according to the length scales—from atomistic to macroscopic—that characterize the underlying phenomena.

Atomic Scales

Atomistic studies of strength, fracture, and chemical reactions are becoming increasingly important in optimizing the performance of materials. For example, modern metallic and ceramic structural materials, as well as composites and artificially structured devices, typically contain large numbers of interfaces separating grains or phases. Fracture at such interfaces, which is frequently influenced by local segregation of solutes and of environmentally introduced impurities such as hydrogen, is often critical in limiting toughness. New fundamental approaches to alloy design, e.g., identification of favorable trace elements that will improve interfacial toughness, should follow from basic understanding of the atomistics of interfacial fracture. One example, so far understood only empirically, is that the polycrystalline-ordered Ni3Al alloy normally fractures easily along grain boundaries, but may be made ductile by addition of trace boron atoms, which, apparently, segregate at the boundaries in such a way as to strengthen them. An opposite example is the weakening of quenched and tempered martensitic steels by grain-boundary segregation of trace elements such as phosphorus, sulfur, tin, antimony, and, especially, hydrogen.

Analysis and modeling at the atomic scale should be useful in two primary ways. The first is by providing accurate, quantum mechanical calculations of material properties (interfacial energies, solute binding energies, dislocation core configurations and energies, and so on), which are needed in continuum theories of deformation or fracture but which are not easily or accurately measured. Dramatic improvements in our ability to make such calculations have been achieved in recent years, and the impact of these developments is only now beginning to be felt. The second way in which atomic-scale modeling is becoming useful is in exploring the dynamics of complex, many-atom processes. Such calculations necessarily involve departures from rigorous quantum mechanical principles, for example, the use of pair potentials or a modern improvement like the “embedded atom method.” Examples of processes for which dynamic modeling is currently being attempted include fracture at a crack tip, chemical bond formation during separation of fracture surfaces, the motion of dislocations, interaction of glide and grain-boundary dislocations, nucleation of martensitic transformations, and entanglements of long-chain molecules during deformation and crazing of polymeric materials.



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