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57 for X? = 10 ~ at Τ = 668 Κ and Τ = 1136 Κ. Discuss the results. 0 6 5. e. 7). 6. 10(f) at T . Show how you could calculate ΔH% and A S ^ given ΔΗ® and AS® where these are the standard enthalpies and entropies of formation for v and υ respectively. 2 2 2 2 2 Additional General References R. A. Swalin, Thermodynamics of Solids, John Wiley, 1972, is a good and quite complete i n t r o d u c t o r y treatment of the thermodynamics of defects; see Chapters 13 and 14. C. P. F l y n n , Point Defects and Diffusion, Clarendon Press, 1972, is a detailed mathematical discussion; see C h a p t e r 2.

Henceforth, we will use the Gibbs rather than Helmholtz free energy, although cognizant of this small discrepancy. 6. 23) with respect to l/T to obtain the enthalpy of formation of the vacancies, 4 5(AG°/^r) d\nX ΔΗ* — Λ— = Τ = — v (2-24) which is a form of the Gibbs-Helmholtz equation. This enthalpy of vacancy formation is the quantity most amenable to direct experimental measure­ ment, rather than the absolute concentration of defects as a function of 42 II Point Defects in Elemental Crystalline Substances temperature.

F r o m about 2100 to 2500°C, vacancypositron trapping causes a pronounced decrease in the mean lifetime. At the highest temperatures most positrons decay from the trapped state causing the mean lifetime to approach a fixed value. T h e binding energy between a vacancy and a positron can be as large or even larger than the vacancy formation energy. 2 lists values of ΔΗ„ as obtained from positron annihilation experiments. Values of ΔΗ® obtained from methods other than positron annihilation are included for comparison.

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