Brillouin spectroscopy of incommensurate Ba2NaNb5O15 at its 105-K phase transition.

Abstract

We have performed Brillouin studies of acoustic-phonon behavior in barium sodium niobate above and below its phase transition at ${T}_{0}$=105 K. Anomalies in sound velocity and attenuation are observed for the sound waves corresponding to the ${C}_{11}$ and ${C}_{22}$ elastic coefficients. Above ${T}_{0}$ the sound-velocity anomalies display lambda-shaped dips of algebraic form ${V}_{\mathrm{jj}}$(T) =${V}_{\mathrm{jj}}$(\ensuremath{\infty})-\ensuremath{\beta}/(T-${T}_{C}$), with ${T}_{C}$ several degrees lower than the actual transition temperature ${T}_{0}$; this is the form expected for free energies dominated by linear coupling between strain and the order parameter. Below ${T}_{0}$, ${V}_{\mathrm{jj}}$(T)=${V}_{\mathrm{jj}}$(\ensuremath{\infty})-\ensuremath{\beta}'/(${T}_{c}^{\mathcal{'}}$-T The attenuation displays an increase of approximately 100% as the transition temperature is approached from above or below. By combining sound-velocity and attenuation data through a Landau-Khalatnikov approach, we are able to extract a single relaxation time and find that this time \ensuremath{\tau} satisfies the expected mean-field dependence characteristic of critical slowing down: ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1}$(T)=${\ensuremath{\tau}}_{1}^{\mathrm{\ensuremath{-}}1}$(T-${T}_{C}$)/${T}_{C}$+${\ensuremath{\tau}}_{2}^{\mathrm{\ensuremath{-}}1}$.For ${C}_{11}$ we determine ${\ensuremath{\tau}}_{1}$=(2.0\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ s; ${\ensuremath{\tau}}_{2}$=(2.0\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$ s, and for ${C}_{22}$ we find ${\ensuremath{\tau}}_{1}$=(1.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ s and ${\ensuremath{\tau}}_{2}$=(8.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ s. These values may be compared with those at the upper transition (${T}_{I}$=573 K) of ${\ensuremath{\tau}}_{1}$=1.7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$ s and ${\ensuremath{\tau}}_{2}$=5.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ s from P. W. Young and J. F. Scott [Ferroelectrics 52, 35 (1983)]. The present data are compatible with Schneck's hypothesis that a second I-C phase exists in the range 12--105 K.