Study of grain boundary polarization by two-probe and four-probe impedance spectroscopy
Four-probe impedance spectra of polycrystalline cation conductors: NASICON, Na β-alumina and Ag β-alumina, were measured in the frequency range from 10 Hz to 100 kHz with the aid of high sensitivity, high input impedance preamplifiers. Dispersion associated with the grain boundary polarization was observed below room temperature. The frequency dependent part of the conductivity of grain interiors was seen in the four-probe spectra below 200 K. Two-probe impedance spectra were measured for samples with platinum electrodes over the frequency range 0.01 Hz to 10 MHz. The spectra were analyzed by nonlinear least-squares fitting of equivalent circuits. The circuit composed of two sections connected in series: (i) resistance R g parallel to constant phase element P gi , (ii) parallel combination of resistance R gb , constant phase element P gb and capacitance C gb , was found to be a good model of the dispersion seen in the four-probe spectra and was also part of the circuit used to simulate the two-probe spectra. The results obtained by the two-probe and four-probe methods for the resistance of grains, R gi , and total resistance, R t =R gi +R gh , are compared. The advantages and limitations of the two methods are discussed.