Free energies in the presence of small amplitude fluctuations, e.g. in concentration, can be evaluated using an approximation introduced by Ginzburg and Landau to describe magnetic field gradients in superconductors. This approach allows one to approximate the free energy as an expansion in terms of the concentration gradient ∇ ∇ c , a vector. Since free energy is a scalar and we are probing near its minima, the term proportional to ∇ ∇ c is negligible. The lowest order term is the quadratic expression κ κ ( ∇ ∇ c ) 2 , a scalar. Here κ κ is a parameter that controls the free energy cost of variations in concentration c .