Electronic Localization by Structural Distortion - ACS Publications

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

High-Temperature-Phase Bi4RhI2: Electronic Localization by Structural Distortion Bertold Rasche*,‡,† and Michael Ruck‡,¶ ‡

Department of Chemistry and Food Chemistry, TU Dresden, Dresden, Germany Max Planck Institute for Chemical Physics of Solids, Dresden, Germany

¶

S Supporting Information *

ABSTRACT: The metal-rich compound Bi4RhI2 was discovered in a thorough investigation of the Bi−Rh−I phase system. The monoclinic crystal structure was solved via single-crystal X-ray diffraction. It consists of infinite strands of face-sharing distorted square antiprisms 1∞[RhBi8/2]2+, which are separated by iodide ions. Bi4RhI2 is the high-temperature phase related to the weak three-dimensional topological insulator Bi14Rh3I9 (Bi4.67RhI3) and forms peritectically at 441 °C, where Bi14Rh3I9 decomposes. The structure of Bi4RhI2 is compared with Bi4RuI2 and Bi9Rh2I3, all three sharing a similar intermetallic strand-like structure, although their overall count of valence electrons differs. A chemical bonding analysis of Bi4RhI2 via the electron localizability indicator reveals a complex bonding pattern with covalent bonds between rhodium and bismuth, as well as between bismuth atoms and suggests a possible explanation for the formation of this structure type. Band structure calculations indicate a narrow band gap of 157 meV, which was verified by resistivity measurements on a pressed powder pellet and on single crystals. In a broader context, this strandlike structure type accounts for unusual physical phenomena, such as the transition into a charge-density-wave phase.

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INTRODUCTION With the discovery of the first weak three-dimensional topological insulator (TI), Bi14Rh3I9, the Bi−Rh−I phase system came into focus.1,2 Driven by the need to provide optimal parameters for the growth of crystals, studies of the ternary phase diagram in the vicinity of Bi14Rh3I9 were initiated. The combination of differential scanning calorimetry (DSC) and powder X-ray diffraction (PXRD) revealed that the new phase, Bi4RhI2, has almost the same composition as Bi14Rh3I9 (Bi4.67RhI3) and forms in the course of the peritectic decomposition of the latter.2 At the time, we were not able to provide further information on this so-called “phase X”. Besides the relation to Bi14Rh3I9, Bi4RhI2 is also related to an entire family of phases, because of its structure. This family hosts several structures with transition-element centered strands of bismuth, tellurium, or selenium held together by halides in an ionic matrix (examples include Te4MoBr, Te4MI, and (Se2M)2I, where M = Nb or Ta).3−7 This becomes interesting, as some of them, such as (Se4Ta)2I, exhibit a transition from a metal to a charge-density-wave phase and can therefore host 1D electrons.6 Most prominent is the relationship of Bi4RhI2 to two specific compounds of this family: Bi 4 RuI 2 and Bi 9 Rh 2 I 3 .8,9 Compared to the ruthenium compound, the exchange for rhodium, which has one electron more than ruthenium, leads to structural distortions, while this distortion evolves further for the even more electron-rich Bi9Rh2I3, because of a slightly increased bismuth content (Bi4.5RhI1.5). © XXXX American Chemical Society

Here, we present the crystal structure of Bi4RhI2, the formerly unknown “phase X”, as it was solved from data of single-crystal X-ray diffraction. Its structure and bonding patterns are compared to the related compounds Bi4RuI2 and Bi9Rh2I3. The second part is a comprehensive analysis of the chemical bonding, among others with the density functional theory (DFT)-based real-space analysis via the electron localizability indicator (ELI-D). It reveals trends going hand in hand with the changing electron count. Based on the analysis, we can assign oxidation states to the atoms in Bi4RhI2 and classify the new structure into the family.

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RESULTS AND DISCUSSION Synthesis and Structure. Synthesis of Bi4RhI2 followed the thorough DSC analysis recently presented, which revealed that the phase is stable between 441 °C, where it forms in the peritectic decomposition of Bi14Rh3I9, and 475 °C, where it decomposes peritectically into a homogeneous Bi−I melt and Bi2Rh(aP12).2 Bismuth, rhodium, and BiI3, in a molar ratio of Bi:Rh:I = 4:1:2, were ground in an argon-filled glovebox and sealed in an evacuated silica ampule (p < 0.1 Pa). Phase-pure powders of Bi4RhI2 (see Figure S1 in the Supporting Information) were obtained by annealing the mixture at 458 °C for 5 d, followed by quenching to room temperature in Received: February 22, 2018

