Electrical conductivity in ternary systems

The ideal behavior in the case of electric conductivity is not defined physically, as we deal with scalar quantities, for which the total derivative does not exist and the simple additivity rule may thus not be used. However, the electrical conductivity is thermally activated and the additivity of activation energies of pure components is enabled. Based on this idea the additivity of logarithms of the electrical conductivity may be accepted as the ideal behavior. It should be, however, emphasized that there are two kinds of electrical conductivities, i.e. the conductivity, k, and the molar conductivity, X. The concept of the additivity of logarithms is recommended to apply to the molar conductivity, as the concentration course of the molar conductivity is smoothed by multiplying the conductivity with the molar volume. The ideal course of the electrical conductivity in the ternary system can be then expressed in the form 

For the excess electrical conductivity of the real ternary system, the validity of the general Redlich-Kister s type equation can be proposed. For the description of the composition dependence of electrical conductivity in the ternary system, the following equation could then be used 

The first term represents the ideal behavior, the second one the binary interactions, and the third term the interactions of all the three components. 

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