Impedance spectroscopy of brushite composites and a scaling approach to the dispersion behavior of inhomogeneous ionic conductors

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Abstract
The conductivity of composites prepared from ceramics is studied. The conductivity has an ionic character and the complex impedance behaves similar to many other inhomogeneous ionic systems. The dependence on the frequency is nonanalytical in form and can be described with some exponents that appear to depend on the concentration. We develop a Monte Carlo algorithm and perform a comprehensive computer simulation of the system. A network analysis reproduces the behavior of the complex impedance so that we can connect experimentally measured quantities to the internal structure of the system. Our theory predicts the values of the exponents and gives their dependence on the structure of a particular system. The most important parameter is the width of the distribution of the local conductivities. When the width increases, the exponents describing the frequency behavior reach universal values that are independent of the particular features of the system. The developed theory can be applied to understand impedance spectroscopy data for various inhomogeneous ionic conductors and some electronic conductors as well.