Grain boundary solute segregation

It is thought that controlled amounts of B, N, and S or Se in solute form segregate to the grain boundaries hence, inclusions are not involved. 

For Type-B diffusion along a grain boundary, Eq. 9.9, which holds for selfdiffusion, takes the form of Eq. 9.15 for solute diffusion when simple McLean-type segregation occurs with cf/c L = k. Show that this causes Eq. 9.13, which holds for self-diffusion, to take the form... 

Segregation of solutes to a grain boundary lowers its energy. Solutes that have a larger atomic size than the parent atoms occupy positions that are open and smaller solute atoms occupy sites where there is crowding, as shown schematically in Figure 12.11. 

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