Density functional theory investigation of the phonon instability, thermal equation of state and melting curve of Mo

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The phonon instability and thermal equation of state of Mo are extensively investigated using density functional theory. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening in the transverse acoustic (TA) branches of body-centred cubic Mo. When the pressure is raised to 716 GPa, the frequencies along Γ-N in the TA branches soften to imaginary frequencies, indicating structural instability. For face-centred cubic Mo, the phonon calculations predicted the stability by promoting the frequencies from imaginary to real. Within quasi-harmonic approximation, we predicted the thermal equation of state and some other properties including the thermal expansion coefficient α, product αK(T), heat capacity C(V), entropy S, Grüneisen parameter γ and Debye temperature Θ(D). The melting curves of Mo were also obtained successfully.