Phase diagram, electronic, mechanical and thermodynamic properties of TiB2–ZrB2 solid solutions: A first-principles study

Abstract

The stability, electronic and phonon structures, mechanical and thermodynamic properties as well optical spectra of the Ti1−xZrxB2 solid solutions were investigated in the framework of a first-principles approach. The miscibility gap was predicted with the consolute temperature TC = 1973 K and composition xC = 0.4. The negative deviation of the calculated bulk, shear, Young moduli, Debye temperature, Vickers hardness and fracture toughness from the mixing rule is observed. The ideal shear stress of 41.1 GPa for Ti0.5Zr0.5B2 was found to be lower compared to that for TiB2 (43.5 GPa) and ZrB2 (43.1 GPa). The calculated elastic moduli and Poisson ratio exhibit the spatial anisotropy inherent to hexagonal structures. It was shown that the thermodynamic characteristics of the Zr-rich solid solutions could be well reproduced in a temperature range up to 1000–1400 K using the harmonic approximation. The calculated dielectric constants εR(ω) and εI(ω), and optical reflectivity spectra R(ω) for Ti1−xZrxB2 were analyzed in comparison with available optical spectra of parent diborides from other authors.