THE FRACTAL SHAPE OF SUTURED QUARTZ GRAIN-BOUNDARIES - APPLICATION ASA GEOTHERMOMETER

Along grain boundaries of quartz from metamorphic and igneous rocks co mplex interfingering (sutures) may occur. Under the light microscope t he lengths of the sutures range from approximately 10-1000 mu m. The s utured grain boundaries are statistically self-similar over one to two orders of magnitude. They represent fractals. Their mathematical coun terpart are Koch curves which are developed after two to four iteratio ns. 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 dur ing formation of the sutures. On a statistical basis, D can be used as a measure of this temperature and, therefore, as a deformation-relate d thermometer.