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Negative formation energy of a point defect in a solid

  1. Sep 1, 2011 #1
    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)
     
  2. jcsd
  3. Sep 9, 2011 #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.
     
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