Impingement function for nucleation on non-random sites

Many kinetics theories assume that nucleation of a new phase takes place on sites that are randomly located within the parent matrix. In practice, however, nuclei form at non-random sites. These sites could be situated, for example, on grain boundaries or within a heavily deformed grain or deformation band. Applying formal kinetics theories to reactions in which sites are non-randomly located may result in erroneous values calculated for microstructural quantities such as the number of grains per unit of volume, and for kinetic quantities such as the interface velocity. Non-random sites pose particularly difficult problems because formal kinetic equations might still fit measured data even when the nucleation sites are non-random, as will be demonstrated in this study. Therefore, measurement of additional parameters that are able to detect non-randomness, such as the contiguity function recommended by Vandermeer, becomes mandatory. In this work, the concept of an “impingement function” is introduced. Our impingement function aims at replacing the usual relationship between the extended and real volume fractions when nucleation takes place at non-random sites. Knowledge of this impingement function allows treating non-random nucleation sites in a manner that parallels the approach used for random sites. The impingement function by its own definition is directly related to impingement and can be seen both as a fundamental description of non-randomly located nuclei and a factor that relates kinetic properties of extended quantities to the kinetic properties of their corresponding real quantities. The new methodology was tested with the help of cellular automata computer simulation. The analysis of computer simulated data showed that the impingement function was much more sensitive to underlying non-randomness than the contiguity. Even when the non-randomness was apparently not so severe, the impingement function was able to show that impingement was significantly different from the random case.