Cage Adaption by High-Pressure Synthesis: The Clathrate-I Borosilicide Rb8B8Si38.

Rb8B8Si38 forms under high-pressure, high-temperature conditions at p = 8 GPa and T = 1273 K. The new compound (space group Pm3̅n, a = 9.9583(1) Å) is the second example for a clathrate-I borosilicide. The phase is inert against strong acids and bases and thermally stable up to 1300 K at ambient pressure. (Rb+)8(B-)8(Si0)38 is electronically balanced, diamagnetic, and shows semiconducting behavior with moderate Seebeck coefficient below 300 K. Chemical bonding analysis by the electron localizability approach confirms the description of Rb8B8Si38 as Zintl phase.

Introduction

Intermetallic boron compounds are often characterized by high thermal stability[1,2] and are thus frequently studied as candidate materials in application oriented research, e.g., in the context of thermoelectrics.[3−8] The often complex crystal structures provide a favorable basis for the required low heat conductivity, and a number of extensive studies focused on low-density binary and ternary borides.[4] More recent interest was directed on framework compounds of abundant elements such as boron-rich chalcogenides B6X (X = S, Se), boron suboxide B6O, or boron carbide.[5−8] Borosilicides with high boron content typically form framework structures comprising [B12]2– dodecahedra.[1] In boron-rich compounds like Li2B12Si2[9] or Tb0.68B12Si3.04,[10] the dodecahedra are interconnected via exo-bonds or Si2 dumbbells. In Na8B74.5Si17.5, multicenter bonds in closo-clusters go along with four-bonded silicon atoms interconnecting the clusters.[11]

By comparison, silicon-rich borosilicides are rare. One of the few examples is clathrate-I type K7B7Si39, comprising four-bonded boron in the polyanion.[12] In contrast, most of the alkali metal silicon clathrates of the heavier homologues Al and Ga A8–Z8–Si38+ (A = Na, K, Rb, Cs, Z = Al, Ga with x < 0.55, y < 0.9) have already been prepared,[13−17] of which Na8Al8Si38, K8Al8Si38, Rb8Al8Si38, and Rb8Ga8Si38 adopt nonmetal-deficient and electron-precise compositions in agreement with the Zintl rule. Nevertheless, subsequent attempts to prepare further boron-containing clathrate-I phases remained unsuccessful at ambient pressure. At this stage, the synthesis strategy was reconsidered by taking into account the beneficial effect of elevated pressures as evidenced by the recent preparation of the borosilicide LiBSi2 comprising a [Si2B–] framework of four-bonded atoms[18] and the theoretical prediction of quenchable sodalite-type RbB3Si3.[19]

In the scope of the present work, the influence of high-pressure conditions on the formation of a clathrate-I borosilicide is investigated. We find that high-pressure synthesis grants access to the clathrate-I Rb8B8Si38 showing remarkable thermal stability. The adaption of the crystal structure to cage filling and boron substitution is discussed, and the chemical bonding is studied by quantum chemical methods in direct space. Finally, thermal and electronic transport properties are reported.

Experimental Section

Synthesis

Sample handling, except for high-pressure synthesis and washing procedure, was performed in argon-filled glove boxes (MBraun, H2O and O2 < 0.1 ppm). Rubidium (Chempur, 99.95%) and silicon (Chempur, 99.9999%) were used to synthesize the precursor compound Rb12Si17 in a closed tantalum tube by annealing at 750 °C for 7 h and slow cooling to room temperature within 8 h. Amorphous boron (Alfa Aesar) was cleaned and activated in a streaming hydrogen plasma.[20] High-pressure, high-temperature preparation started from educt mixtures with ratio Rb:B:Si = 3.25:2:5, which were thoroughly ground in agate mortars. The powders were filled into boron nitride crucibles before being placed in MgO octahedra with an edge length of 18 mm. The high-pressure, high-temperature syntheses were conducted using a multianvil press comprising a Walker-type module.[21] Calibration of pressure and temperature had been realized prior to the experiments by recording the resistance changes of bismuth and thermocouple-calibrated runs, respectively. A pressure of p = 8 ± 1 GPa was applied, and the samples were heated to T = 1273 ± 127 K within 15 min. After annealing for 300 min, the samples were quenched under load. The reaction products were washed with ethanol and deionized water to remove traces of highly reactive Rb4Si4, followed by washing with ethanol and acetone and drying at room temperature. The compound is air stable and inert against strong acids and bases.

