High-Pressure Synthesis of β-Ir4B5 and Determination of the Compressibility of Various Iridium Borides.

A new iridium boride, β-Ir4B5, was synthesized under high-pressure/high-temperature conditions of 10.5 GPa and 1500 °C in a multianvil press with a Walker-type module. The new modification β-Ir4B5 crystallizes in a new structure type in the orthorhombic space group Pnma (no. 62) with the lattice parameters a = 10.772(2) Å, b = 2.844(1) Å, and c = 6.052(2) Å with R1 = 0.0286, wR2 = 0.0642 (all data), and Z = 2. The structure was determined by single-crystal X-ray and neutron powder diffraction on samples enriched in 11B. The compound is built up by an alternating stacking of boron and iridium layers with the sequence ABA'B'. Additionally, microcalorimetry, hardness, and compressibility measurements of the binary iridium borides α-Ir4B5, β-Ir4B5, Ir5B4, hexagonal Ir4B3- x and orthorhombic Ir4B3- x were carried out and theoretical investigations based on density function theory (DFT) were employed to complement a comprehensive evaluation of structure-property relations. The incorporation of boron into the structures does not enhance the compressibility but leads to a significant reduction of the bulk moduli and elastic constants in comparison to elemental iridium.

Introduction

Over the past few years, metal borides attracted major interest within the scientific community, as many of them have outstanding physical properties, such as a high hardness (ReB2, WB4, FeB4, IrB1.35[1−4]), extremely low compressibilities (ReB2, OsB[1,5]), superconductivity (MgB2, NbRuB[6,7]), and outstanding high melting points (ZrB2, HfB2[8]). As a result of their high thermal stabilities, borides are often used in high temperature applications.[9] Most borides can be synthesized at ambient pressure, which makes these materials interesting for industrial applications, as this synthesis route is relatively inexpensive and easily accessible.[1,3,4,8−10]

In contrast to the limited experimental work on borides synthesized under high-pressure conditions, various theoretical studies predicted the possible synthesis of FeB4, ReB4, TaB4, IrB2, and IrB4, among others, under high-pressure conditions.[11−14] Specifically, the existence of a new iron-tetraboride FeB4 with interesting physical properties like outstanding hardness and superconductivity was originally predicted by Kolmogorov et al.[15] and Bialon et al.,[16] who suggested that FeB4 could be synthesized under high-pressure conditions. In 2014, Gou et al. successfully synthesized FeB4 under high-pressure conditions at a pressure of 15 GPa and a temperature of 1573 K.[2] Later on, the predicted orthorhombic structure as well as the superconductivity of FeB4 were confirmed by experiment.[2,15,16] In addition to FeB4, only very few further borides such as, e.g., Fe2B7, MnB4, Co5B16, and CrB4 were synthesized under high-pressure conditions.[2,17−24]

In order to expand the available limited data, the focus in this work is the synthesis of new iridium borides under high-pressure conditions. Up to now, already six binary iridium borides are known, namely, Ir4B5+ (formerly IrB1.35),[10,25−27] Ir5B4+ (formerly IrB1.1),[10,25,26] and the high and low temperature modification of Ir4B3– (formerly IrB0.9).[10,28] These phases were synthesized via high temperature syntheses by Aronsson et al.[25,26] and by Rogl et al.[28] More recently, Zeiringer et al. reinvestigated the chemical compositions and structures of these iridium borides and suggested a slightly different labeling for a more suitable specification of the phase width.[10] In 2016, Xie et al. successfully used a mechanochemical approach to synthesize two new iridium borides, namely, IrB2 and IrB.[29] Rau et al. and Latini et al. investigated the hardness of Ir4B5+ (formerly IrB1.35) and Ir5B4+ (formerly IrB1.1) and discovered that very thin films of both phases show a high hardness of 49.8 at a load of 0.49 N for Ir4B5+ and 43 GPa at 0.49 for Ir5B4+.[3,30] With the exception of the hardness of those phases, very little is known about other properties, such as compressibility, of the iridium borides. Numerous predictions of novel iridium borides with varying Ir:B ratio, which possibly could be synthesized under high-pressure/high-temperature conditions and are expected to show interesting mechanical properties, have been made.[10,12−14,31−34]

In this context, our experiments led to the successful synthesis of a new modification of Ir4B5 which crystallizes in the centrosymmetric space group Pnma in a new crystal structure type. Due to the extremely low scattering cross section of boron in comparison with iridium for X-rays, it is practically impossible to reliably determine the exact position and occupation of the boron atoms solely on the basis of X-ray diffraction data. Therefore, neutron powder diffraction data on 11B-enriched samples were used in combination with X-ray diffraction methods to determine the structure. In addition to the synthesis of the new modification, we examined the compressibility, hardness, and thermodynamical properties of various other iridium borides.

