Soliton interpretation of relation between driving force and velocity of interface motion in martensitic transformation

Abstract

The relationship between the driving force for a martensitic transformation, ΔG, and the motion velocity of the martensite/parent interface, υ, is derived for the Hamiltonian of a one-dimensional atomic chain with a nonlinear periodic potential model suggested by Peyrard and Remoissenet [Phys. Rev. B 26, 2886 (1982)] as ΔG = (2ma/π2)ω[C/√1-υ2/C 2](4.02692-2.931 92r - 0.762 24r2), where m is the atomic mass, a the spacing of the one-dimensional lattice, r the shape parameter indicating the periodic lattice potential and C and ω are the characteristic velocity and frequency of the system, respectively. This result shows that the velocity of interface motion increases as the driving force increases. This equation is valid for different materials, regardless of whether the softening for martensitic transformation exists. © 2000 American Institute of Physics.