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The solid-state phase transformation from an amorphous solid into a nanocrystalline (NC) phase is studied from a thermodynamic point of view. The thermodynamic quantities of the interfaces (including the excess volume, excess energy, enthalpy, entropy, and the Gibbs free energy), which constitute a significant component in the NC materials, were calculated based on a quasiharmonic Debye approximation. By means of thermodynamic equilibrium conditions and quantitative calculations, we found that the structural characteristics of the interfaces are closely correlated with the grain-size limits crystallized from the amorphous phase. With a decrease in grain size, the excess volume as well as the excess energy of the interfaces formed during the crystallization will be reduced or, in other words, with the NC samples crystallized from the amorphous solids, a smaller grain size might be always associated with interfaces containing a smaller excess volume. This conclusion is in good agreement with experimental data of various systems for elements and alloys.
K. Lu (Sun,) studied this question.