Experimental Section

Synthesis

The starting materials iridium (99.9+%, ChemPur, Karlsruhe, Germany) and amorphous boron (99.9+%, ChemPur, Karlsruhe, Germany) or crystalline 11B (99.9+% purity, 99.8+% enrichment, Ceradyne 3M, St. Paul, USA) were used for all phases. For the synthesis of β-Ir4B5, a stoichiometric Ir:B ratio of 1:3 was used. Experiments with a Ir:B ratio of 1:1.2 did not lead to the synthesis of β-Ir4B5 and showed that some excess of boron is necessary for the successful synthesis. The mixture was ground in a ball mill (Pulverisette 7-Premium Line, Fritsch, Idar-Oberstein, Germany) with an internal bowl volume of 80 mL for 100 min. Seven tungsten carbide balls were used as milling media with a ball to powder weight ratio of 1:15. Afterwards, the powder was inserted into a crucible made from hexagonal boron nitride (HeBoSint P100, Henze BNP GmbH, Kempten, Germany) and inserted into a 14/8 assembly. The sample was compressed to 10.5 GPa within 4.5 h by a high-pressure device consisting of a hydraulic 1000 t press (mavo press LPR 1000-400/50, Max Voggenreiter GmbH, Mainleus, Germany) and a Walker-type module (Max Voggenreiter GmbH) with eight tungsten carbide cubes (HA-7% Co, Hawedia, Marklkofen, Germany). The mixture was heated from ambient temperature to 1500 °C within 5 min. The temperature was held for 30 min and afterwards reduced to 700 °C in 1 h. After decompression, the sample was isolated from the surrounding assembly parts by mechanical separation. A more detailed description of this setup can be found in the literature.[35,36]

Samples of α-Ir4B5 were synthesized in an arc melter (MAM-1, E. Bühler GmbH, Hechingen, Germany) by annealing the elements in an Ir:B ratio of 1:1.5. The powders were mixed in an agate mortar and pressed into pellets of 5 mm diameter. Prior to the experiment, a titanium getter (99.95%) was molten to absorb any remaining traces of oxygen from the atmosphere in the reaction chamber. During the synthesis, the pellet was not molten but annealed by the plasma several times from different sides. The temperature could thus not be determined exactly but must have been close to the melting point at the sample surface. A temperature gradient from the surface to the bulk must be assumed.

Samples of Ir5B4 could be synthesized in a custom-built tube furnace from the elements at 1223 K. The starting materials were mixed in an agate mortar in a Ir:B ratio of 1.25:1 and pressed into a dense pellet of 5 mm in diameter. The pellet was placed in a ceramic crucible and heated to 1223 K. The temperature was held for 24 h before switching the furnace off. The analysis of the powder X-ray diffraction pattern of Ir5B4 revealed that no side phases were present after the synthesis. The orthorhombic and hexagonal modifications of Ir4B3– were synthesized simultaneously from the same pellet. This was achieved by annealing the compacted powder with the plasma beam at low powers, which did not suffice to melt the elements. Since the phase transformation takes place at moderate temperatures (1373–1473 K), the temperature gradient from the surface to the bulk of the pellet in this method enabled us to obtain both modifications at once.

Crystal Structure Determination

The powder X-ray diffraction pattern of β-Ir4B5 was obtained in transmission geometry from a flat powder sample of the product. The measurements were carried out in transmission geometry using a STOE STADI P powder diffractometer equipped with Mo-Kα1-radiation (Ge(111) monochromator λ = 0.7093 Å) in the 2θ range of 2.0–90.2° with a step size of 0.015°. As a detector, a silicon microstrip solid state detector (Dectris Mythen 1K) was used. The lattice parameters shown in Table were obtained through a Rietveld analysis of the powder pattern using the program TOPAS.[37] The Rietveld analysis of the powder pattern (Figure ) revealed a very weak amorphous halo which can be explained by some unreacted amorphous boron, some weak reflections (e.g., at 10.9, 16.9, and 23.0°) which can be assigned to the compound IrB2 (ReB2-type), and a few additional reflections (12.1, 12.7, and 18.2°) which could not yet be assigned to any known phase and presumably belong to an unknown minor impurity phase.

Table 1

Crystal Data and Structure Refinement of β-Ir4B5 (Standard Deviations in Parentheses)

empirical formula	β-Ir4B5
molar mass, g·mol–1	822.86
crystal system	orthorhombic
space group	Pnma (no. 62)
Powder Data
powder diffractometer	STOE Stadi P
radiation	Mo-Kα1 (λ = 0.7093 Å)
a, Å	10.758(2)
b, Å	2.837(2)
c, Å	6.038(3)
V, Å3	184.32(4)
Single-Crystal Data
single-crystal diffractometer	Bruker D8 Quest Kappa
radiation	Mo-Kα (λ = 0.71073 Å)
a, Å	10.772(2)
b, Å	2.844(1)
c, Å	6.052(2)
V, Å3	185.47(2)
formula units per cell, Z	2
calculated density, g cm–3	14.73
crystal size, mm3	0.050 × 0.045 × 0.040
temperature, K	292(2)
absorption coefficient, mm–1	142.8
F(000)	666
θ range, deg	3.8–39.9
range in hkl	–19 ≤ h ≤ 19, –5 ≤ k ≤ 5, –9 ≤ l ≤ 10
total no. of reflections	7081
independent reflections	651
reflections with I ≥ 2σ(I)	624
data/parameters	651/32
absorption correction	multiscan
goodness-of-fit on F2	1.262
final R indices [I ≥ 2σ(I)]	R1 = 0.0271
	wR2 = 0.0635
final R indices (all data)	R1 = 0.0286
	wR2 = 0.0642
largest diff. peak and hole, e Å–3	5.07/–3.76

Figure 1

Rietveld plot of β-Ir4B5. The experimental powder diffraction pattern is shown in black, the calculated pattern is shown in red, and the difference plot is shown in blue. The reflection positions of β-Ir4B5 are shown in green, and those of IrB2, in blue.

