Use the following free energy model to describe the thermodynamics of a binary solution, = [() 2 ()2] () = 2(1 )2 Where w and are positive constants. c=0 and c=1 are the equilibrium compositions. (1) Calculate the interfacial energy and interface width in terms of w and . (2) Calculate the kc and kmax of the system in terms of w and for a solid solution with overall composition c0, where c0 is within the spinodal region. (3) For the alloy in (2), schematically plot the amplification factor R as a function of the wavelength =2/k