XRPD

Sample characterization was done with a Guinier camera (Huber G670, CuKα1 radiation λ = 1.54056 Å, germanium monochromator, measurement range 5° ≤ 2θ ≤ 100°, Δ2θ = 0.005°). Rietveld refinements were performed using synchrotron data (Desy Hamburg, PETRA III, Beamline P02.1, λ = 0.20720 Å) recorded at room temperature. Reflection positions were corrected using LaB6 standard (NIST), and unit cell parameters were calculated from least-squares refinement. Crystallographic calculations were performed with the WinCSD program package.[22]

Thermal Analysis

Thermogravimetry and differential thermal analysis was conducted simultaneously with a NETZSCH STA 449C device (Netzsch-Gerätebau GmbH, Selb, Germany) using a Knudsen cell made of tantalum and heating rates of 10 K min–1 under an argon atmosphere.

Metallography

Specimens were embedded in paraffin and polished with a suspension of diamond powders (grain sizes 6, 3, and 0.25 μm). Wavelength-dispersive X-ray spectroscopy (WDXS) was carried out with a Cameca SX100 electron microprobe equipped with a tungsten cathode. Ni3B, Mg2Si, and RbI were used as standards. The analysis comprehended intensity measurements of the B–Kα, Si–Kα, and Rb-Lα lines. The X-ray emission lines were excited at an electron beam of 7 keV and a beam current of 100.00(1) nA for B, 15 keV and 8.00(1) nA for Si, and 15 keV and 40.00(1) nA for Rb, respectively. The WDX spectrometer was equipped with LPC3, TAP, or LPET monochromator crystals.

NMR

Nuclear magnetic resonance (NMR) experiments were performed on a Bruker Avance 500 spectrometer with a magnetic field of B0 = 11.74 T. The standard Bruker MAS probe for 2.5 mm ZrO2 rotors was used for 29Si experiments, whereas the static probe (NMR Service GmbH, Erfurt, Germany) was used for 11B experiments. The 29Si and 11B signals were referenced to 1 vol % tetramethylsilane (TMS) and BF3 × Et2O with the reference frequencies of 99.3596 and 160.4588 MHz, respectively. In the case of 29Si, the Hahn-echo sequence (90°−τ–180°−τ–acquisition) with a 90° pulse of 1.8 μs, interpulse delay of 100 μs and the recovery time of 5 s was applied. The MAS rotation rate was 30 or 29 kHz. For the 11B spectra, the signal acquisition was achieved after a single pulse of 2.5 μs and recovery times of 30 s.

Electronic Structure Calculations and Chemical Bonding Analysis

For quantum chemical computations on Rb8B8Si38, the mixed occupation of the 16i position in space group Pm3̅n was described by an ordered structure model in space group P4̅3n with boron and silicon each located on an 8e position. Moreover, the coordinate of the boron atoms 1/2 – x was optimized to a value of x = 0.1812 by total energy calculations being markedly different to x = 0.1912(2) for the averaged Si2/B2 position from X-ray structure refinements.

The electronic structure was calculated by means of the all-electron, full-potential local orbital (FPLO) method.[23] All results were obtained within the local density approximation (LDA) to the density functional theory using the Perdew–Wang parametrization for the exchange-correlation effects.[24] A mesh of 12 × 12 × 12 k points was used for calculations.

Chemical bonding analysis in position space was performed within the approach of combined topological analysis of electron density (ED) and electron localizability indicator (ELI). The analysis of the ED was made on the basis of the quantum theory of atoms in molecules (QTAIM).[25] ELI[26,27] was calculated in the ELI-D representation by a module implemented in FPLO.[28] The topological analysis of ED and ELI-D was carried out by the program DGRID.[29]

Transport Properties

Electrical resistivity, thermal conductivity, and Seebeck coefficient were measured simultaneously on a physical property measurement system with thermal transport option (PPMS, Quantum Design). Rb8B8Si38 powder was cold pressed to a plate (2.6 × 1.4 × 0.25 mm3) and contacted in a four-terminal configuration using flat gold-plated copper leads and silver epoxy (Epotek H20e). The uncertainty of resistivity and conductivity was estimated to amount to ±50% and that of the Seebeck coefficient to 25% because of uncertainties in sample geometry.

Magnetic Susceptibility

Powder samples were measured in open quartz tubes with a squid magnetometer (MPMS XL-7, Quantum Design) from 1.8 to 300 K in external fields between 0.2 mT and 7 T.

