carbon atoms through vacancies. This model has been implemented to numerical studies of a segregation problem under irradiation of binary alloys [@anthony72; @ohl73; @oh72; @oswt74; @sth73; @ow74; @jl76; @jl77; @ropw78; @jl78; @wol79], where $A$- and $B$-type atoms diffuse over vacancies and interstitials. We simplified the segregation problem for diffusion of carbon atoms over vacancies in one-dimensional ($1D$) case, and solved analytically the non-linear differential equations for carbon atoms- and vacancies- concentrations. The obtained results show that a vacancy created, say in the middle of the sample, diffuses to the edge of the sample. We think that boundary of samples can be considered as an “ extended defect” like dislocations, grain boundaries or a hole of a big size. Therefore, the vacancies diffuse and are incorporated, commonly say around extended defects in the sample.

The paper is structured as follow: the computational method, employed for our [*ab-initio*]{} calculations is described in the next Section II. Section III presents the obtained results of [*ab-initio*]{} DFT calculations. Section IV provides our analytic investigation of diffusion-segregation problem for carbon atoms through vacancies, and migration of the vacancies toward the sample boundary. Our conclusions and speculations are given in Section V.

Computational methods
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SIESTA 