Ab initio study of the LiH phase diagram at extreme pressures and temperatures

The effect of anharmonic vibrational contributions to the finite-temperature pressure-driven B1-B2 structural phase transition of LiH is studied by using the stochastic self-consistent harmonic approximation method in combination with ab initio density functional theory and the quasiharmonic approximation. Contrary to previous experimental results based on multiple-shock compression, we find that the B1-B2 transition pressure is not significantly reduced at high temperatures. Moreover, we find that the B2 phase is dynamically unstable at low temperatures within harmonic theory in a wide range of pressures where its enthalpy is lower than that of the B1 phase, and the inclusion of anharmonic effects stabilizes the B2 phase in this pressure range. Our results imply that a third, yet unknown phase must exist in the phase diagram of LiH, in addition to the B1 and B2 phases, in order to explain the shock compression result.

Figure 1

(a) Phonon dispersion of LiH B1 as a function of pressure along the high-symmetry points of the Brillouin zone. (b) The frequency of the transverse acoustic mode of the B1 phase at $\mathbf{X}$ as a function of pressure. Our results are represented by lines, and the results from Refs. [10, 30] are represented by open symbols and solid orange squares, respectively.

Figure 2

(a) Phonon dispersion of LiH B2 as a function of pressure along the high-symmetry points of the Brillouin zone. (b) Frequency at two $\mathbf{q}$ points at a denser $\mathbf{k}$ mesh of $40\times 40\times 40$ for different values of pressure.

Figure 3

Relative energy $\delta E=E(\mathrm{d}-\mathrm{B}2)-E\left(\mathrm{B}2\right)$ is plotted as a function of the monoclinic angle at (a) $V/V_0$ = 0.32, (b) $V/V_0$ = 0.30, and (c) $V/V_0$ = 0.28. $\delta E<0$ indicates that the distorted B2 ($\mathrm{d}-\mathrm{B}2$) is more stable than the B2 phase in LiH.

Figure 4

Comparison of phonon dispersions and the phonon density of states (ph DOS) of (a) and (b) B1 and (c) and (d) B2 at $T=300$ K (dashed orange line) and $T$ = 1800 K (blue line) obtained by SSCHA calculations with the corresponding results obtained at $T=0$ K (gray line) obtained using HA. Note that the anharmonic effects to phonon dispersions and the phonon DOS at $T=0$ K are shown by the dotted cyan line in (c). For B2, the phonon DOS has been shown only for stable phonons.

Figure 5

(a) Phonon dispersions of LiH B2 as a function of volume fractions at $T$ = 300 K. (b) A zoomed-in region of (a) along $\mathrm{\Gamma }-\mathbf{X}$.

Figure 6

B1-B2 phase diagram. Blue and pink regions represent the regions of phase stability of B1 and B2, respectively, obtained from SSCHA. The blue line represents the transition line obtained from QHA. The red line represents the transition line suggested by Ref. [15]; the orange star represents the position of the appearance of electrical conductivity observed by these authors.

Figure 7

Equation of states (EOS) at $T=$ 0, 300, and 1800 K. The solid black and blue lines represent the EOSs of B1 and B2, respectively, at $T$ = 0 K; the solid (dotted) orange and red lines represent the EOSs of B1 and B2, respectively, at $T=$ 1800 K (300 K). The insets show the percentage of change of volume $\mathrm{\Delta }V/V_0$ at the corresponding transition pressures at a given temperature (shown by green horizontal lines).