Aerospace and Mechanical Engineering
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AEM Research: Equilibrium maps provide
a guide to nanostructures

AEM researchers Ellad Tadmor, Ryan Elliott, and Subrahmanyam Pattamatta are to be published in the prestigious Proceedings of the National Academy of Sciences for their work addressing the challenges involved in the design of nanostructures - namely their stochastic or apparently random response to external loading.

Nanostructures are technological devices constructed on a nanometer length scale more than a thousand times thinner than a human hair. Due to the unique properties of matter at this scale, such devices offer great potential for creating novel materials and behaviors that can be leveraged to benefit mankind. When nominally identical nanostructures are subjected to mechanical, thermal, electrical, or magnetic external loading they often respond differently.

"The common explanation for this behavior is that nanostructures are too small to contain statistically equivalent internal defect populations," explains Elliott, AEM associate professor and Russell J. Penrose Faculty Fellow. "This leads to a response that is highly sensitive to external fluctuations in loading."

Although this explanation is valid, a more fundamental issue is involved. Indeed, the sensitivity to loading fluctuations is due to the fact that the potential energy function relating the energy of a nanostructure to the arrangement of its atoms has a very large number of minima each of which corresponds to a possible equilibrium state. Further, the potential energy changes in time as the loading evolves create a multitude of possible response scenarios. (This is depicted schematically in the accompanying figure.)

"In contrast to existing methods for modeling nanostructures that tend to ignore the potential energy complexity, our work describes a new approach for constructing a special kind of diagram called an "Equilibrium Map" (EM)," says Tadmor, AEM professor. "Specifically an ideal EM fully characterizes it and describes all possible responses of a nanostructure to any given loading."

Given such a tool, it is possible to say definitive things about the response of nanostructures in different limiting cases and to model the response efficiently at any desired loading rate. The latter is important since due to the nature of standard methods for simulating nanostructures they must typically resort to loading rates many orders of magnitude faster than reality in order to make the computations feasible. In contrast, the EM-based methodology provides an exciting new temporal multiscale approach for the direct simulation of experiments.

Summary for "Mapping the stochastic response of nanostructures" by Subrahmanyam Pattamatta, Ryan S. Elliott and Ellad B. Tadmor, Proceedings of the National Academy of Sciences, Vol. 111, No. 17, E1678-E1686 (2014).

A schematic of the possible behaviors of a compressed nickel nanoslab. As the compression increases with time, the initially perfect structure (bottom) develops defects associated with minima on its evolving potential energy surface. The sequence of states observed in repeated experiments on nominally identical nanostructures is highly stochastic and rate dependent. Each colored line in the figure represents one such realization obtained using a new computational method described in the paper by S. Pattamatta et al..
Image courtesy of Subrahmanyam Pattamatta, Ryan Elliott and Ellad Tadmor.

Last Modified: 2014-05-05 at 11:15:57 -- this is in International Standard Date and Time Notation