Microstructure and its Evolution

Modeling Microstructure and its Evolution. Until this point, we have emphasized the virtues of modeling efforts built from the smallest scales up. However, as we have already noted, in many instances it is preferable to construct our theoretical vision on the basis of continuum models. We have already made reference to the critical role of microstructure in determining material properties and it is in this arena that we will consider a case study in continuum modeling. In particular, we consider the problem of a two-phase microstructure in which second-phase particles are dispersed through a matrix and the question under consideration concerns the temporal evolution of this microstructure. In particular, the modeler can ask questions both about the temporal history of particle size and shape as well as about its privileged terminal shape. 

In the previous section, we showed one quantitative scheme for treating microstructure and its evolution. Earlier in the chapter we discussed the geometrical... 

The current part of the present chapter has had as its aim the use of the study of microstructural evolution as a case study in the techniques for bridging scales described earlier in the chapter. The examples that were recounted in our discussion of microstructure and its evolution drew from a variety of the resources discussed earlier in the chapter in the context of bridging scales . In particular, we have seen how kinetic Monte Carlo models adopt an information passage philosophy in which calculations of one type are used to inform those of another. Similarly, the description of solidification, including information on the local crystal orientations, using a linkage of cellular automata with continuum descriptions of heat flow illustrates how more than one computational scheme may be brought under the... 

Metastability. Much of the use and analysis of real materials involves systems that are metastable. Unlike the robust tools that are available for the evaluation of systems that are in terminal privileged states (i.e. equilibria), the study of metastable systems is presently characterized by ideas that are based upon perturbations about the equilibrium state, or else ad hoc hypotheses that remain, as yet, unjustified. Our discussion of microstructure and its evolution was based upon a range of clever and fascinating ideas, but I at least am unable to escape the feeling that the treatment of the material s history was implicit and present primarily by virtue of initial conditions, whereas a more fundamental treatment of such metastable systems might demand a more detailed accounting for that history. 

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