows significant deviations from spherical symmetry (structuring [38], Figure 6, left pannel). Quantitative characterization of this trend and comparison to the recent results for YGa6, YGa and t-Y5Ga3 [55] reveals fingerprints for the participation of the penultimate shell in the bonding interactions [38,56]. In the valence region of silicon, five different ELI-D maxima are observed. Three of them are located on (or close to) the shortest Si-Si contacts ( Figure 6) indicating covalent Si-Si bonding. Two remaining ones are located on the outer side of the Si2-Si3 dumbbell suggesting lone pairs. In an isolated Si2 molecule, each basins of these maxima would have contacts with one core basin of silicon, i.e., it would reflect a lone pair such as in RhBi4 [57], CoBi3 [58] or hp-CuBi [59]). In BaSi3, each of these attractors represents a five-center bond SiBa4.
Integration of the electron density within the bonding basins ( Figure 6, right pannel) yields the values 2.34 and 1.75 for the Si1-Si1 and Si2-Si3 dumbbells, respectively, as well as 2.18 for the Si1-Si3 contact. Consequently, the shortest Si-Si distances correspond 2c-2e bonds in good approximation. The calculated population of the lone-pair basin of Si3 amounts to 2.34 electrons, which is close to the value of two as predicted by the 8-N rule. Yet, the three-bonded Si1 atom does not show any basin resembling a lone-pair. The Si2 atom is single-bonded with a calculated population of the lone-pair basin of 3.77 electrons, which is still below the predicted six on basis of the 8-N rule. The analysis evidences that the interpretation of the crystal structure of BaSi3 as a CaGe3-type packing with slightly tilted Si2 dumbbells is insufficient. Further analysis of the chemical bonding in BaSi 3 was realized by applying the electron localizability approach. The ELI-D distribution in the penultimate shell of the barium atoms shows significant deviations from spherical symmetry (structuring [38], Figure 6, left pannel). Quantitative characterization of this trend and comparison to the recent results for YGa 6 , YGa and t-Y 5 Ga 3 [55] reveals fingerprints for the participation of the penultimate shell in the bonding interactions [38,56]. In the valence region of silicon, five different ELI-D maxima are observed. Three of them are located on (or close to) the shortest Si-Si contacts ( Figure 6) indicating covalent Si-Si bonding. Two remaining ones are located on the outer side of the Si2-Si3 dumbbell suggesting lone pairs. In an isolated Si 2 molecule, each basins of these maxima would have contacts with one core basin of silicon, i.e., it would reflect a lone pair such as in RhBi 4 [57], CoBi 3 [58] or hp-CuBi [59]). In BaSi 3 , each of these attractors represents a five-center bond SiBa 4 . Instead, the bonding analysis yields direct evidence for a more adequate description of the atomic arrangement (Figure 7). The Si2 dumbbells (Si1)2 and Si2-Si3 are oriented in an almost perpendicular way. However, the condensation of these diatomic units proceeds exclusively via three-bonded Si1 and Si3 atoms. The Si2 atoms form a single bond to the Si3 atoms and are arranged above and below the puckered sheets formed Si1 and Si3. These special covalent segments are interconnected by barium cations interacting with the anionic substructure by polar five-center Si2Ba4 and Si3Ba4 bonds.
In agreement with the electron balance and the calculated band structure, electrical resistivity measurements on BaSi3 between 2 and 305 K show a positive slope above approximately 25 K indicating metal-type conductivity behavior (Figure 8). At room temperature and zero-field, the value for BaSi3 amounts to ρ300 K = 2906 μΩ cm with a residual resistance ratio (RRR) ρ293 K/ ρ4 K = 1.5. In comparison to analogue high-pressure phases of germanium [12,13,19,27], the resistivity is high and shows only weak temperature dependence which is typical for polycrystalline silicides [60]. The changes of both resistivity and susceptibility below 6 K are attributed to traces of superconducting BaSi2 [61]. The little overall resistivity changes down to 110 mK in conjunction with the minor magnetic susceptibility change (Figure 8) clearly evidence that these changes do not originate from a bulk superconducting state. Integration of the electron density within the bonding basins ( Figure 6, right pannel) yields the values 2.34 and 1.75 for the Si1-Si1 and Si2-Si3 dumbbells, respectively, as well as 2.18 for the Si1-Si3 contact. Consequently, the shortest Si-Si distances correspond 2c-2e bonds in good approximation. The calculated population of the lone-pair basin of Si3 amounts to 2.34 electrons, which is close to the value of two as predicted by the 8-N rule. Yet, the three-bonded Si1 atom does not show any basin resembling a lone-pair. The Si2 atom is single-bonded with a calculated population of the lone-pair basin of 3.77 electrons, which is still below the predicted six on basis of the 8-N rule. The analysis evidences that the interpretation of the crystal structure of BaSi 3 as a CaGe 3 -type packing with slightly tilted Si 2 dumbbells is insufficient.
Instead, the bonding analysis yields direct evidence for a more adequate description of the atomic arrangement ( Figure 7). The Si 2 dumbbells (Si1) 2 and Si2-Si3 are oriented in an almost perpendicular way. However, the condensation of these diatomic units proceeds exclusively via three-bonded Si1 and Si3 atoms. The Si2 atoms form a single bond to the Si3 atoms and are arranged above and below the puckered sheets formed Si1 and Si3. These special covalent segments are interconnected by barium cations interacting with the anionic substructure by polar five-center Si2Ba 4 and Si3Ba 4 bonds.  In agreement with the electron balance and the calculated band structure, electrical resistivity measurements on BaSi 3 between 2 and 305 K show a positive slope above approximately 25 K indicating metal-type conductivity behavior (Figure 8). At room temperature and zero-field, the value for BaSi 3 amounts to ρ 300 K = 2906 µΩ cm with a residual resistance ratio (RRR) ρ 293 K /ρ 4 K = 1.5. In comparison to analogue high-pressure phases of germanium [12,13,19,27], the resistivity is high and shows only weak temperature dependence which is typical for polycrystalline silicides [60].
The changes of both resistivity and susceptibility below 6 K are attributed to traces of superconducting BaSi 2 [61]. The little overall resistivity changes down to 110 mK in conjunction with the minor magnetic susceptibility change (Figure 8) clearly evidence that these changes do not originate from a bulk superconducting state.
Materials 2019, 12, x FOR PEER REVIEW 10 of 13 Figure 8. Temperature-dependent electrical resistivity ρ of BaSi3 at zero-field between 2 and 305 K. Insets: Low-temperature electrical resistivity of BaGe3 between 0.11 and 2.0 K at zero-field. The normalization was performed to eliminate changes originating from different measurement geometries. The second inset shows the temperature dependence of the magnetic susceptibility χ between 1.8 and 10 K measured in a field of 0.2 mT. The subtle decrease is attributed to a small amount of superconducting impurity, but bulk superconductivity can clearly be ruled out.  . Temperature-dependent electrical resistivity ρ of BaSi 3 at zero-field between 2 and 305 K. Insets: Low-temperature electrical resistivity of BaGe 3 between 0.11 and 2.0 K at zero-field. The normalization was performed to eliminate changes originating from different measurement geometries. The second inset shows the temperature dependence of the magnetic susceptibility χ between 1.8 and 10 K measured in a field of 0.2 mT. The subtle decrease is attributed to a small amount of superconducting impurity, but bulk superconductivity can clearly be ruled out.