Scalar-relativistic calculations of the band structure for selected ordered and disordered supercells have been performed using Quantum-ESPRESSO code based on the density functional method.
For the solid solutions Ti1-xNbxB2 and Ti1-xZrxB2, it was found that at T=0 K the Ti1-xNbxB2 solutions are thermodynamically stable (negative mixing energy), while Ti1-xZrxB2 ones are unstable (positive mixing energy). The obtained negative values of mixing energy for all Ti1-xNbxB2 solutions indicate the possibility of formation of stable continuous substitutional solid solutions. It was established that the reason for their strengthening is strengthening of the interatomic interaction between the xy-planes in the z-direction. That is confirmed by calculations of the partial densities of electronic states and partial charges, which show an increase in the charge on the pz orbitals of boron atoms as compared to the px and py orbitals for compositions close to equiatomic.
With temperature decreasing down to the critical 1973 K, the Ti1-xZrxB2 solid solutions are assumed to decompose according to the spinodal or binodal mechanisms. Taking the phonon component into account reduces the critical temperature of decomposition. The study of mechanical properties of Ti1-xNbxB2 and Ti1-xZrxB2 has shown that they do not correlate with the stability of the solid solutions and change almost linearly depending on their composition.
To establish possible routes for the structural transition from B1-SiC to B3-SiC under decompression, first-principles molecular dynamics (FPMD) was used. Intermediate states were analyzed for the presence of symmetry using a group-theoretic approach and analysis of phonon spectra. The transition route was shown to depend on the volume and configuration of the initial cells, modeling temperature, and the presence of soft phonon modes, freezing of which leads to structural transformation. We have found two possible routes of the B1 to 3C structural transition:
Fm3m -- Imm2 -- I4m2 -- F43m
Fm3m -- I4mm -- Cc -- F43m
In order to determine the mechanical and thermodynamic characteristics and stability of the solid solutions TiC-SiC and NbC-SiC, the corresponding first-principle calculations were performed. The calculated mixing energy is positive for both systems, which means that the formation of solid solutions at low temperatures is energetically unfavorable. To determine stability of solid solutions at finite temperatures, we constructed spinodal and binodal curves taking into account the phonon and configuration components. For the Ti1-xSixC system, the structures B1 and B3 were considered because titanium carbide is stable in the B1 structure, while silicon carbide – in B3. The structure B1 was shown to be energetically favorable in the range $0 <= x <0.5$, while the structure B3 in the range $0.5 <= x <=1.0$. Similar calculations for the Nb1-xSixC system have revealed that they are dynamically unstable over a wide concentration range.
Although both TiC-HfC and TiC-TaC systems show a positive deviation of the cell volume from linearity, the TiC-HfC system is unstable, while the TiC-TaC system is stable. The study of mechanical properties revealed that the modulus of elasticity and hardness for TiC-HfC have a negative deviation from linearity, while for TiC-TaC it is positive. To establish the reasons for strengthening of the TiC-TaC solid solutions and instability of TiC-HfC ones, an analysis of their electronic structures was performed. It was shown that the strengthening is mainly caused by the contribution of the metal component of the chemical bond, while the energetic instability of the TiC-HfC solutions is mainly due to the significant difference in the volumes of TiC and HfC cells.
Stability of all possible combinations of solid solutions based on transition metals of IV, V and partially VI groups has been analyzed as well. It was shown that all alloys based on transition metal carbides of different groups are mutually soluble, except for ZrC-VC and HfC-VC, which have large difference in the cell volumes of carbides they consist of. Thus, the mixing energy depends mainly on the difference in the cell volumes of the composing carbides and the difference in filling of the energetic metal bands in them. The corresponding calculations show that the maximum strength of such carbide compositions is expected for the number of valence electrons within 8.50--8.75.
The developed research methodology as well as the obtained results will be useful for interpretation of phase transitions and strengthening mechanisms and prediction of mechanical and thermodynamic properties for other solid solutions. The obtained properties of refractory alloys based on borides and carbides of transition metals and SiC can also be useful in the design of new promising superhard materials.
