Reply to comments by Almond and West on Na β-alumina immittance data analysis

Abstract

We begin by summarizing the background of the present controversy. Because the Almond/West data on Na β-alumina are the only published small-signal ac results for the low temperature range from 83 K to 151 K, they are particularly important and deserve careful and full analysis. We first discuss the data themselves, pointing out certain deficiences in them, and then compare the somewhat subjective analysis methods employed by Almond and West with the more objective ones we have used. Next, we discuss appropriate fitting models and show that the model used by Almond and West is equivalent to one long used in the ionic conductor field. We then examine the analysis and interpretation of fitting results in some detail. The main original contribution of Almond and West in this area is their complete identification of a parameter ω p appearing in their fitting model with the average thermally activated hopping frequency, ν H. Our detailed examination of this assumption indicates that there is, so far, no strong theoretical basis for it and no fully trustworthy experimental evidence for it either. We have re-analyzed the data for all nine temperatures between 83 K and 151 K by complex nonlinear least squares fitting and find that better fits than we earlier obtained for the three highest temperatures are possible, giving results in this range much closer to the earlier ones of Almond and West. Nevertheless, thermal activation plots still exhibit strong, well defined breaks and discontinuities between 102 K and 110 K, possible evidence for a glass-like transition in this material. Finally, for comparison with future measurements and results for Na β-alumina in the low temperature regime, we have tabulated all our fitting estimates.