Frenkel notion

In terms of formal point defect terminology, it is possible to think of each silver or copper ion creating an instantaneous interstitial defect and a vacancy, Ag and VAg, or Cu and Vcu as it jumps between two tetrahedral sites. This is equivalent to a high and dynamic concentration of cation Frenkel defects that continuously form and are eliminated. For this to occur, the formation energy of these notional defects must be close to zero. 

The notion of point defects in an otherwise perfect crystal dates from the classical papers by Frenkel88 and by Schottky and Wagner.75 86 The perfect lattice is thermodynamically unstable with respect to a lattice in which a certain number of atoms are removed from normal lattice sites to the surface (vacancy disorder) or in which a certain number of atoms are transferred from the surface to interstitial positions inside the crystal (interstitial disorder). These forms of disorder can occur in many elemental solids and compounds. The formation of equal numbers of vacant lattice sites in both M and X sublattices of a compound M0Xft is called Schottky disorder. In compounds in which M and X occupy different sublattices in the perfect crystal there is also the possibility of antistructure disorder in which small numbers of M and X atoms are interchanged. These three sorts of disorder can be combined to give three hybrid types of disorder in crystalline compounds. The most important of these is Frenkel disorder, in which equal numbers of vacancies and interstitials of the same kind of atom are formed in a compound. The possibility of Schottky-antistructure disorder (in which a vacancy is formed by... 

Figure 1 is a schematic representation of Frenkel s notion an atom or ion can get dislodged from its normal site to form etn interstitial-vacancy pair. He further proposed that they do not always recombine but instead may dissociate and thus contribute to diffusional transport and electrical conduction. They were free to Wcuider about in a "random walk" mcuiner essentially equivalent to that of Brownian motion. . . this meant they should exhibit a net drift in an applied field. 

The model of free volume going back to the classical papers of Frenkel and Firing [48, 80, 144-147] has been widespread in the physics of liquid and solid states of matter. Some concepts allowing improvement in the nature of fluctuation free volume have been offered in the last 15 years [148-150]. Nevertheless, there is one more aspect of the problem, which has not been mentioned earlier. As a rule, the application of free volume theory for the description of the properties of amorphous bodies is based on a notion that the free volume characterises the structure of the indicated bodies. This postulate is due to a considerable extent to the absence of a quantitative model of the structure of the amorphous condensed state, including the structure of amorphous state polymers. Strictly speaking, one should understand that by structure we mean distribution of body elements in space [151]. It is evident that free volume microvoids cannot be structural elements and at best only mirror the structural state of the studied object. Taking the introduction of some structural elements (relaxators, see for example, [148]) into consideration has practically no influence on the structural representation of free volume. 

The concept of the molecules local ordering in a liquid (in contrast to no gas structure ) appeared in the 1920-ies, when Stuart introduced the notion of cybotactic area [79]. The ideology of the particles aggregation in the liquid systems has had a long history (see papers [73,77,80-82]), the attempts to express this idea quantitatively within the colloidal approximation go back to the works of Smolukhovsky [83] and Osvald [84]. The further development of the liquid state theory is connected with the works of Ya. Frenkel, J. Bernal et al. (e.g. see [73,80-82]). 

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