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Control or removal of non-metallic inclusions during the secondary refining process is one of the most important operations in producing high-quality steel products. The first step in controlling or removing inclusions is to understand the behavior of inclusions. Many different types of inclusions are produced in refining processes. Different shapes might arise from different formation and growth mechanisms. Therefore many different theories of inclusion formation and growth have been reported. Dekkers et al. have reported that the major aspect of alumina inclusions is their agglomerate-cluster shape. Some researchers have adopted the concept of fractals to specify the shapes of the clusters. For fractal clusters, the most important parameter might be the fractal dimension, which accounts for many of the characteristic properties of clusters, such as their compactness. Particularly, the removal behavior of inclusions in the steel-making process strongly depends on the fractal dimension of inclusions. However, it is very difficult to find reports on fractal dimension analysis. Only the value of 1.8 was reported by Tozawa et al. based on the cross-sectional images of inclusions. The present research focuses on the shape of alumina inclusions produced by Aluminum deoxidation in a low-carbon-steel RH refining process. The observed alumina inclusions exhibited irregularly spaced clusters composed of many small inclusions, a finding similar to those of other reports. One of the interesting characteristics of alumina inclusions is that the inclusions are composed of many small particles of similar size and shape. Inclusion shape can be analyzed using fractal theory and identified by fractal dimension. The fractal dimension of clusters shows a relation between the number of particles and to the radius of the clusters, as shown in Eq. (1):

Measurement of the 2-Dimensional Fractal Dimensions of Alumina Clusters Formed in an Ultra Low Carbon Steel Melt during RH Process