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Abstract
A model is developed which describes the conductivity of a mixture of touching particles of two or three different species as a function of the volume fractions of the species present. The approach is based on an effective-medium treatment, in which the contact resistance between particles is taken to be a variable. It is shown that if a linear distribution of contact resistances exists in the sample then the deviation from the normal effective-medium solution (or percolation theory) is fairly small. If, however, a higher density of high values of contact resistance between particles exists, then substantial deviations from the normal effective-medium solution may occur and are recognizable as the behaviour that is observed in many practical systems.
A simple model of the effect of unequal particle size between species is presented within the framework of effective-medium theory, and demonstrates semiquantitatively how the relative particle size between species affects the value of volume fraction at which the threshold for conduction occurs, and the value of resistivity for a given volume fraction.
The resistivity as a function of composition of a thick-film system of NiO/CoO is presented and the theoretical models are fitted as an example of their application.