In the literature, a majority of studies on thermal properties of nanocrystals have taken the thermal features of interfaces as a representative of those of the whole nanocrystal. This treatment may cause big errors in predicting some important parameters such as the transition temperatures and critical sizes of phase for transformation in nanocrystalline materials, when the grain size is larger than several tens of nanometers. In the present paper, a model to calculate the thermodynamic functions of the whole nanocrystal has been developed with the consideration of the effects of both the interfaces and the crystal in the grain interior. The expressions of the enthalpy, entropy and Gibbs free energy, as a functions of the excess free volume at interfaces, temperature and grain size, are derived for single_phase nanocrystals. Using the Co nanocrystal as an example, thermal features of interfaces and the bulk nanocrystal have been compared with the conventional. Furthermore, the characteristics of β_Co→α_Co phase transformation in nanocrystalline materials are studied, the transformation temperatures at different levels of grain size, as well as the critical grain sizes at different temperatures, are predicted and compared with experimental results.
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