  Titanium carbide (TiC) nanocrystals were recently proposed as the carrier of
the mysterious 21$\mum$ emission feature observed in post-asymptotic giant
branch stars, based on their close spectral match and the presolar nature of
meteoritic TiC nanograins (which reveals their stellar ejecta origin). But we
show in this {\it Letter} that the Kramers-Kronig dispersion relations, which
relate the wavelength-integrated extinction cross section to the total dust
mass, would impose a lower bound on the TiC mass. This Kramers-Kronig lower
limit exceeds the maximum available TiC mass by a factor of at least
$\simali$50, independent of the absolute value of the ultraviolet/visible
absorptivity of nano TiC. The TiC model is therefore readily ruled out by the
Kramers-Kronig physical principle.
