Mass transport at interfaces in single component systems
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Mass Transport at Interfaces in Single Component Systems
W.W. MULL1NS
Mass transport at interfaces is induced by a gradient of chemical potential along the interface; typicall~r at surfaces, this is caused by a gradient in curvature and, at grain boundaries, by a gradient of normal stress. In addition, interface mass transport in metallic conductors is induced by strong electric fields/currents. On a sufficiently small scale, depending on the temperature, this interface transport dominates bulk diffusion. Continuum equations that specify the interface fluxes in terms of the preceding driving forces and continuity equations that describe the consequences of a divergence of these fluxes are presented; the chemical potential whose gradient is used as a driving force is that in local equilibrium with an element of interface. The equations are subject to boundary conditions at interface junctions that require the total emerging flux to vanish and that require, at junctions that pass flux freely, the chemical potential to be continuous. With the use of several approximations, solutions of the equations are given to describe, in a unified way, basic models of surface morphological evolution, Coble creep and diffusion-based models of sintering, and electromigration. Some of the approximations, not necessarily made simultaneously, are (1) isotropy of interface properties, both within the interface and with regard to the interface orientation; (2) surface slopes everywhere small compared to a reference plane; and (3) steady-state stress in grain boundaries. Limitations and possible extensions of the framework are discussed.
W.W. MULL1NS, University Professor Emeritus of Applied Science, is with the Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890. Professor Mullins received a Ph.D. in physics from the University of Chicago in 1955 under C.S. Smith. He was employed at the Westinghouse Research Laboratories in Pittsburgh from 1955 to 1960 and then at Carnegie Mellon University (then CIT), where he served as Head of the Department of Metallurgical Engineering and Materials Science from 1963 to 1966 and as Dean of the then College of Engineering and Science from 1966 to 1970. In 1985, he was appointed University Professor of Applied Science. His research has concentrated on the areas of the morphology of phase transformations, the capillarity-induced evolution of surfaces, the thermodynamics of stressed solids and solid surfaces, and the mathematical theory of grain boundary motion, grain growth, and coarsening. He was awarded a Fulbright and Guggenheim fellowship in METALLURGICAL AND MATERIALS TRANSACTIONS A
1961, received the Mathewson Gold Medal in 1963 and the Philip M. McKenna Memorial Award in 1981, was elected to the National Academy of Sciences in 1984, received a Professional Achievement Citation from the University of Chicago Alumni Association in 1990 and a Humboldt senior fellowship in 1992, and was named the Mehl Memorial Lecturer for 1994.
The Institute of
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