The phenomenological formalism, which yields Fick's Laws for diffusion in single phase multicomponent systems, is widely accepted as the basis for the mathematical description of diffusion. This paper focuses on problems associated with this formalism. This mode of description of the process is cumbersome, defining as it does matrices of interdiffusion coefficients (the central material properties) that require a large experimental investment for their evaluation in three component systems, and, indeed cannot be evaluated for systems with more than three components. It is also argued that the physical meaning of the numerical values of these properties with respect to the atom motions in the system remains unknown. The attempt to understand the physical content of the diffusion coefficients in the phenomenological formalism has been the central fundamental problem in the theory of diffusion in crystalline alloys. The observation by Kirkendall that the crystal lattice moves during diffusion led Darken to develop the concept of intrinsic diffusion, i.e., atom motion relative to the crystal lattice. Darken and his successors sought to relate the diffusion coefficients computed for intrinsic fluxes to those obtained from the motion of radioactive tracers in chemically homogeneous samples which directly report the jump frequencies of the atoms as a function of composition and temperature. This theoretical connection between tracer, intrinsic and interdiffusion behavior would provide the basis for understanding the physical content of interdiffusion coefficients. Definitive tests of the resulting theoretical connection have been carried out for a number of binary systems for which all three kinds of observations are available. In a number of systems predictions of intrinsic coefficients from tracer data do not agree with measured values although predictions of interdiffusion coefficients appear to give reasonable agreement. Thus, the complete connection has not been made, even for binary systems. The theory has never been tested in multicomponent systems. An alternative path to understanding diffusion behavior in multicomponent systems is presented which is based upon a kinetically derived version of the flux equations. While this approach has problems of its own, it has the potential for providing a new range of insights into the process, and for devising simple models for predicting composition evolution in multicomponent systems.

Structure is at the heart of the materials science paradigm connecting processing with properties. In the hierarchy of structures that exist in materials microstructure offers the richest variety of structural arrangements. This variety is often conveniently accessible, e.g., simply by heat treatment or mechanical deformation. Exploration of the relation between properties and microstructure serves to establish a target range of microstructural states that will perform. In order to attain a target microstructure it is necessary to understand what microstructures are, and how they evolve in processing. This presentation focuses upon the set of tools that must be combined to achieve this control: 1. Geometry 2 Thermodynamics 3. Kinematics 4. Kinetics. The content of these tools is reviewed briefly and their uses illustrated in developing an understanding of how microstructures evolve. In this development an attempt is made to carry the description of each microstructural process as far as possible without making simplifying assumptions. The study of microstructures with this rigorous point of view was termed by F.N. Rhines, "microstructology".