Small single-crystals of β-Ir4B5 were selected by mechanical fragmentation using a polarization microscope. A Bruker D8 Quest Kappa diffractometer with Mo-Kα radiation (λ = 0.71073 Å) was used to collect the single-crystal intensity data at room temperature. A multiscan absorption correction (SADABS-2014[38]) was applied to the intensity data sets. The structure solution and parameter refinement (full matrix least squares against F2) were performed by using the SHELX-13 suite with anisotropic displacement parameters for all atoms.[39,40] To ensure that no symmetry operations were missing, the final solution was checked with PLATON.[41] All relevant details of the data collection and the refinement are listed in Table , the positional parameters are listed in Table , and the important bond lengths are listed in Table . The program Diamond was used for the graphical representation (Figures –7) of the structure.[42]

Table 2

Atomic Coordinates (Wyckoff Position 4c for All Atoms) and Equivalent Anisotropic Displacement Parameters Ueq (Å2) of β-Ir4B5a

atom	x	y	z	Ueqb	s.o.f.
Ir1	0.59904(3)	1/4	0.2719(5)	0.0057(2)	1
Ir2	0.84838(3)	1/4	0.3555(5)	0.0055(2)	1
B1	0.5713(9)	3/4	0.528(2)	0.007(2)	1
B2	0.801(2)	3/4	0.097(2)	0.008(2)	1
B3	0.008(2)	1/4	0.557(3)	0.007(3)	0.5

Data collected by single-crystal X-ray diffraction.

Ueq is defined as one-third of the trace of the orthogonalized U tensor.

Table 3

Interatomic Distances (Å) in β-Ir4B5 (Space Group Pnma), Derived from Single-Crystal Data

2 × Ir1–B1	2.128(8)	Ir2–B1	2.16(2)
Ir1–B1	2.20(2)	2 × Ir2–B2	2.172(7)
Ir1–B2	2.25(2)	Ir2–B2	2.18(2)
Ir1–B3	2.22(2)	2 × Ir2–B3	2.17(2)
2 × Ir1–B3	2.25(2)	Ir2–B3	2.11(2)
2 × Ir1–Ir1	2.8445(2)	Ir2–Ir1	2.9489(4)
Ir1–Ir2	2.9489(4)	Ir2–Ir1	2.8082(5)
Ir1–Ir2	2.7332(5)	2 × Ir2–Ir2	2.8445(2)
Ir1–Ir2	2.8082(5)
4 × B1–B2	2.02(2)	2 × B3–B3	1.59(2)
2 × B1–B1	2.12(2)

Figure 2

Rietveld plot of β-Ir4B5 derived from the neutron data. The experimental powder diffraction pattern is shown in black, the calculated pattern is shown in red, and the difference plot is shown in blue.

Figure 7

Structures of (a) α-Ir4B5 and (b) β-Ir4B5.

Neutron Powder Diffraction

Neutron powder diffraction was carried out at the neutron source FRM II at the Heinz Maier-Leibnitz Zentrum (MLZ), Garching, Germany, using the high-resolution neutron powder diffractometer SPODI with a Ge(551) monochromator (λ = 1.5481 Å). The data were collected in a range of 160° by a bank consisting of 80 3He detector tubes. A detailed description of the high-resolution neutron powder diffractometer can be found in the literature.[43,44] Due to the high absorption cross sections of B and Ir, the samples were placed in a glass capillary with a diameter of only 1 mm for the measurement and measured for 90 min. The probe exhibits a packing density of around 2.39 g/cm3 within the capillary. The packing density in combination with the atomic scattering factors of the used elements and the absorption leads to an attenuation factor for the sample of 2.546 cm–1, which was used during the Rietveld refinement.[45,46] The Rietveld refinement was carried out using the program TOPAS[37] and was used to determine the boron positions and occupancy. Due to the complicated synthesis process, the sample, which was used for the neutron diffraction, was relatively small and therefore the ratio of peak intensity to background was rather weak. The analysis of the neutron data, however, could unambiguously verify the results of the X-ray structure determination (Figures and 2, Supporting Information Tables S1 and S2).

Further details of the crystal structure investigation may be obtained from the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany (fax: +49-7247-808-666; e-mail: crysdata@fiz-karlsruhe.de, http://www.fiz-karlsruhe.de/request) on quoting the deposition number CSD-433663.

