Fractal analysis of experimentally, dynamically recrystallized quartz grains and its possible application as a strain rate meter

Fractal analysis of experimentally recrystallized quartz grain shapes has been employed to study the relationship between the microstructures of dynamically recrystallized quartz grains and the deformation conditions such as temperature and strain rate. Samples used are quartz aggregates deformed under high temperature (800 °C, 900 °C and 1000 °C) and high confining pressure (400 MPa). The fractal dimension is useful to quantify the shapes of the recrystallized quartz grain boundaries. At each set of conditions, the fractal dimension is determined as the slope of a log—log plot of the length of the grain boundaries (perimeters) against the grain size, calculated as diameters of circles having the same areas as the actual grains. The results show that the shapes of grains are self-similar, and the fractal dimensions, D, change systematically, being dependent on both temperature and strain rate. The skew of the grain boundary, defined as D − 1, and showing the degree of the serration, may be proportional to the logarithm of the Zener-Hollomon parameter that includes a component of the Arrhenius term. This relation indicates that strain rate can be calculated from the fractal dimension and the temperature. It may therefore provide a new paleo-strain rate meter for plastically deformed natural rocks.