Presence of solute atoms in host element at high temperature leads to creation of vacancies which are the reason for diffusion, but I cant get any correlation between concentration of solute atoms and vacancies concentration?
In crystals, the natural concentration of vacancies is temperature-dependent given by an Arrhenius term, where the activation energy is the energy required for vacancy formation. In the dilute limit, solute atoms do not significantly modify the natural vacancy concentration. For higher solute concentrations, if there is a positive or negative correlation between vacancy and solute concentration cannot be said in general. It depends on how the presence of a solute atom (or a cluster of them) modifies locally the energy required for vacancy formation. Note that in the case of favorable vacancy formation near the solute atoms, a part of the vacancies is bound to them. BR, René
Dear Mohamed Ibrahim
Hi
There is a PDF in the below link that explains the diffusion process and how to model the diffusion rate.
https://nanohub.org/resources/5949/download/ch06_diffusion.pdf
René Hammer Thank you very much
But I have misunderstanding about differentiating between vacancy formation energy and activation energy for diffusion, Is there any difference between them?
Dear @Mohamed Ibrahim,
there exist several processes which allow solute atoms through the host material. Not all of them require vacencies. For instance smaller atoms can move as interstitials and then the vacency formation energy is clearly not a directly diffusion determining quantity. Furthermore, most materials are not perfect and for instance dislocations, grain boundaries and free surfaces can be significant pathways for diffusion. BR René
René Hammer
Prof Rene, can you help me understand how the type of solute atom will affect the characteristics of vacancy diffusion?
Dear Mohamed Ibrahim ,
the dominating process for substitutional solute atoms diffusing through a host lattice is to exchange their place with the vacancies present in the host. The diffusion coefficient is therefore dependent on the vacancy concentration (which is independent of the solute atoms) and the migration barriers an atom has to overcome on its way into a vacant site. The latter is where the solute atom, for instance, its size and binding to the host and the chemical bonds of the host lattice itself come into the game. Ab initio calculations provide the answers and the parameters can be fed into e.g. models like the five frequency model for FCC materials. You can find more details and more advanced topics, for instance, in the following publication:
Article First principles impurity diffusion coefficients
BR,
René
Dear Prof Rene
May you answer this question?
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 ?
thank you in advance
René Hammer
Presence of interstitial atoms with bigger size than host atoms posses stress field in the lattice,I want to understand how this stress field affect diffusion process and also what will happen if stress field increases via increasing solute concentration?
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