Dust grains in the planet forming regions around young stars are expected to be heavily processed due to coagulation, fragmentation and crystallization. This paper focuses on the crystalline silicate dust grains in protoplanetary disks. As part of the Cores to Disks Legacy Program, we obtained more than a hundred Spitzer/IRS spectra of TTauri stars. More than 3/4 of our objects show at least one crystalline silicate emission feature that can be essentially attributed to Mg-rich silicates. Observational properties of the crystalline features seen at lambda > 20 mu correlate with each other, while they are largely uncorrelated with the properties of the amorphous silicate 10 mu feature. This supports the idea that the IRS spectra essentially probe two independent disk regions: a warm zone (< 1 AU) emitting at lambda ~ 10 mu and a much colder region emitting at lambda > 20 mu (< 10 AU). We identify a crystallinity paradox, as the long-wavelength crystalline silicate features are 3.5 times more frequently detected (~55 % vs. ~15%) than the crystalline features arising from much warmer disk regions. This suggests that the disk has an inhomogeneous dust composition within ~10 AU. The abundant crystalline silicates found far from their presumed formation regions suggests efficient outward radial transport mechanisms in the disks. The analysis of the shape and strength of both the amorphous 10 mu feature and the crystalline feature around 23 mu provides evidence for the prevalence of micron-sized grains in upper layers of disks. Their presence in disk atmospheres suggests efficient vertical diffusion, likely accompanied by grain-grain fragmentation to balance the efficient growth expected. Finally, the depletion of submicron-sized grains points toward removal mechanisms such as stellar winds or radiation pressure.
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