Nonlinear impedance of vanadate glass-ceramics containing BaTiO3

The nonlinear impedance of vanadate glasses doped with BaTiO3 was measured. Samples of the composition of x[BaO,TiO2]–(80 − x)V2O5–20Bi2O3 where x = 5, 10 and 15 in mol% were prepared by a conventional melt quenching technique. The melting was performed in alumina crucibles at the temperature of 1273 K–1373 K. The melts were poured on a preheated (573 K) brass plate and pressed by another plate to obtain flat circular pellets of 1–2 mm thickness and 10–20 mm in diameter. A subset of as-quenched samples was heat treated in air at the temperature of 633 K (close to the crystallization temperature) for 6 h and cooled with the furnace. For the electrical measurements gold electrodes were evaporated at the preheated samples. Nonlinear Impedance measurements were carried out in the frequency range from 1 mHz to 1 MHz and the temperature range from 153 K to 423 K, with the ac voltage of 1 Vrms with Concept 40 broadband dielectric spectrometer. The higher harmonic components (harmonic 0, harmonic1 and harmonic2) were measured up to frequency of 1000 Hz. Here the impedance for harmonic components was defined as the ratio of the voltage base wave to the n-th harmonic current component: Zn∗= U0∗/In∗, where Zn⁎ including the base wave generally depend on the sample voltage U1⁎ base wave amplitude. From Zn⁎ allother independent variables are calculated. The dependence of current density on the cosinusoidal electric field E(t)= E0cos(ωt) leads to the following expression:j´ = σ´0hE0 cos (ωt) + σ´1hE0 cos (2ωt) + σ´2hE0 cos (3ωt) + …Where σ´0h denotes base conductivity, while σ´1h, σ´2h etc. are higher harmonics conductivity. The admittivity for harmonic components with n ≥1, is calculated from relation σ⁎n = i2πfε0ε⁎n.