The Universal Instability of the Separation Boundary Between a Non-Hydrostatically Stressed Elastic Crystal and its Melt
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THE UNIVERSAL INSTABILITY OF THE SEPARATION BOUNDARY BETWEEN A NON-HYDROSTATICALLY STRESSED ELASTIC CRYSTAL AND ITS MELT MICHAEL A. GRINFELD Department of Mathematics, Rutgers University, New Brunswick, NJ 08903
ABSTRACT
In the absence of surface tension and external force fields, the equilibrium between a hydrostatically stressed crystal and its melt is neutral with respect to the perturbations associated with particle transfer from one region of the boundary into another. However, under the action of arbitrary small nonhydrostatic components of the stress field in the elastic crystal, the neutral equilibrium is transformed to an unstable equilibrium [1]. This instability is very general in nature; for example, for it to be seen the liquid media need only to be able to dissolve the solid phase or in some way to assist the transport of particles along the crystal's surface. In contrast, the surface tension, roughly speaking, stabilizes the shape of the interphase boundary but it cannot suppress the instability generated by the nonhydrostatic components of the stress field in the region of sufficiently long perturbations. Until now the basic instability mechanism discussed here seems to have escaped the attention of theorists. This mechanism allows one to look in a completely new way at a broad range of phenomena. We discuss tentative manifestations and role of this instability in low temperature physics, in materials science, in theory of crystal growth, and, in particular, in theory of epitaxy and of the StranskiKrastanow pattern of growth of thin crystalline films.
Phase transformation waves and stress driven instability
Up to now we do not have any clear general approach for describing the dynamics of heterogeneous systems with phase boundaries. This is a conceptually difficult general problem, clouded by serious deficiency in our knowledge concerning the nature of the interphase layers and the processes occurring within them. In one special important practically case, however, a potentially perspective simple approach for the description of dynamics of heterogeneous systems with phase boundaries may be proposed. The approach allows one to formulate a full system of relations which is sufficient for investigation of the slowly propagating phase boundary. Here we have in mind an asymptotic case when the dynamical processes under consideration have the characteristic time scale of evolution much longer than the characteristic time of establishing the phase equilibrium on the boundary. In these situations it looks reasonable to rely on so called "instantaneous kinetics" Mat. Res. Soc. Symp. Proc. Vol. 237. 01992 Materials Research Society
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approximation, i.e., in essence, to use the conditions of the phase equilibrium on the boundary while dealing with the dynamical problems. Applying the "instantaneous kinetics" approximation to the melting- freezing waves propagating along the phase boundary separating solid and liquid phases He-4 Andreev and Parshin [2] established the following dispersion relation:
c
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