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DOI: 10.1021/acs.inorgchem.8b00464 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. (a) Crystal structure Bi4RhI2 at 296 K. (b) One intermetallic strand with surrounding iodide ions in detail. Bi−Bi bonds are drawn up to 338 pm, Bi−I bonds up to 330 pm, Bi···I connections up to 369 pm (details are given in Table S4 in the Supporting Information); ellipsoids represent 99% probability. (c, d) Crystal structure and intermetallic strand for Bi4RuI2.8 (e, f) Crystal structure and intermetallic strand for Bi9Rh2I3.9

(bΔT) = −3.3 × 10−5 K−1, and Δc/(cΔT) = −4.4 × 10−5 K−1, and a slight increase of the monoclinic angle (by 0.15°). Compared to the direction along the intermetallic strands a, the other two directions shrink more pronouncedly. That can be understood in terms of the predominantly covalent bonding within the strands, in contrast to the mostly ionic bonding between the I ions and the intermetallic strands (see below). On the other hand, the atomic positions vary the most in the xparameter, by a maximum of 2.6 pm, compared to a maximum of −1.67 pm for the y- and z-parameters. Nevertheless, this is still 99.90% metal base) and ruthenium (Riedel-de Haen, >99.00% metal base) were used without further purification. BiI3 was synthesized from the elements and sublimed twice.10 Powder X-ray Diffraction (PXRD). Powder X-ray diffraction (PXRD) was performed on a PANalytical X’Pert Pro Powder diffractometer in Bragg−Brentano geometry equipped with a Ge(111) monochromator, a rotating sample stage, and a PIXcel detector, using Cu Kα1 radiation (λ = 154.056 pm). The data were collected using a divergence slit that kept the illuminated sample area constant with a silicon single-crystal sample holder to reduce diffusive X-ray scattering. Single-Crystal X-ray Diffraction (SCXRD). Single crystals were measured on a four-circle diffractometer Bruker-Nonius Kappa APEX II CCD, with a Mo tube (λ(Mo Kα1) = 71.073 pm), a graphite(002)monochromator, and a CCD detector. Integration as well as polarization and Lorentz factor corrections of the data were conducted within the APEX2 suite. Optimization of the experimental crystal shape description based on equivalent reflections in the corresponding Laue class and the numerical absorption corrections were performed with X-Red and X-Shape.22,23 Jana2006 was employed for the structure solution with charge flipping methods.24,25 The refinement was conducted in the SHELX2014 program suite.26 Graphical representations of the structures were developed with Diamond.27 Electrical Resistivity. Powders were cold-pressed to cylindrical pellets in a sapphire die cell. The electrical resistivity was measured between 4 K and 320 K, using four platinum contacts in the Van-derPauw setup. Single crystals were contacted with four gold wires (50 μm) that were glued to the crystal with graphite paste (Dupont 7105 + diluter 8260), which dries in air at room temperature. Magnetization Measurements. The samples were filled in precalibrated silica tubes. The magnetization was measured in fields of ν0H = 2 mT, 0.1 T, 3.5 T, and 7 T in a SQUID magnetometer (Model MPMS-XL7, Quantum Design). The data were corrected for small ferromagnetic impurities (most probably introduced during preparation) with an Honda-Owen type correction28,29 and for paramagnetic impurities with a respective Curie term in the fit. No significant superconducting volume fraction was observed in the magnetic susceptibility measurements. Quantum Chemical Calculations. All scalar- and full-relativistic calculations were performed with the Full-Potential Local-Orbital (FPLO) code,30 version 14.00, within the local density approximation (LDA) using the parametrization PW92.31 The Blöchl corrected linear tetrahedron method with a 15 × 6 × 7 k-mesh for Bi4RhI2 (setting according to P21/c, not P21/n, as FPLO cannot handle the latter), a 12 × 12 × 12 k-mesh for Bi4RuI2 (primitive cell with a = b = c = 901.6 pm and α = β = γ = 43.6°) and a 13 × 8 × 12 k-mesh for Bi9Rh2I3 was employed, after checking for convergence with respect to the number of k-points (min. 9000 k-points). Spin−orbit coupling (SOC) was implemented on the level of the four-component Dirac equation. Topological invariants were calculated according to the supplement of ref 1. The basis states that were treated as valence states are listed in Table 1. Mulliken population analysis32 was directly provided by FPLO. Charges according to the quantum theory of atoms in molecules (QTAIM) developed by Bader33 were calculated with the DGrid program package34 via a topological analysis of the electron density, which was provided by an FPLO module.35

