The fractal shape of sutured quartz grain boundaries: Application as a geothermometer

Along grain boundaries of quartz from metamorphic and igneous rocks complex interfingering (sutures) may occur. Under the light microscope the lengths of the sutures range from approximately 10-1000 μm. The sutured grain boundaries are statistically self-similar over one to two orders of magnitude. They represent fractals. Their mathematical counterpart are Koch curves which are developed after two to four iterations. The fractal (Hausdorff-Besicovitch) dimensions D of sutured quartz grain boundaries from different grades of metamorphism are between ca. 1.05 and 1.30. The D-value decreases with increasing temperature during formation of the sutures. On a statistical basis, D can be used as a measure of this temperature and, therefore, as a deformation-related thermometer.