By Richard J. Borg and G. J. Dienes (Auth.)
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Extra info for An Introduction to Solid State Diffusion
T h e mathematics are nicely related to atomic motion in a clear, understand able way. L. A. Girifalco, Atomic Migration in Crystals, Blaisdell, 1964, provides a lucid discussion of the basic physics with an absolute m i n i m u m of mathematics. S. C h a n d r a s e k h a r , "Stochastic Problems in Physics and A s t r o n o m y " Rev. Mod. Phys. 15, 1 (1943), goes far beyond the mathematical knowledge needed for this text. Nevertheless, C h a p t e r 1, pages 1-20 is one of the best and most rigorous derivation of the relation b e t w e e n diffusion and r a n d o m walks.
29) to represent the number of ways of arranging single vacancies on lattice sites in a manner which creates n o new divacancies. The second term defines the number of different ways of arranging divacancies on (z/2)N lattice sites exclusive of those sites already occupied by the N mono-vacancies. 29) can be much simplified without significant loss of accuracy if one remembers that both N and N are much smaller than N . 30). 30) - N„ \\N„ ! 24) which, as usual, is simplified by Stirling's formula.
Kirkendall, Metals Trans. AIME, 171, 130 (1947). l Technol. 13, Tech. Pub. 4 T h e marker movement experiment of Smigelskas and Kirkendall. The distance between the o p p o s i n g sets of M o wires was found to decrease with the time of the diffusion anneal, thus d e m o n s t r a t i n g that Z n diffuses faster than Cu. Aside from marker movement experiments, there now exists an over whelming number of independent methods, such as quenching and dilation experiments from which the validity of the vacancy mechanism can be inferred.
An Introduction to Solid State Diffusion by Richard J. Borg and G. J. Dienes (Auth.)