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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-( d σ/ 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.
Physics of the Solid State – Springer Journals
Published: May 1, 2004
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