Nanomaterials have attracted the attention of researchers from various fields due to their unique features (that are otherwise absent in the bulk) such as quantum confinement, high surface to volume ratio, ability for surface modification etc. Since the discovery of fullerenes and carbon nanotubes, several synthesis techniques have been developed for nanomaterial growth. However, different control parameters in different synthesis techniques often result in nanostructures with varying defects that may alter their fundamental behavior. Such defects or disorder in the crystal lattice can lead to the disruption of lattice symmetry. The defect-induced symmetry lowering (or breaking) effects play a vital role in the determination of fundamental material characteristics. Thus, it is very important to characterize the defects in order to understand their effects on the nanomaterial properties. This thesis describes the effects of defects in low dimesional systems such as ZnO nanowires, graphene and carbon nanotubes are studied.;Firstly, it describes the synthesis and characterization of ZnO nanostructures and discusses the effects of surface states, defects and dopants on their optical and magnetic properties. An unexpected presence of ferromagnetic (FM) ordering in nanostructured nonmagnetic metal oxides has been reported previously. Though this property was attributed to the presence of defects, systematic experimental and theoretical studies to pinpoint its origin and mechanism were lacking. While it is widely believed that oxygen vacancies are responsible for FM ordering, surprisingly annealing as-prepared samples at low temperature (high temperature) in flowing oxygen actually enhances (diminishes) the FM ordering. For these reasons, we have prepared, annealed in different environments, and measured the ensuing magnetization in micrometer and nanoscale ZnO with varying crystallinity. We further find from our magnetization measurements and ab-initio calculations that a range of magnetic properties in ZnO can result, depending on the sample preparation and annealing conditions. For example, within the same ZnO sample we have observed ferro- to para- and diamagnetic responses depending on the annealing conditions. We also explored the effects of surface states on the magnetic behavior of nanoscale ZnO through detailed calculations.;In the case of grapheme, we have observed new combination modes in the range from 1650 to 2300 cm-1 in single-(SLG), bi-, few-layer and incommensurate bilayer graphene (IBLG) on silicon dioxide substrates. A peak at ∼1860 cm-1 (iTALO- ) is observed due to a combination of the in-plane transverse acoustic (iTA) and the longitudinal optical (LO) phonons. The intensity of this peak decreases with increasing number of layers and this peak is absent for bulk graphite. The overtone of the out-of-plane transverse optical (oTO) phonon at ∼1750 cm-1, also called the M band, is suppressed for both SLG and IBLG. In addition, two previously unidentified modes at ∼2200 and ∼1880 cm-1 are observed in SLG. The 2220 cm -1 (1880 cm-1) mode is tentatively assigned to the combination mode of in-plane transverse optical (iTO) and TA phonons (oTO+LO phonons) around the K point in the graphene Brillouin zone. Finally, the peak frequency of the 1880 (2220) cm-1 mode is observed to increase (decrease) linearly with increasing graphene layers.;Finally, we find that the high curvature in sub-nm SWCNTs leads to (i) an unusual S-like dispersion of the G-band frequency due to perturbations caused by the strong electron-phonon coupling, (ii) an activation of diameter-selective intermediate frequency modes that are as intense as the radial breathing modes (RBMs), and (iii) a clear observation of the IR modes.
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