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Astron. Astrophys. 349, 243-252 (1999)

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3. Carbon grains

While carbon is expected to constitute a major fraction of the circumstellar dust in carbon stars, its exact form is still unclear. Carbon has the unique property that the atoms can form three different types of bonds through sp1, sp2 (graphite) and sp3 (diamond) hybridization.

A number of observations of late-type stars contradict the presence of graphite as the dominant dust type (e.g. Campbell et al. 1976; Sopka et al. 1985; Martin & Rogers 1987; Gürtler et al. 1996). The far-infrared (FIR) data of late-type stars generally show a dust emissivity law of [FORMULA] with a spectral index of [FORMULA]. While graphite grains have a FIR emission proportional to [FORMULA] (Draine & Lee 1984), a [FORMULA] behaviour can be expected in a very disordered two-dimensional material like amorphous material (Huffman 1988; Jäger et al. 1998).

Amorphous carbon grains therefore seem to be a very good candidate as the common type of carbon grains present in circumstellar envelopes. Another possibility could be small diamond grains. Presolar diamond grains have been identified from primitive (unaltered) meteorites (carbonaceous chondrites) and are the most abundant (500 ppm) of the presolar grains discovered so far (Lewis et al. 1987). At least 3% of the total amount of carbon present at the formation of the Solar System was in the form of diamonds (Huss & Lewis 1994). The place of origin of the presolar diamonds is still unknown, but since they can only have formed under reducing conditions Jorgensen (1988) has suggested C-rich AGB stars as the place of formation of the majority of the presolar diamond grains.

It has been suggested by Krüger et al. (1996) that the surface growth processes on carbonaceous seed particles in circumstellar envelopes will take place at sp3 bonded carbon atoms rather than at sp2 bonded ones, which suggests that the grain material formed in circumstellar envelopes could be amorphous-diamond like carbon. Presolar diamonds extracted from meteorites have a median grain size of about 2 nm (Fraundorf et al. 1989), meaning that each diamond contains a few hundred to a few thousand carbon atoms. The presolar diamonds therefore seem to actually consist of a mixture of diamond (core) and hydrogenate amorphous carbon (surface) having about 0.46 the volume fraction of pure diamond (Bernatowicz et al. 1990).

Several spectra of presolar diamonds from various meteorites have been published (Lewis et al. 1989; Colangeli et al. 1995; Mutschke et al. 1995; Hill et al. 1997; Andersen et al. 1998; Braatz et al., submitted to Meteorit. Planet. Sci.) and even though a number of artifacts tends to be present in all the spectra, the general trend is that the presolar diamonds have an absorption coefficient that is twice that of pure diamond and a factor of a hundred less than the "diamond-like" amorphous carbon of Jäger et al. (1998).

There exists a wide variety of possible amorphous carbon grain types, which fall in between the categories "diamond-like" and "graphite-like" amorphous carbon. We have calculated dynamical models using various laboratory data of amorphous carbon to determine the possible influence of these different grain types on the structure and the wind properties of C-rich AGB star models.

3.1. Laboratory measurements of amorphous carbon

Laboratory conditions are far from the actual space conditions where grains are produced or processed, but experiments in which physical and chemical parameters are controlled and monitored do give the option of selecting materials which may match the astronomical observations. When choosing which amorphous carbon data to use one is faced with the fact that due to the various processes used in the sample preparation, differences often appear between the measurements of various authors. Another major problem is that the optical properties of amorphous carbon are most often obtained by different techniques in different wavelength regions. Extinction measurements of sub-micron-sized particles is the most common technique in the infrared. In the visible and ultraviolet, reflectivity and transmission measurements are often obtained on bulk samples.

[FIGURE] Fig. 1. Calculated extinction efficiency of amorphous carbon from optical constants published by Maron (1990), Rouleau & Martin (1991), Preibisch et al. (1993), Zubko et al. (1996) and Jäger et al. (1998), see Table 1 for annotations. The extinction efficiency factors were calculated from the optical constants (n and k) in the Rayleigh approximation for spheres.

Bussoletti et al. (1987a) have determined the extinction efficiencies for various types of sub-micron amorphous carbon particles and spectroscopically analysed them in the wavelength range 1000 Å - 300 µm. In their paper they present an updated version of the data already published from 2000 Å to 40 µm (Borghesi et al. 1983, 1985a) and new data obtained in the UV/vis (1000-3000 Å) and in the FIR (35-300 µm). The sub-micron amorphous carbon grains were obtained by means of two methods: (1) striking an arc between two amorphous carbon electrodes in a controlled Ar atmosphere at different pressures (samples AC1, AC2 and AC3; where the numbers refer to different accumulation distances from the arc discharge); (2) burning hydrocarbons (benzene and xylene) in air at room pressure (samples BE and XY). The smoke was collected on quartz substrates. For the UV/vis spectroscopy the quartz substrates on which the particles had been collected were used directly while the dust was scrapped from the substrate and embedded in KBr pellets for the IR spectroscopy. Bussoletti et al. (1987b) suggest that the extinction efficiencies, [FORMULA], for the AC samples should be corrected by a factor of 5 due to an experimental underestimation of the pellet density. This correction gives an agreement with the data by Koike et al. (1980).

