geometrically general random alloy is still very much an open issue.

DETERMINATION OF PHENOMENOLOGICAL INTERACTIONS FROM ELECTRONIC STRUCTURE CALCULATIONS

Opportunity 9: Substantial improvements in the determination of phenomenological potentials from electronic structure calculations will be accelerated.

The abstraction of phenomenological parameters (i.e., both their formulation and extraction of actual values) from detailed calculations at one time/distance scale to be used at the next higher level remains one of the outstanding challenges of this field. Phenomenological interactions pass information from the lowest time and distance scales in the hierarchy of Figure 4.1 , speeding up the calculations by not dealing with the finer-scale complexity and by increasing the realism in the larger scale. This process is based on the fact that the larger scales average over many of the details of the smaller scale. An important issue to remember is that since the approaches used for the larger-scale problems only incorporate part of the detail of the finer scale, it must be ensured that the proper details are represented correctly. Electronic structure calculations can now reliably determine the electronic properties of tens of atoms (including transition metals), and this can be extended easily to hundreds. Approximate replacements for the self-consistency process can extend this even further. Another tactic that can extend the range of electronic calculations is to calculate accurate results for a region of importance surrounded by a medium of lesser significance. Such embedding schemes that deal with the properties of clusters in a medium have been partially successful with improvements “on the horizon” for years. A real problem remains in the determination of a parameterization. However, although the extraction of parameterizations for coherent alloys has been demonstrated, even the formulation of a chemically and geometrically general formulation of parameterization is a largely unsolved problem. To expand the scale further means proceeding from quantum-level treatments to atomic-level simulations. The basis of this step is to characterize the electronic structure properties in terms of approximate systems such as cluster expansions, embedded atoms, potential induced breathing models, and tight-binding representations. A significant limitation of such schemes is the issue of charge transfer. Nonetheless, they have a wide range of applications. To treat longer-range interactions, albeit with reduced accuracy, polarizable atom-type models can be applied for nonmetallic systems.

Such interchanges between the time and distance scales shown in Figure 4.1 are exemplified by dislocation mesoscale dynamics. The interactions in question include core repulsions, attractions between opposite-sign dislocations on the same slip system, and creation and annihilation mechanisms. All of these can be obtained from large-scale molecular dynamics simulations. They then provide the interaction laws for dislocation dynamics, where the fundamental “particles” are defects rather than atoms. In turn, the behavior of a large number of dislocations under various loading conditions provides information for microstructural continuum models. Finally, these latter simulations allow constitutive laws (or models) to be constructed for use in continuum engineering simulations at the macroscopic level. Occasionally, there are phenomena that are already able to be modeled by a continuum description on the time and distance scales accessible to molecular dynamics, but usually the links between overlapping parts of the chain shown in Figure 4.1 must all be used to obtain practical (macroscopic) modeling information.



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