The Mesoscale Interface Mapping Project

The Mesoscale Interface Mapping Project (MIMP) is an NSF MRSEC involving researchers in the Materials Science and Engineering, Mathematical Sciences, and Electrical and Computer Engineering Departments at CMU (http://mimp.mems.cmu.edu/).

Nearly all technologically useful materials are granular in structure, including metals and ceramics from interconnects on chips to airframes. The grain structure is responsible for many aspects of material behavior. Moreover, the grain boundary properties are responsible for additional features of material behavior, especially durability and lifetime properties, and here we enter the domain of a new discipline sometimes referred to as grain boundary engineering. The idea of MIMP is to determine the grain boundary energies and mobilities (rates of evolution) by direct interrogation of various materials.

This interrogation relies on a tantalizing idea. The force balance at triple junctions where three grains meet provide relations for the energy in terms of geometric and crystallographic quantities. Experiments are designed to scan samples (OIM microscopy) providing a vast amount of information about these triple junctions. The first job of the math sciences group is to reconstruct the energy from this information. Two salient aspects here are that the data has an unusual structure and, from the analytical viewpoint, the function is reconstructed via the boundary conditions its satisfies rather than its equation of motion. Many other questions arise. Can we prove anything about their long-term behavior? Can we simulate them? What information do simulations really provide?

The participants are David Kinderlehrer, Shlomo Ta'asan, and Florin Manolache (the Math Sciences systems manager.) Five postdoctoral fellows have been involved. Richard Jordan (Los Alamos National Laboratories on NSF and DOE fellowships), Chun Liu (Penn State), Darren Mason (Michigan State Materials Science Dept.), and currently Ira Livshits and Michal Kowalczyk.

This is a project that could not be successfully formulated, let alone successfully accomplished, without joint mathematics and materials science collaboration. It is an example of how mathematical sciences can play a vital role at the frontiers of interdisciplinary research. The successful pursuit of the project goals require new concepts in the treatment of data structures and the investigation of new problems in the computation of vast systems of partial differential equations. Come in and help.

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