Crystal Structure and Physical Properties of the Cage Compound Hf₂B_2–2δIr_5+δ

Abstract

Hf₂B_2–2δIr_5+δ crystallizes with a new type of structure: space group Pbam, a = 5.6300(3) Å, b = 11.2599(5) Å, and c = 3.8328(2) Å. Nearly 5% of the boron pairs are randomly replaced by single iridium atoms (Ir_5+δB_2–2δ). From an analysis of the chemical bonding, the crystal structure can be understood as a three-dimensional framework stabilized by covalent two-atom B–B and Ir–Ir as well as three-atom Ir–Ir–B and Ir–Ir–Ir interactions. The hafnium atoms center 14-atom cavities and transfer a significant amount of charge to the polyanionic boron–iridium framework. This refractory boride displays moderate hardness and is a Pauli paramagnet with metallic electrical resistivity, Seebeck coefficient, and thermal conductivity. The metallic character of this system is also confirmed by electronic structure calculations revealing 5.8 states eV^–1 fu^–1 at the Fermi level. Zr₂B_2–2δIr_5+δ is found to be isotypic with Hf₂B_2–2δIr_5+δ, and both form a continuous solid solution.

Short abstract

Hf₂Ir_5+δB_2−2δ is a cage compound with a three-dimensional anionic boron−iridium framework composed of [B₂Ir₈] units with cavities bearing the hafnium cations. Zr₂Ir_5+δB_2−2δ is found to be isotypic with Hf₂Ir_5+δB_2−2δ, and both form a continuous solid solution.

1. Introduction

The structural chemistry of metal borides displays a vast diversity.¹ The inherent electron deficiency of boron can be seen as the main ingredient necessary for the high structural complexity.² Depending on the metal to boron ratio, the formation of multicenter B–B bonds gives rise to the evolution of boron-based framework structures with increasing dimensionality.³⁻⁵ The boride’s crystal structures are characterized by strong covalent boron–boron and metal–boron bonds.^6,7

This gives rise to interesting structure–properties relationships which have been topic of the solid-state sciences for decades. The inherent hardness,⁸ wear resistance, and chemical inertness⁹ of borides belong to the group of phenomena which have been observed and studied from the very beginning of research on this class of materials.⁶ Applications such as abrasives, cermet-based specialty cutting tools,¹⁰⁻¹³ or tough alloy surface coatings¹⁴ take advantage of these properties.

Other technologically demanding developments are ultrahigh-temperature boride-based ceramics¹⁵ and ceramic coatings¹⁶ as well as the field of superhard materials, where alternatives to diamond and cubic boron nitride are sought. The increasing surge in theoretical and experimental research activities focusing on ReB₂^17,18 and OsB₂¹⁹ also raised significant interest in other transition-metal polyborides.²⁰⁻²⁵ The high electron concentration of heavy 5d transition metals, leading to high elastic moduli, in combination with the highly directional covalent bonds is important for the physical properties of this category of superhard borides. For that reason, research has currently intensified on elucidating and understanding the influence of boron incorporation in heavy transition metals.

HfB₂ with a hexagonal AlB₂ type of structure and a high melting point of 3400 °C also belongs to this family of refractory diborides.^26,27 It has found its way into nuclear applications as neutron absorber materials²⁸ and high-temperature ceramic composites.^29,30

Also, platinum metals and their interaction with boron have been the targets of investigation,³¹⁻³⁵ which have been directed toward an understanding of their distinct structural chemistry and/or exploration of their mechanical properties. The binary iridium boron system has been studied thoroughly,^36,37 and recent attention is mainly due to joint theoretical and experimental classification of some iridium borides as potentially superhard materials.³⁸⁻⁴⁰

The structural diversity significantly increases for the numerous families of ternary and higher multicomponent transition-metal-based borides.^4,41−44 Taking alone the large structural variety of noble-metal-based ternary and higher boride systems and combining them with all the possibilities of a diverse interplay between physical properties, such as superconductivity and magnetism, the considerable interest in explorative studies can be easily motivated and explained.⁴⁵⁻⁵²

