Heterogeneous growth of cordierite in low P/T Tsukuba metamorphic rocks from central Japan
This paper examines the spatial statistics of matrix minerals and complex patterned cordierite porphyroblasts in the low-pressure, high-temperature (low P/T) Tsukuba metamorphic rocks from central Japan, using a density correlation function. The cordierite-producing reaction is sillimanite + biotite + quartz = K-feldspar + cordierite + water. The density correlation function shows that quartz is distributed randomly. However, the density correlation functions of biotite, plagioclase and K-feldspar show that their spatial distributions are clearly affected by the formation of cordierite porphyroblasts. These observations suggest that cordierite growth occurred through a selective growth mechanism: quartz adjacent to cordierite has a tendency to prevent the growth of cordierite, whereas other matrix minerals adjacent to cordierite have a tendency to enhance the growth of cordierite. The density correlation functions of complex patterned cordierite porphyroblasts show power-law behaviour. A selective growth mechanism alone cannot explain the origin of the power-law behaviour. Comparison of the morphology and fractal dimension of cordierite with two-dimensional sections from a three-dimensional diffusion-limited aggregation (DLA) suggests that the formation of cordierite porphyroblasts can be modelled as a DLA process. DLA is the simple statistical model for the universal fractal pattern developed in a macroscopic diffusion field. Diffusion-controlled growth interacting with a random field is essential to the formation of a DLA-like pattern. The selective growth mechanism will provide a random noise for the growth of cordierite due to random distribution of quartz. Therefore, a selective growth mechanism coupled with diffusion-controlled growth is proposed to explain the power-law behaviour of the density correlation function of complex patterned cordierite. The results in this paper suggest that not only the growth kinetics but also the spatial distribution of matrix minerals affect the progress of the metamorphic reaction and pattern formation of metamorphic rocks.