Abstract
Using the model of fast phase transitions and previously reported equation of the Gibbs–Thomson-type, we develop an equation for the anisotropic interface motion of the Herring–Gibbs–Thomson-type. The derived equation takes the form of a hodograph equation and in its particular case describes motion by mean interface curvature, the relationship ‘velocity—Gibbs free energy’, Klein–Gordon and Born–Infeld equations related to the anisotropic propagation of various interfaces. Comparison of the present model predictions with the molecular-dynamics simulation data on nickel crystal growth (obtained by Jeffrey J. Hoyt et al. and published in Acta Mater. 47 (1999) 3181) confirms the validity of the derived hodograph equation as applicable to the slow and fast modes of interface propagation.This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.
Highlights
Anisotropy of interfaces plays a crucial role in the formation of equilibrium shapes [1], changing of growth direction of crystals to the preferable one at a critical
A kinetic phase field model [21,22], which would be reduced to the single equation of motion called ‘the hodograph equation of interface’, is used [23,24]
Model, we follow the analysis of Wheeler & McFadden [14] who obtained the sharp interface limit corresponding to the case for which the diffuse interface width is small compared to a characteristic macroscopic length scale
Summary
Anisotropy of interfaces plays a crucial role in the formation of equilibrium shapes [1], changing of growth direction of crystals to the preferable one at a critical. We extend the description of anisotropic interfaces to the highly rapid regimes of their motion with the appearance of local non-equilibrium effects [20]. With this aim, a kinetic phase field model [21,22], which would be reduced to the single equation of motion called ‘the hodograph equation of interface’, is used [23,24]. Using the formalism of the Cahn–Hoffman ξ -vector and the presently developed anisotropic phase field model, we follow the analysis of Wheeler & McFadden [14] who obtained the sharp interface limit corresponding to the case for which the diffuse interface width is small compared to a characteristic macroscopic length scale. Electronic supplementary material, [26] and appendix A add the material for the derivation of the present hodograph equation applicable to the slow and fast modes of interface propagation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
