Grain Boundary Diffusion Controlled Precipitation as a Model For thin Film Reactions
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GRAIN BOUNDARY DIFFUSION CONTROLLED PRECIPITATION AS A MODEL FOR THIN FILM REACTIONS K. Barmak*, K.R. Coffey** *Department of Materials Science and Engineering, Lehigh University, 5. E. Packer Ave., Bethlehem, PA 18015, ** IBM, ADSTAR, 5600 Cottle Rd., San Jose, CA 95193 ABSTRACT In order to arrive at a model for nucleation in the reaction of polycrystalline thin films, we have made use of a transport model that combines atom transport across interface reaction barriers with transport along grain boundaries. Through this transport model, the boundary chemical potential, .li, and a characteristic length Li for each specie are defined. Lj and the ratio of grain size to Li determine the spatial variation and the time evolution of the boundary chemical potential respectively. Nucleation of the product phase is modeled as a process whose driving force is determined by these position dependent (and time dependent) boundary chemical potentials. Thus thin film reactions become similar to precipitation from bulk homogeneous supersaturated solid solutions. Numerical calculations, however, show that boundary diffusion results in low "effective" driving forces for nucleation which can lead to heterogeneous nucleation of even the first phase. The model provides a new approach to phase selection by re-evaluation of the driving force and considers the effect of product and reactant grain structure to be fundamental to the reaction process.
INTRODUCTION Within the framework of existing models of solid-solid reactions it is difficult to reconcile observations of nucleation limited first phase formation with either the large free energies of formation of these phases or with the driving forces that would be expected from the assumption of local equilibrium at interfaces 1 -4 . In this paper, we will present a model that explains this nucleation limited first phase formation and provides a new approach to selection of phases by re-evaluating the "effective" driving force, Ageff, for product phase nucleation. Since in this model Ageff is determined by grain and interphase boundary diffusion, the grain
structure of the reactants and products is considered to be fundamental to the reaction process. Before discussing the model, the experimental results for the formation of NbA13 in multilayer thin films of Nb/A13,4 , which led to the development of the model, will be discussed briefly. NbA13 is the first phase to form in the reaction of Nb/Al layers and the most striking finding is that the formation of this phase is a two-stage process. The two stages manifest themselves as two separate maxima in calorimetry experiments. The first stage has been quantitatively described 5 by proposing that nucleation barriers allow growth from only a fixed areal density of pre-existing nucleation sites in the plane of the interface. The growth of the nuclei into grains occurs two-dimensionally, with the growth direction parallel to the plane of the original interface. The first calorimetry maxima then represent the termination of the interfacial react
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