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

摘要

The pressure-induced phase transition, elasticity behavior, thermodynamicproperties, and $P\mathtt{-}T$ phase diagram of $\alpha$, $\omega$, and $\beta$equiatomic HfTi alloy are investigated using first-principlesdensity-functional theory (DFT). The simulated pressure-induced phasetransition of the alloy follows the sequence of$\alpha\mathtt{\rightarrow}\omega\mathtt{\rightarrow}\beta$, in agreement withthe experimental results of Hf and Ti metals. Our calculated elastic constantsshow that the $\alpha$ and $\omega$ phases are mechanically stable at ambientpressure, while the $\beta$ phase is unstable, where a critical pressure of18.5 GPa is predicted for its mechanical stability. All the elastic constants,bulk modulus, and shear modulus increase upon compression for the three phasesof HfTi. The ductility of the alloy is shown to be well improved with respectto pure Hf and Ti metals. The Mulliken charge population analysis illustratesthat the increase of the d-band occupancy will stabilize the $\beta$ phaseunder pressure. The phonon spectra and phonon density of states are studiedusing the supercell approach for the three phases, and the stable nature of$\alpha$ and $\omega$ phases at ambient pressure are observed, while the$\beta$ phase is only stable along the [110] direction. With the Gibbs freeenergy calculated from DFT-parametrized Debye model as a function oftemperature and pressure, the phase transformation boundaries of the $\alpha$,$\omega$, and $\beta$ phases of HfTi are identified.