Microscopic mechanism of stability in yttria-doped zirconia

The relaxed configurations of yttria-stabilised zirconia (YSZ) between $3$ and $10$ mol. $\%$ Y$_2$O$_3$ were modeled within the pseudopotential technique. In the displacive limit of the double-well potential model, the vibration mode corresponding to the soft phonon in pure $c$-ZrO$_{2}$ has been calculated for each Y$_2$O$_3$ composition. These anharmonic vibrations, associated with stabilization of YSZ, have been investigated within the self-consistent phonon approximation that makes obtainable the fine structure in spectral density. In studying the phonon dynamics, we propose to use the displacement probability density which can quantify very accurately the transition temperature needed to stabilize the YSZ cubic phase.