A concise derivation of the contact conditions at a migrating sharp interface

Abstract

A sharp interface model can be used to simulate the kinetics of diffusional phase transformations provided the transformation process is controlled by migration of the interface and by diffusion of components in the bulk phases only. The contact conditions at the migrating sharp interface can be derived by applying the principles of mass balance and maximum dissipation. A concise derivation of the contact conditions on this basis is presented in this work.

The kinetics of diffusive phase transformations in the light of trans-interface diffusion

“…[1,2,19,23]. It has been derived in [15] that trans-interface diffusion for a mathematically and physically sharp interface must vanish and that the driving force at the migrating interface is the jump of the chemical potentials of a substitutional component, being equal for all substitutional components, and zero for interstitial components. This result is in accordance with the diffusion potentials for substitutional and interstitial components becoming zero in the limit of a zero interface thickness δ, lim d !…”

“…The rate of Gibbs energy available for trans-interface diffusion becomes zero for equal jumps of the chemical potentials ½½l A ¼ ½½l B . The contact conditions for the chemical potentials of the substitutional and the interstitial components at a migrating sharp interface are derived in [15]. However, Gibbs energy dissipation due to trans-interface diffusion is attributed to the QSI.…”

“…A schematic sketch of the situation is presented in Figure 1. The rate of Gibbs energy _ G for the migrating sharp interface follows from, see [15]:…”

“…Efforts have been made to use sharp interface models and introduce the deviation from local equilibrium by a finite interface mobility [13]. The concise contact conditions at a migrating sharp interface can be found in [14] and for alloys with substitutional and interstitial components in [15]. However, information about a concise value of the interface mobility is required.…”

Kinetics of diffusive phase transformations: From local equilibrium to mobility-driven migration of thick interfaces

“…Thereby, the contact conditions at the migrating sharp interface differ from the contact conditions for local equilibrium. The jumps of the chemical potentials of the interstitial components at the sharp interface with a finite mobility are zero, those of the substitutional components at the interface are all equal and deviate from zero prior to equilibration [4,5].…”