Phase stability and mechanical properties of rhenium borides by first‐principles calculations

Abstract

The phase stability and elastic properties of Re-B system were systematically investigated by use of the density functional theory. The formation enthalpies are negative for Re(3)B, Re(7)B(3), Re(2)B, ReB, Re(2)B(3), and ReB(2), indicating that they are thermodynamically stable. Re(7)B(3), Re(2)B, ReB, Re(2)B(3), and ReB(2) are mechanically stable. Combining the study of enthalpy and pressure relationship with the convex hull, it was found that the ground state phases are Re(3)B, Re(7)B(3), and ReB(2) at zero pressure, in agreement with the experimental observations. At the pressure of 90 GPa, Re(3)B, and ReB(2) are the most stable phases.

Indentation strength of ultraincompressible rhenium boride, carbide, and nitride from first-principles calculations

“…If we set Φ = 0 (so σ zz = 0) in the calculation, it is equivalent to require that all the five stress components (except σ xz ) become negligible during the structural relaxation, which is the relaxation procedure used in the previous calculations of pure ideal shear stresses [28][29][30][31][32][33][34][35][36][37][38][41][42][43][44][45][46][47][48] that neglect the effects of the normal compressive pressure and geometry (indenter angles) of the indenter. Our test calculations for the lattice vectors of the equilibrium structure of Re, Re 3 N, Re 2 N, Re 2 C, Re 2 B and ReB 2 , their bulk moduli and Poisson's ratios are given in Table I, which agree well with the previous calculation results 19,[21][22][23][24]54,55 . The bulk moduli are obtained by fitting the energy-volume curves near the equilibrium structures to the Murnaghan equation, and the Poisson's ratios are evaluated from the calculated elastic constants.…”

“…6), we estimate that the (asymptotic) Vickers hardness of ReB 2 and Re 2 C are about 20-30 GPa and 15-25 GPa, respectively, which are consistent with the experimental results. 4,8,9,17 This explains the differences between the measured (asymptotic) Vickers hardness (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) of ReB 2 and the previous theoretical hardness predications (35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50) in which the normal compressive pressure beneath the indenter are neglected in the calculations. 58 The higher pure shear ideal strength of ReB 2 (35.3 GPa) and Re 2 C (27.2 GPa) suggests that they are suitable for applications in abrasive tools and wear-resistant coatings where compressive pressures normal to their scratching surfaces are not high.…”

“…It is difficult to compress their volumes by hydrostatic pressure, which results in their high bulk moduli. However, in indentation hardness tests the uniaxial normal compressive pressure beneath the indenter can cause a large lateral volume expansion of the valence electrons in these structures as indicated by their large Poisson's ratios [19][20][21][22][23][24] . We examine how this lateral expansion affects the mechanical strength under indentation of these compounds with different chemical elements and compositions.…”

In situ study of the formation of rhenium borides from the elements at high-(p, T) conditions: Extreme incompressibility of Re7B3 and formation of new phases

“…The bulk modulus derived from stress-strain calculations agrees with the eos-based value. The values for the c ij obtained here from stress-strain calculations for ReB 2 and Re 7 B 3 agree with those obtained earlier by DFT calculations [27,32,47]. It is worth to mention that the agreement is good although these calculations were performed with other functionals, other pseudopotentials and other DFT-implementations.…”

“…The DFT data are internally consistent, as the bulk modulus obtained from stress-strain calculations is in very good agreement with the value obtained from the eos. An LDA-based calculation [32] gave c ij values similar to those observed here, and a theoretical bulk modulus of 404 GPa, which, as expected, is slightly larger than the WC-GGA value (385 GPa) obtained in the present study. A PBE-GGA value computed by Ref.…”