Diffusion Equation and Cottrell Atmosphere Dragging of Edge Dislocation in High Concentration Solid Solutions

Abstract

The purpose of this paper is to obtain the Cottrell atmosphere and its dragging stress τ_d of an edge dislocation moving with the constant velocity v in concentrated solid solutions. Using the Fermi-Dirac distribution and Einstein’s relation, the diffusion equation of the concentrated solutions is derived as
(Remark: Graphics omitted.)
where J is the diffusion flux, D the mutual diffusion coefficient, c the local concentration of solute atoms, Ω the volume occupied by a lattice point, and W the energy change when a solvent atom is interchanged with a solute atom. It is shown that Takeuchi-Argon’s theory and their numerical results are applicable to the concentrated solutions only by replacing c₀ with c₀(1−c₀), where c₀ is the average solute concentration, in their final results. The method of computer experiment by Yoshinaga and Morozumi is slightly modified and applied to the concentrated solutions. The results at |A⁄akT|\lesssim2 are approximated fairly well by the equation,
(Remark: Graphics omitted.)
where A=(1+ν)μbv_ε⁄3π(1−ν), ν Poisson’s ratio, μ the shear modulus, b the Burgers vector, v_ε the volume difference between solute and solvent atoms, V=va⁄D, a the lattice constant of the imaginary lat-tice moving with the dislocation, V₀\simeq1.2, i₁\simeq0.29 and i₂=0.16. The velocity v_c which gives maximum τ_d is given by v_ca⁄D\simeq1.3; this becomes different from the result of Cottrell, v_c\simeqDkT⁄A, especially at |A⁄akT|→0.