Lattice dynamics inBaxSr1−xTiO3single crystals: A Raman study

Abstract

The lattice dynamical properties of ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{TiO}}_{3}$ 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 $5--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}.$ We present the data on the composition and temperature dependence of the phonon modes in ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{TiO}}_{3}$, in particular, the soft modes. At low temperatures, the well-defined $E$ and ${A}_{1}$ soft modes have been observed in the crystals of all compositions studied. For low $\mathrm{Ba}$ 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 $x\ensuremath{\gtrsim}0.2$, i.e., in the composition range of the ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{TiO}}_{3}$ 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 $\mathrm{Ba}$ content. However, no first-order Raman scattering in the cubic phase was observed in ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{TiO}}_{3}$ of compositions studied, in contrast to pure ${\mathrm{BaTiO}}_{3}$. The temperature behavior of the ${A}_{1}$ soft mode indicates that the ferroelectric phase transition is of the first order in ${\mathrm{Ba}}_{x}{\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{TiO}}_{3}$ with $x\ensuremath{\gtrsim}0.2$, and turns into the second order for smaller $\mathrm{Ba}$ concentrations.