TABLE OF CONTENTS The phenomenological description of diffusion is embodied in Fick's two laws, which are empirical statements that relate the diffusive flow of matter to concentration gradients. To illustrate these laws, consider a single-phase dilute binary alloy in which the constituents are inhomogeneously distributed and let C be the concentration of the minor constituent. The concentration is a function of position and time and the concentration gradient induces a flow of matter. Fick's first law states that the flux of the diffusing species in a given direction has a magnitude proportional to the concentration gradient in that direction. That is, if J 1 is the flux along the x 1 axis, then
where D 1 is a proportionality factor called the diffusion coefficient. The negative sign expresses the fact that diffusion occurs from regions of high concentration to regions of low concentration.
If ( x 1, x 2, x 3) are the points in a Cartesian coordinate system with unit vectors ( i 1, i 2, i 3), then we would expect that an equation similar to (17.1.1) to hold for each of the three directions along the coordinate axes. For isotropic systems such as gases and liquids, this turns out to be the case. Furthermore, for such systems the diffusion coefficient is experimentally found to be the same in all directions. In nonhomogeneous systems, however, such as crystals with a low degree of symmetry,...
