  In recent papers convincing evidence has been presented for chemical
stratification in Ap star atmospheres, and surface abundance maps have been
shown to correlate with the magnetic field direction. Radiatively driven
diffusion in magnetic fields is among the processes responsible for these
inhomogeneities. Here we explore the hypothesis that equilibrium
stratifications can, in a number of cases, explain the observed abundance maps
and vertical distributions of the various elements. The investigation of
equilibrium stratifications in stellar atmospheres with temperatures from 8500K
to 12000K and fields up to 10 kG reveals considerable variations in the
vertical distribution of the 5 elements studied (Mg, Si, Ca, Ti, Fe), often
with zones of large over- or under-abundances and with indications of other
competing processes (such as mass loss). Horizontal magnetic fields can be very
efficient in helping the accumulation of elements in higher layers. A
comparison between our calculations and the vertical abundance profiles and
surface maps derived by magnetic Doppler imaging reveals that equilibrium
stratifications are in a number of cases consistent with the main trends
inferred from observed spectra. However, it is not clear whether such
equilibrium solutions will ever be reached during the evolution of an Ap star.
