%0 Journal Article
%T Wagner-Vengrenovich Distribution
%A Bohdan V. Ivanskii
%A Anatolii V. Moskalyuk
%A Sergey V. Yarema
%A Igor I. Panko
%A Miroslav O. Stasyk
%J ISRN Nanomaterials
%D 2013
%R 10.1155/2013/651576
%X The process of coarsening of nanoclusters or nanocrystals (NCs) is investigated for the case when cluster growth (dissolution) is governed simultaneously by both diffusion along dislocation pipes and the rate of formation of chemical connections (chemical reaction) at cluster surface, namely, Wagner¡¯s growing mechanism. For that, the total flow of atoms to (from) a cluster is represented by two parts, namely, diffusion part and the Wagner (kinetic) one. The dependence of the rate of growth of NC on the ratio of the parts of the total flow has been determined as well as the NC¡¯s size distribution function referred to as the Wagner-Vengrenovich distribution. Computed distribution is compared with experimentally obtained histograms. 1. Introduction Ostwald¡¯s ripening (OR) is the final stage of formation of a new phase as a result of phase transformation, such as decay of oversaturated solid solutions. Nanoclusters or nanocrystals (NCs) of new phase having different sizes interact through the Gibbs-Thomson effect that results in dissolution of small NC and growth of large ones. Diffusion growth of NC under matrix of volume diffusion (ls-mechanism) has been firstly studied by Lifshitz and Slyozov [1, 2]. Wagner has showed later [3] that beside diffusion mechanism, another mechanism of NC growth is possible, which is governed by the rate of formation of chemical connections (chemical reaction) at NC surface (w-mechanism). The theory developed in the cited papers is referred to as the LSW theory. Practical verification of this theory shows that in many cases, it is proper for the description of experimental data on temporal behavior of the mean NC size and the NC size the distribution function, while in other cases the LSW theory must be refined. In this connection, NC growth is considered in papers [4, 5] as a result of combined action of two growing mechanisms, diffusion (ls) and Wagner¡¯s (w) ones. In the framework of the modified LSW theory and taking into account both mechanisms of growing (ls and w), we can obtain a size distribution in the form of the generalized Lifschitz-Slyozov-Wagner distribution [4]. This distribution can refer to a much wider range of the experimental histograms than each of the Lifschitz-Slyozov (LS) and Wagner¡¯s ( ) distributions separately. The products of nanotechnologies [6¨C8] become new objects of applying the LSW theory. As sizes become 100£¿nm and less [9], the characteristics of both separate NCs and of the system as a whole change cardinally that provides practically useful properties. The OR is among probable factors
%U http://www.hindawi.com/journals/isrn.nanomaterials/2013/651576/