An unfolding procedure for estimation of three-dimensional bivariate size-orientation distribution of microcracks

Quantitative Characterization and Representation of Global Microstructural Geometry

“…Recent developments in designbased stereology enable efficient estimation of total surface area per unit volume and total length per unit volume in the anisotropic microstructures as well (Ref [9][10][11][12][13][14][15][16][17][18]. These designbased stereological measurements have also been used in several recent experimental studies ( Ref 11,43,45,[55][56][57][58][62][63][64][65][66][67][68][69]. The quantitative metallographic methods for estimation of volume fraction, total surface area per unit volume, and the total length of per unit volume are described in the following sections.…”

“…Until recently, most of the stereological techniques for estimation of microstructural distributions were limited to the estimation of the size distributions of randomly oriented geometrically similar particles/voids of simple shapes (for example, spheres, ellipsoids) that differ only in size (Ref 6-8, 12, 85-91). Progress in stereology now enables efficient estimation of true bivariate sizeshape (Ref 92) and size-orientation ( Ref 38,45) distributions, as well as trivariate size-shape-orientation distributions of particles/voids (Ref 39) in a three-dimensional microstructure from the measurements performed on few metallographic planes. Nonetheless, all of these techniques do require that the particles/voids of interest be of known convex shape.…”

Flower-like Fe2O3/reduced graphene oxide composite for electrochemical energy storage

“…In addition, the existence of micro-crack in the Fe 2 O 3 NPs on Fe 2 O 3 /graphene composite may form a multi-channel structure to facilitate transport of ions and electrons [25], which will greatly improve the electrochemical property. Commonly, because of the stable crystalline structure of Fe 2 O 3 NPs, the typical micro-crack or defect was hardly generated, except for the special cruel experimental conditions [27][28][29].…”