An Introduction to Solid State Diffusion by Richard J. Borg and G. J. Dienes (Auth.)


By Richard J. Borg and G. J. Dienes (Auth.)

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The factor 2 Iv arises because, unlike divacancies, the vacancy and impurity are distinguishable entities, and hence reversing them on their adjacent lattice sites gives rise to a different complexion. i\j. JV . 44) and ΔΞ = k ln = k[\n Ω + In Q + ln Q ] € 7 v = Δ 5 + ΔΞ + Iv 7 υ ΔΞ . 45). 7 LF=N LE l r Iv v + N *E 0 + B N bE rB - T(N, A S / + N AS: + N ltt v fB AS;„) - TAS . 45) W e again make use of Stirling's approximation, neglect the vibrational Thermodynamics of Simple Defects 47 entropy, a n d calculate the individual chemical potentials μ,, μ , and μ Ιυ dAF —— = AE, - TAS, a Ν, 3AF AE 3AF = AE Iv V + kT \n{N Iv - TAS V - N,) - kT In Ν, = μ, L - TAS ν + kT In 2 + kT In - N L + kT \n(N N fv - kT In N lu - Ν ) - kT In N„ = μ„.

Yet both radiation damage and sputtering form an area of solid state kinetics and are at least deserving of mention. D. The Vacancy Mechanism T h e vacancy mechanism is by far the most general and important of all the diffusion mechanisms. All cases of substitutional diffusion which have been carefully investigated appear to operate through a vacancy mechanism. As the n a m e indicates, a diffusive j u m p occurs only via an exchange of position with an adjacent vacancy. Consequently, a flux of diffusing atoms in any given direction, requires a vacancy flux of equal magnitude in the opposite sense.

V where a is the effective average number of complexing sites per disloca­ tion, and J_ stands for dislocation. ) + (F ±V F ° „ ) = 0. 63) This assumes that the total dislocation count remains the same, although the n u m b e r of available sites for vacancy binding decreases as vacancies Problems 51 become attracted to dislocations. Thus, if the complex concentration is given by (a° - a')(±) = ( J . v)= V A ' . 61). Problems 1. W h a t are the contributions to the vacancy formation enthalpy in elemental crystals?

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