In conclusion, we have shown that the cubic-totetragonal phase transition in zirconia upon cooling can be partly described within the framework of anharmonic phonon theory. Conventional SC1 theory based only on frequency renormalisation from fourth order force constants fails to describe an adequate softening of the phonon mode responsible for the transition. Inclusion of third order force constants through the bubble selfenergy results in a further mode softening and lead to a FIG. . Di↵usion in cubic zirconia from AIMD at 2500 K and entropic stabilisation from defect concentration a Displacements from equilibrium of four selected oxygen atoms as a function of time. The dashed line indicates the displacement that should occur along all three axes to enter the interstitial site, while the dotted line indicates the displacement at should occur along one direction to enter another oxygen site. b Di↵usion mechanism showing one oxygen entering an interstitial site immediately followed by another oxygen atom occupying its original position. A Frenkel defect pair is thus created, and an oxygen site is vacant allowing for easy ionic di↵usion. The schematic is inspired by ref. . c Entropic contribution from Frenkel defect pairs following a simple configurational model of Voronin given in Eq. 2. The interstitial concentration is given as the fraction of occupied interstitials.