Given the recent interest in the platinum-group-metal superalloys, related intermetallic compounds for high-temperature oxidation-resistant structural applications,^53−59,65 and the concomitant need for brazing alloy systems, a detailed knowledge of ternary Ir-based phase diagrams is desirable. Joining small casted parts of such alloys helps to minimize size-dependent casting defects; transient liquid phase (TLP) bonding,⁶⁰ a technology developed for joining and repairing Ni-based superalloys,^61,62 could be an obvious choice. To achieve this, a melting-point depressant is placed between the two mating surfaces, which is typically a boride-based eutectic, where the highly diffusive boron reduces the melting point, due to low-lying eutectic formation. As an example, a eutectic is formed in the Ir-rich part (37.5 atom % boron) of the binary Ir–B system at 1259 °C.^22,35 One could therefore envision employing boron as a melting-point depressant also in Ir–Zr–Hf-based superalloys,⁶³⁻⁶⁵ in a way similar to Ni-based superalloys joining technologies. However, as is known from numerous studies when boron is used as a melting point depressant, it is very difficult to avoid the precipitation of brittle borides.^66,67 They have a detrimental effect on the mechanical properties as well as on the corrosion resistance. This is a strong motivation for investigating the occurrence of Ir–Zr/Hf-based borides, their crystal structures, and thus the structure–properties relationships in these materials.

The isothermal sections of the phase diagrams of Zr–Ir–B and Hf–Ir–B ternary systems at 1100 °C were investigated some time ago.⁶⁸ Three ternary borides—hexagonal ZrIr₃B₄ (HfIr₃B₄ type) (also reported later as a ZrIr₃B_3.76 composition⁶⁹) as well as ∼ZrIr₃B₂, and ∼ZrIr₅B₄ with unknown structures—were detected in the Zr–Ir–B system. Additionally, cubic Zr₂Ir₆B (K₂PtCl₆ type) was reported later to exist.⁷⁰ However, five compounds have been reported to occur in the Hf–Ir–B system: tetragonal Hf₃Ir₅B₂ (Ti₃Co₅B₃ type⁷¹), hexagonal HfIr₃B₄ (its own type of structure⁶⁹), HfIr₃B_0.45 (structure type CaTiO₃⁶⁸), and ∼HfIr₃B₂ and ∼HfIr₅B₄ with unknown structures.

In light of the aforementioned interest in Ir-rich ternary borides, we started to search for these last two compounds, which yielded as a byproduct the ternary phase Hf₂B_2–2δIr_5+δ with a new type of crystal structure and its Hf_2–xZr_xB_2–2δIr_5+δ solid solution.

2. Experimental Section

Samples with the nominal compositions ZrIr_2.7B_1.6, HfIr_2.7B_1.6, and Hf₂Ir₅B₂ were prepared from Zr powder (Alfa-Aesar, 98.5% metals base, with Hf 2% nominal content), Zr crystal bar (Haines & Maassen, 99.9% metals base, with 280(20) ppm of Hf as analyzed by ICP-OES), Hf powder (Chempur, 99.8% metals base, with 2.9(1)% Zr as analyzed by ICP-OES), Hf pellets (Haines & Maassen, 99.9% metals base, with 0.11(1)% Zr as analyzed by ICP-OES), Ir powder (Chempur, 99.9%), and B crystalline powder (Chempur, 99.99%). First, B and Ir powders were pressed into a pellet, placed in a ZrO₂ crucible, enclosed in an evacuated Ta tube, and annealed at 1270 K for 4 days. This led to (i) homogeneous Ir–B precursors with rather low melting points (see the Introduction) and (ii) suppression of the competing formation of HfB₂ in the second step of synthesis. Then, this pellet was arc-melted with Hf pieces under an Ar atmosphere on a water-cooled copper hearth (mass losses <2%). Further heat treatment was performed between 1470 and 1570 K for several weeks. All described handlings and procedures were carried out in Ar-filled gloveboxes (MBraun, p(O₂/H₂O) ≤ 1 ppm).

The obtained samples were characterized by powder X-ray diffraction (PXRD) with a Huber G670 imaging plate Guinier camera and Cu Kα1 radiation (λ = 1.54056 Å, using a curved germanium (111) monochromator). Phase analysis and indexing have been carried out using the WinXPow program package.⁷² High-resolution powder XRD was performed at the BM20 beamline of the European Synchrotron Radiation Facility (Grenoble, France) (λ = 0.45920 Å) on powder enclosed in a quartz capillary with an outer diameter of 0.3 mm. The images collected on a Pilatus 100K detector⁷³ were integrated with the PYFAI library.⁷⁴ Indexing of PXRD patterns and Rietveld refinement of the crystal structure were performed using the WinCSD software.⁷⁵

