Is the normal to superionic transformation occurring in type-II fast-ion conductors a real thermodynamic phase transition?

Fedorov has written a Comment on our recent paper J. Phys. Chem. C 112, 1267 (2018) in which he suggests that the transformation from a normal ($\alpha$) to a superionic ($\beta$) state occurring in type-II fast-ion conductors (e.g., CaF$_{2}$ and Li-based superionic materials) cannot be regarded as a phase transition in a rigorous thermodynamic sense. Fedorov's arguments for such a criticism can be summarized as follows: (1) the available heat capacity data for the $\alpha \to \beta$ transformation do not reproduce the expected behaviour for a thermodynamic phase transition, (2) there is not evidence for molar volume discontinuity during the superionic $\alpha \to \beta$ transformation, and (3) the $\alpha \to \beta$ transformation is symmetry preserving. Here, we demonstrate either by reproducing experimental data published by other authors or by explaining some simple solid-state arguments that the statements put forward by Fedorov are incorrect and do not correspond to reality. In fact, based on mounting experimental evidence, the normal to superionic phase transformation occurring in type-II fast-ion conductors can be rigorously considered, and should be referred to, as a phase transition. Notwithstanding, it remains less obvious to establish with generality which is the order of the $\alpha \to \beta$ phase transition.