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

Cazorla et al. (preceding Comment) criticize our recent results on the high-$PT$ phase diagram of ${\mathrm{CaF}}_2$ [Phys. Rev. B 95, 054118 (2017)]. According to our analysis, Cazorla et al. have not converged their calculations with respect to simulation cell size, undermining the Comment's conclusions about both the high-$T$ behavior of the $P\overline{6}2m-{\mathrm{CaF}}_2$ polymorph, and the use of the QHA in our work. As such, we take this opportunity to emphasize the importance of correctly converging molecular-dynamics simulations to avoid finite-size errors. We compare our quasiharmonic phase diagram for ${\mathrm{CaF}}_2$ with currently available experimental data, and we find it to be entirely consistent and in qualitative agreement with such data. Our prediction of a superionic phase transition in $P\overline{6}2m-{\mathrm{CaF}}_2$ (made on the basis of the QHA) is shown to be accurate, and we argue that simple descriptors, such as phonon frequencies, can offer valuable insight and predictive power concerning superionic behavior.

Figure 1

Pressure-temperature phase diagrams for ${\mathrm{CaF}}_2$. Blue lines are the QHA results of our work [1], points with error bars are from [5], and green lines are from [6]. The green asterisk marks a possible triple point according to Ref. [6]. The light-gray band running diagonally up and to the right is where $d^2\alpha /d{T}^2$ changes sign in the QHA, and pertains to its validity, as discussed in Sec. 3.

Figure 2

Mean-squared displacement of F and Ca ions in $P\overline{6}2m-{\mathrm{CaF}}_2$ in our 216-atom AIMD-$NVT$ simulation at $T=2500$ K. The pressure is $20.0\pm 1.0$ GPa.

Figure 3

Mean-squared displacement of F and Ca ions in $P\overline{6}2m-{\mathrm{CaF}}_2$ in our 864-atom AIMD-$NVT$ simulations at $T=2500$ and 3000 K. The pressure is $P=19.9\pm 0.4$ GPa at both temperatures. These are to be compared directly to Fig. 2 of the Comment [5]. Note that, in clear contrast to the claims made in [5], there is no unphysical diffusion of Ca ions at either temperature, and the system is not in a melt state at 3000 K. The high diffusion of F ions at 3000 K is indicative of a superionic state.