Single crystals were mechanically extracted from an arc-melted and annealed sample made by using Hf powder containing a considerable amount of Zr (see above) as a Hf source with the composition HfIr_2.7B_1.6. For Hf₂Ir₅B₂ and Zr₂Ir₅B₂, attempts to isolate single crystals of sufficient quality failed. Single-crystal XRD was performed on a Rigaku AFC7 diffraction system equipped with a Saturn 724+ CCD Detector (Mo Kα radiation, λ = 0.710730 Å, graphite monochromator). The crystal structure solution and refinement were performed using the WinCSD program package.⁷⁵

Differential scanning calorimetry has been performed by means of a DSC NETZSCH 404 C instrument in the temperature range 300–1870 K. Both Zr₂B_2–2δIr_5+δ and Hf₂B_2–2δIr_5+δ reveal no thermal effects either during heating or upon cooling, suggesting that the studied samples do not melt in the mentioned temperature range.

For microstructural studies, small pieces of the new ternary boride were embedded in a conductive resin, polished, and ground. The obtained polished surface was investigated using a Zeiss Axioplan 2 light-optical microscope and a Jeol JSM-7800F scanning electron microscope. The chemical composition was analyzed by means of energy dispersive X-ray spectroscopy (EDXS, Quantax 400 EDXS system, Bruker) and wavelength dispersive X-ray spectroscopy (WDXS, SX 100 setup, Cameca) with Ir metal and HfB₂ as reference materials. WDXS measurements on a sample synthesized from Hf metal pellets (see above) confirmed the Hf:Ir ratio to be very close to 2:5, while the total composition (i.e., Hf_1.9(1)Ir_4.9(1)B_2.0(3)) deviated slightly from the nominal composition due to the inaccuracy of the estimation of the small (i.e., 1.6 mass %) boron amount.

The magnetic susceptibility was measured in the temperature range 1.8–400 K in external fields between 0.1 and 7 T using a SQUID magnetometer (MPMS-XL7, Quantum Design). The electrical resistivity, Seebeck coefficient, and thermal conductivity were simultaneously measured using the TTO option of a Physical Property Measurement System (PPMS, Quantum Design).

Electronic structure calculation and bonding analysis for Hf₂B₂Ir₅ were carried out using the experimental values of the lattice parameters and the atomic coordinates for the ordered model without multiple substitution (δ = 0). The electronic density of states for Hf₂B₂Ir₅ was obtained within the local density approximation (LDA) to the density functional theory (DFT). Calculations were performed by using the all-electron, full-potential local orbital method (FPLO, version 9.01-35)⁷⁶ by employing the exchange-correlation potential of Perdew and Wang.⁷⁷ The first Brillouin zone was sampled by a mesh of 20 × 20 × 20 (8000) k points.

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 former type of analysis forms the basis of the quantum theory of atoms in molecules (QTAIM).⁷⁸ ELI was calculated in the ELI-D representation⁷⁹⁻⁸¹ by a module implemented in the FPLO package.⁸² Topological analyses of the ED and the ELI-D were carried out by the program DGrid.⁸³ To obtain the atomic charges from ED and bond populations for bonding and lone-pair basins from ELI-D, both the ED and the ELID were integrated within the space regions (basins), bounded by zero-flux surfaces in the according gradient field. The procedure proposed follows the QTAIM.⁷⁸ A combined analysis of ED and ELI-D allows obtaining basic information for the description of the bonding situation in solids, in particular for intermetallic compounds.

3. Results and Discussion

3.1. Crystal Structure

Since single crystals were originally extracted from samples made from Hf powder containing considerable amounts of Zr (see the Experimental Section), the crystallographic details on the single-crystal diffraction performed on Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05) are given in Table 1. An analysis of the extinction conditions indicated the two possible space groups Pba2 (No. 32) and Pbam (No. 55). Starting with the centrosymmetric space group, we applied direct methods to find the positions of heavier Hf and Ir atoms. Further differential Fourier calculations allowed localization of boron atoms. During the refinement the displacement parameter B_eq for Hf was found to be twice as large as that of Ir atoms. Thus, this position was assumed to be occupied by a statistical mixture of Hf and Zr (cf. the composition of the initial hafnium powder in the Experimental Section). The content of Zr in this position is higher in comparison to the initial powder, indicating a special suitability of the atomic environment for occupancy by zirconium. At this stage, the residual value was relatively low (0.042). Nevertheless, an analysis of the difference electron density reveals an additional peak at the 2d site (0,1/2,1/2). Because of spatial collision with the boron atoms (d = 0.91 Å), it was assumed that this position is occupied by iridium, i.e. the random replacement of ca. 5% of boron pairs by single iridium atoms, as this was already found in Mg₂Rh_1–xB_6+2x.⁹⁸ This minor substitution significantly reduced the residual value to 0.037. The final values of atomic coordinates and displacement parameters for Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05) are given in Table 2, and the anisotropic displacement parameters are collected in Table 3.

