The field of nanoscience and nanotechnology deals with materials whose at least one dimension is less than one hundred nanometers. High resolution transmission electron microscope (HRTEM) is better compared to other imaging tools in the sense that it can probe atomic structure throughout full thickness of the specimen with a lateral resolution of angstrom range. The phase information of the wave function gets lost while being recorded in the detector but phase contains useful information about the materials such as electrostatic potential distribution. This phase can be retrieved using exit wave reconstruction which does not require complicated experimental setup. The combination of exit wave reconstruction technique and density functional theory (DFT) provides a very powerful means of synergistic atomic-scale materials investigation. HRTEM with developed techniques can provide atomic-scale informations about nano-materials e.g. interface, heterostructure and nanoclusters with angstrom spatial resolution. Using density functional theory we first investigate the structural, elastic and mechanical properties of high-k dielectric gadolinium oxide (Gd2O3). Our calculations indicate that all phases of Gd2O3 are soft and ductile in nature indicating that they can be grown as thin films. We show that TEM based iterative algorithm can be used to remove amorphous carbon induced artefacts from experimentally recorded micrographs to investigate the qualitative nature of the sharpness/diffuseness of the interface. Moreover, we show how to get the thickness of a specimen along the electron beam direction using electron channelling theory. Finally, using DFT calculations we show the possibility of chemical gradation in II-VI semiconductor/semiconductor nanoheterostructure (CdSe/ZnTe) driven by thermodynamic force.