Modeling to determine bulk modulus dependence on size, shape and dimensionality of nanomaterials

In the present study, a simple model is presented to study the shape, size and dimension effect on the bulk modulus of nanomaterials. The bulk modulus dependence on group velocity and mass density of material is taken into account. A qualitative melting temperature model for nanocrystals is extended to express the bulk modulus of nanocrystal in terms of its melting temperature. In view of the model proposed, Bulk modulus increases with increase in size of nanomaterials. The nanomaterials of Si, Cu, Al, Au, Ag, Pt are considered in the present study. The shape effect on bulk modulus is studied for spherical, hexahedral and tetrahedral, octahedral, icosahedral nanoparticles, cylindrical and hexagonal nanowires, nanofilms. Among the considered shapes, the drop in bulk modulus with size reduction is maximum for tetrahedral NP's, however, this decrease is noted least for thin films. The predicted model results are compared with the experimental data and simulated data available and are found in good accord with the available experimental and theoretically simulated results that justify the present model theory for study of elastic behavior of nanomaterials.