Table 1. Crystallographic Data for Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05)) and Hf₂B_2-2δIr_5+δ (Space Group Pbam, Z = 2).

	Hf2–xB2–2δZrxIr5+δ (x ≈ 0.5, δ ≈ 0.05)	Hf2B2–2δIr5+δ
diffraction material	single crystal	powder
crystal shape	irregularly shaped
cryst size (mm3)	0.015 × 0.030 × 0.040
diffraction system	Rigaku AFC-7	BM20
radiation, λ (Å)	Mo Kα, 0.710730	synchrotron, 0.45920
sin θ/λmax	0.775	0.766
unit cell params (powder data)
a (Å)	5.6290(9)	5.6300(3)
b (Å)	11.270(2)	11.2599(5)
c (Å)	3.8444(5)	3.8328(2)
V (Å3)	243.9(1)	242.97(3)
calcd density ρ (g cm–3)	17.79	18.26
h, k, l ranges	–5 ≤ h ≤ 8	0 ≤ h ≤ 8
	–17 ≤ k ≤ 15	0 ≤ k ≤ 17
	–4 ≤ l ≤ 5	0 ≤ l ≤ 5
abs cor	numerical
abs coeff (mm–1)	180.29	65.51
N(hkl) measd	1592	518
N(hkl) obsd	461
observation criterion	F(hkl) ≥ 4σ(F)
no. of refined params	34	17
RF, RI, RW, RP	0.037; 0.040	0.045, 0.068
residual peaks (e Å–3)	–4.19/5.68

Table 2. Atomic Coordinates and Occupational and Displacement Parameters for Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05) and Hf₂B_2–2δIr_5+δ.

atom	site	occ	x	y	z	Beqa/Biso (Å2)
Hf2–xB2–2δZrxIr5+δ (x ≈ 0.5, δ ≈ 0.05)
M	4g	0.76(1) Hf + 0.24(1) Zr	0.2871(2)	0.1128(1)	0	0.56(3)
Ir1	2b	1	0	0	1/2	0.55(3)
Ir2	4h	1	0.0340(2)	0.24666(7)	1/2	0.33(2)
Ir3	4g	1	0.7797(2)	0.13189(7)	0	0.42(2)
Ir4	2d	0.05(1) Ir	0	1/2	1/2	0.6(3)
B	4h	0.949(6) B	0.612(5)	0.058(3)	1/2	0.6(4)
Hf2B2–2δIr5+δ
Hf	4g	1	0.290(1)b	0.1128(6)	0	0.7(2)
Ir1	2b	1	0	0	1/2	0.8(2)
Ir2	4h	1	0.036(2)	0.2462(5)	1/2	0.8(2)
Ir3	4g	1	0.781(1)	0.1319(6)	0	0.7(2)
Ir4	2d	0.06 Ir	0	1/2	1/2	1.3(4)
B	4h	0.94(2) B	0.580(30)	0.088(15)	1/2	1.2(4)

^aB_eq = 1/3[B₁₁a*²a² + ... + 2B₂₃b*c*bc cos α] for M and Ir1–Ir3 in Hf_2–xZr_xIr_5+δB_2–2δ (x ≈ 0.5, δ ≈ 0.05), B_iso for all other atoms.

^bEstimated standard deviations are calculated by the method of Bérar and Lellan.⁹⁹

Table 3. Anisotropic Displacement Parameters for Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05).

atom	B11	B22	B33	B12a
Hf	0.54(5)	0.49(4)	0.65(4)	–0.06(3)
Ir1	0.71(5)	0.39(4)	0.54(4)	0.02(4)
Ir2	0.34(3)	0.30(3)	0.37(3)	–0.05(2)
Ir3	0.44(4)	0.37(3)	0.47(3)	0.08(3)

^aB₁₃ = B₂₃ = 0 for all Hf and Ir positions.

