2002MNRAS.332..513S

We have modelled dust envelopes and discs around oxygen-rich asymptotic giant branch (AGB) stars using optical properties of amorphous and crystalline silicate dust grains, paying close attention to the infrared observations of the stars including the Infrared Space Observatory (ISO ) data. Using the opacity functions for various mixtures of amorphous and crystalline silicates, we have calculated the radiative transfer model spectral energy distributions (SEDs) for the dust envelopes and discs. We have compared the model results with the observed SEDs of the stars. Using the averaged single grain population model for mixed amorphous and crystalline silicates, we find that spherical envelope models with about 10 to 20 per cent of crystalline silicates produce the observed crystalline emission features for high mass-loss rate AGB stars and there is virtually no evidence of the existence of crystalline silicates for low mass-loss rate stars. This would confirm the idea that crystalline silicates form only in dense envelopes around high mass-loss rate O-rich AGB stars. Additionally, we find that the crystalline content is higher for more dusty stars. For a spherical dust envelope, we argue that a fraction of silicates initially condensed in amorphous form may subsequently be annealed to become crystalline form in the inner region of the outflowing envelope. If dust formation temperature is 1000K, the inner region of the envelope is hot (about 900-1000K) during an extended period of time (several hundred days) for a known crystallization process - annealing. The process may not be effective for low mass-loss rate stars because the dust formation temperature is believed to be lower for weaker stellar winds. We have investigated the model SEDs produced by the geometrically thin and optically thick dust disc heated by a spherical dust envelope as well as a central star. We find that the crystalline silicate emission features are produced by the spherical envelope, not by the dust disc. The crystalline absorption features at the same wavelengths are produced by the dust disc.