3. Results and Discussion

The X-ray powder diffraction pattern of Rb8B8Si38 (a = 9.9583(1) Å) reveals the clathrate-I-type crystal structure[30] with space group Pm3̅n (Figure and Table S1). Rietveld refinements using binary Rb8Si46– as a structure model show that the smaller 20-atom dodecahedral and the larger 24-atom tetrakaidecahedral cages are fully occupied by Rb1 (Wyckoff position 2a) and Rb2 (6d), respectively (Table and Table S2 and Figure S1). In the framework, position Si1 (6c) is fully occupied by silicon atoms, whereas enlarged displacement parameters for Si2 on position 16i and Si3 on site 24k point to mixed B/Si occupancy. Indeed, position 16i shows a distinctly reduced electron density, which is compatible with the occupancy of 9.36(6) Si2 and 6.64 B atoms. The slightly decreased electron density at position 24k is assigned to a mixture of 22.68(9) Si3 and 1.32 B atoms. The total number of boron atoms amounts to 7.96(15) per formula unit and equals, and thus, the alkali metal content within the estimated error. The final composition Rb8B8Si38 is consistent with an electron-balanced Zintl phase. Composition analysis by wavelength-dispersive X-ray spectroscopy resulted in Rb8.1(1)B8.5(1)Si37.4(1) (normalized to 100%, this corresponds to Rb15.0(1)B15.8(1)Si69.2(1)), which is in fair agreement with the composition refined in the diffraction experiment (Rb8B8Si38) considering the known experimental limits in the quantitative analysis of light elements like boron.

Figure 1

Powder X-ray diffraction pattern of Rb8B8Si38 (synchrotron radiation, λ = 0.20709 Å) with the results of the crystal structure refinement.

Table 1

Atomic Coordinates and Displacement Parameters Beqa (in Å2) for Rb8B8Si38 (space group Pm3̅n, a = 9.9588(2) Å), for the Anisotropic Displacement Parameters see Table S2

atom	site	x	y	z	Beqa
Rb1	2a	0	0	0	1.03(2)
Rb2	6d	0.25	0.5	0	1.43(3)
Si1	6c	0.25	0	0.5	1.39(7)
Si2/Bb	16i	0.1912(2)	x	x	1.56(4)
Si3/Bc	24k	0	0.2973(2)	0.1243(2)	1.43(5)

Beq = 1/3[B11a*2a2 + ... 2 B23b*c*bc cos α)]; Berar factor: 6.1.

Si0.585(4)B0.415.

Si0.945(4)B0.055.

The obtained powder diffraction data preclude the refinement of split atom positions.[12] Therefore, the short distance d(16i-16i) of 2.029(2) Å represents a mean value resulting from the superposition of d(Si2–Si2) and d(B–Si2). In a similar vein, d(16i-24k) = 2.277(2) Å resembles an average of Si–Si and Si–B distances. Contacts d(6c–24k) = 2.376(2) Å and d(24k–24k) = 2.475(2) Å appear as basically regular silicon–silicon distances d(Si1–Si3) and d(Si3–Si3), respectively, because of the low substitution level of position 24k (Si3) (Table S3). A peculiar feature of Rb8B8Si38 (and also K7B7Si39) is the predominant substitution of silicon atoms on position 16i (Si2). The site typically shows the shortest interatomic framework distances, e.g., in the related binary silicon clathrates K8–Si46[31] or Rb6.15Si46[32,33] and is thus best suited for accommodating the small boron atoms. Position 6c (Si1),[34,35] which is preferred by larger substitution atoms like transition metals, is avoided by boron as the resulting local configuration and interatomic distances would be unfavorable for sp3-hybridized boron atoms. The substitution of Si by the heavier homologues Al or Ga in Rb8Al8Si38 and Rb8Ga8Si38 affects all Si sites, although it appears predominantly at 6c.[14,16]

Comparison of lattice parameters (Figure , Table S3) reveals reduced values for ternary clathrate-I borosilicides[12] in relation to their binary analogs,[32,33,36−40] e.g., the unit cell of Rb8B8Si38 (a = 9.9583(1) Å) is significantly smaller than that of Rb6.15Si46 (a = 10.27188(6) Å)[32,33] in which the dodecahedral cages are almost empty. The lattice parameter is connected to the framework contacts of position 16i and the metal-network distances in the small cages (Figure ) by the relationAs boron substitution and rubidium defects mainly affect positions, which are located on the body diagonal of the unit cell, the shortening of the framework distances d(16i–16i) in the ternary phase (Table S3) goes along with a pronounced contraction of the lattice.

