Resistivity anomaly during the process of separation of phases of a binary alloy

It is well known that when one follows, isothermally, the process of separation of phases of certain binary alloys using electrical-resistivity measurements, an anomalous behavior is observed. The theoretical explanation of this anomaly has been controversial. Two aspects of that theory are discussed that have not received enough attention in the literature. The first is the real effect that an exponential damping term produces on the resistivity anomaly when the mean free path is not a free parameter but rather depends on the wave vector. This leads to an integral equation of the Volterra-type, the solution of which, by the iterative method of Newmann, exhibits rapid convergence when the time constant of the damping factor is associated with the internal mean free path of a Guinier--Preston zone. The second aspect concerns a possible reconciliation of the ideas of Rossiter and Hillel concerning a semiphenomenological model that reproduces well the clustering process. This model takes into account the effect of scattering by zones, separately, through the microstructure and through the boundaries, with a weight function that determines the centers by which the electron is scattered. The results obtained when this model is applied to the binary Al--Zn alloy are completely satisfactory.