Individual multi-walled carbon nanotubes (MWCNTs) were exposed to the electron beam of 200 kV energy and high resolution transmission electron micrographs were recorded at several time intervals. Interestingly, the nucleation of diamond nanoparticles with in the highly disordered MWCNT matrix upon electron-irradiation is observed. This happens without any assistance of high pressures and temperatures. High pressure X-ray diffraction experiments were performed on core/shell structures which suggest that even the closed structures of carbon resist any inward pressure, thereby ruling out the possibility of a hypothetical internal pressure under the electron irradiation conditions. Our experiments suggest that the transformation of graphitic carbon into diamond in the size window of a few nanometers is possible due to the stability of the diamond and a selective dissolution effect of 200 kV electrons on graphite. A mechanism for the same is proposed.