4 Dust condensation sequence

The dust condensation sequence in O-rich circumstellar regions is expected to go as follows (Tielens 1990):

${\rm Al_{2}O_{3}, Alumina}$
$\Downarrow$
${\rm Ca_{2}Al_{2}SiO_{7}, Augite}$
$\Downarrow$
${\rm CaMgSi_{2}O_{6}, Diopside}$	${\rm Mg_{2}SiO_{4}, Forsterite}$
$\Downarrow$	$\Downarrow$
${\rm MgAl_{2}O_{4}, Spinel}$	${\rm MgSiO_{3}, Enstatite}$
$\Downarrow$	$\Downarrow$
${\rm CaAl_{2}Si_{2}O_{8}, Anorthite}$	${\rm (Mg,Fe)_{2}SiO_{4}, Olivine}$

Figure 18: The laboratory spectra of some minerals in the predicted condensation sequence. In a) two spectra are shown for amorphous alumina, where the solid line represents a porous sample and the dashed line is a compact sample. These spectra both come from the Jena optical constants database (http://www.astro.uni-jena.de/Group/Subgroups/Labor/Labor/odata.html), as do the spectra in b) and c). In d), two polytypes of SiO2 are shown. The solid line is a form of amorphous silica (from Nyquist 1971) and the dashed line is one of the crystalline polytypes, tridymite (Hofmeister et al. 1992). The x-axis is wavelength in $\mu$m, the y-axis is normalized extinction

According to condensation thermodynamics, the silicate condensation sequence starts with the nucleation of alumina (Al₂O₃) from the circumstellar gas at about 1760 K. The first silicate is expected to form by a gas-solid reaction with alumina, to form Ca₂Al₂SiO₇. As the temperature drops, further gas-dust reactions occur so that Mg substitutes for Al to form CaMgSi₂O₆. The aluminium released and the remaining alumina are converted to spinel (MgAl₂O₄). As further cooling occurs the CaMgSi₂O₆ and the spinel form a solid-solid reaction, producing the feldspar anorthite (CaAl₂Si₂O₈). At even lower temperatures ($\sim$ 1440 K) forsterite (Mg₂SiO₄) starts to condense out. Forsterite continues to form until the temperature has dropped to $\sim$ 1350 K when it reacts with gaseous SiO to produce enstatite (MgSiO₃). Finally, at $\sim$ 1100 K reactions with gaseous iron will convert some enstatite into fayalite (Fe₂SiO₄) and forsterite. Kinetics also plays an important role in determining which silicates form in the outflows of AGB stars. Depending on the density structure of the circumstellar region the condensation sequence will cease at different points. Thus, if the density drops rapidly with distance from the star, the only dust expected to form will be various high temperature oxides (e.g. Al₂O₃, CaTiO₃, ZrO₂), which will form very close to the star. If the densities are a little higher further out in the circumstellar shell gas-grain reactions can take place, allowing the formation of calcium-aluminium silicates. If the density is high enough a little further out still magnesium silicates may form as rims on the Ca-Al silicates. For magnesium silicates to nucleate, there need to be very high densities a long way out, which is highly unlikely. Feldspars, such as anorthite (CaAl₂Si₂O₈) are not expected to form, as the solid-solid reaction requires unrealistically high densities. Finally, Fe can only be incorporated into Mg-silicates if, initially, most of the iron is in gaseous form (rather than solid, metal form) and if the density is high enough at large distances from the star where fayalite (Fe₂SiO₄) can survive. Figure 18 shows the laboratory spectra of major minerals that are expected to form, together with that of SiO₂ which is a likely to be a step in the formation of silicates.

Another possible sequence of condensation mentioned by SP98 involves chemistry determined by the C/O ratio. In this case, less evolved stars with low C/O ratios would exhibit silicate features while somewhat more evolved stars, with C/O ratios closer to unity, could have spectra dominated by Al₂O₃. According to the standard scenario (e.g. Salpeter 1974), stars with low C/O ratios ($\ll$1), have an abundance of oxygen atoms to form dust and therefore we should see strong silicate features. However, in stars with higher C/O ratios (but still less than unity) less oxygen would be available and therefore aluminium oxide features could dominate because aluminium is more oxidizing than magnesium and so uses up the available oxygen first (see SP98 for details).