Estimation of the average size of plane convex loops in three dimensional microstructure

Abstract

Evolution of microstructures leads to formation of lineal microstructural features, which can be often regarded as plane convex loops. Average loop size is an important stereological parameter for characterization of such features. It is shown that the perimeter averaged caliper diameter $\text{D}{}_{\mathrm{p}}$ is a quantitative descriptor of the average loop size. This parameter is related to the total perimeter of the loops per unit volume, L_v, and the total planar area enclosed by the loops per unit volume, A_v, as follows: $\text{D}{}_{\mathrm{p}}\text{=}\text{4A}{}_{\mathrm{v}}\text{L}{}_{\mathrm{v}}$ A practical example involving experimental measurement of $\text{D}{}_{\mathrm{p}}$ is discussed.