Due to solute atoms diffusion, substitutional atoms diffuse by vacancies diffusion, so I am asking, if the concentration of solute atoms increases, so what will be the effect on vacancies mobility ?
That problem sounds like a good application for Monte Carlo simulations since these can account for "blocked by occupation" scenarios. I just had a quick look and found this:
Article Kinetic Monte Carlo simulations of vacancy diffusion in nond...
Fig. 5 of this work should be what you are looking for, I suppose.
Mr. Ibrahim,
A direct answer to your question can be obtained through a solution of the Fick’s second law, which connects the concentration with a function called ''diffusion.'' Depending on the boundary conditions and the model of the diffusion-function you are completely able to describe your model system. Very frequently, there is used the approximation to the latter function as a coefficient, which is constant during the experiment. It is described within the framework of the Einstein's model equation for the diffusion function, which is applicable to non-interacting particles, which are presented as spheres. Looking at your simple system (diffusion of vacancies, which, perhaps, do not interact mutually; and, perhaps, you approximate the atoms to spheres) most probably, the Einstein's model equation shall be applicable, as well.
For complex, real system, very frequently the Einstein's model equation of the diffusion function appears inapplicable to describe exactly the system. For instance, you could pay attention to our stochastic dynamic treatment of real mass spectrometric phenomena. Please, consider reference [1], where we have introduced our own-authored (to me and my co-author) model of the discussed function, which corresponds excellent-to-exact to the experiment in chemometric terms.
[1] Journal of Molecular Liquids, 292 (2019) 111307
Stochastic dynamic electrospray ionization mass spectrometric diffusion parameters and 3D structural determination of complexes of AgI–ion – Experimental and theoretical treatment
Bojidarka Ivanova, Michael Spiteller
If you are referring to solid state diffusion, there are a number of standard monographs which give the underlying theoretical treatments, which are well developed, e.g.
Shewmon, P. (Ed) (2016) Diffusion in Solids Springer
J. S. Kirkaldy (John Samuel) ; David J Young (David John)
Diffusion in the condensed state
London ; Brookfield, VT, USA : Institute of Metals, 1987
For the liquid state:
H.J. V. Tyrrell and K R Harris, Diffusion Liquids, Butterworths 1984
E L Cussler, Diffusion, Cambridge UP
Mr. Ibrahim,
Reference [DOI: 10.1103/PhysRevMaterials.2.123403] shown in the posting by Mr. Weippert, approximates the system again within the framework of the Einstein's model equation (please, consider equation 2; page 2 in the main text of the paper.) But, it is applicable to ideal systems, as I have mentioned in my posting to your question, above.
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