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 p atterned cordierite porphyroblasts in the low-pressure, high-temperature (l ow PIT) Tsukuba metamorphic rocks from central Japan, using a density corre lation function. The cordierite-producing reaction is sillimanite + biotite + quartz= K-feldspar + cordierite + water. The density correlation functio n shows that quartz is distributed randomly. However, the density correlati on functions of biotite, plagioclase and K-feldspar show that their spatial distributions are clearly affected by the formation of cordierite porphyro blasts. 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 den sity correlation functions of complex patterned cordierite porphyroblasts s how power-law behaviour. A selective growth mechanism alone cannot explain the origin of the power-law behaviour. Comparison of the morphology and fra ctal dimension of cordierite with two-dimensional sections from a three-dim ensional diffusion-limited aggregation (DLA) suggests that the formation of cordierite porphyroblasts can be modelled as a DLA process. DLA is the sim ple statistical model for the universal fractal pattern developed in a macr oscopic diffusion field. Diffusion-controlled growth interacting with a ran dom field is essential to the formation of a DLA-like pattern. The selectiv e growth mechanism will provide a random noise for the growth of cordierite due to random distribution of quartz. Therefore, a selective growth mechan ism coupled with diffusion-controlled growth is proposed to explain the pow er-law behaviour of the density correlation function of complex patterned c ordierite. The results in this paper suggest that not only the growth kinet ics but also the spatial distribution of matrix minerals affect the progres s of the metamorphic reaction and pattern formation of metamorphic rocks.