The topological entropy and separation of grain boundary networks
Dr. Jeremy Mason, Lawrence Livermore National Laboratory
Date: Thursday, November 08, 2012
Place: EA 409
Historically, principles guiding the rational design of polycrystalline materials have focused on structures the scale of a single grain or smaller. The opportunity to engineer a microstructure at longer length scales as well depends fundamentally on the availability of suitable language and concepts to describe the statistical features of ensembles of grains in a microstructure.
Our research is based on the construction of a combinatorial object, known as a swatch, that gives a complete description of the grain boundary network topology in a small region. By considering the frequencies of swatch types, or of local grain boundary configurations, the statistical features of the grain boundary network topology may be encoded as a discrete probability distribution. This allows us to calculate the topological entropy of a microstructure, or even a distance between microstructures that indicates the degree of their topological similarity or difference.
The intention of this research is to provide the community with a rigorous means to measure, e.g., microstructure variability for a given processing condition, or the degree to which some processing route accurately produces a target microstructure.
Prepared by LLNL under Contract DE—AC52—07NA27344.