Fractal growth of graphite nodules in iron

It has been found from a large number of statistical tests that graphite nodules in malleable iron grow with time according to a power law. The growth of the nodules and their fractal dimension have been investigated experimentally as a function of annealing time. Based on the assumption of carbon-diffusion-controlled growth in the initial stage, the growth equation is R _G = K ₁ t ^1/(D-1), where R _G is the radius of the graphite nodules, t the time, D the fractal dimension and K ₁ a constant. Assuming cementite-dissolution-controlled growth in the later stages of growth, the relation is R _G = K ₃ t ^3/D , where K ₃ is a constant. The fractal dimension, or the aggregate state of the graphite nodules, strongly influences the growth process.