Lattice stability of ordered Au-Cu alloys in the warm dense matter regime

In the warm dense regime, where the electron temperature is increased to the same order of the Fermi temperature, the lattice stability of elemental metals depends on its electronic band structure as well as its crystal structure. It has been believed that the $d$ electron excitations yield the phonon hardening as in noble metals, whereas the crystal structure symmetry can prevent phonon hardening at a specific point in the Brillouin zone as in alkali metals. Here, we extend this concept to binary alloys (Au and Cu) in the L1$_0$ and L1$_2$ structures. By performing first principles calculations on phonon dispersions, we demonstrate that warm dense alloys in the L1$_0$ and L1$_2$ structures show phonon softening and hardening behaviors, respectively. This suggests that for the L1$_0$ the effect of crystal structure symmetry overcomes that of weakened electron screening due to the $d$ electron excitations.