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

Highlights: • For the first time, first-principles investigations of TiB₂–ZrB₂ solid solutions were performed. • The phase diagram of the random TiB₂–ZrB₂ alloys was constructed and analyzed. • The negative deviation of the calculated B, G, E, H_V and K_IC from the mixing rule was observed. • The optical spectra of Ti_1-xZr_xB₂ are similar to the spectra of the parent diborides. • The calculated elastic moduli and Poisson ratio exhibit spatial anisotropy. The stability, electronic and phonon structures, mechanical and thermodynamic properties as well optical spectra of the Ti_1−xZr_xB₂ solid solutions were investigated in the framework of a first-principles approach. The miscibility gap was predicted with the consolute temperature T_C = 1973 K and composition x_C = 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 Ti_0.5Zr_0.5B₂ 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 ${\epsilon }_R\left(\omega \right)$ and ${\epsilon }_I\left(\omega \right)$, and optical reflectivity spectra $R\left(\omega \right)$ for Ti_1−xZr_xB₂ were analyzed in comparison with available optical spectra of parent diborides from other authors.