Planetesimal were the first planetary objects to form in the solar system, which later grew to make the proto-planets. Most of these bodies were differentiated as a result of internal heating. Several differentiated bodies have, then, been accreted following the giant impacts to create the terrestrial planets. As a result of these impacts, the newly formed Earth was molten and completely differentiated. Subsequent crystallization has given rise to Earth's current structure. In order to bring new constraints on the differentiation and melting relationship in the planets we have studied natural and synthetic samples corresponding to different stages of planetary evolution through state of the art electron microscopy techniques. We have, first, looked at carbonaceous materials in a ureilite meteorite (Almahata Sitta MS-170). Thin sections from ureilite diamonds were prepared with the focused ion beam (FIB) are observed by transmission electron microscopy and spectroscopy. The morphology of graphite bands in diamonds indicated that they result from the diamond to graphite transformation during a shock event. Moreover, the diamonds in this meteorite with crystallite sizes as large as ~20 ÎŒm can only form under static high-pressure condition of planetary interiors. We have, also, found three types of diamond inclusions in our samples. The majority of these inclusions are euhedral Fe-S inclusions. However, each of these inclusions has three phases, namely: kamacite (Fe, Ni), troilite (FeS), and schreibersite ((Fe, Ni)3 P). The chemical analysis of the intact inclusions shows them to be a stoichiometric phase, (Fe, Ni)3(S, P), that can only form above 21 GPa. The ureilite parent body (UPB) should have had the size about that of Mars to exert necessary pressure to grow the diamond inclusions in the core-mantle boundary. The other two types of inclusions are the Al- and Mg- free chromite, Cr2FeO4, and Ca-Fe phosphates that were previously observed only in iron meteorites. Our results suggest that the diamonds and their inclusions were formed from an S-rich metallic liquid. In the second part of the thesis, we have studied melting and fractional crystallization of the lower mantle using a laser-heated diamond anvil cell (LH-DAC). San Carlos olivine is used as a proxy to the mantle composition. The recovered samples are first analyzed with the 3D chemical tomography using a dual beam FIB instrument. The molten region in all the samples at pressure range from 30 to 71 GPa have at least three distinct zones: a ferropericlase shell (Fp), an intermediate bridgmanite (Brg) region and the Fe-rich melt core. Thin sections from the center of the same samples are analyzed with TEM and energy-dispersive x-ray (EDX) spectroscopy. The results from the samples heated at 45 GPa for 1, 3, and 6 minutes demonstrated that the temperature gradient in the heated zone shrinks through the time and, thus, the crystallization continues toward the center of the heating. Consequently, the melt becomes richer in iron. The melt core also gets more iron-rich with increasing pressure. In fact, in ~70 GPa we observe an Fe-O core with small Si and Mg concentration. This implies that the melt at the bottom of the mantle could become denser than the solid phases and sink down. The presence of the iron-rich melt or the oxides crystallizing from such a melt can explain the ultra-low velocity zones (ULVZs) found in the seismic surveys of the core-mantle boundary.