Jeremy Mason Lawrence Livermore National Laboratory Rigorous quantification of the grain growth microstructure in two and three dimensions While a variety of approaches have been proposed to simulate the evolution of grain boundaries during grain growth, comparing the results of different simulations or the results of simulations with a physical microstructure remains difficult. We suggest that this is partly due to the absence of a rigorous definition of the conjectured steady state grain growth microstructure, and partly due to the inability to adequately measure the approach to that state. We address this situation by placing a metric on the space of grain boundary network topologies. Specifically, we use the frequencies of local grain boundary configurations to encode the statistical features of the grain boundary network topology as a discrete probability distribution. This allows us to calculate a distance between microstructures that indicates the degree of their topological similarity or difference, and to rigorously quantify the grain boundary network topology of the grain growth microstructure. Prepared by LLNL under Contract DE-AC52-07NA27344.