  We recently proposed a high-pressure and high-temperature P-62m-symmetry
polymorph for CaF2 on the basis of ab-initio random structure searching and
density-functional theory calculations [Phys. Rev. B 95, 054118 (2017)]. We
revisit this polymorph using both ab-initio and classical molecular dynamics
simulations. The structure undergoes a phase transition to a superionic phase
in which calcium ions lie on a bcc-symmetry lattice (space group Im-3m), a
phase not previously discussed for the group-II difluorides. We demonstrate
that modelling this phase transition is surprisingly difficult, and requires
very large simulation cells (at least 864 atoms) in order to observe correct
qualitative and quantitative behaviour. The prediction of superionic behaviour
in P-62m-CaF2 was originally made through the observation of a lattice
instability at the harmonic level in DFT calculations. Using superionic
alpha-CaF2, CeO2, beta-PbF2 and Li2O as examples, we examine the potential of
using phonons as a means to search for superionic materials, and propose that
this offers an affordable way to do so.
