Fractal dimensions of recrystallized quartz grain boundaries and grain fabrics

We measured the fractal dimensions of dynamically recrystallized quartz grain boundaries subjected experimentally to various deformation conditions (temperature 800°C to 1000°C and strain rate 10^-6 to 10^-4 sec^-1). We investigated both the individual fractal dimension D₁ for each grain, using the box-counting method, and the collective fractal dimension D_C for whole grain fabric, using the area-perimeter method. The individual fractal dimension D_I showed an inverse variation with grain size and converged to the value of D_C as the grain size increased. During dynamic recrystallization, grain boundary serration would be modified by neighboring grain interactions including bulging, nucleation, and boundary migration. The pattern of variation of D_I appears to suggest that a restricted range of shapes results from grain boundary serration or smoothing processes as the grain is growing or being consumed.