Consider the case of a cube-shaped solid forming heterogeneously at a 90 edge of the container such that two sides of the cube-nucleus are in contact with the walls of the container as shown below. a) Find the relation between the surface energies Ws and WL. (Hint: Start with the energy balance) b) Derive the equation for the change in the free energy for the nucleation of this nucleus (Ghetero). c) Find the critical cube edge length, a, and the energy barrier to nucleation, G, for this shape of nucleus. d) Does this heterogeneous nucleation model provide an easier nucleation path for the cubic nucleus than the homogeneous nucleation? ws= Energy of the wall-solid interface wL= Energy of the wall-liquid interface Ls= Energy of the liquid-solid interface