Carbon related systems have attracted a large amount of attention of the science and technology community during the last few decades. In particular, graphene and carbon nanotubes have remarkable properties that have inspired applications in several fields of science and engineering. Despite these properties, creating structurally perfect samples is a difficult objective to achieve. Defects are usually seen as imperfections that degrade the properties of materials. However, defects can also be exploited to create novel materials and devices. The main topic of this thesis is studying the effect of isotope doping on the phonon properties of graphene. The advantage of the isotope enrichment technique is that only phonon frequencies or thermal properties can be modified without changing the electrical or chemical properties. We calculated the values of the phonon lifetimes due to isotope impurity scattering for all values of isotopic fractions, isotopic masses and for all wave-vectors using second order perturbation theory. We found that for natural concentrations of 13C, the contribution of isotopic scattering of optical modes is negligible when compared to the contribution from the electron-phonon interaction. Nevertheless, for atomic concentrations of 13C as high as [rho] = 0.5 both the isotopic and electron-phonon contributions become comparable. Our results are compared with recent experimental results and we find good agreement both in the 13C atomic density dependence of the lifetime as well as in the calculated spectral width of the G-band. Due to phonon scattering by 13C isotopes, some graphene phonon wave-functions become localized in real space. Numerical calculations show that phonon localized states exist in the high-energy optical phonon modes and in regions of flat phonon dispersion. In particular, for the case of in-plane optical phonon modes, a typical localization length is on the order of 3 nm for 13C atomic concentrations of [rho] ~~ 0.5. Optical excitation of phonon modes may provide a way to experimentally observe localization effects for phonons in graphene.
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