Mechanism of Polaronic Conduction in Olivine Phosphates: An Influence of Crystallite Size

We report the polaronic conduction mechanism in transition-metal phosphate with different crystallite sizes by performing broadband ac conductivity measurements. The conductivity spectra exhibited a frequency-independent dc conductivity at low frequencies, and the conductivity becomes frequency-dependent above the characteristic frequency. The temperature dependent dc conductivity has been analyzed within the framework of Mott's model of polaronic conduction, which exhibits nonArrhenius behavior within the hopping conduction region. The apparent non-Arrhenius behavior is divided into three different regions depending on the type of lattice phonons associated with the bound charge carrier. Interestingly, at high temperatures, the dc conductivity is primarily determined by the polaron concentration, and it varies with temperature. To ascertain the temperature dependent polaron concentration variation at high temperatures, the frequency-dependent conductivity spectra have been analyzed by scaling procedure individually on three distinct regions. The application of the Summerfield scaling law on the ac conductivity spectra at low-and intermediate-temperature regions follows the time-temperature superposition principle (TTSP). On the other hand, at high temperatures, the scaling of the ac conductivity spectra with the Summerfield scaling law was found to exhibit pronounced deviations. The scaling of the ac conductivity spectra at high temperatures was improved significantly using the random barrier model. We suggest that at high temperatures, the number density of polarons performing a long-range hopping process becomes a temperature-dependent quantity and increases with temperature.