Additionally, a close to single-phase ternary sample of Hf₂B_2–2δIr_5+δ (inset to Figure 1) was prepared from Hf metal with significantly reduced Zr content (see the Experimental Section) and characterized with high-resolution synchrotron (HRS) XRD at BM20 at ESRF.

Figure 1.

Powder XRD pattern for Hf₂B_2–2δIr_5+δ (red, calculated profile; black circles, measured intensities; black tick marks, reflection positions; black line in the bottom panel, difference intensity curve). Inset: microstructure of an annealed sample.

As the initial model for the Rietveld structure refinement, the atomic parameters from Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05) (Table 2) were used. The refinement converged with low reliability factors (Table 1) and physically reasonable displacements for all atoms (Table 2). Whereas from the laboratory X-ray powder diffraction data the additional position of Ir cannot be reliably refined, the high-resolution synchrotron data clearly confirm this crystallographic disorder. The experimental, calculated, and differential diffraction intensities for Hf₂B_2–2δIr_5+δ are shown in Figure 1. The crystal structures of both Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05) and Hf₂B_2–2δIr_5+δ reveal a unique atomic architecture and thus have to be considered as a new structure type.

The indexing of the HRS XRD pattern as well as the comparison of the theoretically calculated and experimentally observed intensities also confirmed the Hf₂B_2–2δIr_5+δ structure type for Zr₂B_2–2δIr_5+δ (a = 5.6290(2) Å, b = 11.2697(3) Å, c = 3.8444(1) Å). However, the presence of numerous impurity phases (e.g., ZrIr₄B₃⁶⁹ and Zr₂Ir₆B⁷⁰) did not allow us to refine the atomic coordinates and displacement parameters for this boride in a reasonable way.

The interatomic distances in the structure of Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05) are given in Table 4 (data for Hf₂B_2–2δIr_5+δ can be found in Table S1 in the Supporting Information). The Hf–B, Hf–Hf, Hf–Ir, and B–B distances are close to or exceed the sums of atomic radii of the elements (r_Hf = 1.56 Å, r_Ir = 1.36 Å, and r_B = 0.83 Å⁸⁴).

Table 4. Selected Interatomic Distances (in Å) for Hf_2–xB_2–2δZr_xIr_5+δ (x ≈ 0.5, δ ≈ 0.05).

Ma–B (×4)	2.73(2)–2.78(2)	Ir3–B (×2)	2.30(2)
Ma–Ir (×10)	2.781(2)–2.878(1)	Ir3–Ir (×6)	2.7234(9)–2.7351(9)
Ma–Hf (×3)	3.494(2)–3.8444(6)	Ir3–Hf (×4)	2.781(1)–2.878(1)
Ma–Ir4 (×2)	2.5975(8)	Ir3–Ir4 (×2)	2.8952(7)
Ir1–B (×2)	2.28(3)	B–B	1.82(4)
Ir1–Ir (×6)	2.7281(7)–2.7864(4)	B–Ir (×4)	2.24(3)–2.30(2)
Ir1–Hf (×2)	2.8148(9)	B–Hf (×4)	2.72(2)–2.78(2)
Ir1–Ir4 (×2)	2.8145(4)	B–Ir4	0.91(3)
Ir2–B	2.24(3)
Ir2–Ir (×7)	2.7234(9)–2.816(1)
Ir2–Hf (×4)	2.829(1)–2.852(1)
Ir2–Ir4	2.8616(8)

^aM = Hf_0.76Zr_0.24.

The coordination polyhedra of atoms in the structure of Hf₂B₂Ir₅ (ordered model without multiple substitution) are depicted in Figure 2 (top). Hafnium atoms are at the centers of 18-vertex [HfHf₆Ir₈B₄] polyhedra. This polyhedron can be understood as being formed on the basis of a [HfHf₆] octahedron. Ir1 and Ir2 are at the centers of distorted [Ir1Hf₄Ir₆B₂] and [Ir2Hf₄Ir₇B] cuboctahedra, thus having as the closest environment [Hf₄Ir₄] distorted cubes. Ir3 is located in a distorted [Ir3Hf₄Ir₆B₂] icosahedron typically occurring in the CeCo₃B₂ structure type.⁸⁵ Finally, the location of boron atoms can be geometrically described in different ways. They center trigonal prisms [BHf₄Ir3₂] which share their rectangular [Hf₄] face in pairs forming rhombic prisms. The B atoms are relatively close to each other (d_B–B = 1.87(5) Å), forming B₂ dumbbells—a structural unit that is well-known in the chemistry of metal-rich intermetallic borides.^1,86 For δ ≠ 0, a single iridium atom is located in the center of such a cuboctahedron. The [B₂Hf₄Ir3₄] rhombic prisms are tetracapped by each two Ir1 and two Ir2 atoms, respectively, which result in [B₂Hf₄Ir3₄Ir1₂Ir2₂] entities (reminiscent of distorted cuboctahedra) forming slabs along the [001] direction and sharing their corners in the [100] direction (see Figure 2, top, and Figures S1 and S2). Such a description indicates a close crystallographic relationship of the Hf₂B_2–2δIr_5+δ type with the homologous series of the borides based on α-Fe (W) and AlB₂ types.^1,87

