A comprehensive understanding of melting temperature of nanowire, nanotube and bulk counterpart

Surface energies of nanostructures are of considerable interest, and thermodynamic methods have provided valuable insight into the physics and chemistry of these systems. Although the effect of surface energy on melting behaviors of nanostructures has been widely investigated in theoretical calculations and simulations, from the thermodynamics at the nanometer scale point of view, the comprehensive understanding of the fundamental physical and chemical issues involved in nanostructures' melting is still lacking. For instance, nanostructures with negative curvature, such as nanotubes, show different melting behaviors compared with the nanostructures with positive curvature such as nanowires, and both nanotubes and nanowires exhibit abnormal melting temperature compared with that of the bulk counterparts. Herein, we put forward a general model to elucidate the melting temperature of the nanostructures with positive and negative curvatures based on the surface energy at the nanometer. Further, the surface mean square relative atomic displacement (MSRD) of these nanostructures has been studied from the perspective of the size-dependent cohesive energy consideration, which can provide the atomic understanding of the nanostructures' melting. Theoretical analyses indicate that both melting temperatures of the nanostructures with the positive and negative curvatures decrease with decreasing dimensionality, and the surface MSRDs show different size effects in the systems with the positive and negative curvatures, respectively. The melting temperature of the surface with the negative curvature is higher than that of the surface with the positive curvature, and both melting temperatures are smaller than that of the bulk counterpart when the size of nanostructures is less than a threshold value. The unique melting behaviors of nanostructures are attributed to the size- and curvature-dependent surface energy of nanostructures. These results provide new insight into the fundamental understanding of the melting temperature of nanostructures.