: In nanocrystalline (NC) materials, when grain size is decreased, the atomic fraction of grain boundary (in comparison with conventional polycrystalline materials) is increased. Therefore, this matter could be change the properties of this materials, especially thermodynamics properties. Thereupon, study of thermodynamic properties of these materials with align=left Keywords: Nanocrystalline, Grain boundry, Triple junction, Quad node, Grain boundary regions, Equation of state, Allotropic transformation
