**Greater diffusion rate of carbon atoms from nonlinear migration in
micro-cell and spatially heterogeneous stable states in FCC iron**

J Wang and Q Tao and LM Fu and W Lai and CJ Shen and Z Sun and AD Shan, JOURNAL OF MATERIALS SCIENCE, 53, 15952-15968 (2018).

DOI: 10.1007/s10853-018-2755-9

The nonlinear migration of C atom between nearest interstitial sites in fcc iron has been studied in the paper. It reveals an optimum migration pathway in the preferred crowdion direction in its infancy; the pathway is finally along the tetrahedral direction. This nonlinear tendency can be intensified by a repulsive force from another near neighbor C atom in the crowdion direction. We introduce an interaction model based on Coulomb's force, which indicates that this nonlinear migration mechanism is a foregone conclusion with a certain atomic geometric configuration. However, for a multiple-C system, we find that there exists a typical preferred orientation, which is a continuously stable structure maintained by the C atoms migrating in the crowdion direction. The first neighbor migrated structure is the main formation as a result of this preferential orientation. Based on this, we derive a novel diffusion equation by introducing a proportionality coefficient k(rho,) which can be closely related to the C structures absorbed on the surface during carburization. The diffusion coefficient will increase dramatically with a small perturbation of K rho. Moreover, a spatially heterogeneous occupation is introduced on a much larger scale. The results not only show that it is a relatively stable state but that the C diffusion coefficient is significantly larger than that of the other disorder-free C states. Meanwhile, it provides a repulsive force for nonlinear migration in the micro-cell. As a result, a greater diffusion rate will be achieved from both spatial heterogeneity and the nonlinear migration of C atoms.

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