Vacancy formation energy, defined

The energetics of non-stoichiometric surfaces can be characterized in two different ways. One consists in defining the vacancy formation energy Evf. It is the energy required to extract one neutral oxygen atom from the... 

If a vacancy is created in an otherwise perfect lattice, the implication is that an additional atom must now occupy the surface of the crystal. The basic idea behind the vacancy formation energy is that it is a measure of the difference in energy between two states one being the perfect crystal and the other being that in which an atom has been plucked from the bulk of the crystal and attached to the surface. From a computational perspective, the vacancy formation energy may be defined as... 

Point (microscopic) defects in contrast from the macroscopic are compatible with the atomic distances between the neighboring atoms. The initial cause of appearance of the point defects in the first place is the local energy fluctuations, owing to the temperature fluctuations. Point defects can be divided into Frenkel defects and Schottky defects, and these often occur in ionic crystals. The former are due to misplacement of ions and vacancies. Charges are balanced in the whole crystal despite the presence of interstitial or extra ions and vacancies. If an atom leaves its site in the lattice (thereby creating a vacancy) and then moves to the surface of the crystal, it becomes a Schottky defect. On the other hand, an atom that vacates its position in the lattice and transfers to an interstitial position in the crystal is known as a Frenkel defect. The formation of a Frenkel defect therefore produces two defects within the lattice—a vacancy and the interstitial defect—while the formation of a Schottky defect leaves only one defect within the lattice, that is, a vacancy. Aside from the formation of Schottky and Frenkel defects, there is a third mechanism by which an intrinsic point defect may be formed, that is, the movement of a surface atom into an interstitial site. Considering the electroneutrality condition for the stoichiometric solid solution, the ratio of mole parts of the anion and cation vacancies is simply defined by the valence of atoms (ions). Therefore, for solid solution M X, the ratio of the anion vacancies is equal to mJn. 

The earliest vacancy-mediated melting theories were essentially instability theories, which predicted the temperature at which the free energy of formation of vacancies becomes negative (an example of such arguments can be found in the section on KTHNY theory above). More recent theories (such as O Reilly s) view melting as a vacancy condensation transition. Vacancy-mediated melting theories have never enjoyed wide acceptance because the concept of a vacancy is ill-defined in the liquid phase, and because such theories seem to be inapplicable to substances that contract upon melting. 

Vacancies are quite common in many crystals, both in close-packed metallic structures as well as in open covalent structures. The creation of a vacancy costs some energy, due to the breaking of bonds, which is called the formation energy This is defined as the energy of the crystal containing a vacancy, that is, one atom fewer than the ideal crystal which has N atoms, denoted as — 1), plus the... 

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