  We present spectroscopic observations of a large sample of Herbig Ae stars in
the 10 micrometer spectral region. We perform compositional fits of the spectra
based on properties of homogeneous as well as inhomogeneous spherical
particles, and derive the mineralogy and typical grain sizes of the dust
responsible for the 10 $\mu$m emission. Several trends are reported that can
constrain theoretical models of dust processing in these systems: i) none of
the sources consists of fully pristine dust comparable to that found in the
interstellar medium, ii) all sources with a high fraction of crystalline
silicates are dominated by large grains, iii) the disks around more massive
stars (M >~ 2.5 M_sun, L >~ 60 L_sun) have a higher fraction of crystalline
silicates than those around lower mass stars, iv) in the subset of lower mass
stars (M <~ 2.5 M_sun) there is no correlation between stellar parameters and
the derived crystallinity of the dust. The correlation between the shape and
strength of the 10 micron silicate feature reported by van Boekel et al. (2003)
is reconfirmed with this larger sample. The evidence presented in this paper is
combined with that of other studies to present a likely scenario of dust
processing in Herbig Ae systems. We conclude that the present data favour a
scenario in which the crystalline silicates are produced in the innermost
regions of the disk, close to the star, and transported outward to the regions
where they can be detected by means of 10 micron spectroscopy. Additionally, we
conclude that the final crystallinity of these disks is reached very soon after
active accretion has stopped.
