Fractal theory for the temperature dependence of the constant-phase element of solid electrolytes

The temperature dependence of the constant-phase element (CPE) is described in terms of fractal representations of grain boundaries of a polycrystalli ne electrolyte, both inside it and at the electrode-sample interface. The s imple expression alpha(i) = d(i) is used to relate the fractal dimensionali ty d(i) of the boundary to CPE alpha(i) of the ith crystallite. CPE of a sa mple comprising a large number of crystallites is determined by averaging a lpha(i) from the density of distribution of fractal dimensionalities n(d(i) ) of boundaries of individual crystallites (normal distribution). Selecting , as an example, beta = beta(0)T(-1)exp(-Delta b x 1000/T) as a parameter o f the normal distribution beta(T) allows one to make comparisons with the e xperiment using two parameters, beta(0) and Delta b. To determine beta(T), beta is also represented through the diffusion coefficient, capacitance, re sistance, and average area of boundaries of crystallites.