Vacancy-energy model

As up to now the 2(z+ I) gj and gig coefficients cannot be experimentally determined or theoretically calculated, for numerical calculations a simple bondbreaking model has been applied (modified vacancy-energy model of Cheng et al. (1967)), where the bond-energy change when displacing an A or B atom from the lattice to the surface is — [(z-/)eAA + CABJ/2 or - [ (z - /)Cab + /Cbb 1 /2 respectively. 

Let us recall that this vacancy-energy model is incorrect, because it does not take into account local rearrangements of atoms around a vacancy after its creation. Indeed, as noted by Kim (1984), as the ratio of the number of surface sites to the total number of atoms in a typical crystal is of the order of 10, many pure-B surface layers will be formed when creating = 10 vacancies if Another process must... 

Non-stoichiometry in solid solutions may also be handled by the compound energy model see for example a recent review by Hillert [16]. In this approach the end-member corresponding to vacancies is an empty sub-lattice and it may be argued that the model loses its physical significance. Nevertheless, this model represents a mathematically efficient description that is often incorporated in thermodynamic representations of phase diagrams. 

Oxygen vacancy energies, Ed (0), for the surface sites 0(1-3) at the V20s(010) surface with and without surface relaxation. All data are obtained for the V10O31H12-O (= V10O30H12) model cluster [126], In addition, the table contains values of charges and relaxation dis-... 

Fig 3. Oxygen vacancy level and overlap population diagrams around the vacancy by model clusters of (In40 ) and (In40,(,) . MO energy of the defective cluster is alligned with that of the perfect crystal at the top of the 0-2p band. 

There are two ways in which the volume occupied by a sample can influence the Gibbs free energy of the system. One of these involves the average distance of separation between the molecules and therefore influences G through the energetics of molecular interactions. The second volume effect on G arises from the contribution of free-volume considerations. In Chap. 2 we described the molecular texture of the liquid state in terms of a model which allowed for vacancies or holes. The number and size of the holes influence G through entropy considerations. Each of these volume effects varies differently with changing temperature and each behaves differently on opposite sides of Tg. We shall call free volume that volume which makes the second type of contribution to G. 

From the discussion of location of hydrogen and muonium in the lattice, it is clear that the bond-center position is the lowest-energy site in many semiconductors. In GaAs and Si, this site has only recently been experimentally associated with anomalous muonium, which is relatively immobile (Kief et al., 1987, 1988). The agreement between theoretical results for hyperfine parameters (Van de Walle, 1990) and experiment allows an unambiguous identification of Mu with the bond center. Other models, such as the vacancy model proposed by Sahoo etal. (1985, 1989), are no longer considered acceptable candidates for Mu. ... 

Considerable attention has also been paid to modelling the thermodynamics of defects. This includes, for example, studies of the enthalpies of formation of vacancies or interstitial atoms and the association energies associated with the clustering of such defects. It is usually crucial to allow for the relaxation of the... 

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