Evolution of Heterogeneous Systems

Document Type

Book

Publication Date

1-1-2023

Abstract

In this chapter we apply the ideas and methods developed in previous chapters to the dynamics of heterogeneous systems and obtain the celebrated time-dependent Ginzburg-Landau equation of the order parameter evolution. This equation will be applied to various heterogeneous states of the system. Its application to an equilibrium state shows that the criteria of the dynamic and local thermodynamic stability coincide. In case of a plane interface, this equation yields a traveling wave solution with a finite thickness and specific speed proportional to the deviation of the system from equilibrium. To better understand properties of such solution, we use the thermomechanical analogy, which was found useful for the equilibrium states. The drumhead approximation of the Ginzburg-Landau equation reveals various driving forces exerted on a moving interface and allows us to study evolution of droplets of a new phase. We extend the definition of the interfacial energy into the nonequilibrium domain of the thermodynamic parameters (phase diagram) and analyze growth dynamics of the antiphase domains using the Allen-Cahn self-similarity hypothesis. The analysis reveals the coarsening regime of evolution, which is observed experimentally. In this chapter we finish up column 4 of the beams and columns FTM configuration in Fig. P.1.

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