1 4·3(Bi6p) − 2(Bi4−Bi6 bond) − 4· (I−) = 8 2

Structurally, this square of Bi atoms is related to a fragment from Bi4RuI2, which was originally discussed as Bi04 and later as 8,20 Bi2− 4 . This electron distribution derived from ELI-D and comparison to Bi4RuI2 finally can be translated into a coordination chemistry picture with rhodium as a central atom. The [(Bi2)Bi2I1I2/2] “ligand” and the [(Bi2)Bi2I4/2] “ligand” donate eight electrons each. For rhodium, with its nine valence electrons, this makes 9 + (8+8)/2 = 17 valence electrons. Forming a multicenter Rh−Bi−Rh bond (Figure 4c), it achieves the advantageous 18-electron count. Within the three presented compounds, this analysis demonstrates exemplarily, how the localization of electrons in covalent bonds can stabilize the same type of structure with different (valence) electron counts and lead to “‘electronprecise”’ compounds with a gap in the DOS at the Fermi level. As a consequence, structural distortions occur. This approach might even shed new light on the broader family of compounds, to which, additionally, the more heteropolar Te4MoBr, Te4MI, and (Se2M)2I with M=Nb or Ta belong.3−7 In the latter structures, strands of square antiprisms of chalcogenides host electron-poor transition-metal atoms that are separated by short and long distances (various patterns). These structures are polarized inversely to the 5− bismuth compounds discussed here, e.g., [Mo5+][(Te2− 2 )2Br] 3 (charges assigned by the authors). All in all, this structure type seems to be very flexible, with respect to the constituting elements and charge distribution. That is of interest, as the strands under certain conditions, as, e.g., in (Se4Ta)2I, can host 1D-electrons, resulting in unique transport phenomena, such as charge density waves.6

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CONCLUSION We have introduced the new compound Bi4RhI2 as the hightemperature phase to the weak 3D-TI Bi 14 Rh 3 I 9 . Its intermetallic strand structure has been compared to the two closest relatives of an entire family of structures, revealing the influence of the electron count on the local and global structural arrangement. A comprehensive analysis of bonding situation, with the DFT-based ELI-D method allows a formal assignment of charges and therefore to fit Bi4RhI2 into the family. Moreover, the bonding analysis explains the calculated electronic structure of a narrow gap semiconductor, that was E

DOI: 10.1021/acs.inorgchem.8b00464 Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

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Table 1. Basis States (Adjusted Atomic Wave Functions) That Were Treated as Valence States for the Elements Used atom Ru Rh I Bi

4p 4p 4p 5p

4d 4d 4d 5d

5s 5s 5s 6s

5p 5p 5p 6p

5d 5d 5d 6d

6s 6s 6s 7s

6p 7p

Chemical bonding was characterized via the electron localizability indicator (ELI-D, ϒσD).17,18 The ELI-D field was computed from the converged SCF calculations using the ELI-D module35 for the FPLO program package.30 The field maxima (attractors) can mark out various bonding features, such as atomic shells, lone pairs, and chemical bonds. Topological analysis of ELI-D was performed in the DGrid 4.6 program34 by a procedure similar to that of the Quantum Theory of Atoms in Molecules by Bader.33 The integration of electron density within the resultant basins yielded the electron count for all bonding features. The atomic contributions into the bonding basins were computed via integration of the intersection between the bonding ELI-D basin and the respective QTAIM basins for atomic constituents. The ELI-D localization domains were visualized in real space with the Paraview program package.36

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00464. Detailed data on the structure solved from single-crystal X-ray diffraction (atomic positions, anisotropic displacement parameters, distances), calculated electronic band structure, resistivity and magnetization measurements and results of the quantitative Bader and ELI-D analysis (PDF) Accession Codes

CCDC 1823422−1823423 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, U.K.; fax: +44 1223 336033.

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REFERENCES

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valence states 4s 4s 4s 5s

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Bertold Rasche: 0000-0002-9691-1903 Present Address †

Department of Chemistry, University of Oxford, Oxford, United Kingdom Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Ms. I. Kuhnert for support with the DSC experiments, Dr. A. I. Baranov for helpful discussions concerning the ELI-D results, and Dr. W. Schnelle and Mr. R. Koban for the magnetization and resistivity measurements. We are indebted to ZIH TU Dresden for computational facilities. We acknowledge the financial support from the German Research Foundation (DFG) in the framework of the SPP1666 and the Research Fellowship RA 3120/1-1. F

DOI: 10.1021/acs.inorgchem.8b00464 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b00464 Inorg. Chem. XXXX, XXX, XXX−XXX