Abstract
If a drop of a dilute mixture of milk in water is placed under a microscope and observed by transmitted light, small fat globules can be seen. These globules are about 1 µm in diameter and continually make small movements hither and yon. These movements, which are called Brownian motion, give a continual mixing and are the cause, or mechanism, of the homogenization, whose rate could be measured in a macroscopic diffusion experiment. For example, if a drop of the same milky solution is placed in water, it will tend to spread out, and the mixture will ultimately become homogeneous. In this latter experiment a concentration gradient is present, a flux of fat globules1 exists, and a diffusion coefficient could be measured. This is not quite an after-lunch experiment though, since turbulent mixing must be avoided and diffusion occurs quite slowly (D = 10−8 cm2/sec).
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Notes
A readable, interesting treatment of Brownian motion can be found in the translation of Einstein’s original papers. (A. Einstein, Investigations on the Theory of Brownian Movement, Dover Publications, New York, 1956.)
For an advanced, complete treatment which deals more with mathematics and less with physical phenomena, see N. Wax (ed.), Selected Papers on Noise and Stochastic Processes, Dover Publications, New York, 1954.
For further reading on the random walk problem, G. Gamov, One, Two, Three … Infinity, Viking Press (1947), Chap. 8, gives a very readable introduction.
J. Manning, Diffusion Kinetics for Atoms in Crystals, Van Nostrand, 1968, gives a more detailed discussion of its use in diffusion problems.
A solution of this type is given in the first few pages of B. S. Chandrasekhar, Revs. Modern Phys., 15 (1943) 1.
This article is also reprinted in N. Wax (ed.), Selected Papers on Noise and Stochastic Processes, Dover Publications, New York, 1954.
Or see M. N. Barber, B.W. Ninham, Random and Restricted Walks, Gordon & Breach, (1970) Chap. 8.
For a more detailed discussion of the problem see Chap. 7 of C. P. Flynn, Point Defects & Diffusion, Clarendon-Oxford Press, (1972).
C. Zener, in W. Schockley (ed.), Imperfections in Nearly Perfect Crystals, p. 289, John Wiley & Sons, Inc., New York, 1952
or C. P. Flynn, Point Defects & Diffusion, Clarendon-Oxford Press, (1972), pp. 335–7.
C. Wert, C. Zener, Phys. Rev., 76, (1949) 1169.
R. A. Johnson, in Diffusion, ASM, Metals Park, OH, 1973, pp. 25–46.
The energy changes given here are those of F. Fumi, Phil. Mag., 46 (1955) 1007.
The discussion given here follows that of H. Huntington, G. Shim, E. Wajda, Phys. Rev., 99 (1955) 1085.
A. Kuper, H. Letaw, L. Slifkin, C. Tomizuka, Phys. Rev., 98 (1955) 1870.
R. Simmons, R. Balluffi, Phys. Rev., 119 (1960) 600.
R. Emrick, Phys. Rev., 122 (1961) 1720.
See also, H. Bakker, Diffusion in Crystalline Solids, ed. G. E. Murch, A. S. Nowick, Academic Press, 1984, p. 189–258.
The reader who is not familiar with this law will find it discussed under this title or “equilibrium constant” in most books on thermodynamics or physical chemistry, e.g., L. Darken, R. Gurry, Physical Chemistry of Metals, chap. 9, McGraw-Hill Book Company, Inc., New York, 1953.
J. N. Mundy, Phys. Rev. B3 (1971) 2431.
See also N. Peterson, J. Nucl. Matl., 69, (1978) 3.
J. Federer, T. S. Lundy, Trans, AIME, 227, (1963) 592.
J. M. Sanchez, D. de Fontaine, Acta Met., 26, (1978) 1083.
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Shewmon, P. (2016). Atomic Theory of Diffusion. In: Diffusion in Solids. Springer, Cham. https://doi.org/10.1007/978-3-319-48206-4_2
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