Finite size effect on critical transition temperature of superconductive nanosolids

A simple and unified model is developed for finite size effect on the critical transition temperature of superconductive nanosolids, which is based on the size-dependent Debye temperature of crystals within the McMillan expression. In the model, two material and structure dependent parameters of D0 and α are used, which, respectively, are the critical size at which all atoms of a low-dimensional material are located on its surface, and the ratio of the mean square vibrational amplitude between surface atoms and interior atoms, In light of this model, the critical transition temperatures of superconductive nanosolids can decrease or increase with the dropping size of nanosolids depending on the bond strength changes of interfacial atoms. The predicated results are consistent with the available experimental results for superconductors MgB2 and Nb thin films, Bi and Pb granular thin films and nanoparticles, Al thin films and nanoparticles.