Figure 2

Lattice parameter vs cage filling level x for clathrate-I borosilicides MBSi46– in comparison to binary clathrates MSi46 (M = Na, K, Rb, Cs). Full symbols indicate products synthesized at ambient pressure, open symbols denote high-pressure products. Experimental errors are smaller than the size of the symbols.

Figure 3

Clathrate-I arrangement with emphasis on the network of interconnected dodecahedral cages. Interatomic distances d(Rb1–Si2) (red) and d(Si2–Si2) (green) are oriented along the unit cell diagonal.

On the other hand, the value for the lattice parameter of Rb8B8Si38 (a = 9.9583(1) Å) is strikingly similar to that of K7B7Si39 (a = 9.952(1) Å)[12] in which half of the dodecahedral cages are empty. For describing the framework adaption to the larger rubidium atoms, a model is applied in which the metal-centered dodecahedra (yellow in Figure ) are surrounded by Rb2 and Si1 atoms adopting Zeolite A topology.[41] The atoms of this 24-atom sodalite cage (gray in Figure ) remain unaffected by boron substitution and alkali metal deficit. The edge length of the polyhedron, l = 1/4 a √2, directly scales with the lattice parameter because the metal (6d) and Si1 atoms (6c) occupy special positions without variable parameters. Because the lattice parameters of K7B7Si39 and Rb8B8Si38 are nearly identical, the sodalite cage adopts practically the same size in both crystal structures. Nevertheless, the size of the inner dodecahedral cage can still adapt to the radius of the metal atom. Replacement of potassium by the larger rubidium atoms goes along with longer distances between metal and framework and between Si3/B–Si3/B in the smaller 20-atom polyhedron (Figure ). Simultaneously, distances Si2/B–Si2/B and, to a lesser extent, Si1–Si3/B become shorter (Table S3).

Figure 4

Adaption of the clathrate-I structure to framework substitution, cage filling and size of the filler atom. Increasing distances are denoted in blue, decreasing ones in red. The size of the sodalite cage (gray) scales with the lattice parameter as the constituting atoms Rb2 and Si1 are located on the special positions 6d and 6c, respectively. The polyhedron encircles the smaller dodecahedron (yellow). Twenty-four-atom cages around Rb2 (shown in Figure S1) are omitted in this description of the clathrate-I structure.

The local arrangement of boron and silicon atoms is characterized by solid-state NMR spectroscopy. The 11B NMR spectrum shows a strong, slightly asymmetric signal centered at −25 ppm, and a weak signal at 60 ppm, agreeing with two boron positions as evidenced by the X-ray diffraction experiment (Figure ). Boron pairs do not occur as the presence of [BSi4] and [BBSi3] entities in the tetrahedral framework would result in a more complex 11B NMR spectrum. Therefore, only one out of two neighboring Si2 positions (site 16i) is substituted by boron atoms. The slight asymmetry of the stronger signal is attributed to the axial symmetry of the Si2 position and positional disorder. The 29Si NMR spectrum shows a broad signal extending from −100 ppm to 600 ppm (Figure , inset), which is assigned to the superposition of different local configurations. Similar spectra have also been observed for other substituted silicon clathrates.[42] Absence of an NMR Knight shift indicates a low density of states at the Fermi level, which is in line with the electron-balanced composition obtained from structure refinement.

Figure 5

11B and 29Si NMR spectra of Rb8B8Si38 at room temperature. Signal at 60 ppm is indicated by an arrow.

The topological features of the partially substituted and compressed clathrate-I framework motivate investigation of chemical bonding. For quantum chemical calculations, an ordered structure representation in space group P4̅3n[43] models the disordered silicon and boron distribution in the framework of Rb8B8Si38. The noncentrosymmetric subgroup allows for a transformation of the mixed occupied 16i position of space group Pm3̅n into two 8e positions in P4̅3n, which are alternatively occupied by B and Si, respectively. The coordinates of the boron position are optimized by total energy calculations. In the calculated density of states (Figure ) the range at low energies (<6 eV) is dominated by the s states of boron and silicon, whereas their p states are located in the region below the Fermi level, reflecting the bonding within the framework. Consistent with the charge transfer in the Zintl model, the s states of rubidium are empty and contribute to the density of states above the Fermi level.

Figure 6

Calculated electronic density of states for an ordered structure model of Rb8B8Si38 (space group P4̅3n).

