Abstract
AbstractWe present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry-breaking structural changes of the crystal unit cell and reveals the importance of a mechanochemical spinodal, defined as the region in strain–composition space, where the free-energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechanochemical spinodal decomposition are variationally derived from a free-energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher-order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests that mechanochemical spinodal decomposition should occur in metal hydrides such as ZrH2−2c. The rich physics that ensues is explored in several numerical examples in two and three dimensions, and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high-temperature ceramics.
Highlights
Spinodal decomposition is a continuous phase transformation mechanism occurring throughout a solid that is far enough from the equilibrium for its free-energy density to lose convexity with respect to an internal degree of freedom
The latter could include the local composition as in classical spinodal decomposition described by Cahn and Hilliard,[1] or a suitable non-conserved order parameter as in the theory by Allen and Cahn[2] for spinodal ordering
A key requirement for continuous transformations is that order parameters can be formulated to uniquely describe continuous paths connecting the various phases of the transformation
Summary
Spinodal decomposition is a continuous phase transformation mechanism occurring throughout a solid that is far enough from the equilibrium for its free-energy density to lose convexity with respect to an internal degree of freedom The latter could include the local composition as in classical spinodal decomposition described by Cahn and Hilliard,[1] or a suitable non-conserved order parameter as in the theory by Allen and Cahn[2] for spinodal ordering. The existence of a single, continuous free-energy density surface for all phases participating in a transformation implies, by geometric necessity, the presence of domains in order parameter space, where the free-energy density is non-convex Reaching those domains through supersaturation (by externally varying temperature or composition) makes the solid susceptible to a generalised spinodal decomposition
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