We use the density functional inspired model for alloying and lattice vibrations to study the relaxation of the intermetallic binary systems Ni - Al and Cu - Au. In one case the data set is made up of first-principles results for the intermetallics in their cubic form. In the other case the data set is mostly experimental. The parametrization is performed in the direct space and it resembles a parametrization for an Ising Hamiltonian, though with distance dependent pair interactions. In both cases three-body and many-body interactions were not needed, and the pair interactions did not go beyond the second-neighbour shell.