The effective charges in Rb8B8Si38 are analyzed within the Quantum Theory of Atoms in Molecules (Figure ).[25] In accordance with the electronegativity values, the Rb atoms carry positive (Rb1+0.68, Rb2+0.76) and the B atoms negative charges (−0.72), whereas Si atoms exhibit values around zero (Figure , top). For comparison, the QTAIM charges for the hypothetical binary compound Rb8Si46 using structure data[21] are Rb1+0.59, Rb2+0.57, Si1–0.07, Si2–0.09, and Si3–0.12. Evidently, the presence of the more electronegative boron atoms in Rb8B8Si38 induces a higher charge transfer from the rubidium atoms onto the framework. This finding is also in accordance with the smaller lattice parameter of the boron-substituted clathrate because of increased Coloumb interactions. With the boron atoms carrying a negative charge of −0.72 and effective charges of the silicon close to zero, the electron balance is in agreement with the Zintl model. However, the Coulomb contributions to the stabilization of the structure in the Rb compounds is less significant than in binary clathrates of Ba[44] or Sr[45] because of the lesser charge transfer.

Figure 7

Chemical bonding in Rb8B8Si38. (Top) Shapes and effective charges of QTAIM atoms visualizing the charge transfer in the structure. (Bottom) Distribution of the electron localizability indicator in the (100) plane and positions of ELI-D maxima shown by the isosurface of ELI-D = 1.6 with the populations of bond basins.

Further confirmation of the Zintl-phase character of the new borosilicide is obtained from the distribution of the electron-localizability indicator (ELI-D; Figure bottom). The spherical ELI-D distribution around the Rb nuclei and the absence of the last shell confirm charge transfer from the rubidium atoms to the framework. Each Si–Si and B–Si contact exhibits an ELI-D attractor, and the populations of the basins are close to two electrons. As these basins consist of Si and B contributions, the covalent two-atomic character of the Si–Si and Si–B bonds is evidenced.

TG/DTA measurements of Rb8B8Si38 reveal thermal decomposition at 1305(10) K (Figure ) plus a feature at 1130(5) K which is attributed to a side phase or recrystallization of the product. The mass loss is consistent with the evaporation of the Rb atoms, and the decomposition product only shows reflections of α-Si in XRPD. The high thermal stability, the balanced composition, and the complex crystal structure are preconditions for materials with potential thermoelectric properties.

Figure 8

Thermogravimetry (black curve) and differential thermal analysis (blue curve) of Rb8B8Si38 taken upon heating and cooling in the range 298 K ≤ T ≤ 1473 K with a heating rate of 10 K min–1.

The electrical resistivity of Rb8B8Si38 with ρ(300 K) = 0.02 Ω m is in the range of doped α-Si or α-Ge[46] and shows a semiconductor-like temperature dependence dρ/dT < 0 (Figure ). The Seebeck coefficient is negative, indicating electrons as dominating charge carriers. As expected, the thermal conductivity of κ(300 K) = 2 W K–1 m–1 is small. The thermoelectric figure of merit ZT = S2Tρ–1κ–1 amounts to values close to zero because of the low charge carrier concentration (Zintl limit). The magnetic susceptibility χ of Rb8B8Si38, measured in the temperature range of 1.8–400 K, denotes diamagnetic behavior and remains constant between 100 and 400 K (Figure ). The paramagnetic upturn below 100 K is typical for minor paramagnetic impurity phases. The sum of the diamagnetic increments for Rb1+, B3+ and α-Si[47,48] amounts to χ = – 4.04 × 10–4 emu mol–1, which is only slightly smaller than the measured value. Measurements at 0.2 mT did not show any transition into the superconducting state.

Figure 9

(a) Electrical resistivity ρ(T), (b) Seebeck coefficient S(T), and (c) thermal conductivity κ(T) of Rb8B8Si38.

Figure 10

Magnetic susceptibility of Rb8B8Si38 in the temperature range of 1.8–400 K. The dashed line denotes the sum of the diamagnetic increments.

Summary

The preparation of the new clathrate-I Rb8B8Si38 underlines the potential of high-pressure synthesis to access new tetrahedral borosilicide frameworks. The description of the clathrate-I crystal structure type as a sodalite arrangement enclosing interconnected dodecahedral units emphasizes the separation into a static and a flexible partial structure. The variable part of the clathrate-I crystal structure allows for the specific adaption to various filler and substitution atoms. Analysis of the electron density in Rb8B8Si38 underlines charges in an anionic clathrate framework of covalently four-bonded Si0 and B– following the Zintl model. The chemical bonding is in agreement with the 8-N rule and fully consistent with the semiconducting behavior in electronic transport measurements and the calculated electronic density of states. Characterization of the thermoelectric properties reveals acceptable values for thermal conductivity and Seebeck coefficient, but the still significant electrical resistivity requires further optimization by appropriate doping.