Resolution of the diffusional paradox predicting infinitely fast kinetics on the nanoscale

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33 Citations (Scopus)


In our paper, we offer a natural resolution for a long-standing paradox in diffusion. We show that the growth rate of the diffusion zone (reaction layer) should not go to infinity with decreasing time (as 1t), just because the diffusion permeability of the interface is finite. Expression for the changeover thickness X* between the linear and parabolic regimes of the interface shift in phase separating binary A(B) systems is derived in the framework of a deterministic atomistic model for diffusion. X* lies typically between 0.01 and 300 nm, depending on the composition dependence of the diffusion coefficient and the phase separation tendency of the alloy. While in ideal binary alloys with composition independent diffusivity, the deviation from the parabolic law practically cannot be observed, in real systems (where the diffusion coefficient can change several orders of magnitude with the composition), measurable deviations are expected as it was experimentally observed very recently in the NiCu and AuNi systems. We also offer an atomistic explanation for the phenomenological interface transfer coefficient K. It measures the finite interface permeability (proportional to the jump frequency across the interface) and thus it controls the shift of the interface at short times (diffusion distances). Although it is almost exclusively accepted in the literature that linear growth kinetics are the result of interface reaction control, our results suggest that the linear or nonparabolic growth of a reaction layer on the nanoscale cannot be automatically interpreted by an interface reaction.

Original languageEnglish
Article number035426
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
Publication statusPublished - Feb 27 2006

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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