  Using electron diffraction on free-standing single-walled carbon nanotubes we
have determined the structural indices (n,m) of tubes in the diameter range
from 1.4 to 3nm. On the same free-standing tubes we have recorded Raman spectra
of the tangential modes and the radial breathing mode. For the smaller
diameters (1.4-1.7nm) these measurements confirm previously established radial
breathing mode frequency versus diameter relations, and would be consistent
with the theoretically predicted proportionality to the inverse diameter.
However, for extending the relation to larger diameters, either a yet
unexplained environmental constant has to be assumed, or the linear relation
has to be abandoned.
