Space functions in radial anisotropic growth

In radial anisotropic growth, at time r of nucleation, the surface of the initial grain is completely covered with a layer of the new solid with negligible thickness, and we nornmlly see the development of this layer on the surface of the grain. 

The grains are characterized by their shapes, initial characteristic sizes, and current sizes (at time f). The first fom columns of Table A. 1.1 of Appendix 1 provide the selected grain shapes and their characteristics. 

We provide calculations for the spherical grains, which show the procedure and their use with other grain shapes. Tables of Appendix 2 recapitulate the results for the various shapes of grains. 

We now consider the two possible directions of development (inward and outward) and for each of them, the rate-determining step can be a reaction step at the internal interface or the external interface or diffusion through the layer of the formed solid. Therefore, we have six possibilities. 

Inward development with the rate-determining step located at the internal interface (A/B) 

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