Instability Analysis of Strained Interfaces Via a Discrete Atom Method
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JONG K. LEE Department of Metallurgical and Materials Engineering Michigan Technological University, Houghton, MI 49931
ABSTRACT The morphological instability of an epitaxially-strained, thin film is studied by means of a discrete atom method in a dislocation-free, two-dimensional crystal. The instability of the film-substrate interface is also examined in conjunction with the migration of the free surface. The results show that a mobile film-substrate interface can accelerate merger between the two surfaces, and anisotropic effects facilitate island formation. In addition, the instability of a curved interface is discussed with the results on the morphological evolution of coherent precipitates. A circular, soft precipitate in an isotropic matrix undergoes a series of shape transitions before reaching its equilibrium shape. As in the strained thin film case, transition begins with interfacial waves induced by the coherency strain. The waves then develop small lobes, which coarsen into a lower density of larger lobes. The larger lobes eventually coarsen as the equilibrium shape is approached. Anisotropic effects suppress some of the interfacial waves.
INTRODUCTION The microstructural development of elastically strained two-phase systems has been a subject of great interest. Two well-known cases are the formation of islands during thin film processing and the development of spatial correlations during coarsening of coherent precipitates in nickel-
base superalloys. However, our understanding of this subject has been severely limited due to the absence of a computational technique through which one can analyze the elastic state associated with arbitrarily-shaped,coherent precipitates in an elastically inhomogeneous system. Eshelby was the pioneer in the field of coherency strain, who devised the classic equivalency method [1-4]; however, the shape had to be limited to an ellipsoid. Since his work, several numerical techniques have been developed, but most involve either computations of an elastically homogeneous state, or approximate solutions for integro-differential equations when faced with an inhomogeneous system [5-10]. A new technique, called the Discrete Atom Method (DAM), has been recently introduced to accurately analyze coherency strain under an isotropic elasticity condition [11]. In this work the DAM is utilized to address morphological evolution of coherent precipitates and instability of an epitaxially-strained thin film. Problems based upon both isotropic and anisotropic elasticity in a two-dimensional, dislocation-free crystal are discussed.
DISCRETE ATOM METHOD Since the DAM was described in detail elsewhere [11], only a brief review is presented here. A two-dimensional triangular lattice with Hookean nearest neighbor interaction is elastically isotropic [12]. If the atomic bond energy is expressed in the form of k(r - a) 2/2, both Lam6 constants, X and [t, are equal to 0.433k, where k is the spring constant, r is the interatomic distance, and a is 63 Mat. Res. Soc. Symp. Proc. Vol. 356 * 1995 Ma
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