tructural transformation, pressure dependent elasticity behaviors, phonon,and thermodynamic properties of the equiatomic TiZr alloy are investigated byusing first-principles density-functional theory. Our calculated latticeparameters and equation of state for $\alpha$ and $\omega$ phases as well asthe phase transition sequence of$\alpha$$\mathtt{\rightarrow}$$\omega$$\mathtt{\rightarrow}$$\beta$ areconsistent well with experiments. Elastic constants of $\alpha$ and $\omega$phases indicate that they are mechanically stable. For cubic $\beta$ phase,however, it is mechanically unstable at zero pressure and the critical pressurefor its mechanical stability is predicted to equal to 2.19 GPa. We find thatthe moduli, elastic sound velocities, and Debye temperature all increase withpressure for three phases of TiZr alloy. The relatively large $B/G$ valuesillustrate that the TiZr alloy is rather ductile and its ductility is morepredominant than that of element Zr, especially in $\beta$ phase. Elastic wavevelocities and Debye temperature have abrupt increase behaviors upon the$\alpha$$\mathtt{\rightarrow}$$\omega$ transition at around 10 GPa and exhibitabrupt decrease feature upon the $\omega$$\mathtt{\rightarrow}$$\beta$transition at higher pressure. Through Mulliken population analysis, weillustrate that the increase of the \emph{d}-band occupancy will stabilize thecubic $\beta$ phase. Phonon dispersions for three phases of TiZr alloy arefirstly presented and the $\beta$ phase phonons clearly indicate itsdynamically unstable nature under ambient condition. Thermodynamics of Gibbsfree energy, entropy, and heat capacity are obtained by quasiharmonicapproximation and Debye model.
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