How to predict diffusion behaviours in a metallic platings-substrate system?

I want to qualify electroplatings (Ag or Sn for instance) on a Cu substrate. (Ni underplated barrier present or not). Furthermore I want
to have an in-depth look at the ways of characterizing platings regarding solid-solid diffusion properties. In a first approach, I distinguish two problems at least.
For the case of two semi-infinite media in a planar configuration, the following formula well applies
thickness of the "diffusion affected area"=squareroot(diffusionconstant*time)
Temperature enters through the diffusion constant which obeys an Arrhenius law. This provides the basis for a time-temperature correlation. Possibility for this prediction relies on the knowledge of the two constants involved in the Arrhenius law: the pre-exponential factor and the activation energy. Either one trusts values in the tables, if available, or one performs measurements. If one does the latter, one can let the samples in the furnace (inert atmosphere), with different temperatures and/or different times of exposure and then determine the concentration profiles by using a profilometric technique: SIMS or GDS, for what I know. Then, two situations have to be distinguished.
1- The elements are not miscible in every proportion
According (more or less!) to the phase diagram, some new layers are grown. The thickness predicted by the above fundamental formula is the overall thickness of these new layers. In the connector industry, it is this way the growth of intermetallic compounds is mitigated to reasonable low thickness by choosing the mating surfaces according to their diffusion constants and the required "mean" operating temperature during the timelife.
2- The elements are miscible in every proportion (e.g. Cu-Ni)
The concentrations of the elements are continuous functions of the distances from the interfaces. Here it is much more tricky. Indeed, experimental curves are noisy or do not look like a "beautiful" theoretical one obtained with simple assumptions. Then fitting them is not straightforward. This is a first problem.
A second problem, and the most critical in my opinion, is the following: with the case of layers a few microns thick or less on a substrate, the physics is more intrigate than with two semi-infinite bodies. However predicting the behaviour during the lifetime of the system requires formulas as well as an experimental measurement of the diffusion constants! (Even likely less simple than the fundamental one quoted above!). One faces the first problem also!...
Does someone know guidelines to use diffusion-accelerating assesments and to exploit them for predicting the behaviour during the lifetime of a system of a plated metallic substrate? Or may be a simple-minded approach, that is a rough criterion, putting aside any theoretical considerations?
NB: I am aware that diffusion is not the only phenomenom involved in the aging of platings. It is on purpose I put aside corrosion problems on the surface. Diffusion considerations are intended to ensure that the material chosen from corrosion considerations to be on the surface will not be replaced by an other one.
******************************************** Dr Pierre LAURAT Project Manager - Materials Sciences *********************************************
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