Experimental and computational investigations of TiIrB: a new ternary boride with Ti_1+x Rh_2−x+y Ir_3−y B₃-type structure

2.1 Phase analysis and structure refinement

The TiIrB sample was synthesized by arc-melting of the elements as detailed in the Experimental Section. Phase analysis of the arc-melted product by powder X-ray diffraction (PXRD) indicated four crystalline phases in the sample. Subsequent Rietveld refinement of the PXRD pattern in FullProf [12] generated Figure 1, with results summarized in Table 1. Besides the known TiB₂ (AlB₂ type), TiIr (CuAu type) and TiIr₃ (Cu₃Au type) phases, a new phase could be identified whose lattice parameters and space group (Pbam) indicate the Ti_1+x Rh_2−x+y Ir_3−y B₃ structure type.

Figure 1:

Observed (black) and calculated (red) powder X-ray diffraction pattern of TiIrB; the position of the Bragg reflections (green) for TiIrB (top row), TiB₂ (second row), TiIr₃ (third row), and of TiIr (bottom row); the difference curve (blue) obtained from Rietveld refinement.

The refined lattice parameters of the new phase are a = 8.655(2), b = 15.020(2), and c = 3.2271(4) Å. These lattice parameters and the unit cell volume are larger than those reported for quaternary phases containing smaller transition metals, M = Mn–Ni [9], and Rh-containing Ti_1+x Rh_2−x+y Ir_3−y B₃. This is expected since a larger Ti atom replaces the smaller Rh atom. The refined weight fractions (given in Table 1) indicate that the new phase constitutes 27.9(8) wt. % of the sample. To increase the weight fraction of the new phase the amount of iridium in the starting material was increased to a higher ratio, but this change yielded a sample containing less of the targeted phase, even though the formation of TiIr was suppressed. Rietveld refinement was successfully applied to refine the atomic positions and occupational factors for the new phase. For this refinement the asymmetric unit of the Ti_1+x Rh_2−x+y Ir_3−y B₃ parent compound was used as the starting model (Figure 2), replacing Rh with Ti and neglecting all mixed-occupancies in the first run. After convergence, mixed occupancies of Ir and Ti were successfully refined on two out of three possible Ti sites (see Table 2), leading to a refined composition of Ti_0.93(1)Ir_1.07(1)B indicating a phase width with general formula Ti_3−x Ir_3+x B₃. The Ir content mixed on the Ti sites correlates well with the volume of the different coordination polyhedra, with the largest polyhedron exclusively occupied by Ti and the smallest polyhedron containing the highest fraction of Ir. The volume of the polyhedra and how it affects the coloring of the different Ti sites has been discussed in more detail for quaternary compounds containing three transition metals [9]. Given that x is very small, we use the ideal composition, TiIrB, for simplification when referring to the new compound. The refined interatomic distances around the B atoms (Table 3) were all within expected ranges as found in borides containing these transition metals, especially those mentioned above that have the same or similar structures [3, 5, 7], [8], [9], [10], [11]. The flat B₄ units have bond angles of ca. 117°, which agrees very well with the bond angle in the relaxed computational structure (see electronic structure section below). The B–B interatomic distances are provided without uncertainty as the boron positions have not been refined. However, these coordinates match well with the coordinates of the relaxed structure (Table 2). The chemical bonding analysis performed previously for similar borides containing B₄ fragments has indicated that the boron-based interactions are the strongest bonds [3, 5, 7, 8].

Figure 2:

Projected structure of TiIrB (Ti_1+x Rh_2−x+y Ir_3−y B₃ type) as obtained from Rietveld refinement.

2.2 Electronic structure

The electronic structure was calculated with the Vienna ab Initio Simulation Package (VASP) as detailed in the Experimental Section. The resulting structure, after relaxation, had lattice parameters of a = 8.707, b = 15.094, and c = 3.2412 Å which agree with the experimental data. A slight overestimation of all three parameters is observed, as expected from generalized gradient approximation (GGA) calculations. The atomic coordinates after relaxation agree well with the coordinates used for the Rietveld refinement (Table 2).

