UT theoretical chemistry code forum

Dear Prof. Henkelman,

I just had a general conceptual question wrt vacancy migration in a structure. The vacancy formation energies are negative and favourable, however the energy barrier for vacancy migration between the two sites is extremely high (~ 7 eV). I am not sure if this would make sense, can you please explain?

So first, the vacancy formation energy should be positive in the sense that it costs energy to make a vacancy in a material. If it was negative, the material would not be thermodynamically stable.

In terms of a vacancy diffusion barrier, 7 eV sounds pretty high, but I don't know what the material is. Basically, the numbers seem a little fishy (that said knowing nothing about the system).

Thank you for your reply. Yes i meant that removing 1 atom from the structure, the formation energy of the structure is still negative.
But I am not able to understand how then the migration barrier is extremely high.

No, even if the overall formation energy is negative, that is not what's important: if the vacancy formation energy is negative the system will be unstable to vacancy formation.

Sorry if its a simple question but I just want to understand better. I am not able to get the difference between vacancy formation energy and the structure with 1 vacancy defect. Do you mean that the vacancy formation energy = (energy of perfect structure - energy of defected structure) ? And that i was referring to the energy of the defected structure earlier (it being negtive)?
So, did i get it right? the energy of an imperfect crystal is always > energy of perfect crystal. Hence by above formula, energy of defect would be always -ve ?

Normally one would talk about a free energy difference, but let's just assume that the energy is the key component of free energy for solids.

So a negative formation energy of a material means that the material is more stable than your reference components. That does not mean that the material is stable with respect to decomposition to other phases. Stability of a material is typically defined by compositions on a convex hull plot. If you are above the convex hull, then you would thermodynamically like to decompose into structures on the hull.

In terms of a structure with a vacancy - just because a structure with a vacancy has a negative formation energy does not make it stable with respect to other phases. Specifically, the vacancy formation energy describes the energy of the material with a vacancy plus the per-atom reference energy of the vacancy material as compared to the original material. If this is negative, the material would prefer to have a vacancy. But then it will likely prefer to have another vacancy and so the material becomes unstable. The vacancy formation energy of a stable material should be positive (even if the formation energy of a material with a vacancy is negative).

Got it, thanks very much for your reply