Molecular equilibria and condensation temperatures in carbon-rich gases

Abstract

Detailed chemical equilibrium calculations were carried out using a number of different C/O ratios, in order to determine the relative condensation sequence of various phases. For C/O > 1, we calculated the condensation temperatures of graphite, TiC, and SiC, and found that the condensation temperature of graphite is strongly dependent on the C/O ratio, but insensitive to pressure, whereas for TiC and SiC, there is a strong dependence on pressure, but almost no dependence on C/O. In all cases, TiC condenses before SiC. For most regions of P-C/O space when C/O > 1, graphite condenses before TiC and SiC, but for a C/O ratio of about 1.2, TiC condenses before graphite for pressures above approximately 30 dyne/cm^2, and this limiting pressure decreases with decreasing C/O ratio. We found that the main species governing the condensation of graphite, TiC, and SiC were the gas phase species H, H_2, C_2H, C_2H_2, Ti, and Si. By identifying the key equilibria involving these species, a few simple analytic formulae were found that estimate the condensation temperatures, which are generally in good agreement with the detailed calculations, with any differences being easily explained by the neglect of some minor species. These results exhibit the basic dependence of the condensation sequence on C/O, pressure, and temperature for C, TiC, and SiC. To form grains in the winds of an AGB star, the gas density must be high enough for grains to form in a reasonable timescale at or below their condensation temperature. From kinetic considerations and stellar models, we argue that grains are most likely to form in the pressure range 0.2 < P < 40 dyne/cm^2. This requires that for TiC to form before graphite, the C/O range is 1.04 < C/O < 1.2. If graphite begins condensing soon after TiC, then the TiC grain will be embedded in abundant graphite before SiC forms at a temperature ∼170 K lower. These inferences are consistent with previous observations of the presence of TiC crystals embedded in circumstellar graphite spherules found in a meteorite. It is shown that due to the difference between the condensation temperatures of TiC and of SiC, there is a substantial decrease in the amount of available carbon in the gas phase, so that significant graphite condensation will not occur along with SiC. This would appear to explain the occurrence of SiC grains unassociated with graphite in the presolar grain population found in meteorites. The nitrogen chemistry was investigated and it was found that AIN always condenses at a much lower temperature than SiC. However, Al and N are often found in substantial amounts in association with SiC. We infer that these elements must form a solid solution with SiC at higher temperatures. We note that a small amount of SiC forms below the condensation temperature of AIN, due to the formation of CaS grains allowing some Si locked up in gaseous SiS to be released. This additional low temperature SiC could incorporate some AIN. Finally, we briefly investigated the equilibria when C/O ≤ 1. When C/O = 1 or slightly smaller, the results are very sensitive to the data. TiC can form at C/O = 0.98 but at lower temperatures than TiN and TiO. Below C/O = 0.98, no SiC forms. For C/O = 0.9, calculations show that this definitely is in the "oxygen-rich" regime when oxides and silicates but no carbides form. As SiO is one of the next most tightly bound oxides in the gas phase after CO, it is shown that the whole high temperature condensation chemistry takes on oxygen-rich aspects, when C/O < 0.96 for the solar Si/O ratio.

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