Diffusion
Diffusion phenomena are widely involved in many metallurgical transformations and processes and are frequently mentioned throughout the present work. This chapter treats the basic laws of diffusion Before going on to describe three typical cases where its
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8-1 Chemical diffusion General aspects Diffusion is a phenomenon whereby atoms move with respect to their neighbours. In a crystalline solid, the displacement involves jumps onto empry adjacent sites, which may either be lattice interstices or vacancies. It is often facilitated by the presence of crystal defects, such as dislocations, grain boundaries and phase interfaces, which represent continuous accumulations of potential sites. In general, only small solute elements, such as hydrogen, carbon, nitrogen and oxygen, can diffuse via interstitial sites. Larger atoms require the presence of vacancies, with which they exchange positions. An atom must acquire sufficient energy to make a successful jump. The frequency depends on the element concerned and varies strongly with temperature. At high temperatures, extremely high values can be attained, of the order of several billion jumps per second. For each individual atom, the displacement direction is completely random and for macroscopic diffusion to be observed, a gradient in chemical potential is necessary. Chemical diffusion phenomena are important in metallurgy, since they enable a system to evolve towards an equilibrium state. However, they are inherently sluggish, being much slower than thermal diffusion (heat conduction), so that true equilibrium is rarely achieved. It is therefore important to consider the transient situation priOf to the possible establishment of a steady state regime. The fundamentallaws governing macroscopic diffusion were derived by Fick, inspired by Fourier's work on heat conduction. Fick's first mathematical study was published in 1855.
M. Durand-Charre, Microstructure of Steels and Cast Irons © Springer-Verlag Berlin Heidelberg 2004
THE MICROSTRUCTURE OF STEELS ANO CAST IRONS His first law expresses the fact that the flux density J is proportional to the concentration gradient clx : ]
=
ac ax
-Dx-
(8-1-1)
J is the quantity of marter flowing through unit area in unit time. It is expressed in units of kg/m 2/s or atoms/m 2/s, depending on whether a mass flux or an atom flux is considered. Dis the proportionality constant called the diffusion coefficient, expressed in m 2/s, c is the volume concentration in kg/m 3 or atoms/m 3, and x is the distance, in metres. It should be noted that, in the customary scientific approach, c is generally given as a weight or atom fraction rather than as a percentage. The minus sign in Equation 8-1-1 signifies that the flux occurs down the concentration gradient (or more rigorously, down the chemical potential or activity gradient). Any chemi cal potential gradient will therefore tend to decrease and eventually disappear. Fick's first law is only strictly valid for diffusion along the x axis, in a binary system containing a single isotropic phase, at constant temperature and pressure. It is analogous to the heat conduction equation, where the heat flux is proportional to the temperature gradient. It is also similar in form to Ohm's law, where the current is proportional to the difference in electric
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