Colangeli et al. (1995) measured the extinction efficiency in the range 40 nm - 2 mm. They produced three different samples; two by arc discharge between amorphous carbon electrodes in Ar and H2 atmospheres at 10 mbar (sample ACAR and ACH2 respectively) and one by burning benzene in air (sample BE). The samples were deposited onto different substrates for the UV/vis measurements, while in the IR the samples where prepared both on a substrate and by being embedded in KBr/CsI pellets and for the FIR measurements the samples were embedded in polyethylene pellets. These different but overlapping methods gave the possibility of evaluating the difference as a result of embedding the samples in a matrix or by having them on a substrate. Colangeli et al. (1995) found that embedding the samples in a matrix introduces a systematic error (the matrix effect) while the spectra obtained for grains deposited onto a substrate did not suffer from any matrix effect detectable within the accuracy available in the experiment. Therefore the FIR data were corrected for the extinction offset introduced by the matrix.

Jäger et al. (1998) produced structurally different carbon materials by pyrolizing cellulose materials at different temperatures (400o C, 600o C, 800o C and 1000o C), and characterised them in great detail. These materials have increasing sp2/sp3 ratios making the amorphous carbon pyrolysed at 400o C the most "diamond-like" with the lowest sp2/sp3 ratio while the amorphous carbon pyrolysed at 1000o C is more "graphite-like" with the highest sp2/sp3 ratio. The pyrolysed carbon samples were embedded in epoxy resin and reflectance of the samples was measured in the range 200 nm to 500 µm, making this the first consistent laboratory measurement of amorphous carbon over the whole spectral range relevant for radiative transfer calculations of C-rich AGB stars. From the reflectance spectra the complex refractive index, m, was derived by the Lorentz oscillator method (see e.g. Bohren & Huffman 1983, Chap. 9). There is a significant difference between the two low temperature (400o C and 600o C) and the two high temperature samples (800o C and 1000o C). The latter two behave very similar to glassy carbon.

In contrast to grain measurements, the bulk samples by Jäger et al. (1998) give the possibility of investigating the difference between the influence of the internal structure of amorphous material and the morphology of the carbon grains. These two properties can be separated out due to the careful investigation of the internal structures of the four samples and the range of material properties that these four amorphous carbon samples span (from "diamond-like" to "graphite-like").

3.2. Calculated optical properties of amorphous carbon

Several authors have used the data of Bussoletti et al. (1987a) and Colangeli et al. (1995) to obtain the optical constants of amorphous carbon grains.

Maron (1990) used the extinction efficiencies of Bussoletti et al. (1987a) (sample AC2) to derive the optical constants (n and k) by estimating the complex permittivity by a combination of the measured absorption efficiencies, dispersion formulae and Kramers-Kronig relation. The reason for performing these calculations is that the optical constants are needed for modelling emission properties of grains containing various allotropic carbons or having different sizes. Maron (1990) is of the opinion that the differences between the primary extinction efficiencies obtained by Bussoletti et al. (1987a) and Koike et al. (1980) are real and caused rather by the use of different electrodes (amorphous carbon and graphite, respectively) than by an underestimation of the pellet column density as suggested by Bussoletti et al. (1987b). Therefore he did not introduce the correction suggested by Bussoletti et al. (1987b).

Rouleau & Martin (1991) used the AC2 and BE data from Bussoletti et al. (1987a) to produce synthetic optical constants (n and k) which satisfy the Kramers-Kronig relations and highlight the effects of assuming various shape distributions and fractal clusters. One of the complications in determining these optical properties of amorphous carbon material was that in the infrared the extinction measurements were done on a sample of sub-micron-sized particles, while in the visible and ultraviolet the optical constants were obtained by measurements of reflectivity and transmission or by electron energy loss spectroscopy on bulk samples. These diverse measurements were used to produce synthetic optical constants which satisfied the Kramers-Kronig relations.

Preibisch et al. (1993) used the BE sample from Bussoletti et al. (1987a) between 0.1-300 µm and the data of Blanco et al. (1991) between 40-700 µm, using the same technique as used by Rouleau & Martin (1991) for deriving optical constants taking shape and clustering effects into account. Preibisch et al. (1993) extend the available optical constants on the basis of the measurements of Blanco et al. (1991). With these they determine the opacities of core-mantle-particles with varying mantle thickness and pollution.

Zubko et al. (1996) used the extinction efficiencies obtained by Colangeli et al. (1995) to derive the optical constants (n and k) also by use of the Kramers-Kronig approach. These data were used to evaluate the possible shapes of the amorphous carbon grains in space and the possible clustering of the particles.

In this study we have used the derived optical constants of Maron (1990), Rouleau & Martin (1991), Preibisch et al. (1993), Zubko et al. (1996) and Jäger et al. (1998), see Table 1 for details. The extinction efficiency data presented in this paper were calculated in the Rayleigh approximation for spheres.


Table 1. Comparison of the different laboratory data and a list of authors who have obtained optical constants from these data.
1) Given in Rouleau & Martin (1991).

