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

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 ${\mathrm{B}}₁₁{\mathrm{C}}^p$(CBC) and ${\mathrm{B}}₁₂$(CBC), but also of ${\mathrm{B}}₁₂$(CBCB) and ${\mathrm{B}}₁₂({\mathrm{B}}₄$). 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 ${\mathrm{B}}_10.5\mathrm{C}$ and ${\mathrm{B}}₄\mathrm{C}$, we identify in addition to the regularly studied ${\mathrm{B}}₁₁{\mathrm{C}}^p$(CBC) at the composition of ${\mathrm{B}}₄\mathrm{C}$ two low-energy configurations, resulting in a new view of the B-C convex hull. Those are $[{\mathrm{B}}₁₂$(CBC)${\mathrm{]}}_0.67{[{\mathrm{B}}₁₂({\mathrm{B}}₄)]}_0.33$ and $[{\mathrm{B}}₁₂$(CBC)${\mathrm{]}}_0.67[{\mathrm{B}}₁₂$(CBCB)${\mathrm{]}}_0.33$, corresponding to compositions of ${\mathrm{B}}_10.5\mathrm{C}$ and ${\mathrm{B}}_6.67\mathrm{C}$, respectively. As a consequence, ${\mathrm{B}}₁₂$(CBC) at the composition of ${\mathrm{B}}_6.5\mathrm{C}$, previously suggested in the literature as a stable configuration of boron carbide, is no longer part of the $\mathrm{B}\ensuremath{-}\mathrm{C}$ 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 ${\mathrm{B}}₁₂$(CBCB) and ${\mathrm{B}}₁₂({\mathrm{B}}₄$), together with the previously proposed ${\mathrm{B}}₁₁{\mathrm{C}}^p$(CBC) and ${\mathrm{B}}₁₂$(CBC), as the crucial ingredients for modeling boron carbide with compositions throughout the single-phase region.