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 dynamical stability of elemental metals depends on its electronic band structure as well as its crystal structure. It has been known that phonon hardening occurs due to an enhanced internal pressure caused by electron excitations as in close-packed simple metals, whereas phonon softening occurs at a specific point in the Brillouin zone as in body-centered cubic metals. Here, we investigate the dynamical stability of binary ordered alloys (Au and Cu) in the ${\mathrm{L}1}_0$ and ${\mathrm{L}1}_2$ structures. By performing first-principles calculations on phonon dispersions, we demonstrate that warm dense Au-Cu systems show phonon hardening behavior except the lowest frequency phonon mode at point $R$ of AuCu in the ${\mathrm{L}1}_0$ structure. We show that when a phonon mode is stabilized by long-range interatomic interactions at ambient condition, such a phonon will be destabilized by the short-range nature of the warm dense matters.

Figure 1

Crystal structure of ${\mathrm{CuAu}}_3$ (${\mathrm{L}1}_2$), AuCu (${\mathrm{L}1}_0$), and ${\mathrm{AuCu}}_3$ (${\mathrm{L}1}_2$).

Figure 2

The phonon dispersions of (a) Au, (b) Cu, (c) AuCu, (d) ${\mathrm{CuAu}}_3$, and (e) ${\mathrm{AuCu}}_3$ calculated with the PZ and PBE functionals. The experimental data (circles) for (a), (b), and (e) are taken from Refs. [28, 29, 31], respectively.

Figure 3

The phonon dispersions of (a) Au, (b) Cu, (c) AuCu, (d) ${\mathrm{CuAu}}_3$, and (e) ${\mathrm{AuCu}}_3$ for $k_{\mathrm{B}}{T}_{\mathrm{e}}=0,4,$ and 6 eV. The PBE functional is used.

Figure 4

The electron DOS for Au, ${\mathrm{CuAu}}_3$, AuCu, ${\mathrm{AuCu}}_3$, and Cu for $k_{\mathrm{B}}{T}_{\mathrm{e}}=0,4$, and 6 eV. The electron energy is measured from the Fermi level.

Figure 5

(a) The free-energy of ${\mathrm{L}1}_0$ AuCu along the Bain path for different $T_{\mathrm{e}}\mathrm{s}$. The free-energy is measured from the minimum value along $c/a$ with $T_{\mathrm{e}}$ fixed. (b) The phonon dispersion curves of AuCu with $c/a=1$ (i.e., B2) for $T_{\mathrm{e}}=0$ and 4 eV.