Dynamic Central Modes and Photorefractive Effects at TI and TC in Barium Sodium Niobate

Barium sodium niobate (Ba2NaNb5O15) is a tungsten bronze structure that exhibits a complicated sequence of six structural phase transitions, including three incommensurate (IC) phases. The phases are unusual in that all but the highest temperature P4/mbm structure are ferroelectric. Unlike the situation for most incommensurate insulators, in which ferroelectricity develops at low temperatures along the modulation direction, the polarization direction in barium sodium niobate is orthogonal to the modulation(s), permitting some unusual phenomena. In the present study we analyse the thermal and dielectric behaviour at the Curie temperature TC near 830 K as well as that at the Ccm 21–IC(1q) transition near 543 K, the IC(1q)–IC(2q) transition near 565 K and the IC(2q)–P4bm transition at 582 K. The entropy change at 565 K is related to the wall roughening model of Rice et al (1981 Phys. Rev. B 24 2751). Data near TC = 830 K indicate close proximity to a tricritical point, and discussions of critical exponents are presented, all of which are found to be mean field. Because of Na vacancies, transition temperature variation is found among specimens Ba2Na1−xNb5O15 (830 K< TC(x)< 865 K), and the system appears to be describable by the disordered exclusion model as a slightly first-order intrinsic system whose dynamics are suppressed by weak disorder. Near TC the specific heat C(T) is compared with the random bond prediction of Harris (1974 J. Phys. C: Solid State Phys. 7 1671): C(T) = C0(T)/[1+bx2C0(T)], where C0(T) is the intrinsic specific heat of the vacancy-free crystal varying as (TC−T)−1/2 and x is the sodium vacancy concentration. In agreement with Harris’s model, the shifts in TC(x) are to lower T with increasing x and scale as x; the broadening scales as x2; and the effective critical exponent remains unchanged at α = 1/2.

Section: Introductionsupporting

confidence: 71%

High temperature phase transitions in barium sodium niobate: the wall roughening 1q–2qincommensurate transition and mean field tricritical behaviour in a disordered exclusion model

Scott

Hayward

Miyake

2005

“…Formal coupling models have been developed for central peak modes in other phases, such as CsH 2 AsO 4 , KH 2 AsO 4 and Ba 2 NaNb 5 O 16 , for example (Katiyar et al 1971, Oliver et al 1988. In LaAlO 3 a correlation between the central peak and additional elastic softening of all the elastic constants is also clear in the stability field of the low symmetry structure (Carpenter et al 2010).…”

Section: Discussionmentioning

confidence: 99%

Elastic and anelastic relaxations in the relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O₃: II. Strain–order parameter coupling and dynamic softening mechanisms

Carpenter

Bryson

Catalán

et al. 2011

Elastic and anelastic behaviour of single crystal and ceramic samples of Pb(Mg(1/3)Nb(2/3))O(3) has been investigated at frequencies of ~0.1-1.2 MHz through the temperature interval 10-800 K by resonant ultrasound spectroscopy (RUS). Comparison with data from the literature shows that softening of the shear modulus between the Burns temperature and the freezing interval is independent of frequency. The softening is attributed to coupling between acoustic modes and the relaxation mode(s) responsible for central peaks in Raman and neutron scattering spectra below the Burns temperature, and can be described with Vogel-Fulcher parameters. Shear elastic compliance and dielectric permittivity show similar patterns of temperature dependence through the freezing interval, demonstrating strong coupling between ferroelectric polarization and strain such that the response to applied stress is more or less the same as the response to an applied electric field, with a frequency dependence consistent with Vogel-Fulcher-like freezing in both cases. Differences in detail show, however, that shearing induces flipping between different twin orientations, in comparison with the influence of an electric field, which induces 180° flipping: the activation energy barrier for the former appears to be higher than for the latter. Below the freezing interval, the anelastic loss also has a similar pattern of evolution to the dielectric loss, signifying again that essentially the same mechanism is involved in the freezing process. Overall softening at low temperatures is attributed to the contributions of strain relaxations due to coupling with the local ferroelectric order parameter and of coupling between acoustic modes and continuing relaxational modes of the polar nanostructure. Dissipation is attributed to movement of boundaries between PNRs or between correlated clusters of PNRs. Overall, strain coupling is fundamental to the development of the characteristic strain, dielectric and elastic properties of relaxors.

“…This is a characteristic consequence of coupling with the central peak mode (e.g. Katiyar et al 1971, Oliver et al 1988. The broadening reaches a maximum for the TA peak at the same temperature as the central peak achieves maximum intensity and minimum width (figure 14(a)).…”

Section: Dynamic Central Peak and Acoustic Mode Couplingmentioning

confidence: 97%

Elastic relaxations associated with the Pm\bar 3 m –R\bar 3 c transition in LaAlO₃: II. Mechanisms of static and dynamical softening

Carpenter¹,

Sinogeikin²,

Bass³

2009

Brillouin spectra have been collected in situ at temperatures up to ∼1000 K for different crystallographic directions from two single crystal plates of LaAlO(3) perovskite. Elastic moduli derived from these, together with heat capacity, spontaneous strain and Raman data from the literature, have then been used to calibrate the coefficients in a classical Landau free energy expansion for the second order [Formula: see text] phase transition at T(c) = 817 K. The static strain/order parameter coupling model provides a quantitative description of elastic softening between room temperature and ∼700 K, but from ∼700 K up to T(c) additional elastic softening correlates with the development of a central peak in the Brillouin spectra. The presence of quasi-elastic scattering, which reaches maximum intensity ∼5-15 K below T(c), implies a strong dynamical component to the phase transition. Relaxation times estimated from the width of the central peak are of the order of ∼10-100 ps and appear to be more or less constant between ∼700 and 800 K, which is consistent with an intrinsic origin associated with phonon density fluctuations. Central peak width variations and an irregular pattern of acoustic velocity variations in a 20 K temperature interval below T(c) are interpreted in terms of flipping of clusters of tilted octahedra between different ⟨111⟩, ⟨011⟩ and ⟨001⟩ tilt axes. The additional softening beyond that expected from the classical strain/order parameter coupling model can be understood in terms of coupling of acoustic modes with the central peak mode(s).