Determination of the Compressibility

For high-pressure experiments, Boehler-Almax-type diamond anvil cells were used.[47] The cells were loaded with Ne as a pressure-transmitting medium. Samples were placed in holes of 110–130 μm in diameter, which were drilled by a custom-built laser lathe in preindented Re gaskets (40–50 μm in thickness). The pressure was determined using the ruby fluorescence method.[48] Synchrotron X-ray diffraction experiments at high pressures were performed at the beamline P02.2 of the PETRA III synchrotron (DESY, Hamburg, Germany). The diffraction patterns were acquired with a PerkinElmer XRD1621 detector at a wavelength of 0.2902 Å with beams focused to 1.5 × 2.3 μm fwhm by Kirkpatrick–Baez mirrors. In order to improve the sampling statistics, samples were rotated by 20° during the 10 s data acquisition time. A CeO2 standard was used to determine the sample-to-detector distance and for detector calibration during the experiments.[49] The diffraction patterns were corrected and integrated using the FIT2D and DIOPTAS software packages.[50,51] The compressibilities were determined by investigating the dependence of the unit cell parameters upon compression which were obtained by Le Bail refinements. The data were fitted using a third-order Birch–Murnaghan (BM) equation of state[52,53] using the EosFit software package.[54]

Microcalorimetry

Microcalorimetry was performed using a Quantum Design thermal relaxation calorimeter (Physical Properties Measurement System, Quantum Design, San Diego, USA). Powdered samples of boron were thoroughly ground in a tungsten carbide mortar to reduce pores and encapsulated in a copper container (Alfa Aesar, 99.999%). In this case, the heat capacity of copper had to be subtracted afterward. Compacted, polycrystalline fragments of samples from α-Ir4B5, β-Ir4B5, and iridium were prepared so that one flat and polished surface was present to guarantee a good thermal coupling of the sample to the sample holder. We have shown the accuracy of our measurements to be 1% in the temperature region between 40 and 300 K and 2% below 40 K by comparing the measurement of a standard material (Cu, Alfa Aesar, 99.999%) with the values obtained by Lashley et al.[55] The samples were mounted using Apiezon-N grease. All samples weighed between 10 and 25 mg and were measured in the temperature range between 1.8 and 395 K at 150 different temperatures. The temperature steps were reduced logarithmically from 395 to 1.8 K. At each step, the heat capacity was measured three times by the relaxation method using the two-τ model.[55−57]

Hardness Measurements

Hardness measurements were carried out using a Vickers-type microhardness testing machine (HM-210A, Mitutoyo, Japan), equipped with an optical microscope and a 50× lens. A standard square-based diamond pyramid indenter with a 136° apex angle between the opposite faces was used for the indentation. Every indentation spot was generated by applying the following conditions: The loading and unloading times were kept at 5 s before and after the retention time of 15 s. The approaching speed of the indenter was 60 μm/s. We created 10 indentations on the sample surface at each testing load (0.49, 0.98, 1.96, 2.94, 4.9, and 9.8 N). The Vickers hardness (HV) was derived using the equationwith g being the standard gravitational acceleration (m/s2), F the indentation load (N), and d the average diagonal imprint distance (mm). For the conversion to GPa, the results were multiplied by the factor 0.009807.

To provide an optimal specimen with a parallel surface for the hardness measurements, five polycrystalline fragments of β-Ir4B5 were embedded in a high-yield two-component epoxy (UHU Endfest 300, UHU, Brühl, Germany) inside a customized brass ring (5 mm in height, 20 mm in diameter). The entire setup was grounded using diamond coated polishing disks of varying mesh sizes, and the error in parallelism was ±2 μm. The top side, on which we carried out the measurements, was polished to a mirror-like finish using Al2O3 powder with grain sizes of 1 and 3 μm.

Density Functional Theory

In order to obtain a better understanding of the structure–property relations of the synthesized compounds, we performed density functional theory (DFT) calculations employing the CASTEP[58] code. This code implements the Kohn–Sham DFT based on a plane wave basis set in conjunction with pseudopotentials. The plane wave basis set is unbiased (as it is not atom-centered) and does not suffer from basis set superposition errors in comparison to atom-centered analogues. It also makes converged results straightforward to obtain in practice, as the convergence is controlled by a single adjustable parameter, the plane wave cutoff, which was set to 390 eV. All pseudopotentials were ultrasoft and were generated using the WC-GGA to allow for a fully consistent treatment of the core and valence electrons.[59] Brillouin zone integrals were performed by using Monkhorst–Pack grids with spacings of less than 0.028 Å–1 between individual grid points. A simultaneous optimization of the unit cell parameters and internal coordinates was performed in the way that forces were converged to <0.005 eV/Å and the stress residual was <0.005 GPa. Elastic stiffness coefficients were derived by stress–strain calculations.

