A homogeneous chemical composition and microstructure always is desired and seldom attained in practice. Corrosion resistance, age hardening and machinability are just a few material characteristics that are affected by chemical segregation. Chemical segregation creates regions that are either anodic or cathodic relative to the average composition. In a corrosive environment, these regions function as tiny batteries and the anodic regions corrode. Segregation also affects heat treatment of aluminum and steel. In the case of an 356 aluminum alloy casting, solute-rich regions overage, while underaging occurs in the solute-lean regions. On average, the casting may be of the correct hardness, but the microstructure is far from ideal or expected. Homogenization heat treatments often are used to reduce the degree of segregation and improve performance.
The mathematics of diffusion is relatively simple in one dimension; however, the complexity increases dramatically when real microstructures are considered. For example, Fig. 1 shows a hypothetical solute concentration profile measured along the length of a dendrite and intersecting the secondary dendrite arms. As a one-dimensional (1-D) problem, the solute profile can be handled by a series of cosine or sine terms. A more realistic approach would be to consider the secondary arms as an array of cylinders and consider diffusion in a radial direction. Solution of the latter problem requires a series of Bessel functions. A comparison of the 1-D and 2-D solutions shows that the 1-D case always requires a longer time to achieve the same degree of homogenization. Thus, the simpler 1-D case represents an upper bound to the required time.