OsB2 and RuB2, ultra-incompressible, hard materials: First-principles electronic structure calculations
Graphical abstract
Osmium diboride has an unusually large bulk modulus combined with high hardness. The electronic and structural properties of OsB2 and RuB2 have been calculated within LDA. It is shown that the high hardness is the result of covalent bonding between transition metal d states and boron p states.
Introduction
Hard materials are of great interest due to their wide range of important industrial applications. Hardness is a measure of a material’s resistance to penetration, deformation, abrasion and wear. Diamond remains the hardest known material, despite years of synthetic [1], [2] and theoretical [3] efforts to improve upon it. However, even diamond has limitations. It is not effective for cutting ferrous metals, including steel, because of a chemical reaction that produces iron carbide. Cubic boron nitride – the second hardest material known, inferior only to diamond – can be used to cut ferrous metals without risk of reaction. However, it does not occur naturally and is produced by treating hexagonal boron nitride at high pressure and temperature, making it quite expensive. Therefore, the development of a new class of hard materials is of great practical interest. Recently, Cumberland et al. [4] synthesized and measured the mechanical properties of the osmium diboride, OsB2, compound. It was found that it is an ultra-incompressible and hard material with bulk modulus of 365–395 GPa and hardness of ⩾2000 kg/mm2. A material that matches or exceeds the hardness of diamond must contain highly directional, short and strong bonds. Hardness may also be increased by introducing a small covalent bond-forming atom, to a soft transition metal, that hinders the migration of dislocations. Applying this idea, the authors [4] incorporated boron atoms into osmium metal to create localized covalent bonding and, thus, improve its hardness. Directional covalent bonding has also been suggested in ab initio calculations carried out on a related material, RuO2. Here Ru d- and O p-orbitals overlap, resulting in covalent bonding and a high calculated bulk modulus both for this material and for the isovalent and isostructural compound OsO2[5]. Like the volume of the unit cell of OsB2, the individual lattice parameters also decrease linearly with increasing pressure with the b-direction being the most compressible. Interestingly, in the c-direction, OsB2 is even slightly more incompressible than diamond [4]. The crystal structure of the Os–B and Ru–B systems has been determined by X-ray diffraction techniques. The isomorphous phases OsB2 and RuB2 have an orthorhombic structure with two formula units per unit cell [6], [7]. Preliminary experiments indicate that RuB2 also has a high bulk modulus [4].
However, neither the structural nor the electronic properties of OsB2 and RuB2 have been studied theoretically yet. In this Letter, we report a study on transition metal diborides performed in the local density approximation (LDA) and compare the results with the experiment.
Section snippets
Computational details
OsB2 crystallizes in the orthorhombic Pmmn structure (space group No. 59), with lattice constants a = 4.684 Å, b = 2.872 Å and c = 4.076 Å[7]. In the orthorhombic unit cell, two Os atoms were placed in , , z; , , with z = 0.1535 ± 4 × 10−4 and four B atoms in x, , z; , , ; , , z; , , , with x = 0.058 and z = 0.632 [6], [7]. A three-dimensional drawing of the unit cell is shown in Fig. 1 with the characteristic Os–B–B–Os sandwich structure. RuB2 occurs in the same structure [6], [7]
Results and discussion
We optimized both lattice geometry and ionic positions to get a fully relaxed structure of OsB2 and RuB2. The corresponding equilibrium lattice parameters are compared with experiment in Table 1. The agreement between our calculated values and the experimental data is excellent. The ground-state total energies as a function of volume for both compounds are shown in Fig. 2. The bulk moduli and their pressure derivatives were obtained by fitting the total energy curves to a fifth order Birch
Conclusions
In conclusion, we have carried out first-principles electronic structure calculations to study the structural and electronic properties of transition metal diborides. Our calculated structural parameters including the bulk modulus and its pressure derivative are in excellent agreement with available experimental data. Our results show that the transition metal–B bond is covalent in character. Thus, these calculations reveal the importance of directional bonding in creating hard,
References (15)
- et al.
Phys. Rev. B
(1981) - et al.
Philos. Mag. A
(2002) - et al.
Annu. Rev. Mater. Res.
(2001) Mater. Res. Soc. Bull.
(1998)- et al.
J. Am. Chem. Soc.
(2005) - et al.
Phys. Rev. B
(1998) - et al.
J. Chem. Phys.
(1962)