3.3. The nature of silicon carbide

Thermodynamic equilibrium calculations performed by Friedemann (1969a,b) and Gilman (1969) suggested that SiC particles can form in the mass outflow of C-rich AGB stars. The observations performed by Hackwell (1972) and Treffers & Cohen (1974) presented the first empirical evidence for the presence of SiC particles in stellar atmospheres. A broad infrared emission feature seen in the spectra of many carbon stars, peaking between 11.0 and 11.5 µm is therefore attributed to solid SiC particles and SiC is believed to be a significant constituent of the dust around carbon stars.

An ultimate proof for the formation of SiC grains in C-rich stellar atmospheres was the detection of isotropically anomalous SiC grains in primitive meteorites (Bernatowicz et al. 1987). Based on isotopic measurements of the major and trace elements in the SiC grains and on models of stellar nucleosynthesis, it is established that a majority of the presolar SiC grains has their origin in the atmospheres of late-type C-rich stars (Gallino et al. 1990, 1994; Hoppe et al. 1994). For recent reviews see, e.g., Anders & Zinner (1993), Ott (1993) and Hoppe & Ott (1997).

Detailed laboratory investigations on the infrared spectrum of SiC have been presented by the following authors: Spitzer et al. (1959a,b) performed thin film measurements on [FORMULA]- and [FORMULA]-SiC; Stephens (1980) measured on crystalline [FORMULA]-SiC smokes; Friedemann et al. (1981) measured two commercially available [FORMULA]-SiC; Borghesi et al. (1985b) investigated three commercially produced [FORMULA]- and one commercially produced [FORMULA]-SiC; Papoular et al. (1998) measured two samples of [FORMULA]-SiC powders, one produced by laser pyrolysis and one which was commercially available; Mutschke et al. (1999) studied 16 different SiC powders which were partly of commercial origin and partly laboratory products (8 [FORMULA]-SiC and 8 [FORMULA]-SiC); Speck et al. (1999) made thin film measurements of [FORMULA]- and [FORMULA]-SiC and Andersen et al. (1999) have measured the spectrum of meteoritic SiC.

One of the difficulties in interpreting laboratory data lies in disentangling the combination of several effects due to size, shape, physical state (amorphous or crystalline), purity of the sample and possible matrix effects if a matrix is used. There is a general agreement that grain size and grain shape have a crucial influence on the absorption feature of SiC particles. This is particularly demonstrated by Papoular et al. (1998), Andersen et al. (1999) and Mutschke et al. (1999). Papoular et al. (1998), Mutschke et al. (1999) and Speck et al. (1999) have shown that the matrix effect does not shift the resonance feature as a whole as it was assumed by Friedemann et al. (1981) and Borghesi et al. (1985b). While Papoular et al. (1998) and Mutschke et al. (1999) find that the profile is not shifted but altered, Speck et al. (1999) state that the profile is not affected at all, whether a matrix is used in the experimental set up or not. The influence of purity of the laboratory samples was mainly studied by Mutschke et al. (1999). Another issue considered is the effect of the crystal type. Silicon carbide shows pronounced polytypism which means that there exist a number of possible crystal types differing in only one spatial direction. All these polytypes are variants of the same basic structure and can therefore be divided into two basic groups: [FORMULA]-SiC (the hexagonal polytypes) and [FORMULA]-SiC (the cubic polytype). It was found by Spitzer et al. (1959a,b), Papoular et al. (1998), Andersen et al. (1999) and Mutschke et al. (1999) that the crystal structure of SiC cannot be determined from IR spectra, because there is no systematic dependence of the band profile on the crystal type. In contrast, Borghesi et al. (1985b) and Speck et al. (1999) find the contrary result.

In this paper we have used the average value for bulk SiC reflectance spectra of [FORMULA]-SiC as presented by Mutschke et al. (1999) with [FORMULA], [FORMULA] = 795.4 cm-1, [FORMULA] = 1423.3 cm-1 and [FORMULA] = 10 to calculate the optical constants n and k, using the one-oscillator model described in Mutschke et al. (1999). The damping constant [FORMULA] is an "ad hoc" parameter, which in a perfect crystal reflects the anharmonicity of the potential curve. A damping constant of [FORMULA] characterises crystals which are not structurally perfect but still far from amorphousness.

Since there is no systematic dependence of the band profile on the crystal type in the data of Mutschke et al. (1999), we could just as well have used the data of one of their [FORMULA]-SiC samples and would have obtained a similar result.

The optical constants n and k where used to calculate the extinction efficiency for small spherical grains in the Rayleigh limit. Spheres are not necessarily the best approximation for the grain shape of SiC particles in C-rich AGB stars compared to e.g. a continuous distribution of ellipsoids (CDE) as introduced by Bohren & Huffman (1983). The general appearance of the feature as well as the peak position will depend on the grain shape, however, common for all grain shapes of SiC are that the feature will always fall between the transverse (TO) and the longitudinal (LO) optical phonon mode, so the difference will be that a spherical grain shape will give rise to a sharper and narrower resonance than other grain shape approximations.

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© European Southern Observatory (ESO) 1999

Online publication: August 25, 1999