Brillouin spectroscopy of incommensurateBa2NaNb5

Abstract

We have performed Brillouin studies of acoustic-phonon behavior in barium sodium niobate above and below its phase transition at To --105 K. Anomalies in sound velocity and attenuation are observed for the sound waves corresponding to the Cll and C22 elastic coefficients. Above To the sound-ve1ocity anomalies display lambda-shaped dips af algebraic form V~~( T) = V~(oo ) -P/(T -Tc), with Tc several degrees lower than the actual transition temperature To, this is the form expected for free energies dominated by linear coupling between strain and the order parameter. Below To, V~&(T)= V&(00) P'/(T-, ' -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-ghalatnikov approach, we are able to extract a single relaxation time and find that this time~satisfies the expected mean-field dependence

Brillouin scattering, DSC, dielectric and X-ray diffraction studies of phase transitions in antiferroelectric PbHfO3:Sn

“…Fig. 10 shows that 1/s is approximately a linear function of temperature, that is, the relaxation time of the LA mode exhibits a critical slowing down, which can be fitted using the formula [35,36]:…”

Anomalous behavior of acoustic phonon and central peak in Pb[(In1/2Nb1/2)0.65Ti0.35]O3 single crystal

“…The softening of LA mode below T B can be likely attributed to the strain fluctuations associated with PNRs since the polarization fluctuations of PNRs can couple to the strain through ⌬x jj = ͑Q 11 +2Q 12 ͒P s 2 , where Q 11 and Q 12 are the electrostrictive coefficients and P s is the local polarization ͑͗P s ͘ = 0, while ͗P s 2 ͘ 0͒. The relaxation time of the strain fluctuations can be calculated from LA phonon mode assuming the Debye relaxation process for the complex elastic stiffness coefficient ͑c͒ as [23][24][25] …”

High-resolution temperature-dependent Brillouin scattering studies of ferroelectricK3Nb3O6(BMączka1, Hanuza2, Kojima3 2008Phys. Rev. B

“…However, linear dependence of 1 / as a function of temperature is predicted by the Landau theory near the ferroelectric phase transitions. 37 Such behavior is known as a "critical slowing down" where 1 / can be described by formula 38,39 Figure 7 shows, therefore, that at low temperatures, the main contribution to the observed temperature dependence of FWHM of the EЉ-symmetry CP is due to the fluctuations of the polarization and a very clear critical slowing down is observed near T 4 . When temperature increases, contribution from the pseudospin-density fluctuations increases and therefore the critical slowing down is less clearly observed at T 3 .…”