It was shown that the quantized phonon energy, the nano-particles' crystal lattice specific heat and superconductivity transition temperature all related to the phonon'…

Its thermal properties were calculated by means of lattice dynamics. It has been found that the entropy and specific heat of nanocrystalline are higher than that of single crystal.

By using improved variational method, the internal energy per plaquette and the specific heat curves of the Tangent action in SU(2) lattice gauge theory arc worked out.