Effects of configurational disorder on the elastic properties of icosahedral boron-rich alloys based on B6O, B13C2, and B4C, and their mixing thermodynamics.

The elastic properties of alloys between boron suboxide (B6O) and boron carbide (B13C2), denoted by (B6O)(1-x)(B13C2)(x), as well as boron carbide with variable carbon content, ranging from B13C2 to B4C are calculated from first-principles. Furthermore, the mixing thermodynamics of (B6O)(1-x)(B13C2)(x) is studied. A superatom-special quasirandom structure approach is used for modeling different atomic configurations, in which effects of configurational disorder between the carbide and suboxide structural units, as well as between boron and carbon atoms within the units, are taken into account. Elastic properties calculations demonstrate that configurational disorder in B13C2, where a part of the C atoms in the CBC chains substitute for B atoms in the B12 icosahedra, drastically increase the Young's and shear modulus, as compared to an atomically ordered state, B12(CBC). These calculated elastic moduli of the disordered state are in excellent agreement with experiments. Configurational disorder between boron and carbon can also explain the experimentally observed almost constant elastic moduli of boron carbide as the carbon content is changed from B4C to B13C2. The elastic moduli of the (B6O)(1-x)(B13C2)(x) system are also practically unchanged with composition if boron-carbon disorder is taken into account. By investigating the mixing thermodynamics of the alloys, in which the Gibbs free energy is determined within the mean-field approximation for the configurational entropy, we outline the pseudo-binary phase diagram of (B6O)(1-x)(B13C2)(x). The phase diagram reveals the existence of a miscibility gap at all temperatures up to the melting point. Also, the coexistence of B6O-rich as well as ordered or disordered B13C2-rich domains in the material prepared through equilibrium routes is predicted.