I understand that similar to D band, D' band relates to the defect of CNT structure. But in details, how different are D band and D' band? What kind of defect does each band describe?
Both the D and the D' peaks are defect activated bands in sp2 carbon materials, hence the name "D" for defect. In the case of both bands you have a type of resonance Raman effect with the involvement of electronic states around the K and K' symmetry points in k-space (where the electronic dispersion is linear), so in both cases you also see non-zone-center phonons.
The difference between the D and D' bands are in different processes (so called inter- and intra-valley scattering); Further in the case of the D band there is a TO phonon, while in case of the D' band there is a LO phonon involved; The difference between the processes and all the other common bands are best explained in:
Raman spectroscopy in graphene materials, L.M. Malard, M.A. Pimenta, G. Dresselhaus, M.S. Dresselhaus, Physics Reports 473, 51-87 (2009)
A.C. Ferrari, Raman spectroscopy of graphene and graphite: Disorder, electron–phonon coupling, doping and nonadiabatic effects, Solid State Commun. 143, 47-57 (2007)
M.S. Dresselhausa, G. Dresselhaus, R. Saito, A. Jorio, Raman spectroscopy of carbon nanotubes, Physics Reports 409, 47–99 (2005)
In addition to Michael's excellent description, amorphous carbon can contribute to the signal of the D band, but has been shown that it does not contribute to the D' band. We have some (unfortunately not yet published) work that indicates that the D' band best describes defects in the side wall of multiwall carbon nanotubes as statistical correlations were determined between Raman spectral properties involving the D' band and XPS and TGA measurements.
I'm very much curious to see your article. If don't mind, you can upload that work in either arxiv.org or RG and in parallel, you can publish to reputed journal.