The Trouble with Diffusion

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

Interdiffusion in the Mg-Al System and Intrinsic Diffusion in beta-Mg2Al3

Solid-to-solid diffusion couples were assembled and annealed to examine the diffusion between pure Mg (99.96 pct) and Al (99.999 pct). Diffusion anneals were carried out at 573 K, 623 K and 673 K (300 A degrees C, 350 A degrees C and 400 A degrees C) for 720, 360, and 240 hours, respectively. Optical and scanning electron microscopes were used to identify the formation of the intermetallic phases, gamma-Mg17Al12, and beta-Mg2Al3, as well as the absence of the epsilon-Mg23Al30 in the diffusion couples. The thicknesses of the gamma-Mg17Al12 and beta-Mg2Al3 phases were measured and the parabolic growth constants were calculated to determine the activation energies for growth. Concentration profiles were determined with electron microprobe analysis using pure elemental standards. Composition-dependent interdiffusion coefficients in Mg-solid solution, gamma-Mg17Al12, beta-Mg2Al3, and Al-solid solutions were calculated based on the Boltzmann-Matano analysis. Integrated and average effective interdiffusion coefficients for each phase were also calculated, and the magnitude was the highest for the beta-Mg2Al3 phase, followed by gamma-Mg17Al12, Al-solid solution, and Mg-solid solution. Intrinsic diffusion coefficients based on Huemann\u27s analysis (e.g., marker plane) were determined for the similar to Mg-62 at. pct Al in the beta-Mg2Al3 phase. Activation energies and the pre-exponential factors for the interdiffusion and intrinsic diffusion coefficients were calculated for the temperature range examined. The beta-Mg2Al3 phase was found to have the lowest activation energies for growth and interdiffusion among all four phases studied. At the marker location in the beta-Mg2Al3 phase, the intrinsic diffusion of Al was found to be faster than that of Mg. Extrapolations of the impurity diffusion coefficients in the terminal solid solutions were made and compared with the available self-diffusion and impurity diffusion data from the literature. Thermodynamic factor, tracer diffusion coefficients, and atomic mobilities at the marker plane composition were approximated using the available literature values of Mg activity in the beta-Mg2Al3 phase