Size effects in surface segregation

Abstract

The effect of the slab thickness (d) on the segregation behavior has been investigated for a phase separating system in a slab consisting of atomic planes parallel to the free surfaces. The calculations were carried out using the Fowler–Guggenheim approximation in the monolayer limit. It is shown, that by varying the surface fraction ξ, a surface phase transition can occur, similar to a semi-infinite system where a change in temperature can lead to a phase transition (S-shaped segregation isotherm). Furthermore, the existence of a minimum on the free energy curve versus d was examined. It was demonstrated that such a minimum can exist in the nanocrystalline region.

Grain boundary segregation and thermodynamically stable binary nanocrystalline alloys

“…This is unfortunate because most of the experimental nanocrystalline alloys described earlier are nondilute, and not all of them exhibit a strong tendency for segregation ͑e.g., Ni-W͒. Recently, Beke et al 48,49 relaxed some of these assumptions in a statistical model, and considered segregation to free surfaces on onedimensional nanocrystals. The statistical nature of this model is attractive in principle, providing a concrete framework to evaluate the conditions for equilibrium directly from a freeenergy function.…”

Segregation inhibited grain coarsening in nanocrystalline alloys

“…They are based on the only assumption that grain stabilization occurs with saturated boundaries. This, however, can be questioned ͑see the results of our previous article͒, 3 or at least can be fulfilled in very special cases only. Thus-taking also into account the eligible quantity of experimental evidence as well-further analyses of the general case͑s͒ are desirable.…”

“…3 No attempt was made there ͑as it was done by Kirchheim 1 or here above͒ to find a simple relation describing the temperature dependence of 0 . As it was illustrated above this is a rather complicated problem and will be analyzed in a separate article.…”

“…[1][2][3] This segregation induced grain stabilization is due to the gain of the ͑chemical͒ energy related to the increased amount of segregated atoms: for small grain sizes this can be larger than the increase of the free energy caused by the enlarged number of the grain boundaries. This phenomenon, since the stabilization of different nanostructures is a crucial problem in many applications, can have high technological importance as well.…”

Thermal stability of nanomaterials

“…The thermodynamic aspects of the segregation effects have been considered in several studies (see, for example, the publications 21,22,28,56,77,78 ). The patterns of adsorption at crystallite boundaries have been studied since long ago.…”