Publications

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Like other interfaces, equilibrium grain boundaries are smooth at low temperature and rough at high temperature; however, little attention has been paid to roughening except for faceting boundaries. Using molecular dynamics simulations of face-centered cubic Ni, we studied two closely related grain boundaries with different boundary planes. In spite of their similarity, their boundary roughening temperatures differ by several hundred degrees, and boundary mobility is much larger above the roughening temperature. This has important implications for microstructural development during metallurgical processes.

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We describe two geometric structures, the shortest path and the minimum cut, and show that these structures emerge at special threshold points in the highly non-linear electrical response of complex networks. Algorithms which find the shortest path and the minimum cut directly as well as methods for finding the full non-linear response of complex networks are outlined. Scaling laws for the behavior of the shortest path and minimum cut in random networks are then surveyed. Finally, applications of the shortest path and minimum cut to grain boundary controlled polycrystalline materials are elucidated. © 2005 Elsevier Ltd. All rights reserved.

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As current experimental and simulation methods cannot determine the mobility of flat boundaries across the large misorientation phase space, we have developed a computational method for imposing an artificial driving force on boundaries. In a molecular dynamics simulation, this allows us to go beyond the inherent timescale restrictions of the technique and induce non-negligible motion in flat boundaries of arbitrary misorientation. For different series of symmetric boundaries, we find both expected and unexpected results. In general, mobility increases as the grain boundary plane deviates from (111), but high-coincidence and low-angle boundaries represent special cases. These results agree with and enrich experimental observations.

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Percolation theory is now standard in the analysis of polycrystalline materials where the grain boundaries can be divided into two distinct classes, namely 'good' boundaries that have favorable properties and 'bad' boundaries that seriously degrade the material performance. Grain-boundary engineering (GBE) strives to improve material behavior by engineering the volume fraction c and arrangement of good grain boundaries. Two key percolative processes in GBE materials are the onset of percolation of a strongly connected aggregate of grains, and the onset of a connected path of weak grain boundaries. Using realistic polycrystalline microstructures, we find that in two dimensions the threshold for strong aggregate percolation c{sub SAP} and the threshold for weak boundary percolation c{sub WBP} are equivalent and have the value c{sub SAP} = c{sub WBP} = 0.38(1), which is slightly higher than the threshold found for regular hexagonal grain structures, c{sub RH} = 2 sin({pi}/18) = 0.347. In three dimensions strong aggregate percolation and weak boundary percolation occur at different locations and we find c{sub SAP} = 0.12(3) and c{sub WBP} = 0.77(3). The critical current in high T{sub c} materials and the cohesive energy in structural systems are related to the critical manifold problem in statistical physics. We develop a theory of critical manifolds in GBE materials, which has three distinct regimes: (1) low concentrations, where random manifold theory applies, (2) critical concentrations where percolative scaling theory applies, and (3) high concentrations, c > c{sub SAP}, where the theory of periodic elastic media applies. Regime (3) is perhaps most important practically and is characterized by a critical length L{sub c}, which is the size of cleavage regions on the critical manifold. In the limit of high contrast {open_square} {yields} 0, we find that in two dimensions L{sub c} {proportional_to} gc/(1-c), while in three dimensions L{sub c} {proportional_to} g exp[b{sub 0}c/(1-c)]/[c(1-c)]{sup 1/2}, where g is the average grain size, {open_square} is the ratio of the bonding energy of the weak boundaries to that of the strong boundaries, and b{sub 0} is a constant which is of order 1. Many of the properties of GBE materials can be related to L{sub c}, which diverges algebraically on approach to c=1 in two dimensions, but diverges exponentially in that limit in three dimensions. We emphasize that GBE percolation processes and critical manifold behavior are very different in two dimensions as compared to three dimensions. For this reason, the use of two dimensional models to understand the behavior of bulk GBE materials can be misleading.

In the present work the authors describe the adaptation of a standard SEM into a flexible microjoining tool. The system incorporates exceptional control of energy input and its location, environmental cleanliness, part manipulation and especially, part imaging. Beam energetics, modeling of thermal flow in a simple geometry, significant effects of surface energy on molten pools and beam size characterization are treated. Examples of small to micro fusion welds and molten zones produced in a variety of materials (Ni, tool steel, Tophet C, Si) and sizes are given. Future directions are also suggested.

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