Shanker Equation of State is used to study the volume compression of nanocrystalline materials under different pressure. On comparing with the experimental data it gives good results at low pressure, but for higher compression it deviates from the experimental points. Therefore, the Equation of State is modified empirically to study the pressure-volume relation for nanomaterials, namely, n-Rb3C60, n-CdSe (rocksalt phase), n-TiO2 (anatase and rutile phase), Fe-filled nanotube, and γ-Fe2O3, at high pressure. The results obtained from the empirical Equation of State are found to be in better agreement with the available experimental data. 1. Introduction Nanocrystalline materials with particle size of 1–100？nm are of current interest in discovering novel and chemical properties of materials that may differ from those of the corresponding bulk materials. Nanocrystalline crystallites are generally viewed to consist of two structurally distinct components, a crystalline component formed by a small single crystal with random crystallographic orientation and a surface layer characterized by a significant fraction of atoms at grain boundaries. The nanomaterials are very sensitive to external parameters like pressure and temperature. The study of nanomaterials under high pressure and high temperature is considered as a possible path to expand the range of available solid state materials. Pressure application, as for the bulk materials, allows the continuous modification of the interatomic interaction of the nanoobject and constitutes an invaluable tool to explore physical chemical interactions at the nanoscale and their link with physical properties of interest. The physical properties of materials depend strongly on the structure and interatomic distances. High pressure can vary these distances, which implies that we can study relations between structure and properties of the materials. High compression occurs due to high pressure. Due to the pressure many effects happen, such as pressure ionization, modification in electronic properties, phase change, and several phenomenons in applied fields. The knowledge of thermoelastic properties of minerals at high temperature and pressure is required for the understanding of the earth’s deep interior. The study based on the Equation of State at high pressure and high temperature is of fundamental interest because it permits interpolation and extrapolation in to the regions in which the experimental data are not available adequately. They help in planning future high-pressure experiments and are also important in
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