By Richard J. Borg and G. J. Dienes (Auth.)
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Extra info for An Introduction to Solid State Diffusion
Curve a is the instrumental resolution function, b is obtained for an annealed sample ( τ = 146 ps), and c is a consequence of p o s i t r o n t r a p p i n g in voids ( τ ^ 467 ps). [After R. M. J. Cotterill, I. K. MacKenzie, L. Smedskjaer, G. T r u m p y , and J. H. 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.
Nowick, Phys. Rev. 109, 1959 (1958); Phil. Mag. 15, 805 (1967); R. O. S i m m o n s and R. W. Balluffi, Phys. Rev. 117, 52 (1960), ibid 125, 862 (1962), ibid 129, 1533 (1963). 2 II Point Defects in Elemental Crystalline Substances 32 the same for both the x-ray and volume measurement. This is because the local distortion is elastically propagated to the surface of the crystal resulting in a commensurate change in the crystal volume. As shown by E s h e l b y the x-ray measurement and the macroscopic dilatation are altered the same way by the defect strain fields.
117-146. A good review and overview of experimental methods used to determine vacancy concentrations in metals; very large bibliography. W. Schilling, in Properties of Atomic Defects in Metals: Proc. ΙηίΊ. Conf. on Properties of Atomic Defects in Metals, N o r t h Holland Pub. Co. 1978, p . 4 6 5 - 4 8 9 . A n excellent discussion of all the various p h e n o m e n a which affect the properties of self interstitial atoms, such as relaxation volumes, elastic polarizabilities, defect vibrations, geometry of j u m p processes, a n d elastic interactions.