1. Dielectric properties of BT-LMT mixed ceramics Povilas Keburis1, Juras Banys1, Algirdas Brilingas1, Jonas Grigas1, Andrei Salak2, and Victor M. Ferreira3 1Department of Radiophysics, Vilnius University, Lithuania 2Department of Ceramics and Glass Engineering/CICECO, University of Aveiro, Portugal 3Department of Civil Engineering/CICECO, University of Aveiro, Aveiro, Portugal

2. BT-LMT (1-x)BaTiO3-x La(Mg1/2Ti1/2O3) BT ferroelectric,
LMT non-ferroelectric,
Homo- and heterovalent substitutions suppress FE PT in BT and induce relaxor behavior.
The continuous crossover from FE to relaxor behavior.
X = 2.5% of LMT: ferroelectric & relaxor features.
Lead free perovskites for microwave applications.
A.N.Salak, M.P.Seabra, V.M.Ferreira, J.Am.Ceram.Soc. 87, 216 (2004)
A.N.Salak, M.P.Seabra, V.M.Ferreira et al. J.Phys.D: Appl. Phys. 37, 914 (2004)
A.N.Salak, V.V.Shvartsman, M.P.Seabra, A.L.Kholkin, V.M.Ferreira, J.Phys.:Condens. Matter 16, 2785 (2004).

3. Relaxation times distribution
The aim?
Relaxation times distribution
of polar
(nano)clusters.

4. Comparison of the temperature dependences of the real part of dielectric permittivity of homogenous and non-homogenous ceramics 2.5%LMT-BT

5. Temperature dependence of the real and imaginary parts of dielectric permittivity at different frequencies of 2.5%LMT – BT (homogenous).

6. Frequency dependence of the real and imaginary parts of permittivity of 2.5%LMT – BT (homogenous).

7. Frequency dependence of the real and imaginary parts of permittivity measured in different temperatures fitted with Debye

8. Real distribution of relaxation times
The original program performs the direct calculation of relaxation times distribution function g() from the frequency dependence of the complex dielectric permittivity at fixed temperatures according to superposition of the Debye‑like processes:
.    (1)
The basic integral transformations (1) can be presented as the following linear matrix equation:
AX = T, (2)
matrix A components are obtained by proper discretization of the integral transformation kernels, vectors T and X components correspond discretized values of the permittivity and distribution of relaxation times, respectively. Equation (3) is the ill-posed problem, and cannot be solved straightforwardly. It is replaced by the following minimization problem:
 = ||T ‑ AX || +  ||RX||, (3)
 is the regularization parameter, R is the regularization matrix, which corresponds to the second g"() derivative. This constrained regularized minimization problem is solved by least squares technique.

9. Distribution of the relaxation times of BT – 2.5%LMT (homogenous)

10. Temperature dependence of the real and imaginary parts of permittivity at of BT – 2.5%LMT (non-homogenous).

11. Frequency dependence of the real and imaginary parts of dielectric permittivity. Lines are the best fits with the obtained distribution of the relaxation times

12. . Distribution of the relaxation times of 2.5%LMT – BT (non-homogenous)

13. C o n c l u s i o n s
1. BT – 2.5%LMT ceramics exhibit both ferroelectric & relaxor behavior Dynamics of polar nanoclusters cause dielectric dispersion and losses in wide frequency range below the phonon frequencies.

14. Thanks for your attention

15. Students of Vilnius University