Fractal Modelling of the Microstructure Property of Quartz Mylonite During Deformation Process

Abstract

Mylonite is the result of the dynamic metamorphism and minerals in mylonite are deformed gradually with an increase in the degree of metamorphism. Quantifying the degree of deformation including the irregularities of shapes and the frequency distribution of the minerals becomes one of the most challenging efforts in mylonite analysis. Fractal modelling has been demonstrated in this paper to be an effective mean to achieve the above goal. Perimeter-Area fractal model was used to quantify the irregularities in the geometries and Cumulative Number-Area model is used to characterize the irregularities of distribution of quartzs in mylonites, respectively. Examples of quartz from five types of mylonites with different degree of deformation within the foreland of the Moine Thrust Zone in NW Scotland are chosen to study the evolution processes of deformation. As the main mineral component of quartzite mylonite, patterns are extracted from digital photomicrographics of the multiscale-grey image grid data to show quartz grains with different degree of deformation, The areas and perimeters of the quartz grains were calculated by GIS-based image processing technologies. From type one to type five, with an increase in degree of deformation, the corresponding Perimeter-Area exponent \({D_{\rm AP}}\) increases from 1.20, 1.28, 1.38, 1.46, to 1.60, respectively, the fractal dimension \({D_{\rm P}}\) of the perimeter from 1.07, 1.08, 1.17, 1.23, to 1.44, as well as the exponent of Cumulative Number- Area from 0.50, 0.51, 0.58, 0.82, to 0.85, respectively. The result has shown that as increase of the intensity of deformation, the shape of quartz grains tends to be more irregular, grain size tends to be smaller, and the number of grains increases. The results obtained using GSI model has indicated that as an increase in the intensity of deformation, the patterns of quartz grains tends to be more stratified and randomness increases.