Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)

On spinodal decomposition

A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening

Abstract A microscopic diffusional theory for the motion of a curved antiphase boundary is presented. The interfacial velocity is found to be linearly proportional to the mean curvature of the boundary, but unlike earlier theories the constant of proportionality does not include the specific surface free energy, yet the diffusional dissipation of free energy is shown to be equal to the reduction in total boundary free energy. The theory is incorporated into a model for antiphase domain coarsening. Experimental measurements of domain coarsening kinetics in Fe-Al alloys were made over a temperature range where the specific surface free energy was varied by more than two orders of magnitude. The results are consistent with the theory; in particular, the domain coarsening kinetics do not have the temperature dependence of the specific surface free energy.

A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening

Dealloying is a common corrosion process during which an alloy is 'parted' by the selective dissolution of the most electrochemically active of its elements. This process results in the formation of a nanoporous sponge composed almost entirely of the more noble alloy constituents. Although considerable attention has been devoted to the morphological aspects of the dealloying process, its underlying physical mechanism has remained unclear. Here we propose a continuum model that is fully consistent with experiments and theoretical simulations of alloy dissolution, and demonstrate that nanoporosity in metals is due to an intrinsic dynamical pattern formation process. That is, pores form because the more noble atoms are chemically driven to aggregate into two-dimensional clusters by a phase separation process (spinodal decomposition) at the solid-electrolyte interface, and the surface area continuously increases owing to etching. Together, these processes evolve porosity with a characteristic length scale predicted by our continuum model. We expect that chemically tailored nanoporous gold made by dealloying Ag-Au should be suitable for sensor applications, particularly in a biomaterials context.

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Evolution of nanoporosity in dealloying

It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc , and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.

Free Energy of a Nonuniform System. I. Interfacial Free Energy

By finding the saddle point in the expression derived in Paper I (see reference 8) for the free energy of a nonuniform system, we have derived the properties of a critical nucleus in a two‐component metastable fluid.At very low supersaturations, we find that the properties of the nucleus approach those predicted by the classical theory that assumes the nucleus to be homogeneous with an interfacial energy that does not vary with curvature. However, with increasing supersaturation, the following changes occur in the properties of the critical nucleus. (a) The work required for its formation becomes progressively less than that given by the classical theory, and approaches continuously to zero at the spinodal. (b) The interface with the exterior phase becomes more diffuse until eventually no part of the nucleus is even approximately homogeneous. (c) The composition at the center of the nucleus approaches that of the exterior phase. (d) The radius and excess concentration in the nucleus at first decrease, the...

Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid

Free Energy of a Nonuniform System. I. Interfacial Free Energy and Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid

John E. Hilliard

Papers

Free Energy of a Nonuniform System. I. Interfacial Free Energy

Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid

Free Energy of a Nonuniform System. I. Interfacial Free Energy and Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid

On the equilibrium segregation at a grain boundary

An Evaluation of Procedures in Quantitative Metallography for Volume‐Fraction Analysis