We observed the AGB stars S Ori, GX Mon and R Cnc with the MIDI instrument at the VLTI. We compared the data to radiative transfer models of the dust shells, where the central stellar intensity profiles were described by dust-free dynamic model atmospheres. We used Al2O3 and warm silicate grains. Our S Ori and R Cnc data could be well described by an Al2O3 dust shell alone, and our GX Mon data by a mix of an Al2O3 and a silicate shell. The best-fit parameters for S Ori and R Cnc included photospheric angular diameters Theta(Phot) of 9.7+/-1.0mas and 12.3+/-1.0mas, optical depths tau(V)(Al2O3) of 1.5+/-0.5 and 1.35+/-0.2, and inner radii R(in) of 1.9+/-0.3R(Phot) and 2.2+/-0.3R(Phot), respectively. Best-fit parameters for GX Mon were Theta(Phot)=8.7+/-1.3mas, tau(V)(Al2O3)=1.9+/-0.6, R(in)(Al2O3)=2.1+/-0.3R(Phot), tau(V)(silicate)=3.2+/-0.5, and R(in)(silicate)=4.6+/-0.2R(Phot). Our model fits constrain the chemical composition and the inner boundary radii of the dust shells, as well as the photospheric angular diameters. Our interferometric results are consistent with Al2O3 grains condensing close to the stellar surface at about 2 stellar radii, co-located with the extended atmosphere and SiO maser emission, and warm silicate grains at larger distances of about 4--5 stellar radii. We verified that the number densities of aluminum can match that of the best-fit Al2O3 dust shell near the inner dust radius in sufficiently extended atmospheres, confirming that Al2O3 grains can be seed particles for the further dust condensation. Together with literature data of the mass-loss rates, our sample is consistent with a hypothesis that stars with low mass-loss rates form primarily dust that preserves the spectral properties of Al2O3, and stars with higher mass-loss rate form dust with properties of warm silicates.
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