  We present a class of models that describe self diffusion on several fcc(001)
metal substrates within a common framework. The models are found to apply well
for Cu(001), Ag(001), Au(001), Ni(001) and Pd(001).For each of these metals the
models can be used to estimate the activation energy of any diffusion process
using a few basic parameters which may be obtained from experiments, ab-initio
or semi-empirical calculations. To demonstrate the approach, the parameters of
the models are optimized to describe self-diffusion on the (001) surface, by
comparing the energy barriers to a full set of barriers obtained from
semi-empirical potentials via the embedded atom method (EAM). It is found that
these models with at most four parameters,provide a good description of the
full landscape of hopping energy barriers on FCC(001) surfaces. The main
features of the diffusion processes revealed by EAM calculations are
quantitatively reproducible by the models.
