First-principles study of elastic and thermodynamic properties of orthorhombic OsB4 under high pressure
Graphical abstract
Highlights
► The elastic and thermodynamic properties of OsB4 under pressure were studied unified. ► It is predicted that the orthorhombic OsB4 is stable below 50 GPa ► The orthorhombic OsB4 exhibits larger elastic anisotropy under higher pressure. ► The thermodynamic parameters are also successfully obtained by the Debye model.
Introduction
Transition metal borides have attracted considerable attentions from both theoretical and experimental studies due to their chemically inert and extreme hardness as well as high thermal and electrical conductivity [1]. Recently, Kaner et al. have suggested that the introduction of light and covalent-bond-forming elements (B, C, N, and O) into the transition metal (TM) lattices with highly valence-electron density is expected to have profound influences on their chemical, mechanical, and electronic properties [2], [3], [4]. Based on this prospect, recent design of new intrinsically potential superhard materials (Hv ≥ 40 GPa) has concentrated on light element TM compounds with high elastic moduli, in particular the 4d and 5d TM compounds [5], [6], [7], [8]. Following the first synthesized ultra-incompressible material OsB2 [3], extensive experimental and theoretical investigations have been carried out for other TM borides in view of their synthesis is more straightforward. Nowadays, some TM borides such as WB4, ReB2, WB2, RhB1.1, and IrB1.35 has been synthesized and were proposed to be superhard with claimed hardness of >40 GPa [9], [10], [11], [12]. Among these superhard TM borides, WB4 has the largest B contents reported hitherto. WB4 exhibits a unique three-dimensional boron covalent bonding network which consisted of in-plane honeycomb B sublattice and out-of-plane B2 dimer. This is responsible for its high hardness [13].
Up to now, the structures of osmium borides with various stoichiometries (OsB, Os2B3, and OsB2) have been synthesized and some related mechanical properties were also investigated. The obtained results indicated that they are all only hard materials. However, a promising material, osmium tetraboride (OsB4) within WB4-type structure, was proposed to be superhard with claimed hardness of 46.2 GPa but with a much low shear modulus of 52 GPa through first-principles calculations [13]. Recently, Zhang et al. [14] proposed an orthorhombic Pmmn structure for OsB4, which is energetically much superior to the WB4-type structure. This Pmmn structure consists of irregular OsB10 dodecahedrons connected by edges and is stable against decompression into a mixture of Os and B at ambient pressure. The elastic and electronic properties of this orthorhombic structure are also explored at ambient conditions. However, to our knowledge, the investigations on its elastic and thermodynamic properties of the orthorhombic OsB4 under pressures are least studied. Especially, the comprehensive analysis of elastic characteristics (elastic constants, bulk and shear modulus, etc.) under pressures can provide a deeper insight into the response of the crystal to external forces, and obviously play an important role in determining the strength and hardness of materials. Moreover it is essential for many practical applications, such as load deflection, thermoelastic stress, fracture toughness, anisotropic character of the bonding, and structural stability [15]. The physical properties under pressures and temperatures have important guidable significances to accelerate the synthesis of OsB4 and other TM borides.
Here, the aim of this paper is to perform a theoretical investigation of structural, elastic and thermodynamic properties of OsB4 within orthorhombic Pmmn structure under pressures up to 50 GPa by first-principles calculations. The elastic properties of orthorhombic OsB4 under high pressure are investigated for the first time, from which the elastic anisotropy are also determined. In order to further investigate the OsB4, the thermodynamic properties, such as the heat capacity, thermal expansion, Grüneisen parameters and so on are determined by the Debye model.
Section snippets
Total energy electronic structure calculations
In the present work, density functional theory calculations are performed with plane-wave ultrasoft pseudopotential [16] using the generalized gradient approximation with the Perdew–Wang functional [17] as implemented in the CASTEP code [18]. The ionic cores are represented by ultrasoft pseudopotentials for B and Os atoms. The B: 2s2p1 and Os: 4p65d66s2 electrons are explicitly treated as valence electrons. The electronic wave functions are expanded in plane-wave basis set with cutoff energy of
Structural properties
The crystal structure of the OsB4 with Pmmn space group is shown in Fig. 1. To calculate the equilibrium lattice constants and bulk modulus, the total energy is calculated by varying the volume for the Pmmn-OsB4. The calculated E–V data are fitted to the third-order Birch–Murnaghan equation of state (EOS) [29], and the calculated equilibrium structure parameters, bulk modulus, and its pressure derivative are tabulated Table 1 together with other theoretical results for comparison. It is clear
Conclusion
In summary, the structural, elastic, and thermodynamic properties of the ultra-incompressible orthorhombic Pmmn structure of OsB4 under pressures have been predicted by first-principles calculations in combination with the quasi-harmonic Debye model. The obtained results of the ground state structural properties and equation of state are in good agreement with previous theoretical calculations. The elastic constants Cij, polycrystalline aggregate elastic moduli, Debye temperature, and the
Acknowledgments
This work was supported by the Natural Science Foundation of China (No. 11204007), Natural Science Basic Research plan in Shaanxi Province of China (Grant No. 2012JQ1005), Baoji University of Arts and Sciences Key Research (Grant No. ZK11060), and the Fundamental Research Funds for the Central Universities.
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2016, Journal of Solid State ChemistryCitation Excerpt :The pressure effect is investigated in the range of 0–18 GPa. In the quasi-harmonic Debye model [37,38,44,45], the Debye temperature ΘD and the thermal expansion coefficient α are two key quantities. Fig. 9 shows the variations of the thermal expansion with pressures and temperatures.