The extraction of hopping frequencies of mobile fluorine ions in the superionic conductor Ba0.5La0.5F2.5 from electrical modulus spectroscopy data

Abstract

The spectra of the complex electrical modulus M*(ν) = M ^/+iM ^// for a single crystal of the superionic conductor Ba_0.5La_0.5F_2.5 with a fluorite-type structure (sp. gr. $\mathrm{Fm}\overline{3}m$) were studied in the frequency range of 10⁻¹–10⁷ Hz at temperatures of 210–407 K. The diagrams of the complex modulus M ^/(ν), M ^//(ν) take the Cole-Cole form and are characterized by the presence of a distribution of relaxation times of mobile ion carriers. On the frequency dependences of the imaginary part of the complex modulus M ^//(ν), the relaxation peaks are observed, caused by hopping rates of mobile interstitial fluorine ions (charge carriers). Based on the temperature change in the position of relaxation maxima, calculations were made of the activation enthalpy ΔH_h and the average frequency ν_h of carrier jumps. The calculated values of ΔH_h and ν_h are in satisfactory agreement with the results obtained by the Almond-West method for this crystal. Within the framework of the crystallophysical model, the carrier mobility μ_mob and mobile ion concentration n_mob were calculated. Research using the method of modular spectroscopy is of undoubted interest for the further search and creation of fluorine-conducting solid electrolytes.