The critical temperature of a clean, normal (n) and superconducting (s) material is calculated and found to differ very slightly from its bulk value. The order parameter at 0°, Δ(0), is found to be modified much more than its bulk value for periodic structures of various cell widths, superconducting-to-normal metal length ratios, and Fermi-velocity differences in the normal and superconducting regions. At intermediate temperatures, an expression for Δ(T)/Δ(0) as a function of T/Tc and Δ(0)/Tc is given. The free-energy functional Fs − Fn is calculated. As in the case of Δ(T)/Δ(0), numerical calculations are necessary. These integrands are carried out to the point where numerical quadrature is simple and straightforward. Because of the great number of parameters describing our system, we do not perform any numerical calculation. These are left to the interested experimentalist for his particular structure.
Coarse-Grained Free Energy Functions for Studying Protein Conformational Changes: A Double-Well Network Model