Figure 2.

Crystal structure of Hf₂B₂Ir₅: (top) coordination polyhedra of atoms; (bottom) arrangement of the distorted cuboids [Ir1Hf₄Ir₄] (violet) and [Ir2Hf₄Ir₄] (red) and trigonal prisms [BHf₄Ir₂]. [□Ir1₂Ir3₂Hf₂] octahedra are shown as examples.

Structural similarities can be also found with the tetragonal Mo₂FeB₂ type.⁸⁸ In this crystal structure we observe tilted and distorted vertex-connected octahedra [□Fe₄Mo₂]. The voids in this kind of 3D structure are distorted cuboctahedra filled with boron dumbbells (i.e., [B₂Fe₈Mo₄]) (Figure 3a,b). On an equal geometrical footing, one can recognize rhombic prismatic slabs along [001] that can be decomposed into face-sharing trigonal prisms hosting the boron atoms. In Hf₂B_2–2δIr_5+δ, a related scenario is encountered. In order to discern this, one has to bear in mind that the slabs of Ir-centered cuboids can be also represented as [□Ir1₂Ir3₂Hf₂] and [□Ir2₂Ir3₂Hf₂] octahedra which share edges in the ab plane and are vertex-connected along [001] (Figure 2, bottom, and Figures S1 and S2).

Figure 3.

Two-dimensional intergrowth of filled cuboctahedral (square biantiprismatic) and empty octahedral segments in the crystal structures of Mo₂FeB₂ and Hf₂B₂Ir₅ (Hf, Mo, gray spheres; Ir, Fe, blue spheres; B, black spheres).

The tilting angle of the [□Ir₄Hf₂] octahedra in this structure (Figure 3c,d) is smaller than those of [□Fe₄Mo₂] in the Mo₂FeB₂ type (Figure 3a). However, in contrast to Mo₂FeB₂, in Hf₂B₂Ir₅ the unit cell geometry with b ≈ 2a allows the intergrowth of a second layer of octahedra with the opposite tilt direction.

From crystal-chemical reasoning, the structure of Hf₂B_2–2δIr_5+δ can thus be described in multiple ways. This raises the important question of which atomic interactions govern the formation of this compound and thus transcend the aforementioned mere geometrical perspective. This issue was tackled by applying a quantum chemical analysis of chemical bonding with position-space techniques, in particular the electron localizability approach.⁸⁰

An analysis of the calculated electron density on application of the QTAIM reveals a relatively small volume of the Hf species in comparison with the iridium and boron species (Figure 4). Furthermore, the effective charge of hafnium, evaluated by integration over the electron density within the region formed by zero-flux surfaces in its gradient field around the nucleus of Hf, is unexpectedly large (+1.83). It is essentially larger than even the charges of the filler atoms Ba (from +1.1 to +1.4⁸⁹) and Sr (from +1.34 to +1.54^90,91) in intermetallic clathrates. This fact allows us to assume strongly polar interactions of hafnium with its ligands. Along with this assumption, the shape of the Hf QTAIM species is convex and may resemble a sphere. The shapes of the QTAIM atoms of Ir and B are characterized by large close to planar faces, which are typical for covalent interactions. According to the difference in electronegativity, iridium and boron species are negatively charged, whereby the difference between the charges of the anions is much smaller in comparison with that of the hafnium cation (Figure 4).

Figure 4.

Shapes and effective charges of the QTAIM atoms in Hf₂B₂Ir₅.

The distribution of the electron localizability indicator (ELI-D) in Hf₂B₂Ir₅ reveals strong maxima of the functional located on, or close to, the bond lines between the boron as well as between boron and iridium atoms (Figure 5). Moreover, the basin population of the B–B attractor in the dumbbell is around two electrons (2.18). The populations of the basins for boron–iridium bonds are formed by two or by three atomic contributions. For the four B–Ir bonds on each side of the dumbbell, 4.29 electrons are available (approximately one electron per bond). In all cases the contributions of boron and iridium to each basin are similar, indicating weakly polar covalent interactions.

