1. Study of Dielectric Properties of SBN Ceramics
J. Banys, J. Macutkevič, W. Kleeman, R.Grigalaitis, J. Grigas, A. Brilingas
Physics Department, University of Vilnius, Lithuania
Angewandte Physik, Univ. Duisburg, Germany

2. SBN (Sr0,61-xBa0,39Nb2O6: Co3O4 (0,002%)

3. Temperature dependence of the real and imaginary parts of dielectric permittivity of SBN at different frequencies.

4. Frequency dependence of the real and imaginary parts of dielectric permittivity of SBN at different temperatures.

5. Temperature dependence of the real and imaginary parts of dielectric permittivity of poled SBN with E = 2.5 kV/cm at different frequencies.

6. Frequency dependence of the real and imaginary parts of dielectric permittivity of poled SBN with E = 2.5 kV/cm at different temperatures.

7. Frequency dependence of the real and imaginary parts of dielectric permittivity of poled and unpoled samples of SBN.

8. The Havriliak-Negami equation
 – dielectric permittivity when ω →∞
 – the strength of relaxator
τ – the most probable relaxation time
 – the width of Havriliak-Negami distribution of relaxation time
– the asymmetry of Havriliak-Negami distribution
of relaxation time

9. Temperature dependence of the fit parameters: relaxation time , contribution to the static dielectric permittivity , relaxation time distribution parameter  from Cole - Cole equation and ,  from Havriliak - Negami equation.

10. The basic integral transformations can be presented as the following linear matrix equation: AX = T,
where the matrix A components are obtained by proper discretization of the integral transformation kernels, vectors T and X components correspond discretized values of the dielectric permittivity (as initial data) and distribution of relaxation times (as the result), respectively. Equation  is the ill-posed problem, and cannot be solved straightforwardly. It is replaced by the following minimization problem:
 = ||T - AX || +  ||RX||,
where  is the regularization parameter, and R is the regularization matrix, which corresponds to the second g"() derivative. The conditions about nonnegative spectrum g() components are added as the constraints. This constrained regularized minimization problem is solved by least squares technique making use the simplified version of contin program developed by Prowentcher  and later developed for dielectric spectra . [1]
[1] J. Macutkevic, J.Banys, A. Matulis Determination of distribution of relaxation times from dielectric spectra Nonlinear Analysis: Modeling and Control 9 (1) 2004: pp

11. Distribution of the relaxation times at different temperatures of unpoled SBN.

12. Distribution of the relaxation times at different temperatures of poled SBN.

13. Comparison of the distribution of the relaxation times at different temperatures of poled and unpoled samples of SBN

16. CONCLUSIONS
Static permittivity of Sr0,61-xBa0,39Nb2O6 with Co3O4 (0,002%) crystals is very high, the peak value reaches 30,000 at frequencies lower than 1 kHz.
The present results of this crystals show typical relaxor behaviour in a very wide frequency range, from low frequencies to microwaves, and the peaks of  and  move towards higher temperatures with increasing frequency.
The largest relaxation times of unpoled crystals diverge according to the activated dynamical scaling law with the freezing temperature T0  320 K .
The broadening of spectra indicate a strong increase in inter-cluster correlation. Also the size of polar nano regions increases on cooling