Results and Discussion

Crystal Structure of β-Ir4B5

According to the systematic extinctions, the orthorhombic space group Pnma (no. 62) was derived for β-Ir4B5. The dimensions of the unit cell are a = 10.772(2) Å, b = 2.844(1) Å, c = 6.052(2) Å, and V = 185.47(2) Å3 (Table ). The crystal structure was solved via single-crystal X-ray diffraction, but as it is difficult to reliably determine the occupancy and exact positions of the boron atoms solely on the basis of X-ray diffraction data, neutron powder diffraction was carried out afterward to verify the structure solution (Figures and 2). Unless otherwise stated, the crystallographic details used in the following discussion (bond lengths and angles) are based on the excellent single-crystal X-ray data, as the quality of the powder pattern obtained from the neutron diffraction data was too low to deviate exact values from it (Figures and 2, Tables and S2). Nevertheless, the neutron diffraction data generally confirmed the single-crystal X-ray data. Furthermore, the investigations show that β-Ir4B5 possesses a phase width and could therefore be labeled as β-Ir4B5±, as Zeiringer et al. also suggested for other iridium borides.[10] However, in the following, we use the idealized formula β-Ir4B5. Figure shows the structure, which can be described as stacking of alternating puckered boron layers (B, B′) and puckered iridium layers (A, A′) in the stacking sequence ABA′B′ in the c direction of the crystal structure. The boron layers are built up by two parallel boron chains consisting of B1 and B2 atoms. These chains are interconnected via the B1 atoms of each chain, leading to the formation of a unique ribbonlike network of boron atoms (Figure ). The boron–boron distances within the ribbons are 2.024(10) Å for B1–B1 and 2.122(14) Å for B1–B2 and are thus relatively long, but they correspond well to boron–boron distances in other transition-metal borides.[10,17,25,60] These ribbons are located within large cavities formed by eight iridium atoms (Figure ). Between the boron ribbons of each individual layer, iridium atoms form a column of face-sharing trigonal prisms that are partly centered by boron atoms B3. These prisms are connected via the square faces building up a column in the b direction (Figure ). The structure determination based on X-ray data revealed an occupancy of ∼50% for B3 in the centers of the prisms within the column. The neutron data were used to verify the occupancy of around 50% for the B3 position and revealed a site occupancy factor of 55(4)%. The result of the neutron data is congruent with the X-ray data and is reasonable regarding the fact that a full occupancy of the prisms would lead to the formation of a boron chain with a very short boron–boron distance of just 1.589(18) Å (Tables and 3). As the B3 position exhibits an occupancy of marginally above 50%, some chain fragments with very short boron–boron distances may exist within the structure. The B3 positions are slightly shifted from being aligned in a perfectly straight chain (Figure ). As the analysis of the X-ray data did not show any superstructure reflections, we cannot assume an ordering on the B3 site. The alignment within the individual boron layers (B and B′) is identical, but the different layers are rotated and shifted with respect to each other (Figure b). The iridium atoms form a framework with two types of cavities, which are occupied by either the boron ribbons (B1 and B2) or the “chain” of isolated boron atoms (B3) (Figure ). Iridium–iridium distances in the framework range from 2.7332(5) to 2.9489(4) Å, which is similar to the iridium–iridium distances in other borides and metallic iridium.[10,26,28,61,62] Whereas the boron atoms B2 at the edge of the ribbons are coordinated by four iridium and two boron atoms, the boron atoms B1 have four close boron neighbors and four iridium atoms, leading to an 8-fold coordination (4 Ir + 4 B). The bond lengths of Ir–B within the iridium cage range from 2.128(8) to 2.249(11) Å and within the trigonal prism from 2.108(19) to 2.249(11) Å, which is slightly shorter than the sum (2.25 Å) of the covalent radii of the B atom (r = 0.84 Å) and the Ir atom (r = 1.41 Å). The iridium atoms are coordinated by six iridium atoms as well as by seven boron atoms, leading to a 13-fold coordination.

Figure 3

Stacking of alternating puckered boron (red) layers and puckered iridium atoms (light green).

Figure 4

(a) Projection of a boron layer consisting of interconnected (green bonds) zigzag chains (black bonds) forming ribbons. Between the ribbons, half-occupied slightly bent boron chains (light red) are located. (b) Puckered boron layers along [010].

Figure 5

Column of face-sharing Ir6 prisms centered by a half-occupied boron chain.

The closely related α-modification of Ir4B5+ can be synthesized by arc melting and crystallizes in the monoclinic space group C2/m with a = 10.520(1) Å, b = 2.895(1) Å, c = 6.095(1) Å, β = 91.156(2)°, and V = 185.6 Å3.[10,25,27,60] Just like β-Ir4B5, α-Ir4B5 can also be described by a stacking of puckered boron and puckered double metal layers, however, without any displacements of the layers, therefore leading to the simple stacking sequence ABAB (Figure b). The interstices of the metal double layers are filled with boron atoms forming boron chains with rather short B–B distances of 1.61 Å. The boron atoms have a trigonal prismatic environment of iridium atoms, and the structure determination also revealed an occupancy of 50% for these boron positions.[10] The same structural motif can be found in β-Ir4B5, but in contrast to the β-modification, these boron chains in the α-modification are located within the iridium layers and are not part of the boron layers (Figures , 6, and 7). Boron atoms with a trigonal prismatic metal environment are very common and can be found within several other transition metal borides such as Re3B, Ni7B3, and the members of the AlB2 and CrB structure type family.[63−66] In contrast to the arrangement of isolated boron ribbons in β-Ir4B5, the boron atoms within α-Ir4B5 form an infinite boron network with B–B distances of 1.877 Å between B1 and B1 and 2.106 Å between B2 and B2 (Figure ).[10,25−27,60]