Figure 5.

Electron localizability indicator ELI-D in Hf₂B₂Ir₅: (top) distribution of ELI-D in the (002) and (120) planes; (bottom) ELI-D basins and their populations (in e^–) for the two- and three-atom interactions.

These findings suggest that the boron dumbbell cannot be interpreted as an isolated structural unit and therefore—from a chemical bonding point of view—should be considered together with the attached iridium atoms as B₂Ir₈ fragments. Moreover, there are two- and three-center iridium–iridium interactions between the B₂Ir₈ units (Figure 5). The intersection of the atomic basins of hafnium with the bonding basins of the B–B, B–Ir, and Ir–Ir bonds shows a very small contribution of Hf to these bonding interactions. There are no bonding attractors in the vicinity of the hafnium nuclei, indicating a mostly ionic type of interaction in this region of the Hf₂B₂Ir₅ crystal structure and resembling strongly the bonding picture in intermetallic clathrates⁸⁹⁻⁹¹ or in recently found MgSi₅.⁹² Another interesting feature of ELI-D appears in the vicinity of the Ir2 and Ir3 atoms within the cavity bearing hafnium atoms (the bonding basins are shown in gray and dark gray in Figure 5, bottom). Such a local ELI-D maximum reveals a donorlike interaction between the neighboring Ir2 or Ir3 and Hf atoms, being topologically similar to a bonding situation observed in the Ba₈Au_5.3Ge_40.7 intermetallic clathrate, where the ionic interaction of the filler atom Ba with the gold–germanium framework is additionally augmented by a covalent (dative) bonding between Ba and Au.⁹³ Surprisingly, an analysis of chemical bonding leads to the understanding of Hf₂B₂Ir₅ as a cage compound (Figure 6). Its crystal structure is formed by a three-dimensional anionic boron–iridium framework with cavities bearing the hafnium cations. The size of the cavities with 14 vertices is smaller than in the typical clathrates with 15- to 24-atom cages but is similar to the those in MgSi₅⁹² and TmAlB₄.⁹⁴

Figure 6.

Cage-compound representation of Hf₂B₂Ir₅, as obtained from a quantum chemical analysis of chemical bonding.

3.2. Physical Properties

The temperature dependence of the magnetic susceptibility (corrected for the sum of diamagnetic increments) of Hf₂B_2–2δIr_5+δ is depicted in Figure 7a. The susceptibility is on the same order of magnitude as those expected for a Pauli paramagnetic system. The fit of χ(T) to a modified Curie law (C/T + χ₀) for T > 100 K resulted in χ₀ = +[6.3(2)] × 10^–5, in line with metallic behavior. An upturn in χ(T) for T < 100 K can be explained by paramagnetic impurities. No phase or superconducting transitions are detected down to 1.8 K.

Figure 7.

Low-temperature physical properties of Hf₂B_2–2δIr_5+δ: (a) magnetic susceptibility χ with the fit to a modified Curie law; (b) Seebeck coefficient S and electrical resistivity ρ with the fit to the Bloch–Grüneisen law; (c) thermal conductivity κ with electronic (κ_el) and phononic (κ_ph) contributions. κ and κ_ph are biased at higher temperatures due to radiation heat losses which follow roughly a ∝T³ law (cf. dotted lines for expected behavior).

As expected for a metal, the electrical resistivity of Hf₂B_2–2δIr_5+δ increases with temperature in the entire temperature range studied (Figure 7b). ρ(T) fits perfectly to the Bloch–Grüneisen (BG) equation:

1

with n = 5 (implying ρ(T) to be mainly due to electron–phonon scattering), the residual resistivity ρ₀ = 0.99(1) μΩ m, the phonon contribution coefficient A = 0.018(1) μΩ m, and the Debye temperature Θ_R = 285(2) K. However, heat capacity measurements are required to shed more light on the lattice thermal properties. Hf₂B_2–2δIr_5+δ displays only a moderate hardness of HV(0.1) = 13(1) GPa (see the Supporting Information).

The Seebeck coefficient S(T) is small and varies linearly with temperature (Figure 7b), which is again typical for metallic systems.⁹⁵ The positive values of the Seebeck coefficient indicate predominant p-type charge carriers.

