Mathematical analyses of diffusive loss and radiogenic growth

2 Mathematical analyses of diffusive loss and radiogenic growth 

1 Diffusive ioss during cooiing without radiogenic growth 

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 

The fraction of Ar loss can be calculated from the above equation as 

Solid sphere For isotropic diffusion in a spherical mineral of radius a with uniform initial concentration Cq and zero surface concentration, Ar diffusion profile is as follows (Equation 3-68g)  

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