Figure 6

(a) Boron layer in α-Ir4B5 viewed along [001̅] exhibiting the boron network with shorter (green) and longer (black) boron–boron bonds. (b) Layered structure of α-Ir4B5 consisting of boron layers and double iridium layers with boron atoms in the interstices.[10,25,27]

Similar infinite two-dimensional boron networks can also be found within many other borides with a metal vs boron ratio ranging from MB2 to M2B5.[27,61,65,67] The existence of interconnected and isolated boron chains within the same phase, as has been observed here in β-Ir4B5, has only been found in borides possessing the V5B6-structure type. In V5B6, the double chain consists of two antiparallel boron chains that are interconnected. The connection of the two chains leads to the formation of a boron network, which can also be described as a chain of aligned B6 hexagons (Figure ).[68,69]

Figure 8

(a) Double and single boron zigzag chains in V5B6.[68] (b) For comparison, double and single boron chains in β-Ir4B5.

Compressibility

In the pressure regime up to 38 GPa, α-Ir4B5 shows no structural phase transition. The bulk modulus is B0 (α-Ir4B5, third order) = 280(6) GPa with the pressure derivative B′ (α-Ir4B5, third order) = 4.4(4). The lattice parameters show a significant anisotropy in their individual compressibilities, with b being more compressible than the others. The higher compressibility along b can be rationalized by noting that this direction is parallel to the boron plane and the half-occupied boron chain is also oriented in this direction. The normalized unit cell parameters versus pressure are shown in Figure .

Figure 9

Compression behavior of the normalized unit cell parameters of α-Ir4B5 up to 38 GPa (left) and β-Ir4B5 up to 40 GPa (right).

The β-modification of Ir4B5 was investigated up to a maximum pressure of 40 GPa, also showing no indication for a pressure induced structural phase transition (Figure b). The bulk modulus is 249(3) GPa for B0 (β-Ir4B5, third order) with B′ = 3.2(3), which is smaller compared to the α-modification. The new modification β-Ir4B5, which was synthesized under high pressure conditions, shows a lower bulk modulus than α-Ir4B5, which is in conflict with the expected behavior, namely, that high-pressure phases should form more dense structures and are harder to compress. Hence, β-Ir4B5 is not a high-pressure modification of α-Ir4B5. High-pressure diffraction patterns of the two modifications at similar pressures are shown in Figures and S1.

Figure 10

Le Bail refinement of β-Ir4B5 at 8.9(3) GPa. The experimental powder diffraction pattern is shown in red, the background is shown in blue, the calculated pattern is shown in green, and the difference plot is shown in black.

Ir5B4 was investigated up to a maximum pressure of 50 GPa, and there are no indications of a structural phase transition. The bulk modulus is B0 (Ir5B4, third order) = 310(5) GPa with the pressure derivative B′ (Ir5B4, third order) = 3.7(2). The lattice parameters do not show a significant anisotropy in their compression behavior (Figure S2).

We further investigated both modifications of Ir4B3– up to a maximum pressure of 33 GPa. We investigated a mixture of both modifications in one experiment in the same DAC at exactly the same pressure points. By scanning the sample with a high resolution (2 × 2 μm2) grid, we found spots, where either orthorhombic Ir4B3– or hexagonal Ir4B3– were present as the main phase, along with unreacted iridium and the respective other polymorph. The bulk modulus of the orthorhombic modification from fitting a third-order BM EOS is 320(6) GPa for B0 (orthorhombic Ir4B3–, third order) with B′ = 5.2(4). The compression behavior of the lattice parameters shows no anisotropy. Hexagonal Ir4B3– shows a higher compressibility with B0 (hexagonal Ir4B3–, third order) = 279(4) GPa and B′ = 5.2(4) for the third-order fit. The compression behavior of the lattice parameters shows a slight anisotropy.

To obtain a better understanding of the changes introduced by the incorporation of boron into the structures, we collected pressure data of elemental iridium up to a pressure of 50 GPa. We found a bulk modulus of B0 (Ir, third order) = 326(3) GPa with B′ = 5.3(2). A summary of the compressibilities of all phases is given in Table . The compression behavior showing the third-order fits is displayed in Figures and S2–S5, and the pressure dependence of the unit cell parameters is listed in Tables S2–S6.

Table 4

Experimental and Calculated Results of the Compressibilitya

compound	space group	BM order	B0 (GPa) (exp)	B′
α-Ir4B5	C2/m	2nd	292(5)	4
		3rd	280(6)	4.4(3)
		DFT	225(1)
β-Ir4B5	Pnma	2nd	239(3)	4
		3rd	249(3)	3.2(3)
		DFT	265(1)
Ir5B4	I41/a	2nd	304(6)	4
		3rd	310(5)	3.7(2)
		DFT	287(1)
orthorhombic Ir4B3–x	Cmc21	2nd	336(8)	4
		3rd	320(6)	5.5(4)
		DFT	b
hexagonal Ir4B3–x	P6̅m2	2nd	293(4)	4
		3rd	279(4)	5.2(4)
		DFT	b
Ir	Fm	2nd	341(5)	4
		3rd	326(3)	5.3(2)
		DFT	346(1)

The DFT values were obtained from stress–strain relations.