The Hall effect measurements indicated a charge carrier density of ∼10²⁸ m^–3 for Hf₂B_2–2δIr_5+δ, which is on the same order of magnitude as for a good metal. Additionally, it confirmed the holelike electrical conductivity, in agreement with the result observed in S(T).

The thermal conductivity κ(T) for Hf₂B_2–2δIr_5+δ is depicted in Figure 7c. It increases almost linearly with temperature, reaches its maximum value of ∼ 9 W m^–1 K^–1 at around 70 K, and remains almost temperature independent up to 300 K. Normally, a good metallic system is characterized by a well-pronounced maximum in κ(T) centered at ∼100–200 K.⁹⁶ Its absence indicates a higher concentration of point defects.⁹⁷ This finding is in good agreement with the performed electrical resistivity measurements.

We calculated the electronic part of κ(T) by applying the Wiedemann–Franz law κ_el = LTρ^–1, with the Lorenz number L = 2.44 × 10^–8 W Ω K^–2. As one can see from Figure 7c, the lattice thermal conductivity κ_ph dominates κ(T) below 200 K, while for a higher temperature range κ(T) is mainly due to κ_el.

3.3. Electronic Structure

The total and atomically resolved electronic densities of states (DOSs) for Hf₂B₂Ir₅ are presented in Figure 8. The calculations resulted in 5.8 states eV^–1 fu^–1 at the Fermi level E_F, confirming the metallic electronic transport properties of the studied boride. Interestingly, the Fermi level is situated at a local maximum of the DOS, suggesting possible electronic or structural instabilities.

Figure 8.

Calculated electronic densities of states (DOSs) for Hf₂B₂Ir₅ with (a) atomic contributions and (b) orbital projected DOS. The Fermi level is set to 0 eV.

The electronic DOS of Hf₂B₂Ir₅ consists of two energy regions: low-lying states between −11 and −7.5 eV and a broad valence band extending from −7.5 eV to E_F. The low-energy region is mainly due to B(2s) states, while the valence band is dominated by Ir(5d) states with an admixture of Hf(5d) and B(2p) electrons (Figure 8b). Also, the Ir(5d) states are contributing ca. 65% at the Fermi level.

4. Summary and Conclusions

The metal-rich refractory intermetallic borides Hf₂B_2–2δIr_5+δ, Hf_2–xB_2–2δZr_xIr_5+δ, and Zr₂B_2–2δIr_5+δ (x ≈ 0.5, δ ≈ 0.05) have been synthesized. They crystallize with a new orthorhombic structure type, where boron atoms are found in a dumbbell-like arrangement. Approximately 5% of the boron dumbbells are randomly substituted by single iridium atoms. From a crystal-chemical point of view, these dumbbells reside in rhombic prismatic [Ir₈] slabs along [001] which can be decomposed into face-sharing trigonal [Ir₆] prisms hosting the boron atoms. Such boron-centered metal prisms represent a typical structural unit of the hexagonal AlB₂ type. As observed for borides with a high metal to boron ratio, the boron-containing structural units are integrated into a metal matrix which in Hf₂B₂Ir₅ is composed of face-sharing Ir-centered [Hf₄Ir₄] cuboids resembling the elemental α-Fe structure.

Unexpectedly, an analysis of chemical bonding interactions yields a quite different picture of Hf₂B_2–2δIr_5+δ. Apart from the multiple B₂-by-Ir substitutions, this material is a cage compound with a three-dimensional anionic boron–iridium framework with cavities bearing the hafnium cations. Moreover, this bonding situation strikingly resembles that in the large family of Ge-based inorganic clathrates in terms of all basic aspects: covalent bonds in the framework, ionic framework–guest atom interactions, and two-center covalent bonds between the host and the transition-metal component of the framework. The position-space chemical bonding analysis elucidated hitherto unknown similarities between such apparently unrelated intermetallic compounds.

Hf₂B_2–2δIr_5+δ is a Pauli paramagnet with a low DOS at the Fermi level. Metallic behavior was further confirmed by the measurements of electrical and thermal transport properties and was corroborated by electronic structure calculations.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.0c02073.

• Selected interatomic distances, 3D crystal structure representations, and results from micro hardness measurements (PDF)

Accession Codes

CCDC 2012569 contains 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 data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

The authors declare no competing financial interest.

Dedication

The authors dedicate this Article to Prof. Peter Franz Rogl on the occasion of his 75^th birthday.