A model for nonclassical nucleation of solid-solid structural phase transformations
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RODUCTION
MARTENSITIC nucleation in solids has been extensively studied within the framework of the so-called classical nucleation theory (based on linear elasticity for evaluation of the self-energy associated with nucleation and on the assumption of a sharp interface with a constant interfacial free energy). The classical nucleation model[1–4] is known to accurately represent heterogeneous nucleation behavior in the vicinity of equilibrium.* Outside this regime, and * At equilibrium, the potential wells associated with the parent and product phases have the same level of free-energy density.
especially as the condition for lattice instability** is ** At lattice instability, the free-energy density barrier vanishes.
approached, nonclassical nucleation is predicted.[5] Characteristic features of nonclassical nucleation in solid-state transformations which are not predicted by classical theory include the divergence of the size of the critical nucleus and the vanishing of the nucleation energy barrier as the condition for lattice instability is approached. An alternative approach to modeling solid-state phase transitions is based on nonlinear, nonlocal elasticity and can be regarded as a Landau–Ginzburg-type approach wherein the Landau potential (nonconvex free-energy functional) is augmented by a gradient energy contribution resulting from a continuum description of material behavior at atomistic scales.[6] This approach is well suited to the study of critical
Y.A. CHU, Researcher, is with the Chung-Shuan Institute of Science and Technology, Taiwan 32500, Republic of China. B. MORAN, Professor, Department of Civil Engineering, and G.B. OLSON, Professor, and A.C.E. REID, Research Associate, Department of Materials Science of Engineering, are with Northwestern University, Evanston, IL 60208. Manuscript submitted July 28, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
phenomena associated with nonclassical nucleation and has been used in the context of one-dimensional nucleation problems by Olson and Cohen[7] and Haezebrouck.[8] Moran et al.[9] use a strain-based finite-element method together with a perturbed Lagrangian algorithm to study nucleation of a dilatational phase transformation for materials governed by a Landau–Ginzburg potential. Chu and Moran[10] use a displacement-based element-free Galerkin method,[11,12] in conjunction with a Landau–Ginzburg model in two dimensions, for nucleation of a deviatoric (square to rectangular) transformation.[13,14] The restriction to low-dimensional systems is a practical limitation of these spatially resolved methods, which do not favor closed-form analytical solutions. The applications mentioned previously are all numerical and, in two dimensions, tend to be computationally intensive.[10] This method has not been attempted for a true three-dimensional (3-D) system. A new model, extended from the classical nucleation theory and spanning the range from classical to nonclassical nucleation, is introduced here. An attractive feature of this model is that closed-form anal
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