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Calculations have been performed to investigate the pressure-induced solid-solid phase transitions and the mechanical stability for three zinc-blende II-VI semiconductor compounds: ZnS, ZnSe, ZnTe by ab initio plane-wave pseudopotential density functional theory (DFT). Using the generalized gradient approximation (GGA) for exchange and correlation in the scheme of Perdew-Wang 1991 (PW91), the ground state properties and equation of state are obtained, which are well consistent with the experimental data available and other calculations. On the basis of the forth-order Birch-Murnaghan equation of states, the transition pressures P(t) are determined through the analysis of enthalpy variation with pressure. A linear-response approach is used to calculate the frequencies of the phonon dispersion. Finally, by the calculations of phonon frequencies, some thermodynamic properties such as the vibrational contribution to the Helmholtz free energy (F), enthalpy (H), entropy (S), and the heat capacity (C(V)) are also successfully obtained

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