In class we developed the classical theory expression for heterogeneous nucleation on an impurity or a container wall. Often nucleation of a precipitate in a solid occurs at grain boundaries. Assume that a precipitate forms on the grain boundary between two grains ( being the initial phase) as shown below. (a) Calculate the critical size for nucleation in terms of the driving free energy, the appropriate interfacial free energies and the wetting angle, . (b) Calculate the ratio of the work of cluster formation for grain boundary nucleation to that for homogeneous nucleation. (c) The solid state precipitate will likely create a strain in the initial phase as it forms. How would you expect that to influence its nucleation rate