First-principles study of configurational disorder in icosahedral boron-rich solids

Abstract: This thesis is a theoretical study of configurationally disordered icosahedral boronrich solids, in particular boron carbides, using density functional theory and alloy theory. The goal is to resolve discrepancies, regarding the properties of boron carbides, between experiments and previous theoretical calculations which have been a controversial issue in the field of icosahedral boron-rich solids. For instance, B13C2 is observed experimentally to be a semiconductor, meanwhile electronic band structure calculations reveal a metallic character of B13C2 due to its electron deficiency. In B4C, on the other hand, the experimentally observed band gap is unexpectedly smaller, not the usual larger, than that of standard DFT calculations. Another example is given by the existence of a small structural distortion in B4C, as predicted in theoretical calculations, which reduces the crystal symmetry from the experimentally observed rhombohedral (R3m) to the based-centered monoclinic (Cm). Since boron carbide is stable as a single-phase over a broad composition range (~8-20 at.% C), substitution of boron and carbon atoms for one another is conceivable. For this reason, the discrepancies have been speculated in the literature, without a proof, to originate from configurational disorder induced by substitutional defects. However, owing to its complex  atomic structure, represented by 12-atom icosahedra and 3-atom intericosahedral chains, a practical alloy theory method for direct calculations of the properties of the relevant configurations of disordered boron carbides, as well as for a thermodynamic  assessment of their stability has been missing.In this thesis, a new approach, the superatom-special quasirandom structure (SA-SQS), has been developed. The approach allows one to model configurational disorder in boron carbide, induced by high concentrations of low-energy B/C substitutional defects. B13C2 and B4C are the two stoichiometries, mainly considered in this study, as they are of particular importance and have been in focus in the literature. The results demonstrate that, from thermodynamic considerations, both B13C2 and B4C configurationally disorder at high temperature. In the case of B13C2, the configurational disorder splits off some valence states into the band gap that in turn compensates the electron deficiency in  ordered B13C2, thus resulting in a semiconducting character. As for B4C, the configurational disorder eliminates the monoclinic distortion, thus resulting in the restoration of the higher rhombohedral symmetry. Configurational disorder can also account for an excel lent agreement on elastic moduli of boron carbide between theory and experiment. Thus, several of the previous discrepancies between theory and experiments are resolved.Inspired by attempts to enhance the mechanical properties of boron suboxide by fabricating boron suboxide-boron carbide composites, as recently suggested in the literature, the SA-SQS approach is used for modeling mixtures of boron suboxide (B6O) and boron carbide (B13C2), denoted by pseudo-binary (B6O)1–x(B13C2)x alloys. The knowledge of configurational disorder, gained from the previous studies of boron carbide, is applied to model the mixing alloys. By investigating the thermodynamics of mixing between B6O and B13C2, the phase diagram of the (B6O)1–x(B13C2)x alloys is outlined and it reveals the existence of a miscibility gap at all temperatures up to the melting point, indicating the coexistence of B6O-rich and either ordered or disordered B13C2-rich domains in (B6O)1–x(B13C2)x alloys under equilibrium condition. However, a limited intermixing of B6O and B13C2 to form solid solutions at high temperature is predicted, e.g. a solid solution of ~5% B13C2 in B6O and ~20% B6O in B13C2 at 2000 K.