The total Density of States (DOS) and partial Density of States (pDOS) are illustrated in Figure 3. Boron slightly dominates the low-lying part of the valence band between −9 and −12 eV. Iridium states dominate the DOS below the Fermi energy (E _F ) and titanium states dominate above E _F , as expected from their different electronegativities. The Fermi energy is located within a pseudo-gap that extends between −1.5 and 0.5 eV, hinting at an optimized electronic structure and confirming the stability of this phase with an almost ideal composition of TiIrB. However, having a finite DOS at E _F infers metallic character, as expected for this metal-rich boride.

Figure 3:

Total and partial density of states (DOS) plots for TiIrB.

The results of a Bader charge analysis indicate that titanium atoms transfer electron density to Ir and B, as their average valence electron count is 9.81 (instead of 9) and 3.52 (instead of 3), respectively, while that of Ti is 2.67 (instead of 4). Remarkably, the boron atoms in the B₄ zigzag fragments retain higher electron density (charge of −3 per B₄ fragment) compared to the lone boron atoms (charge of −0.025 per lone boron atom). The pDOS of the lone boron atoms and B₄ zigzag fragments are compared in Figure 4. The pDOS of B is almost uniform in the range of −1 to −8 eV (see Figure 3), but when divided into two components, the pDOS of the lone B atoms and the pDOS of the B₄ fragments, significant differences become apparent. The pDOS of the B₄ fragments make up most of the boron pDOS in the range of −1 to −5.5 eV compared to that of the lone boron atoms. Thus, it is reasonable to assume that those states are occupied by the additional electrons that have been transferred to the B₄ fragments from Ti. Because of the charge transfer, the atoms at z = 1/2 form a negatively charged layer containing Ir atoms and B₄ fragments, and a positively charged layer at z = 0 containing Ti and lone B atoms. However, not all valence electrons of Ti have been transferred, so it is plausible to also assume significant metallic bonding between the layers. Furthermore, covalent interactions are expected between the lone boron and the surrounding Ir atoms, as found in similar compounds [3, 5, 7, 8]. Consequently, a complex mixture of covalent and metallic bonding as well as some level of electron transfer are the major characteristics of this metal-rich boride.

Figure 4:

Partial density of states (DOS) plots for the lone boron atoms and the B₄ zigzag boron fragments.

4.1 Synthesis of TiIrB

Ti (99.99%), Ir (99.9%) and B (99% amorphous) were used as purchased from Alfa Aesar, and any air sensitive materials were handled in a glovebox. A starting elemental composition of 1Ti:1Ir:1B was mixed in powder form until a homogenous mixture was obtained before being pressed into a dense pellet. The pellets were then melted in an argon-filled arc furnace. Upon arc-melting, The small metallic bead obtained after arc-melting was powdered and characterized by Powder X-ray Diffraction (PXRD) in a Rigaku MiniFlex 600 instrument with CuKα ₁ radiation (λ = 1.54,059 Å) and a Ge monochromator. The refined experimental values were used to provide the information in Tables 1 –3, and Figures 1 and 2.

CSD 2107342 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.

4.2 Computational methods

DFT calculations were used to investigate the electronic structure of the new compound. The TiIrB structural model was prepared in accordance with the Ti_1+x Rh_2−x+y Ir_3−y B₃ structure type in which the Rh positions were fully occupied by Ti. A model without occupational disorder was used to represent the refined X-ray diffraction data, which showed that less than 12% Ir is mixed on two out of three possible Ti sites. The lattice parameters were relaxed using the projector augmented wave method of Blöchl [13, 14] coded in VASP [15]. All VASP calculations employed the generalized gradient approximation (GGA) with exchange and correlation treated by the Perdew-Burke-Enzerhoff (PBE) functionals [16]. The cutoff energy was 450 eV, and the k-point mesh was 19 × 19 × 19. The global break condition for the electronic SC-loop (E _diff) was 1E − 06, and the Fermi level was set to zero. After relaxation, short-circuit (SC) calculations were run. The DOS calculations utilized the CHGCAR file from the SC calculation, with the number of grid points on which the DOS is evaluated (NEDOS) being 2000, making sure to converge the k-points. Bader charge analysis was also performed, ensuring the k-points were converged to ensure an accurate grid for these calculations [17].