Comment on “High-pressure phases of group-II difluorides: Polymorphism and superionicity”

Nelson et al. [Phys. Rev. B 95, 054118 (2017)] recently reported first-principles calculations on the behavior of group-II difluorides (${\mathrm{BeF}}_2, {\mathrm{MgF}}_2$, and ${\mathrm{CaF}}_2$) under high-pressure and low- and high-temperature conditions. The calculations were based on ab initio random structure searching and the quasiharmonic approximation (QHA). Here, we point out that, despite the inestimable value of such calculations at high-pressure and low-temperature conditions, the high-$P$ high-$T$ phase diagram proposed by Nelson et al. for ${\mathrm{CaF}}_2$ is not in qualitative agreement with the results of previous ab initio molecular-dynamics simulations, nor does it agree with the existing body of experimental data. Therefore, we conclude that the QHA-based approach employed by Nelson et al. cannot be applied reliably to the study of phase boundaries involving superionic phases. This conclusion is further corroborated by additional ab initio calculations performed in the superionic compounds ${\mathrm{SrF}}_2, {\mathrm{BaF}}_2, {\mathrm{Li}}_3\mathrm{OCl}$, and AgI.

Figure 1

High-$P$ high-$T$ phase diagrams proposed for ${\mathrm{CaF}}_2$. (a) Adapted from Ref. [1]; “S/I” stands for superionic phases, and the question mark indicates that the corresponding crystal structure has not been resolved experimentally; green dots and error bars correspond to DAC experiments [1]. (b) Adapted from Ref. [2]; the region colored in pink with the S/I label indicates that the cubic $Fm\overline{3}m$ phase develops unstable phonons; the region colored in light blue with the S/I label indicates that the hexagonal $P\overline{6}2m$ phase develops unstable phonons.

Figure 2

Ionic mean-squared displacements calculated for ${\mathrm{CaF}}_2$ in the hexagonal $P\overline{6}2m$ phase at $P=20\left(1\right)$ GPa and $2500\le T\le 3000$ K. The slope of the curves at long simulation times are proportional to the diffusion coefficients of the ions. (a) The sublattice of ${\mathrm{Ca}}^{+2}$ ions becomes vibrationally unstable. (b) All the ions diffuse, hence the system is a liquid.

Figure 3

Vibrational phonon spectrum calculated in several archetypal superionic materials. (a) ${\mathrm{SrF}}_2$ considering the volume at which it becomes superionic at $P=0$ in our AIMD simulations. (b) ${\mathrm{BaF}}_2$ considering the volume at which it becomes superionic at $P=0$ in our AIMD simulations. (c) Stoichiometric ${\mathrm{Li}}_3\mathrm{OCl}$ considering a volume at which imaginary phonon frequencies appear. (d) AgI considering the volume at which it becomes superionic at $P=0$ in our AIMD simulations.