The phase diagram of Sr$_{1-x}$Eu$_{x}$TiO$_{3}$: Crossover from displacive to order-disorder dynamics

The phase diagram of Sr$_{1-x}$Eu$_{x}$TiO$_{3}$ is determined experimentally by EPR and resistivity measurements and analyzed theoretically in terms of the self-consistent phonon approximation (SPA) as a function of x (0.0 $\le $ x $\le $ 1.0). It is observed that the oxygen octahedral tilting instability temperature T$_{S}$ increases nonlinearly with x. The theoretical analysis demonstrates that a crossover from displacive to order-disorder dynamics takes place for x$\ge $0.25, signaled by a change in the local double-well potential and the soft mode temperature dependence.