Open AccessThe hodograph equation for slow and fast anisotropic interface propagation
Author(s) -
Peter Galenko,
A. Salhoumi
Publication year - 2021
Publication title -
philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.074
H-Index - 169
eISSN - 1471-2962
pISSN - 1364-503X
DOI - 10.1098/rsta.2020.0324
Subject(s) - hodograph , curvature , physics , anisotropy , interface (matter) , classical mechanics , gibbs free energy , statistical physics , mathematical analysis , mechanics , mathematics , geometry , thermodynamics , optics , bubble , maximum bubble pressure method
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. Hoytet al. and published inActa 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)’.