Negative formation energy of a point defect in a solid

In summary, the authors of the conversation discuss the issue of negative formation energies reported for point defects in solids using different simulation techniques. They mention two possible explanations for this phenomenon - the interaction with periodic boundary conditions and incorrect reference chemical potentials. They also address the importance of understanding this issue when calculating equilibrium concentrations of defects. They provide various explanations for the occurrence of negative formation energies, including the distortion of the host material and the release of strain. Ultimately, they suggest that further research and individual case studies are needed to fully understand this topic.
  • #1
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It is very common to see in the literature negative formation energies reported for point defects in solids using different simulation techniques ranging from Density Function Theory to Molecular Dynamics.
The authors rarely comment on what does that mean physically. I will mention here two possible explanations that I can think of and I'd appreciate it if you can share with us your understanding of this issue:

(1) Because of the small size of the systems that can be handled by simulation and because of the common practice (or in sometimes the need) to use periodic boundary conditions, defects interact with its images leading to unphysical lowering of their formation energies.

(2) The result is simply unphysical because the computed reference chemical potential of the species that caused the defect (for example sulfur gas reference for a sulfur defect in a sulfide ) is wrong.


The issue is very important especially when it comes to compute the equilibrium concentration of these defects using the exponential expression: n=n0exo(-E/kT)
 
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  • #2
In my opinion, negative formation energies does not make sense but admittedly there exist a few explanations.

The formation energy is calculated as the difference between relaxed systems where the supercell of host material and the supercell of the point defect should be of the same size. Usually, the formation energies of crystals are of major interest. In this case, the configuration of the host material is already in an (local) energy minimum. Vacancies, interstitials or substitutionals would distort the material and bring it out of its minimum configuration. So from this viewpoint, negative formation energies does not make sense.

If the host material is already strained from the very beginning, an interstitial can give rise to a relaxation. For instance, think of a strained bond close to the added interstitial. The introduction of an interstitial can involve the formation of new bonds which allow the host material to relax.

In amorphous materials, strained bonds exist and an introduced point defect, such as a substitutional, may result in a release of strain. Similar considerations may apply to compressed bonds.

An other explanation might be a change in the supercell size which is varied during the relaxation. But this would mean that both materials would dissolve and form a new material. However, this is only the case for the host materials that have the possibility to expand.

I guess this topic is much easier to discuss on the basis of individual cases - including references from literature.
 

1. What is the significance of negative formation energy of a point defect in a solid?

The negative formation energy of a point defect in a solid indicates that the formation of the defect is energetically favorable. This means that the defect is more likely to form in the solid than to not form, as it would require less energy for the defect to exist than for it to not exist.

2. How is the negative formation energy of a point defect calculated?

The negative formation energy of a point defect is calculated by taking the difference between the total energy of the solid with the defect present and the total energy of the perfect crystal without the defect. This value is then multiplied by -1 to indicate its negative energy.

3. What factors can contribute to a negative formation energy of a point defect?

There are several factors that can contribute to a negative formation energy of a point defect, including the size and charge of the defect, as well as the composition and structure of the solid. Additionally, temperature and pressure can also play a role in the formation energy of a point defect.

4. Can a point defect have a positive formation energy?

Yes, a point defect can have a positive formation energy, indicating that its formation is not energetically favored. In this case, the defect is less likely to form in the solid and its presence would require more energy than its absence.

5. How does the negative formation energy of a point defect affect the properties of a solid?

The presence of a point defect with negative formation energy can significantly alter the properties of a solid. These defects can affect the mechanical, electrical, and thermal properties of the material, and can also influence its chemical reactivity and diffusion behavior.

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