PORPHYROBLAST SPACING AND NUCLEATION TIME SPANS IN WELL EQUILIBRATED METAMORPHIC ROCKS

Nucleation of new minerals in metamorphic rocks takes place in enclaves where metastable assemblages provide the overstepping to allow nucleation. As new minerals nucleate and grow, they reduce the probability of nucleation in nearby matrix by reducing the reaction overstepping as intergranular diffusion brings the adjacent matrix into equilibrium with the porphyroblast.

The region around a prophyroblast where the probability for nucleation has been reduced can be approximated by the characteristic length of diffusion: l = (D*t)^0.5, where l is the distance away from the porphyroblast center that has begun to re-equilibrate with the crystal, D is the effective intergranular diffusion coefficient and t is time. In rocks that are well equilibrated at the end of nucleation (i.e. all metastable assemblages have reacted), the average spacing between porphyroblast centers can be used with an effective intergranular diffusion coefficient to estimate the time span of nucleation. For example, using the fluid saturated effective diffusion coefficient of Carlson (2002), garnet prophyroblasts that nucleated and grew from chlorite breakdown at 525 C in a rock with a matrix crystal size of about 30 microns would have the following average 3D garnet center spacing, depending upon the duration of the nucleation period: 0.1 mm = 10 kyr, 0.2 mm =25 kyr, 0.25 mm=50 kyr, 0.36 mm = 100 kyr, 0.57 mm = 250 kyr, 0.81 mm=500kyr, 1.1 mm =1myr, and 1.8 mm=2.5 myr.

Effective diffusion coefficients are dependant upon temperature, matrix size and shape, and fluid saturation. If the temperature was 575 C (e.g. staurolite forming from chlorite break down), the crystal separations for various time periods of nucleation listed above would double. Characteristic diffusion lengths are also proportional to the inverse of the matrix crystal diameter, so the above average porphyroblast separations would give increased times of nucleation for rocks with a larger matrix crystal size and shortened nucleation times in rocks with a smaller matrix crystal size. Diffusion coefficients for fluid under saturated systems are about 2 to 3 orders of magnitude smaller than those for fluid saturated systems, so the separation distances given above would result in much longer nucleation periods if the rock was under saturated with H₂O.