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Application of Fractal Models to Distinguish between Different Mineral Phases

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Fractal modeling is demonstrated to be an effective and rapid tool to distinguish between mineral phases in rock samples. It supplements work that previously could be performed only by observing the interpenetrational or metasomatic phenomena between different minerals with the aid of mineralographic microscope. The Gejiu tin district in southwestern China was chosen as a study area for the recognition and characterization of the spatial distribution of two phases (Types I and II) of cassiterite. Vector patterns used for this study were extracted from digital photomicrographs and analyzed with the aid of MapGIS. Perimeter–area fractal dimension, cumulative number–area exponent, and shape index were determined in order to quantify geometrical irregularities and spatial cassiterite phase distribution characteristics. The results show that fractal dimensions based on area and perimeter are larger for crystals of Type I than for those of Type II. The mean shape index (SI) increases from 0.54 (Type I) to 0.64 (Type II), indicating an increase in regularity. The number–area exponent also increases from 0.88 to 1.15, indicating the smaller crystals of Type II. The cumulative number–shape index log–log plot shows two separate straight-line segments. One of these probably represents a background shape realized during the original process of natural crystallization, whereas the other likely represents anomalous shapes because of weathering or other superimposed processes. Two parallel lines can be constructed on the perimeter–area log–log plots. The upper line, with a larger intercept, represents crystals with lower SI. The lower line represents crystals with higher SI, indicating that the intercept provides a measure of the irregularity of grains. By combining the perimeter–area model with cumulative number–area plot and shape index, the two phases of cassiterite can be distinguished and characterized. One phase has fewer crystals of large size, and the other has smaller crystals. This difference can be explained by assuming that under higher-temperature conditions, the large cassiterite crystals formed earlier than the smaller crystals. Consequently, the large cassiterites underwent longer, high-intensive weathering than the small crystals so that their shapes became more irregular. The younger, more abundant small cassiterites retained their original regular shapes.

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Correspondence to Renguang Zuo.

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Zuo, R., Cheng, Q., Xia, Q. et al. Application of Fractal Models to Distinguish between Different Mineral Phases. Math Geosci 41, 71–80 (2009).

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