Use of the stereological counting measurements in testing theories of growth rates

Abstract

The characterization of growth during microstructural evolution can be couched in terms of the distribution of interface velocities in the system. Information about this distribution can be obtained from certain average interface velocities that may be determined from global geometric properties that are accessible through stereology. Three such average velocities, each with different weighting factors, have been defined. These velocities are$\overline {v_S }$, the surface area averaged growth rates of the surface elements,$\overline {v_H }$, the curvature averaged growth, and$\overline {v_K }$, the growth rate averaged with respect to the spherical image. It is shown that which of these velocity averages is an appropriate descriptor of growth depends primarily upon the dimensionality of the growth process under study, and is relatively insensitive to the details that govern the kinetics of growth. Thus, in the case of growth of rods, plates, lamallae, and so forth, the change in the characteristic dimensions of the growing phase which generally is the model parameter cannot be accessed except by choosing the velocity average appropriate to the situation. Cases in which some averages actually give information that is unrelated to the growth process under scrutiny, and hence may give misleading results, are emphasized.