The surface energy of nanocrystals

An equation for the surface energy a as a function of the size and shape of an n-dimensional nanocrystal was obtained. The nanocrystal had the form of an n-dimensional parallelepiped with a square base; the ratio between the side edge length and the base edge length f determined the shape of the system. The sigma value was shown to decrease as the number of atoms in the nanocrystal N decreases, and the larger the difference between the shape parameter f and one, the stronger the G(N) dependence. At high temperatures, the surface Helmholtz energy decreased as the temperature T increased, and the smaller the size of the nanocrystal of the given shape or the stronger the deviation of the shape of the nanocrystal at the given N from the thermodynamically stablest shape of the n-dimensional cube, the larger was the -(partial derivative sigma/partial derivative T) value. Nanocrystals were shown to melt when their surface energy decreased to a certain value independent of their size and shape. A polymorphic phase transition to a less dense structure decreased the surface energy. The conditions under which the inequality sigma(N, f; T, p) < 0 was valid, that is, crystal size fragmentation or shape dendritization could be observed, were considered.