At the simplest level of SCPH theory (SC1), corresponding to the first-order expansion of the anharmonic free energy, the fourth-order force constants are included in the self-consistent determination of phonon frequencies . The resulting anharmonic phonon dispersion for cubic ZrO 2 clearly shows that the material is now predicted to be dynamically stable with no imaginary phonon modes (Fig. ). However, it is also noted that the phase is predicted to remain stable at significantly lower temperatures than observed experimentally. This is a result of only including fourth-order force constants, which can lead to an overstabilisation of soft modes .