Thermodynamic stability and properties of boron subnitrides from first principles

Abstract

We use the first-principles approach to clarify the thermodynamic stability as a function of pressure and temperature of three different α-rhombohedral-boron-like boron subnitrides, with the compositions of B 6 N, B 13 N 2 , and B 38 N 6 , proposed in the literature. We find that, out of these subnitrides with the structural units of B 12 (N-N), B 12 (NBN), and [B 12 (N − N)] 0.33 [B 12 (NBN)] 0.67 , respectively, only B 38 N 6 , represented by [B 12 (N − N)] 0.33 [B 12 (NBN)] 0.67 , is thermodynamically stable. Beyond a pressure of about 7.5 GPa depending on the temperature, also B 38 N 6 becomes unstable, and decomposes into cubic boron nitride and α-tetragonalboron-like boron subnitride B 50 N 2 . The thermodynamic stability of boron subnitrides and relevant competing phases is determined by the Gibbs free energy, in which the contributions from the lattice vibrations and the configurational disorder are obtained within the quasiharmonic and the mean-field approximations, respectively. We calculate lattice parameters, elastic constants, phonon and electronic density of states, and demonstrate that [B 12 (N − N)] 0.33 [B 12 (NBN)] 0.67 is both mechanically and dynamically stable, and is an electrical semiconductor. The simulated x-ray powder-diffraction pattern as well as the calculated lattice parameters of [B 12 (N − N)] 0.33 [B 12 (NBN)] 0.67 are found to be in good agreement with those of the experimentally synthesized boron subnitrides reported in the literature, verifying that B 38 N 6 is the stable composition of α-rhombohedral-boron-like boron subnitride.

Phase Diagram of the B–BN System at Pressures up to 24 GPa: Experimental Study and Thermodynamic Analysis

“…Hypothetical α-rhombohedral-boron-like boron subnitride B 38 N 6 predicted from first-principles was never observed in our experiments, even below 7.5 GPa, i.e., in the pressure range where it was claimed to be the only thermodynamically stable boron subnitride. All this clearly illustrate the limitations of the first-principles approach in the case of boron-rich solids, especially under pressure.…”

Chemical vapour deposition of sp2-hybridised B-C-N materials from organoborons

“…116 The electrical and mechanical properties of boron subnitride have mostly been calculated. 117 B6N and B13N2 are predicted to show metallic conduction be while B38N6 should be a semiconductor. Boron subnitride should be a superhard, brittle material with a bulk modulus predicted to be around 230 GPa.…”

“…It was unclear whether N was incorporated in the boron carbide lattice or not. One must also note that the eventual formation of an amorphous phase is usually not considered in thermodynamic calculations in the B-C-N system 116,117 .…”

Mechanical properties of superhard boron subnitride B13N2

“…The variation of ν over the 0. from 530 to 501 GPa which is within the experimental error of Young's modulus evaluation from the present set of nanoindentation data. This allows the conclusion that the theoretically predicted Young's modulus value (387 GPa [13]) is strongly underestimated. Using the relation between Young's (E) and shear (G) moduli for an isotropic material (6) and Poisson's ratio ν = 0.23 [13], the shear modulus of B 13 N 2 was evaluated as G = 209(6) GPa which is sig nificantly higher than the theoretically predicted values (157 GPa [13] and 162 GPa [14]).…”

“…The Young's modulus of E = 515(16) GPa was calculated by Eq. 5 using the experimental E r = 365(8) GPa value (data from 7 independent nanoindentation experiments) under the assumption that Poisson's ratio of B 13 N 2 is equal to ν = 0.23 (theoretically predicted using the Voigt Reuss Hill approach [13]). The variation of ν over the 0. from 530 to 501 GPa which is within the experimental error of Young's modulus evaluation from the present set of nanoindentation data.…”