Dependence of the surface energy on the size and shape of a nanocrystal

An expression is derived for the surface energy σ as a function of the size and shape of a nanocrystal. It is shown that the wider the deviation of the shape parameter f from unity, the more pronounced the decrease in the surface energy σ with a decrease in the number N of atoms in the nanocrystal. The dependences of the average coordination number, the surface energy, and the melting temperature on the number N exhibit an oscillatory behavior with maxima at points corresponding to numbers of atoms forming a defect-free cube. The surface energy decreases with an increase in the temperature T. It is found that the smaller the nanocrystal size or the greater the deviation of the nanocrystal shape from the thermodynamically most stable shape (a cube), the larger the quantity-(dσ/dT). It is established that the nanocrystal undergoes melting when the surface energy decreases to a value at which it becomes independent of the nanocrystal size and shape. The conditions providing fragmentation and dendritization of the crystal are discussed. It is demonstrated that, at N>1000, the dependence σ(N) coincides, to a high accuracy, with the dependence of the surface tension of the nanocrystal on N. The inference is made that bimorphism is characteristic of nanocrystals. This implies that nanocrystals can have platelike and rodlike shapes with equal probability.