Due to the partial occupation of some boron positions in the orthorhombic and hexagonal Ir4B3– phases, no appropriate model calculation could be carried out.

The incorporation of boron into the structures does not enhance the incompressibility but leads to a significant reduction of the bulk modulus in comparison to elemental iridium. This is in contrast to the observations on rhenium or osmium borides, where the incorporation of boron leads to a decrease of the compressibility with respect to the compressibility of the elements.[5,70−72] The investigated phases however follow the trend to become more compressible as the amount of boron in the structures increases. Orthorhombic Ir4B3–, being the most metal-rich phase, almost reaches the bulk modulus of elemental iridium. The new phase β-Ir4B5 on the other hand shows a compressibility which is approaching the rather low value of 224(15) GPa of elemental boron.[73] The findings in this study thus support the statement of Gu et al., who correlated an increasing amount of boron in borides with a decreasing bulk modulus.[5]

Hardness

The hardness of β-Ir4B5 was obtained at different indentation loads in order to allow an extrapolation of the load dependence and in order to enable a comparison to data from earlier studies. The asymptotic response of the material’s hardness to increasing loads is depicted in Figure . In the load regime between 9.8 and 2.94 N, the hardness remains almost constant, showing a hardness of approximately 16 GPa. At lower forces, the hardness increases to a maximum value of HV (0.49 N, β-Ir4B5) = 22.6(2.8) GPa at 0.49 N. The hardness of β-Ir4B5, which ranges from HV (9.8 N, β-Ir4B5) = 15.8(1.2) GPa to HV (0.49 N, β-Ir4B5) = 22.6(2.8) GPa, is significantly lower than the values reported for the α-modification (49.8 at 0.49 N and 18.2 GPa at 9.8 N), or Ir5B4 (43 GPa).[3,30] However, the hardness data for α-Ir4B5 and Ir5B4 were obtained using very thin films consisting of nm-sized crystals on a substrate of different chemical constitution (TiB2/BN composite) which might have resulted in significant overestimation of the values. Furthermore, the XRD pattern of Ir5B4 in the study of Latini et al. (2010) showed indications of an impurity phase which formed during the laser deposition experiments. In contrast, our results are in good agreement with the observation of Samsonov et al. on bulk samples, who found a hardness of only 15.8(8) GPa for Ir5B4.[74] Therefore, we conclude that the bulk hardness of iridium boride phases is not as high as previously assumed on the basis of thin film measurements.

Figure 11

Load-dependent hardness of β-Ir4B5. The data were fitted with an exponential to extrapolate the material hardness at infinitesimal loads. The extrapolation of the fit is indicated by a dashed line.

Microcalorimetry was performed on polycrystalline samples of α-Ir4B5 and β-Ir4B5, which weighed between 20 and 25 mg. The comparison of the heat capacity curves for both modifications can be seen in Figure S6. Both curves show no peaks at low temperatures, and hence, there seems to be no transition into a superconducting state down to 2 K. There is excellent agreement for the ambient temperature values of the heat capacity, enthalpy, and entropy with published data for elemental boron and iridium. The Debye temperature of β-Ir4B5 (444(4) K) is higher than the temperature of α-Ir4B5 (392(4) K), whereas both are in the same temperature range as elemental iridium (420 K) and noticeably smaller than the Debye temperature of elemental boron (1219 K). The herein determined values for the Debye temperature of elemental iridium (343(3) K) and boron (928(9) K) are smaller than the values tabulated in the literature.[75,76] These deviations can arise from different fitting ranges and fitting difficulties. The T3-plots are shown in Figures S7–S10. All derived thermodynamic values, including those of elemental boron and iridium, are listed in Table .

Table 5

Thermodynamical Properties of α-Ir4B5, β-Ir4B5, Elemental Ir, and Elemental B at 298 K

compound	CP (J/mol K)	H2980 (J/mol)	S2980 (J/mol K)	ΘD (K)	reference
α-Ir4B5	291(1)	39770(700)	227(2)	392(4)	this study
β-Ir4B5	223(1)	32930(600)	191(1)	444(4)	this study
Ir elemental	24.8(2)	5232(50)	35.3(3)	343(3)	this study
Ir elemental	25.09	5266	35.49	420	Arblaster[76]
B elemental	11.2(1)	1220(15)	5.93(9)	928(9)	this study
B elemental	11.1(1)	1222(8)	5.90(8)	1219	Thompson and McDonald[75]

