Elasticity behavior, phonon spectra, and the pressure–temperature phase diagram of HfTi alloy: A density-functional theory study

Abstract

The pressure-induced phase transition, elasticity behavior, thermodynamic properties, and P −T phase diagram of α, ω, and β equiatomic HfTi alloy are investigated using first-principles densityfunctional theory (DFT). The simulated pressure-induced phase transition of the alloy follows the sequence of α→ω→β, in agreement with the experimental results of Hf and Ti metals. Our calculated elastic constants show that the α and ω phases are mechanically stable at ambient pressure, while the β phase is unstable, where a critical pressure of 18.5 GPa is predicted for its mechanical stability. All the elastic constants, bulk modulus, and shear modulus increase upon compression for the three phases of HfTi. The ductility of the alloy is shown to be well improved with respect to pure Hf and Ti metals. The Mulliken charge population analysis illustrates that the increase of the d-band occupancy will stabilize the β phase under pressure. The phonon spectra and phonon density of states are studied using the supercell approach for the three phases, and the stable nature of α and ω phases at ambient pressure are observed, while the β phase is only stable along the [110] direction. With the Gibbs free energy calculated from DFT-parametrized Debye model as a function of temperature and pressure, the phase transformation boundaries of the α, ω, and β phases of HfTi are identified.

First-principles study of structural, elastic, and thermodynamic properties of ZrHf alloy

“…The visualizations of all the models are displayed by the VESTA code. [22] One of the two structures was frequently used in a previous study, [23,24] and the other one is built in the same scheme. For The special quasi-random structure (SQS) of ZrHf alloys is generated for the calculation of disordered structure.…”

“…Obviously, all three structures are stable at ground-state, and interaction between acoustic and optical branches exists among all the models, which is similar to TiZr alloys; [23] however, it differs in a way from the TiHf alloys, for which there is no interaction in alpha phase. [24] Compared with the phonon DOS of lamella structures and pure metals, the result of SQS is smoother, possibly resulting from the large cell (16 atoms in one cell) of the quasi-random model. Interestingly, the highest phonon frequency of Hf is about 4.7 THz, and the phonon dispersions of ZrHf alloys above this frequency are not empty.…”