Evolving information complexity of coarsening materials microstructures

The temporal evolution of microstructural features in metals and ceramics has been the subject of intense investigation over many years because deviations from normal grain growth behavior are ubiquitous and strongly dictate observed mechanical and magnetic properties. To distinguish among different grain growth scenarios, we examine the time evolution of the information content of both synthetic and experimental coarsening microstructures as quantified by both a computable information density (CID) and a spectral entropy along with selected metrics and measures of shared information and interaction strength. In these approaches, microstructural evolution is described in terms of two time series representations, namely: (1) strings and their compressed counterparts that reflect the information contained in the configuration of a system over time, and (2) the spectra of graph Laplacians that embody the information contained in a coarsening grain network. These approaches permit one to characterize dynamically evolving microstructures and to identify correlation times associated with different coarsening scenarios. Moreover, as the information content of a system is a proxy for the entropy, a thermodynamic description of grain growth is also described.