Elastic properties, lattice dynamics and structural transitions in molybdenum at high pressures

The structural phase transitions in molybdenum under pressures are investigated on the basis of first principle analysis of elastic constants behavior and phonon dispersions. The definition of the effective elastic constants of nth order (n ⩾ 2), governing the elastic properties of a loaded crystal, is given. The effective elastic constants of second and third order and the phonon dispersions are calculated by DFT methods in the pressure range of P = 0 − 1400 GPa, T = 0 K. The calculation results at P = 0 are in good agreement with the available experimental data. On the basis of the obtained results the stability of the bcc phase of molybdenum under pressure and the possibility of the phase transition are investigated. It is shown that the effective elastic constant C ∼ ′ which corresponds to the tetragonal uniform strain of a loaded crystal undergoes significant softening at P > 400 GPa. In the same pressure range the frequencies of the transverse branch T [ 1 1 ¯ 0 ] [ ζ ζ 0 ] also begin to soften and already at P ≈ 1000 GPa they become imaginary near the wave vector 1 4 1 4 0 . The bcc → dhcp phase transition associated with the softening of C ∼ ′ and the soft mode T 1 1 ¯ 0 1 4 1 4 0 is discussed.