Nucleation in a Concentration Gradient

The process of formation of intermediate phases at interdiffusion is accompanied by a competition between stable and metastable phases. Solid-state amorphizing reactions (SSAR) present a classical example, when at the initial stage a metastable amorphous layer is formed and grows rather than the stable intermetaUides [1-3]. It is clear that the search for possible ways to estabhsh control over phase competition is highly essential for technological processes. Another problem related to phase competition refers to the order of phases formed in thin films and multi-layers [4, 5], 

At long times of annealing, according to the generally accepted theory, three stable flat phase layers must grow with the parabolic law Xi = Quite often real experiment reveals, however, a different behavior - either one stable phase or a metastable crystal or an amorphous layer is formed. Thus, phases compete with each other like different regimes of reaction-diffusion. 

The investigation of the initial stages of reaction-diffusion in multilayers, carried out during recent years, by differential scanning calorimetry (DSC), proved that the stage of intermediate phase nucleation at solid-state reaction does take place. DSC experiments [6-8] have shown that the formation of a new phase in multilayers can involve two stages. For example, the curve illustrating the dependence of heat flux on time at formation of NbAls in multilayers Nb/Al (obtained by deposition) has two maxima. X-ray analysis and electron microscopy confirmed that both peaks correspond to the formation of the phase NbAls. Similar curves with two peaks are obtained for such systems as Co/Al, Ni/Al, Ti/Al, Ni/amorphous Si, and V/amorphous Si. 

Diffusion-Controlled Solid State Reactions. Andriy M. Gusak Copyright 2010 WILEY-VCH Veriag GmbH Co. KGaA, Weinheim ISBN 978-3-527-40884-9 

The mentioned circumstances lead to the necessity of inevitable change of the classical theory of nucleation - both in its kinetic and thermodynamic aspects. Such modifications have been made during the last decades. These modifications are analyzed in this and the next chapters. 

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If the condition. Equation 3.47 is not fulfilled, that is, diffusion permeability of phase 1 is high enough and its nuclei are competitive, the concentration preparation time becomes equal to the incubation time. Equation 3.46. A rigorous theory of nucleation in a concentration gradient and its influence on the incubation period and phase competition was developed by Gusak, Desre, and Hodaj in the series of papers [7, 33-40]. 

Thermodynamics of the Polymorphic Mode of Nucleation in a Concentration Gradient... 

A new possible explanation for phase suppression and for sequential phase growth in thin films is proposed in the context of the nucleation in a concentration gradient approach. Nucleation of intermediate phases at the initial stage of reactive diffusion is influenced by the sharp concentration and chemical potential gradients... 

In Section 5.2, phenomenological models of the first intermediate phase nucle-ation at reactive diffusion in a binary diffusion couple are presented, and methods of thermodynamic analysis of the process, based on the theory of nucleation in a concentration gradient field, are given. We have pioneered the explanation of experimental results using thermodynamic suppression of nucleation rather than kinetic factors [1]. 

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