Microstructure Quantification

From MMGWiki

At its core, the field of materials science and engineering is concerned with understanding and modeling the relationships between a material’s internal structure, its macroscale properties and its processing history. Fundamental to establishing these relationships is the quantitative representation of the material’s internal structure, which includes not only an identification of the constituent local states, but also their spatial placement. Quantifying the microstructure in a given material sample is an arduous task. New surface characterization techniques including scanning probe microscopy, nano-indentation, EBSD (OIM) mapping and a whole host of spectroscopy techniques have exponentially expanded the information researchers can extract from a given material. The tasks of how to combining the data from varied characterization techniques and building 3D datasets from multiple 2D surface scans are by no means trivial. The main thrust of this effort is the development of a rigorous statistical framework based on n-point spatial correlations. These correlations provide a hierarchy of statistical measures of the microstructure. The simplest of these are the 1-point correlations, which essentially reflect the volume fractions of the various distinct constituents. These are termed 1-point statistics because they reflect the probability density associated with finding a specific local state of interest at a point selected randomly in the microstructure. Expanding on this basic concept, the 2-point correlations capture the probability density associated with finding an ordered pair of specific local states at the head and tail of a randomly placed vector r into the microstructure. Current effort in this area is focussed on reconstructions of Representative Volume Elements (RVEs) from 2-pt correlation sets, delineation of the complete set (hull) of theoretically feasible 2-pt correlation sets for a given material system, and the development of a new mathematical framework for exploring efficiently the microstructure-property-processing relationships.

Advanced reconstruction algorithms reproduce original microstructure exactly up to a translation and inversion.