The generalized Vogel-Fulcher-Tamman equation for describing the dynamics of relaxor ferroelectrics

Abstract

Relaxor ferroelectrics (RF) are outstanding materials owing to their extraordinary dielectric, electromechanical, and electro-optical properties. Although their massive applications, they remain to be one of the most puzzling solid-state materials because understanding their structural local order and relaxation dynamics is being a long-term challenge in materials science. The so-called Vogel-Fulcher-Tamman (VFT) relation has been extensively used to parameterize the relaxation dynamics in RF, although no microscopic description has been firmly established for such empirical relation. Here, we show that VFT equation is not always a proper approach for describing the dielectric relaxation in RF. Based on the Adam-Gibbs model and the Grüneisen temperature index, a more general equation to disentangle the relaxation kinetic is proposed. This approach allows to a new formulation for the configurational entropy leading to a local structural heterogeneity related order parameter for RF. A new pathway to disentangle relaxation phenomena in other relaxor ferroics could have opened.

High Entropy Oxide Relaxor Ferroelectrics

“…In relaxors, this dependence obeys an empirical Vogel–Fulcher relation: where f 0 is the limiting response frequency of the dipoles, f is the applied ac field frequency, E a is the activation energy, T f is the static freezing temperature, and k B is Boltzmann’s constant . A Vogel–Fulcher relationship with an extrapolated freezing temperature of around 565 K, as shown in Figure c, may indicate the relaxor ferroelectric behavior of Ba­(5 B )O films. , However, it is noted that the Vogel–Fulcher equation is not always a proper approach for describing the dielectric relaxation in relaxor ferroelectrics . The values of E a (∼0.16 eV) and f 0 (∼3.18 × 10 12 Hz) extracted from the fit are similar to those values obtained for Pb- and BTO-based relaxors …”

New paradigm for configurational entropy in glass-forming systems

“…( 13) has already been used for describing dynamics in glass-forming polyvinylidene difluoride (PVDF), PVDF + Barium-Strontium-Titanate (BST) microparticles composite, 58 and in its parallel form for describing relaxation time in relaxor ceramics. 59 Nevertheless, these tests cannot be considered as a crucial validation of Eq. (13) if recalling the above discussion.…”

Unravelling the mechanisms of adaptation to high pressure in proteins

“…5e and f) for the two proteins is remarkable: it follows the Arrhenius law (τ (T ) = τ 0 exp(E A /RT ), note the sign reversal compared to before, as τ = h/Γ) for Tba PMI, while it follows the Vogel-Fulcher-Tamman (VFT) law (τ (T ) = τ 0 exp DT 0 T −T 0 , where 1/D is the fragility index, not to be confused with the aforementioned pseudo-diffusion coefficient D pseudo , and T 0 is the Vogel temperature) for Tko PMI. The latter is typical of glass-forming systems [40][41][42][43][44][45] , but it has also been observed in proteins and interpreted as the signature of protein-water coupled dynamics [46][47][48][49] . An Arrhenius behaviour arises from activated processes, and it is expected for jump-diffusion, while a VFT behaviour is usually connected with cooperative processes.…”