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The present study provides a simple model to predict the favored phase of Cu 2 S nanosolids upon variation of their size, shape, and temperature. Insight into the phase stability at the nanoscale will aid in the design of new nanomaterials. A study of the solid−solid phase transition demonstrated that the low-chalcocite to high-chalcocite transition temperature of Cu 2 S nanowires increases with increasing wire diameter consistent with recent experimental data. 31 At ambient temperature, the high-chalcocite phase is the most stable phase for nanofilms with a thickness below 1.5 nm, nanowires with a diameter below 3 nm and nanoparticles smaller than 4.5 nm, all in agreement with experimental observations.

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The size-temperature phase diagram of titanium nanoparticles has been obtained by calculating the corresponding Gibbs free energies of the FCC, BCC and HCP structures. It is found that these structures can transform from one into the other at specific sizes and temperature ranges, which is consistent with the available data reported in the literatures. Most importantly, we firstly predict that titanium particles with BCC structure can change to the FCC one in the size range 8.1-27.3 nm and in the temperature range 1156-1715 K.