half-crystal. The diffusion in the crystals is described by Fick's laws. The ratio of the solute concentration in the grain boundary to that in the adjacent atomic layer of the bulk is given by an enrichment ratio, . Most models assume to be a constant, but in practice this is only true for dilute systems with low segregation levels. In this dilute limit, if is one monolayer, is given as . The kinetics of segregation can be described by the following equation: where for grain boundaries and 1 for the free surface, is the boundary content at time , is the solute bulk diffusivity, is related to the atomic sizes of the solute and the matrix, and , respectively, by . For short times, this equation is approximated by: In practice, is not a constant but generally falls as segregation proceeds due to saturation. If starts high and falls rapidly as the segregation saturates, the above equation is valid until the point of saturation. In metal castings All metal castings experience segregation to some extent, and a distinction is made between macrosegregation and microsegregation. Microsegregation refers to localized differences in composition between dendrite arms, and can be significantly reduced by a homogenizing heat treatment. This is possible because the distances involved (typically on the order of 10 to 100 μm) are sufficiently small for diffusion to be a significant mechanism. This is not the case in macrosegregation. Therefore, macrosegregation in metal castings cannot be remedied or removed using heat treatment. Further reading See also Adsorption Absorption (chemistry) BET theory Freundlich equation Langmuir equation Reactions on surfaces Wetting Henry adsorption constant References Materials science Surface science