DFT Calculations

DFT calculations were performed on simplified model structures. We disregarded occupational disorder in the structures and assumed full site occupancies for each phase. These simplifications turned out to be inappropriate for both Ir4B3– modifications, and therefore, no further calculations were carried out for this composition. Ir5B4 was approximated by Ir20B16, α-Ir4B5 by C2/m-Ir8B12 with a full occupation of the Wyckoff position 4i, and β-Ir4B5 by Pnma-Ir8B12. Stress–strain calculations allowed us to obtain the elastic stiffness coefficients c, bulk modulus B, shear modulus G, Young’s modulus Y, Poisson’s ratio υ, Debye temperature ΘD, universal anisotropy index AU, and hardness H (Table ). The calculated Debye temperatures for α-Ir4B5 (324(2) K) and β-Ir4B5 (414(2) K) are in moderate agreement with the experimental values (392(4) K for α-Ir4B5 and 444(4) K for β-Ir4B5). The Debye temperature for elemental iridium (428(3) K) is in excellent agreement with the value from the literature (420 K).[76] The calculated bulk moduli of the three phases are similar to the values obtained by the experimental measurements (Table ). This justifies to some extent the neglect of the partial occupation but, conversely, also indicates that a minor change in the boron content will not influence the physical properties significantly. The values of the calculated and measured hardness however differ considerably for the phases. These deviations can be explained by the fact that the hardness of a material is primarily a surface property and the calculations are volume-based parameters.

Table 6

Elastic Properties from the Elastic DFT-GGA Calculations

	C2/m - “Ir8B12”	Pnma - “Ir8B12”	“Ir20B16”
	α-Ir4B5	β-Ir4B5	Ir5B4	Ir
c11 (GPa)	373(3)	482(4)	494(2)	583(1)
c22 (GPa)	303(3)	390(1)
c33 (GPa)	303(2)	433(4)	460(2)
c44 (GPa)	50(1)	112(1)	72(1)	256(1)
c55 (GPa)	125(1)	102(2)
c66 (GPa)	58(1)	60(1)	162(1)
c12 (GPa)	150(2)	170(2)	221(2)	228(1)
c13 (GPa)	160(2)	122(2)	177(1)
c15 (GPa)	58(1)
c16 (GPa)			40(1)
c23 (GPa)	217(2)	250(2)
c25 (GPa)	–32(1)
c35 (GPa)	7(1)
c46 (GPa)	–29(1)
Bcij (GPa)	225(1)	265(1)	287(1)	346(1)
Gcija (GPa)	63(8)	99(5)	110(6)	222(2)
Ycij (GPa)	180(10)	266(10)	295(15)	550(5)
υcij	0.37(1)	0.33(1)	0.33(1)	0.23
ΘD (K)	324(2)	414(2)	382(2)	428(3)
AUb	2.5(1)	0.7	0.9(1)	0.16(1)
H (GPa)	4.5(5)	8.5(5)	9(1)	25(1)

2G(1 + υ) = Y = 3B(1 – 2υ) for isotropic materials.

AU = 5GV/GR + BV/BR – 6 ≥ 0 (GV and GR Voigt and Reuss estimates of G, BV and BR = Voigt and Reuss estimates of B).[77]

Conclusions

We report the successful synthesis of β-Ir4B5, the first 5d transition metal boride synthesized under high-pressure conditions, as well as the synthesis and characterization of the binary iridium borides orthorhombic Ir4B3–, hexagonal Ir4B3–, Ir5B4, and α-Ir4B5. The structure of the new modification was solved unambiguously by combining single-crystal XRD and complementing neutron diffraction experiments to unequivocally locate the boron atoms and determine their site occupancies. There are some similarities between the structures of β-Ir4B5 with both α-Ir4B5 and the V5B6-structure type; however, the alignment of the double boron chains in combination with the half-occupied single chain in β-Ir4B5 is unique and therefore constitutes a new structure type. Even though the synthesis of β-Ir4B5 was carried out under high-pressure/high-temperature conditions, our findings (compressibility, unit cell volume, microcalorimetry) clearly show that it is not a high-pressure polymorph of Ir4B5. The structure was not among the numerous predicted possible structures. By using microcalorimetry measurements, the heat capacities of α-Ir4B5 and β-Ir4B5 were determined. Both phases do not seem to become superconducting at low temperatures. The hardness measurements revealed a significantly lower hardness for bulk β-Ir4B5 than Latini et al. found for thin films of α-Ir4B5.[30] As the crystal structure and composition for both modifications are similar, the huge difference in the hardness value presumably arises from other reasons. We conclude that the hardness of α-Ir4B5 is either not as high as previously assumed on the basis of thin films measurements or that such observations are at least not extendable to bulk properties. The values for the bulk moduli B0 of the iridium borides vary between 249(3) and 320(6) GPa (third-order BM fits). Iridium borides do not reach the ultra-incompressibility of diamond (443 GPa) and OsB (431–453 GPa), or other incompressible period-6 transition metal borides.[5,71] The incorporation of boron into the structures does not enhance the compressibility but leads to a significant reduction of the bulk modulus in comparison to elemental iridium (B0, third order = 326(3) GPa). These findings for iridium borides are in contrast to the observations on rhenium or osmium borides, where the incorporation of boron leads to a decrease of the compressibility with respect to the compressibility of the elements.[5,70−72] Thus, ongoing research in the field of binary borides is crucial for a better understanding of the exact influence of boron incorporation into heavy transition metals.