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In this paper we present the results of a computational study of diffusion across disordered flake composites in which the flakes are misaligned with respect to the direction of bulk diffusion. We evaluate the effect of flake orientation as well as the influence of boundary conditions and unit-cell types on the predicted barrier properties. Flake orientation impacts very significantly on the barrier properties in flake-filled composites, and usually the key objective in their fabrication is to orient them as close as possible to being perpendicular to the direction of macroscopic diffusion. Our computations are carried out in two-dimensional, doubly-periodic unit cells, each containing up to 3000 individual flake cross-sections. We consider high aspect ratio (α) systems with α=1000, from the dilute (αφ=0.01) and into the very concentrated (αφ=40) regime. The effective diffusivity of the corresponding unit cells is computed from the imposed concentration difference and the computed mass flux, using Fick’s Law. We show that use of cyclic boundary conditions and doubly-periodic unit cells results in effective diffusivities which are in agreement with theory and invariant of the shape of the unit cell. We also show that the use of adiabatic boundary conditions produces erroneous results at high flake concentrations. Finally we compare our results to the predictions of existing literature models and find that the latter deviate significantly from computation at high flake concentrations. [ABSTRACT FROM AUTHOR]

The microstructure of garnet aggregates within a metamorphic vein are investigated to constrain the duration of vein formation. Garnet-bearing veins occur subparallel to the foliation of a host mafic schist in the Sanbagawa metamorphic belt, Japan. Microstructural observations using SEM, EPMA and EBSD reveal that numerous small garnets (10–100 μm diameter) coalesced to form large porphyroblasts within the vein. EBSD analysis of the porphyroblasts reveals that misorientation angles of neighbor-pair garnet grains within the vein have a random distribution. This contrasts with previous studies that found coalescence of garnets in mica schist leads to an increased frequency of low angle misorientation boundaries by misorientation-driven rotation. The random misorientation angle distribution indicates that (1) garnets within the vein grew so fast that they could not rotate within the vein, and thus (2) random orientations of garnets at the nucleation stage were preserved. On the basis of a simple kinetic model that assumes rotation of garnet is rate-limited by diffusion creep of matrix quartz, the time taken for a small garnet grain to rotate 1° is estimated to be 103 – 104 years. This duration may indicate the upper limit of the duration of garnet growth, and of vein formation. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]