Relaxor behavior in lead-free Ba(Ti_1−xSc_x/2Nb_x/2)O₃ ceramics

Abstract

Solid solutions of (1−x)BaTiO 3 -xBaSc 1/2 Nb 1/2 O 3 (BT-BSN) with x = 0.025, 0.05, 0.075, 0.1 and 0.125 were prepared by a high temperature solid-state reaction technique. The effects of the Ba(Sc 1/2 Nb 1/2 )O 3 addition on the phase composition, dielectric properties, as well as polarization-electric field (P-E) loops of the BT-BSN solid solution were investigated. The room-temperature X-ray diffraction analyses of all the ceramics revealed a perovskite phase after sintering at 1350 • C with a composition-dependent symmetry. Temperature and frequency dependence of the dielectric permittivity and losses have been explored: ceramics of compositions x ≤ 0.075 showed normal ferroelectric behavior, while ceramics with x ≥ 0.1 were of relaxor type. The degree of diffuseness and the relaxor effect increase while the transition temperature (T C or T m ) decreases when both scandium and niobium are introduced in the BaTiO 3 lattice. Ceramics of composition x = 0.125 exhibited interesting relaxor characteristics at 10 kHz: T m = 20 K, ε r = 12,000, and T m = 140 K. In addition, modeled using Vogel-Fülcher relation, this same composition showed the fitting parameters: E a = 0.0503 eV, f 0 = 1.129 × 10 14 Hz and T VF = 166.85 K.

Relationship between Crystal Structures and the Relaxor Property of SrBi2(Ta2–xVx)O9 Ceramics

“…The γ values for normal-type ferroelectrics and ideal relaxor-type ferroelectrics are 1 and 2, respectively. 39,40 Figure 8 represents the plot of log(1/ε′ – 1/ε m ) vs log( T – T m ) for SBTV ceramics measured at 1 MHz. A linear relationship was observed in the SBTV ceramics, and the slopes of the fitting curves determined the γ value.…”

Microstructures and physical properties of sol–gel derived Ba2FeMnO6 double perovskite

“…To quantitatively understand the above relaxor‐like dielectric behavior, we utilized a modified Curie–Weiss law to fit the dielectric data, which is expressed by the following equation 53 : $$$$\begin{equation}\frac{1}{{{\varepsilon _{\rm{r}}}}} - {\rm{\;}}\frac{1}{{{\varepsilon _{\rm{m}}}}} = \frac{{{{\left( {T - {T_{\rm{m}}}} \right)}^\gamma }}}{C}\end{equation}$$$$where ε m is the peak value of ε r at T m , C denotes the Curie–Weiss constant, and γ is the diffuseness exponent that lies in a range of 1.0–2.0 54 . The γ values obtained by a linear fitting the plots of Ln(1/ ε r − 1/ ε m ) versus Ln( T − T m ) for the BFMO samples measured at different frequencies (see Figure S3a–e), lie in the range of 1.42–1.63, indicating that the phase transition undergone in the BFMO system is neither a complete diffuse phase transition nor a classical ferroelectric phase transition, but a mixed type between them.…”

“…where ε m is the peak value of ε r at T m , C denotes the Curie-Weiss constant, and γ is the diffuseness exponent that lies in a range of 1.0-2.0. 54 The γ values obtained by a linear fitting the plots of Ln(1/ε r − 1/ε m ) versus Ln(T − T m ) for the BFMO samples measured at different frequencies (see Figure S3a-e), lie in the range of 1.42-1.63, indicating that the phase transition undergone in the BFMO system is neither a complete diffuse phase transition nor a classical ferroelectric phase transition, but a mixed type between them. To determine the activation energy (E a ) involved in the dielectric relaxation process of the BFMO ceramics, the temperature dependence of the angular frequency (ω m ) is fitted by the Arrhenius law 55 :…”

Efecto del BiFeO₃ en las propiedades del sistema ferroeléctrico libre de plomo K_0.5Na_0.5NbO₃

“…Las investigaciones realizadas sobre el fenómeno relaxor, han dado origen a diversas interpretaciones físicas y/o estructurales. El comportamiento puede ser explicado con base en las fluctuaciones composicionales y/o aleatoriedad en los campos eléctricos locales y transiciones de fase inducidas por tensiones, debido a la distribución aleatoria de los iones que ocupan el sitio B dentro de la estructura [40]. Uchino y colaboradores propusieron una ley de Curie-Weiss modificada (también llamada función de Uchino-Nourma) para estimar el grado del relaxor y está definida por la siguiente ecuación [41]: (9) En la expresión anterior C es la constante de Curie y γ es el coeficiente que mide el carácter difuso; γ=1 y 2, representan un sistema ferroeléctrico normal y un sistema ferroeléctrico-relaxor ideal, respectivamente.…”