Lattice stability and thermal equation of state of -La from first-principles calculations

We report a first-principles calculation to investigate the lattice stability and thermal equation of state of β -La. The calculated phonon dispersion curves agree with experimental results at zero pressure. We reproduced the dip in phonon dispersion along the [111] direction successfully. Under compression, we captured a large softening around the L point. When the pressure is raised to 4.67 GPa, the frequencies around the L point along the Γ –L transverse acoustical branches become imaginary, indicating a structural instability. Within the quasi-harmonic approximation, we predicted the accurate thermal equations of state under high pressure and high temperature.