On the basis of a model for size-dependent cohesive energy, the size, shape, and dimensionality effects on melting temperatures of nanocrystals are modeled in a unified form. The model predicts that the melting temperature T_m(D,d,λ) decreases with reducing size D and dimensionality d or increasing shape factor λ. For nanoparticles with the same D values, there is T_m(icosahedron) > T_m(sphere or cube) > T_m(octahedron) > T_m(tetrahedron). Moreover, the ratio of depression of T_m(D,d,X) is about 1:2λ_(wire):3λ_(particle) for thin films, nanowires, and nanoparticles when D is large enough, for example, 6 run. The model is found to be in accordance with available experimental, MD simulation, and other theoretical results for Au, Ag, Ni, Ar, Si, Pb, and In nanocrystals.
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