5.5. Nano Titanium Carbide Grains
Presolar titanium carbide (TiC) grains were first identified in primitive meteorites as nano-sized inclusions embedded in micrometer-sized presolar graphite grains (Bernatowicz et al. 1996). Very recently, von Helden et al. (2000) proposed that TiC nanocrystals could be responsible for the prominent 21 µm emission feature detected in over a dozen carbon-rich post-AGB stars. This mysterious 21 µm feature still remains unidentified since its first detection in the IRAS LRS (Low Resolution Spectrometer) spectra of four post-AGB stars (Kwok, Volk, & Hrivnak 1989). While bulk TiC samples show no resonance around 21 µm (Henning & Mutschke 2001), laboratory absorption spectra of TiC nanocrystal clusters exhibit a strong 21 µm feature, closely resembling the observed 21 µm feature both in position, width and in spectral detail (von Helden et al. 2000).
We have examined the nano-TiC proposal by comparing the maximum available with the minimum required TiC dust mass inferred from the nano-TiC model (see Li 2003). It is found that if the UV/visible absorption properties of TiC nanograins are like their bulk counterparts, the model-required TiC dust mass would exceed the maximum available TiC mass by over two orders of magnitude (also see Chigai et al. 2003; Hony et al. 2003). One may argue that nano TiC might have a much higher UV/visible absorptivity so that the available TiC mass may be sufficient to account for the observed 21 µm emission feature. However, the Kramers-Kronig dispersion relations, which relate the wavelength-integrated extinction cross sections to the total dust mass (Purcell 1969; Draine 2003b), would impose a lower bound on the TiC mass. We have shown that this Kramers-Kronig lower limit exceeds the maximum available TiC mass by a factor of at least ~ 50 (see Li 2003 for details). Therefore, it is unlikely that TiC nanoparticles are responsible for the 21 µm emission feature of post-AGB stars.