Velocity-Dependent Herring Equation

The advanced modification leading to the velocity-dependent Herring equationEquationHerring was given by Müller-Krumbhaar et al. (J Cryst Growth 38:13–22 1977 [1]) on the basis of the Ginzburg-Landau formalism for phase transitionsPhasetransition. This advancement allows for the analysis of interfaces in dynamics (see, e.g., Sect. 7 in the monograph (Statistical physics of crystal growth. World Sientific, Singapore 1996 [2])). Generalization of the Herring equationEquationHerring of Müller-Krumbhaar et al. (J Cryst Growth 38:13–22 1977 [1]) was performed for spatial and temporal variations of the chemical potentialPotentialchemical difference that acts as a driving force at the anisotropic interface motion. Following their work, derivation of the Herring equationEquationHerring for the interface dynamics is given in the present Chapter.