Motion by curvature and impurity drag: resolution of a mobility paradox

ABSTRACTWe consider the problem of solute diffusion and segregation in the grain boundaries moving during a phase transformation in the framework of Cahn's impurity drag model. The concept of a dynamic segregation factor for the diffusion along moving grain boundaries is introduced. The difference between static and dynamic segregation factors may cause the apparent difference of the triple product of the segregation factor, grain boundary width and grain boundary diffusion coefficient for stationary and moving grain boundaries. The difference between static and dynamic segregation is experimentally verified for the Cu(In)-Bi system, for which the parameters of static segregation are well-known. It is shown that the complications associated with the dynamic segregation may be avoided during the study of the discontinuous ordering reaction. From the kinetics of this reaction, the activation energy of the grain boundary self-diffusion can be determined.

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A regular solution model for impurity drag on a migrating grain boundary

Acta Materialia ◽

10.1016/s1359-6454(00)00358-x ◽

2001 ◽

Vol 49 (4) ◽

pp. 589-597 ◽

Cited By ~ 38

Author(s):

M.I. Mendelev ◽

D.J. Srolovitz

Keyword(s):

Grain Boundary ◽

Regular Solution ◽

Regular Solution Model ◽

Solution Model ◽

Impurity Drag

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Chemically induced grain boundary dynamics, forced motion by curvature, and the appearance of double seams

European Journal of Applied Mathematics ◽

10.1017/s0956792501004806 ◽

2002 ◽

Vol 13 (1) ◽

pp. 25-52 ◽

Cited By ~ 4

Author(s):

PAUL C. FIFE ◽

XIAO-PING WANG

Keyword(s):

Free Boundary ◽

Grain Boundary ◽

Extended Model ◽

Forced Motion ◽

Chemically Induced ◽

Thin Film Model ◽

Motion By Curvature ◽

Boundary Model ◽

Grain Boundary Motion ◽

Boundary Dynamics

The free boundary model of diffusion-induced grain boundary motion derived in Cahn et al. [3], Fife et al. [6] and Cahn & Penrose [4] is extended, in the case of thin metallic films, to account for bidirectional motion, together with the appearance of S-shapes and double seam configurations. These are often observed in the laboratory. Computer simulations based on the extended model are given to illustrate these and other features of bidirectional motion. More generally, the extension accounts for the motion of grain boundaries whose traces on the film's surface are curved. The new free boundary model is one of forced motion by curvature, the forcing term possibly changing sign due to the bidirectionality. The thin film model is derived systematically under explicit assumptions, and an adjustment for grooving is included.

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