Lattice dynamics in Ba_xSr_1-xTiO₃ single crystals: A Raman study

The lattice dynamical properties of Ba_xSr_1-xTiO ₃ single crystals with x=0.05, 0.1, 0.2, 0.35, and 0.5 have been studied by Raman spectroscopy in the temperature range 5-300 K. We present the data on the composition and temperature dependence of the phonon modes in Ba_xSr_1-xTiO₃, in particular, the soft modes. At low temperatures, the well-defined E and A₁ soft modes have been observed in the crystals of all compositions studied. For low Ba content (x<0.2) the soft modes extrapolate to zero and remain underdamped in the entire temperature range, indicating the displacive type of the ferroelectric phase transition. For x≳0.2, i.e., in the composition range of the Ba _xSr_1-xTiO₃ phase diagram where three ferroelectric phases exist, the soft modes exhibit less softening and become heavily damped in the temperature range corresponding to the orthorhombic and tetragonal phases. This demonstrates that the order-disorder-type behavior becomes stronger with increasing Ba content. However, no first-order Raman scattering in the cubic phase was observed in Ba_xSr _1-xTiO₃ of compositions studied, in contrast to pure BaTiO₃. The temperature behavior of the A₁ soft mode indicates that the ferroelectric phase transition is of the first order in Ba_xSr_1-xTiO₃ with x≳0.2, and turns into the second order for smaller Ba concentrations.