The Determination of Spatial Homogeneity in Multiphase Mixtures

Abstract

The modifications of the properties of composite materials by controlling the ratio, size, shape, orientation and spatial distribution of the second phase particles is a well known phenomena. Although there are technique available for the quantifying of most of these parameters, there is no established technique for the determination of the spatial homogeneity; yet this property is also highly influental on the behavior of the material. The aim of this paper is to introduce a fully automated technique to determine the spatial homogeneity of second phase particles.The technique presented in this paper was based on the technique reported by Eisenkolb and Lange and Hirlinger. In this technique the image area was divided by a grid having equal size squares (Fig.1). In a homogeneous mixture the proportion of the second phase would be the same in each square. However, because of the finite size and the agglomeration of particles, the proportion of the second phase varies. This variation is best represented by Relative Standard Deviation, Srel, which is defined as the standard deviation divided by the average. As finer grid sizes are used Srel would naturally increase. It was assumed that for a random dispersion Srel increases linearly as the size of the grid squares becomes smaller. In this study it was shown mathematically that this increase becomes faster when agglomerations are present.