Structural models of increasing complexity for icosahedral boron carbide with compositions throughout the single-phase region from first principles

Abstract

We perform first-principles calculations to investigate the phase stability of boron carbide, concentrating on the recently proposed alternative structural models composed not only of the regularly studied B 11 C p (CBC) and B 12 (CBC), but also of B 12 (CBCB) and B 12 (B 4). We find that a combination of the four structural motifs can result in low-energy electron precise configurations of boron carbide. Among several considered configurations within the composition range of B 10.5 C and B 4 C, we identify in addition to the regularly studied B 11 C p (CBC) at the composition of B 4 C two low-energy configurations, resulting in a new view of the B-C convex hull. Those are [B 12 (CBC)] 0.67 [B 12 (B 4)] 0.33 and [B 12 (CBC)] 0.67 [B 12 (CBCB)] 0.33 , corresponding to compositions of B 10.5 C and B 6.67 C, respectively. As a consequence, B 12 (CBC) at the composition of B 6.5 C, previously suggested in the literature as a stable configuration of boron carbide, is no longer part of the B-C convex hull. By inspecting the electronic density of states as well as the elastic moduli, we find that the alternative models of boron carbide can provide a reasonably good description for electronic and elastic properties of the material in comparison with the experiments, highlighting the importance of considering B 12 (CBCB) and B 12 (B 4), together with the previously proposed B 11 C p (CBC) and B 12 (CBC), as the crucial ingredients for modeling boron carbide with compositions throughout the single-phase region.

Effect of temperature and configurational disorder on the electronic band gap of boron carbide from first principles

“…6, the unoccupied midgap states of 3 C appear as the two sharply defined peaks in the band gap, and their origin is attributed to the presence of the rhombic B 4 chain. As demonstrated in the previous theoretical studies of boron carbide [31][32][33][34][35], one of the peaks is assigned as the split-off valence states, while the other peak appears as impurity states. As the concentration of B 12 (B 4 ) increases, the unoccupied defect states widen and form an impurity band, eventually overlapping with the conduction band.…”

“…As the concentration of B 12 (B 4 ) increases, the unoccupied defect states widen and form an impurity band, eventually overlapping with the conduction band. We note that the overlapping of the impurity band, arising from a high concentration of B 12 (B 4 ), with the conduction band was previously predicted for boron-rich boron carbide B 10.5 C, represented by [B 12 (CBC)] 0.67 [B 12 (B 4 )] 0.33 [33][34][35]. However, in the dilute limit, the sharpness of these states indicates an impurity-band-type character.…”

“…This can be attributed not only to the complexity of the icosahedral structure but also to the similar characteristics of boron and carbon atoms, i.e., the atomic form factor for x-ray diffraction [38] and the nuclear scattering cross sections ( 11 B and 12 C) for neutron diffraction [7,39]. As a consequence, there has so far been no unambiguous experimental spectroscopic evidence to explicitly characterize structural defects existing in boron carbide, and several investigations of defects inducing configurational disorder in boron carbide have by far been based mostly on the theoretical simulations [2,19,[30][31][32][33][34][35][40][41][42][43][44]. The structural model of the ideally stoichiometric B 4 C is given by B 11 C p icosahedra and linear CBC chains, as it has been demonstrated by several theoretical studies [17,19,[40][41][42] to be the most favorable configuration from the thermodynamics aspect.…”

“…%, the C p atoms residing in the B 11 C p icosahedra rather than C atoms residing in the linear CBC chains tend to be replaced by B atoms, hence resulting in the formation of electron-deficient B 12 (CBC). Second, recent theoretical works on boron carbide [31][32][33][34][35] revealed that entirely compensating for the electron deficiency in B 12 (CBC) through the addition of B 12 (B 4 ), in which the B 12 (CBC)-to-B 12 (B 4 ) ratio is 2, can considerably lower the total energy of the material. We note that the rhombic B 4 chains were originally proposed by Yakel [5], based on the x-ray diffraction data of boron-rich boron carbide, and furthermore, most recently the existence of rhombic chains was observed experimentally by Rasim et al [34] through high-resolution transmission electron microscopy of boron carbide, reasonably justifying the structural model of B 4.3 C employed in the present work.…”

“…Recent theoretical studies demonstrated that electron deficiency in the idealized B 12 (CBC) can be compensated either by a thermally activated configurational disorder of boron and carbon atoms [30] or via a combination of different intericosahedral chain motifs, for example, the linear CBC and CBCB as well as rhombic B 4 chains [31][32][33][34][35]. The latter has been suggested from the thermodynamics aspect to be the most plausible explanation of how boron carbide retains its semiconducting state within the homogeneity range.…”