Investigators: J. A. Simmons, L. A. Bendersky, W. J. Boettinger, J. W. Cahn, J. R. Manning and J. A. Warren

Technical Description:

The focus of this work is to identify areas of process technology where quantitative modeling can lead to the production of improved materials at reduced cost. The project was initiated to foster interactions between mathematical modeling and materials science with emphasis on the development of new mathematical techniques. It involves extensive interactions with mathematicians and computational scientists outside of NIST funded by the ARPA Computational and Applied Mathematics Program and includes, as an important aspect, the organization of workshops and symposia to enhance the dialog between mathematicians and material scientists. With the advent of large scale parallel processing, computational modeling of material microstructure development as a function of processing conditions offers a promising method of predicting process results. Because understanding of materials science is becoming more quantitative and computational capabilities are becoming more profound, there are new opportunities both to apply presently available mathematical techniques to materials processing and to develop new mathematics for this technology. Recent project work has emphasized applications to microstructural evolution, including modeling of alloy solidification, solid-state diffusive transformations, and incorporation of stress effects. This work is now being redirected to focus on thin film technology.

Technical Objectives:

• To involve mathematicians in the development of new mathematics needed to treat practical materials science problems.

• To model effects arising from complex conditions that arise in real materials processes, including ordering processes, thin films, and facetted surfaces, where discontinuities abound.

Anticipated Outcome:

• Predictive mathematical models will be developed that can be incorporated into materials processing systems. This will allow control and improvement of material products and reduction of materials processing costs.

• Improved interactions will be developed between the materials and mathematics communities to facilitate cooperative efforts even beyond the direct topics treated in this project.

Accomplishments for FY 1995:

• Developed geometric measure theory important for understanding the effect of anisotropic surface energies on interface facetting during both solidification and grain growth. Microstructural facetting strongly influences interface properties.

• Developed and applied new Master Equation techniques to model ordering processes in alloys. Time sequences were obtained showing the growth of ordered domains, which are crucial in the development of alloy properties.

Impacts and Technical Highlights:

• Mathematical models and comparisons with experiment developed in the current work have verified assumptions being incorporated by the ARPA-funded industrial Investment Casting Cooperative Arrangement into commercial software for casting design and the NIST-sponsored Consortium on Casting of Aerospace Alloys in models for processing aerospace materials.

• A symposium on "Mathematics of Thermodynamically Driven Microstructural Evolution", Oct. 29-Nov 1, 1995, TMS/ASM Materials Week Meeting, Cleveland, Ohio was organized as part of this project, bringing together mathematicians and material scientists to focus on this topic. The symposium was jointly sponsored by ASM International, the Society of Industrial and Applied Mathematics (SIAM), The Minerals, Metals and Materials Society (TMS), Advanced Research Projects Agency (ARPA), and NIST.

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Last modified: Mon Jan 06 09:46:15 1997 Metallurgy Webmeister