By Richard J. Borg and G. J. Dienes (Auth.)
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O. L. ] Experimental Methods 37 Appendix B, then one can apply simple first order kinetics to derive, say, the enthalpy of defect formation. Taking single equilibrium vacancies for our example and assuming no dissociation, after trapping we write for the disintegration rate of the trapped positrons ~ = <°Χ ν λ (2-8) Χ where λ , is the specific rate or decay constant which is the reciprocal of the m e a n lifetime of trapped positrons, o is the energy averaged cross-section for trapping, and X is the mol fraction of vacancies.
Referring to Fig. 2, note that if the A g is a radioactive tracer, each j u m p into a nearest neighbor position consists of a displace ment of a/2. 2 A schematic illustration of the interstitialcy mechanism. T h e atoms or ions X a n d Θ c a n b e the same a n d are differently labeled only for ease of visualization. A t o m X c o m m e n c e s in a n interstitial position, b u t displaces atom Θ from its original substitutional site i n t o a n adjacent interstitial position. Hence, if this is an ionic crystal, a measurement of the ionic conductivity will lead to twice the value of D as will be obtained by direct tracer techniques.
D. Franklin, Chap. 9, p. 27, Point Defects in Solids, Eds. J. H. Crawford and L. M. Slifkin, Plenum Press (1972). T h e value of ΔΗ® for Fe is estimated indirectly. a b 1. Experimental Methods There are relatively few techniques capable of accurately measuring the equilibrium concentration of vacancies. As a rule, one measures only the enthalpy of formation as the result of varying some specific property which reflects the concentration as a function of temperature. A. Quenching T h e most common technique applied to metals for the measurement of vacancy concentrations is to quickly quench a wire made from the material of interest from a succession of temperatures and measure the change in electrical resistance at liquid He temperature, which is proportional to the change in vacancy concentration, which in turn is a function of the initial annealing temperature.