Minerals grain boundaries

Plane sheet bounded by two parallel plane surfaces Suppose the mineral grains can be treated as thin wafers so that Ar loss is through two parallel surfaces. Define the two surfaces to be = a. For the initial condition of uniform initial concentration Co and the boundary condition of zero surface concentration, Ar... 

A full treatment of this problem is unavailable. The simplest case would be a bimineralic rock. The mineral grains are randomly distributed with variable grain sizes. Even if both minerals are diffusionally isotropic, all grains of the same mineral are equal in size and shape, and the mineral grains are regularly spaced, the problem still has not been solved. One complication is that grain boundary diffusion is much more rapid than volume diffusion. 

Figure 6.1 A TEM image of an ultramicrotome slice of an anhydrous, porous, chondritic IDP, L2009 E2. Dark areas are mineral grains, while the light areas are void spaces. The boundary of the particle is shown by the solid line. This particle is an aggregate of minerals of diverse compositions (TEM image from L.P. Keller).

The statements above have introduced several concepts that need to be defined and expanded upon. A system is a grouping of atoms, minerals, rocks, and/or gases and waters under consideration within a single volume of space, the boundaries of which can be defined as is convenient. A system could be one mineral grain, a drop of rain, a water-logged soil, a well-mixed lake, or a regional groundwater/rock system tens of kilometers in diameter. 

When rocks and minerals are stressed above their tensile strength they break. Commonly, rocks fracture along joints, fissures, or planes that have developed during cooling, tectonism, sedimentary processes, or along lines of weakness at the mineral grain boundaries. When buried rock masses are... 

The kinds of substitution mechanisms that may be relevant to super-low concentration elements such as Pa involve intrinsic defects, such as lattice vacancies or interstitials. Vacancy defects can potentially provide a low energy mechanism for heterovalent cation substitution, in that they remove or minimise the need for additional charge balancing substitutions. Formation of a vacancy per se is energetically unfavourable (e.g., Purton et al. 1997), and the trace element must rely instead on the thermal defect concentration in the mineral of interest, at the conditions of interest. Extended defects, such as dislocations or grain boundaries, may also play a key role, but as these are essentially non-equilibrium features, they will not be considered further here. 

Eiler JM, Baumgartner LP, Valley JW (1992) Intercrystalline stable isotope diffusion a fast grain boundary model. Contrib Mineral Petrol 112 543-557... 

Several models for diffusive transport in and among minerals have been discussed in the literature one is the fast grain boundary (FGB) model of Eiler et al. (1992, 1993). The FGB model considers the effects of diffusion between non-adjacent grains and shows that, when mass balance terms are included, closure temperatures become a strong function of both the modal abundances of constituent minerals and the differences in diffusion coefficients among all coexisting minerals. 

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