Bulk aluminum at high pressure: A first-principles study

The behavior of metals at high pressure is of great importance to the fields of shock physics, geophysics, astrophysics, and nuclear materials. We study here bulk crystalline aluminum from first principles at pressures up to $2500\mathrm{GPa}$—soon within reach of laser-based experimental facilities. Our simulations use density-functional theory and density-functional perturbation theory in the local-density and generalized-gradient approximations. Notably, the two different exchange-correlation functionals predict very similar results for the $\mathrm{fcc}\to \mathrm{hcp}$, $\mathrm{fcc}\to \mathrm{bcc}$, and $\mathrm{hcp}\to \mathrm{bcc}$ transition pressures, around 175, 275, and $380\mathrm{GPa}$, respectively. In addition, our results indicate that core overlaps become noticeable only beyond pressures of $1200\mathrm{GPa}$. From the phonon dispersions of the fcc phase at increasing pressure, we predict a softening of the lowest transverse acoustic vibrational mode along the [110] direction, which corresponds to a Born instability of the fcc phase around $725\mathrm{GPa}$.

Figure 1

(Color online) (a) Enthalpy of the bcc phase ($3e$ and $11e$ GGA) relative to the enthalpy of the fcc phase ($3e$ and $11e$ GGA, respectively). (b) Enthalpies for hcp and bcc phases relative to the enthalpy of the fcc phase. The $\mathrm{fcc}\to \mathrm{hcp}$, $\mathrm{fcc}\to \mathrm{bcc}$, and $\mathrm{hcp}\to \mathrm{bcc}$ transition pressures are 175, 275, and $380\mathrm{GPa}$, respectively.

Figure 2

(Color online) (a) The $c∕a$ ratio of the hcp phase plotted with increasing pressure. (b) Volume vs pressure for the fcc, hcp, and bcc phases plotted relative to the fcc phase.

Figure 3

(Color online) The frequencies of the two nondegenerate acoustic phonon modes at $X$ calculated with both the $3e$ and $11e$ pseudopotentials and plotted as a function of increasing pressure.

Figure 4

(Color online) (a) The lowest energy branch of phonon dispersion for fcc Al with increasing pressure. (b) As above, enlarged around $\Gamma$, in the $K\to \Gamma$ direction. A steady flattening is observed with increasing pressure.

Figure 5

(Color online) Elastic constants as obtained from the sound velocities along the [100], [110], and [111] directions. According to the Born criterion, the fcc phase becomes mechanically unstable when $\Delta c=c_{11}-c_{12}=0$; this occurs around $725\mathrm{GPa}$.