Equilibrium Unstable Point Defects in Solids
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EQUILIBRIUM UNSTABLE POINT DEFECTS IN SOLIDS
V.M. KOSHKIN Polytechn. Inst., Department of Phys. Chem., Frunze str. 21, 310002, Kharkov, Ukraine ABSTRACT
It is shown that in addition to Frenkel's and Schottky's defects there is another type of equilibrium defects, such as an unstable pairs (UP) : vacancy and interstitial atom. UP has the life time of the order of 10-10 10- 12 s, independent of temperature. The review of the unstable pairs physics is presented. Numerous experimental evidences of equilibrium UP in semiconductors, insulators, especially in superionic crystals, and metals are discussed. POINT DEFECTS INSTABILITY ZONE
When analyzing Frenkel's pairs (FP), the interstitial atom (i) and the vacancy (v), left by it, are supposed to be independent. Meanwhile, in conceptully important work [1], where kinetics simulation of radiation defects has been investigated by the method of molecular dynamics, it was found that if the atom knocked out moves off its site not further than ro, then this atom i without activation at any low temperature returns to its vacancy. The physical nature of this phenomenon has been cleared in [2], where the analytical expression for the radius ro of the zone of absolute instability (IZ) in the case of i-v Coulomb interaction was obtained: ro= 13(zizve 2d/eUm) 1/2 ,
(1)
where Um is the migration energy of the self-interstitial ion; Zie, Zve are the i, v charges, respectively; e is the electron charge; d is the interatomic distance; E is the high- frequency dielectric constant; 13 is the coefficient of the order of unity defined by the relief of i migration potential. The expression (1) is obtained under assumption on the migration energy for v being much more than for i, confirmed by many experimental data for semiconductors, insulators and metals (the characteristic energy of v and i migration are 1-2eV and 0.03-0.2 eV, Mat. Res. Soc. Symp. Proc. Vol. 291. 01993 Materials Research Society
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respectively). So, r0 is the IZ radius for i around fixed v. The values z0~ 10-30 A for the Coulomb IZ calculated by (1) are in a good agreement with the experimental data obtained by Balzer, Kuznetsov, Smirnov and others. In metals with the Coulomb interaction screened by free charge carriers the i-v interaction can be considered as elastic. The estimate r 0 ~3-10 A for such an interaction found in [3] agrees with the experimental data by Biget, Thompson and the molecular dynamics results by Vineyard et al. Thus, IZ is the charachteristic feature of crystals of various types. PAIRS "VACANCY-INTERSTITIAL UNSTABLE EQUILIBRIUM DEFECTS
ATOM"
AS
If an excited atom does not escape from IZ then it returns to its vacancy for very short time rup 1010 -10- 1 2 s estimated in [4]. As shown in [4,5] the equilibrium concentration nup of unstable pairs with short life time in the first approximation is the following: nup=(4nr03/3d 3 ) exp (-Eup/kT),
(2)
where k is the Boltzmann constant, T is the temperature. Clearly, nup increases with increasing ro. The mean energy Eup of UP formation has a fol
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