I think the best way is to measure photo luminescence if possible.
XRD and TEM observation may give a solution; FWHM can be estimated from the particle size according to the Scherrer equation. If there is a deviation between the estimated FWHM and actual FWHM with the XRD, the deviation can be attributed to the defect.
First what defects do you mean? Intrinsic (vacancy / interstitial / ....) or extrinsic (due to dopants) ?
1. Go for FT Raman analysis as the first step. The modes obtained will decipher the defects.
2. Try to record the photo-luminescence(PL) spectrum of your sample as the next step and this complements Raman spectra. It works for both intrinsic and extrinsic, of semiconducting and semi-insulating materials. By knowing the PL response you can more or less predict the crystal quality or purity of the samples. PL determines the impurity defect levels that includes atomic vacancies and substitutional defects.
3. An XPS analysis will clearly show the defect states
4. Positron annihilation lifetime spectroscopy (PALS) gives much more clear details about the defects in the sample. PALS is inert for self interstitial or impurities in sample. PAS is very sensitive tool to detect vacancies, vacancy clusters or dislocations. Anyway I don't think that one can vouch for the defect concentration, defect size or type and its relation with the positron life time.
Defects in carbon nanostructures can be introduced by both vacancies and external doping. Defects may be visualized by transmission electron microscopy (TEM) .Also, The ratio of intensity of D/G bands in Raman spectroscopy is a measure of the defects present on graphene structure.
Thank you very much for your comments. I would like to clearify my question here. I am asking for both types of defects i.e. vacancy (e.g. Oxygen vacancies or metal vacancies in metal oxide semiconductors) and impurities or doping (e.g. metal ion doping in some other semiconductors). How to measure or count the approximate number of these defects by experimental technique or data else by theoretical way like some formulae etc. In general i know Frankel or schottky defect equations. I need experimental way like RBS spectroscopy or any characterizations tools or by electrical property measurements etc. Plz guide me for the same. Thank you