Focusing on physical metallurgy and materials, Materials Week '97, which incorporates the TMS Fall Meeting, features a wide array of technical symposia sponsored by The Minerals, Metals & Materials Society (TMS) and ASM International. The meeting will be held September 14-18 in Indianapolis, Indiana. The following session will be held Tuesday morning, September 16.

*Program Organizers:* F.G. Yost, Sandia National Laboratories, Albuquerque, NM 87185; A.J. Markworth, Dept. of Materials Science, The Ohio State University, Columbus, OH 43210-1179; J.E. Morral, Dept. of Metallurgy, University of Connecticut, Storrs, CT 06269-3136; L. Brush, Dept. of Materials Science and Engineering, University of Washington, Seattle, WA 98195

*Room:* 201

*Session Chair:* J.E. Morral, Dept. of Metallurgy, University of Connecticut, Storrs, CT

**LINEAR AND NONLINEAR MODIFICATIONS OF THE DIFFUSION EQUATION:** *John W. Cahn,* Materials Science and Engineering Laboratory, NIST, Gaithersburg, MD 20899

There has been increased interest in the formulation of the diffusion equations, modified to reflect specific complications of various applications. Many of these applications will be described later in this symposium. The modified equations can be nonlinear and may contain source or sink reaction terms, higher gradients, nonlocal terms, surface diffusion, etc. The study of these modified equations has often yielded valuable insights into the phenomena being studied, as well as results that sometimes deviate from what is expected from the linear diffusion equation in surprising ways. Various physical problems will be discussed to illustrate how modifications to the equations originate, and what qualitative effects these have on solutions.

**9:00 am INVITED**

**RELAXING THE ASSUMPTION OF LOCAL THERMODYNAMIC EQUILIBRIUM AT INTERFACES IN STRESSED DIFFUSION COUPLES:** *William C. Johnson,* Department of Materials Science and Engineering, Thornton Hall, University of Virginia, Charlottesville, VA 22903-2442

Impediments to establishing local thermodynamic equilibrium at an interface during a diffusional phase transformation will affect the motion of the interface, the interfacial compositions, and the composition profiles in each phase. A continuum theory on interfacial motion will be presented which accounts for deviations in chemical equilibrium at the interface and impediments to interface motion. Results are applied to the motion of a planar interface in a stressed, binary diffusion couple and show that large, time-dependent deviations in the interfacial compositions with respect to the stress-free equilibrium compositions are possible. This work is supported by NSF under Grant DMR-9496133.

**9:30 am INVITED**

**DIFFUSION AT LATTICE STEPS-AN ATOMIC VIEW:** *Gert Ehrlich, *Materials Research Laboratory and Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Steps on a crystal surface dramatically alter the ordinary diffusion of atoms over the surface and play a vital role in the growth of crystals. The atomic events taking place at steps are now accessible to direct examination by taking advantage of the unique ability of the field ion microscope to image individual metal adatoms without significant perturbation. Recent studies of jump processes which take place when atoms attempt to incorporate at ascending and descending steps on closepacked fcc surfaces have revealed a variety of unexpected phenomena, such as atom interchange and funneling, which will be briefly reviewed. Supported by the Department of Energy under Grant No.DEFG02-9lER-45439.

**10:00 am INVITED**

**THE EFFECTS OF COARSENING ON CASCADES OF SPINODAL DECOMPOSITION IN MULTICOMPONENT ALLOYS:** *David J. Eyre, *Department of Mathematics, University of Utah, Salt Lake City, UT 84112

Cahn-Hilliard equations suitable for multicomponent alloys are employed to study spinodal decomposition. Numerical simulations of spinodal decomposition show that the phase separation into multiple phases proceeds via a sequence or cascade of separations, and that coarsening of the solution is required before subsequent phase separation can take place. Numerical simulations suggest that this coarsening can delay phase separation for long times. In this talk, results of an investigation into the role of coarsening in secondary phase separation will be presented.

**10:30 am BREAK**

**10:40 am**

**DIFFUSIONAL EVOLUTION OF ARBITRARILY SHAPED PRECIPITATES UNDER ELASTIC FIELDS:** *P.H. Leo,* Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455

We study the diffusional evolution of arbitrarily shaped precipitates embedded coherently in an infinite elastic matax. We develop two distinct approaches to this problem. The first is a sharp interface method, where the composition and elastic fields are calculated by using a boundary integral method, and-the precipitate-matrix interface is tracked through its normal velocity. The second is a diffuse interface (Cahn-Hilliard) model, where microstructure is tracked by the evolution of smooth composition and displacement fields. In both formulations, nonlinearities enter through the curvature of the precipitate-matrix interface. We compare the two formulations. We also give results for precipitate shapes and motions as a function of elastic inhomogeneity, interfacial energy anisotropies and elastic anisotropies.

**11:00 am**

**SIMULATION OF MICROSTRUCTURE IN 422 STAINLESS STEEL DURING NITRIDING:** *Carlene Hannigan,* Advanced Technology Center, The Torrington Company, Torrington, CT 06790; Caian Qiu, J.E. Morral, Department of Metallurgy and Materials Engineering, Institute of Materials Science, University of Connecticut, Storrs, CT 06268

Microstructure evolution in commercial 422 stainless steel (Fe-11.3Cr-0.8Mn-1.0Mo-0.8NI-1.0W-0.2C wt %) has been investigated during nitriding by computer modeling. The nitriding process is simulated by means of the finite difference program DICTRA, which assumes diffusion control and local equilibrium. Composition profiles and diffusion paths have been calculated for various nitrogen potentials at the surface.

**11:20 am**

**LINEAR RESULTS FROM THE NON-LINEAR FORM OF THE DIFFUSION EQUATION WHEN ANALYZING DIFFUSION COUPLE DATA:** Yoon-Ho Son, New-Tech Co., Ltd, Daegu, Korea; *J.E. Morral, *University of Connecticut, Storrs, CT

When the diffusivity of a material is independent of concentration, the so-called "diffusion equation" is linear. Several methods of analyzing diffusion couple data to measure the diffusivity have been developed based on this linear form. However if the diffusivity is proportional to concentration, then the diffusion equation is nonlinear via a term proportional to the concentration gradient squared. Despite significant changes in concentration profiles that can result from the non-linear term, it has been found numerically that no detectable error is introduced when using the constant diffusivity, "square root diffusivity analysis" on diffusion data. The analysis always gives a diffusivity which is the average of initial alloy diffusivities. This observation has been made for all possible variations of the diffusivity in binary systems and for selected variations of the diffusivity matrix for ternary systems. The conclusion is that the "square root diffusivity analysis" can be applied to diffusion couples with significant concentration differences without necessarily introducing error.

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