  A number of cool white dwarfs with metal traces, of spectral types DAZ, DBZ,
and DZ have been found to exhibit infrared excess radiation due to
circumstellar dust. The origin of this dust is possibly a tidally disrupted
asteroid that formed a debris disk now supplying the matter accreting onto the
white dwarf. To reach any clear conclusions from the observed composition of
the white dwarf atmosphere to that of the circumstellar matter, we need a
detailed understanding of the accretion and diffusion process, in particular
the diffusion timescales. We aim to provide data for a wide range of white
dwarf parameters and all possible observed chemical elements. Starting from
atmosphere models, we calculate the structure of the outer envelopes, obtaining
the depth of the convection zone and the physical parameters at the lower
boundary. These parameters are used to calculate the diffusion velocities using
calculations of diffusion coefficients available in the literature. With a
simple example, we demonstrate that the observed element abundances are not
identical to the accreted abundances. Reliable conclusions are possible only if
we know or can assume that the star has reached a steady state between
accretion and diffusion. In this case, most element abundances differ only by
factors in the range 2-4 between atmospheric values and the circumstellar
matter. Knowing the diffusion timescales, we can also accurately relate the
accreted abundances to the observed ones. If accretion has stopped, or if the
rates vary by large amounts, we cannot determine the composition of the
accreted matter with any certainty.
