Brillouin spectroscopy of the incommensurate—commensurate phase transition in barium sodium niobate

Abstract

Small angle and large-angle Brillouin scattering have been used to measure the sound velocity and damping of longitudinal waves propagating along (C, and perpendicular to (C'J the incommensurate axis in Ba,NaNb,O,, . For each mode strong dispersion is observed, with relaxation time 2 m of order 1.3 x lo-" s near T. For C , , T (~ satisfies with 2nr, = (1.08 & 0.13) x lo-'' s;2zr1 = (8.5 + 0.7) x lo-" s; and thediffusivity D = 1.3 cm'/s. This approximately 65 times larger than the thermal diffusivity of entropy fluctuations and implies a dynamic "central mode" for right-angle geometry light scattering of -60GHz. This mode is ten times the width observed for phason (soliton) diffusion by Lyons et al. in BaMnF,; it is not directly observed in the present work. For LA sound waves perpendicular to the incommensurate axis r;i(T) = T ; ' + Dq';that is, T, and D are the same as for C , , but ro' is neligible. T,, is interpreted as due to amplitude mode-acoustic mode interaction; T, and D are interpreted as interaction of acoustic modes with mobile defects, presumably soliton-like kinks in the incommensurate structure. +This paper summarizes the

Anomalies of Brillouin Light Scattering in Selected Perovskite Relaxor Ferroelectric Crystals

“…F c = γSP 2 for electrostrictive coupling, where γ is the electrostrictive coefficient. The coupling between the strain and polarization affects both the static and dynamic parts of the complex elastic constant C , as given by [ 73 , 74 , 75 , 76 ]: C * (ω) = C ∞ − Δ C …”

“…For bilinear coupling, the elastic constant softens as /T − T c / −1 on both sides of the transition. For electrostrictive coupling, the elastic constant abruptly decreases to a lower value at T c [ 73 , 76 ]. Brillouin scattering measures the dynamic part of C according to Equation (11): C(ω) = ρV 2 (ω) where ρ is the bulk density of the crystal and V is the corresponding velocity of the acoustic phonon.…”

“…Therefore, a linear coupling between the polarization and strain should exist in the quasi-static region below T * [ 62 ]. Moreover, according to Young and Scott, Equation (12) applies to any form of coupling, such as bilinear or electrostrictive coupling and the coupling between the acoustic phonon mode and other excitations, which are altogether not connected with the order parameter [ 76 ]. This relaxation mechanism was used to describe the relaxation behavior of the acoustic phonon mode across commensurate–incommensurate phase transition in Ba 2 NaNb 5 O 15 where the exact form of the coupling was not known [ 76 , 77 ].…”

Quantum critical points in ferroelectric relaxors: Stuffed tungsten bronze K3Li2Ta5OSmith1, Gardner2, Morrison3 et al. 2018Phys. Rev. Materials3020View full textAdd to dashboardCite

“…Orthorhombic distortions can occur when the A1 site distorts from the perfect square channel, and in this case with K on the A1 site would explain the existence of orthorhombic distortions for higher K content. Within TTBs, it is not unprecedented to have orthorhombic distortion and expansions of the unit cells from P4/mbm (Z = 2) cell; other examples [52][53][54][55][56][57][58] include Ba2NaNb5O15 or Ba4La0.67Nb10O30. Ba2NaNb5O15 has five structural phase transitions as the temperature is lowered, some incommensurate, all of which are orthorhombic distortions in the ab-plane.…”

“…In TTBs it is not unprecedented to have orthorhombic distortion and expansions of the unit cells from the P 4/mbm (Z = 2) cell. Other examples [56][57][58][59][60][61][62] in the ab plane. From the analysis reported here, there is a high likelihood that at least one phase transition occurs in the region of 25-50 K. Variable temperature PXRD was used in an attempt to probe any possible changes in structures.…”