Consider the free energy functional of an inhomogeneous system that depends on a non-conserved order parameter η and temperature T, written in one-dimension as: G= ∫ [Go+ α [T- Tc]η^2 + Cη^3+ Bη^4+ D(∂η/∂η)^2 ].dx

Tc is the critical temperature.

Required:
a. Plot the equilibrium value of the order parameter as a function of temperature for a homogeneous system both for cases of constant C ≠ 0 and for vanishing C as T passes through the critical temperature. Choose representative values or ratios of the coefficients, you should not need particular values.

b. Explain how, using the free energy functional above and Gibbs' definition of the surface properties you would construct an expression for the surface en- ergy/surface tension of an interface separating an infinite ordered phase η = 1 and an infinite disordered phase η = 0.

c. Explain how and why the diffraction patterns (intensity vs. angle) change as a material alloy in going from ordered to disordered state. Can these patterns be used to investigate the kinetics of ordering?