Determination of Heterogeneity for Manganese Dendrites using Lacunarity Analysis

Abstract

The surface patterns of natural and experimental deposits are important as they are a result of the internal microstructure. For this purpose, lacunarity analysis is applied to determine the heterogeneous nature of deposit surface patterns. In this study, images were digitally moved onto square mesh to determine the heterogeneous situation of manganese dendrite patterns on the natural manganese surface. The relation between the lacunarity values of the images and the box size were examined. The lacunarity values corresponding to the box size values was estimated using the gliding-box algorithm. This relation was determined numerically as a power-law function using nonlinear regression method. It has been shown that the system examined with the generated numerical model function can be defined with three specific parameters. As a result, it has been shown that it is possible to describe the relationship between numerical solution-based lacunarity-box size and also with a third-order nonlinear differential equation. With this study, the lacunarity-box size value on different system images can be determined by using the gliding box algorithm and calculating the coefficient value from the power-law relationship.