Direct Fitting of Grazing-Incidence Neutron and X-ray Reflectivity Profiles using the Kinematic Approximation

At present, neutron and X-ray reflection data have been analysed either by modelling, using the optimal-matrix method, or by the fitting of partial structure factors arising from application of the kinematic approximation. Here the direct and simultaneous fitting of neutron and X-ray reflection profiles measured for a series of isotopic variations of the same interface is described. The interface is described as consisting of several components, which are either groups of atoms in a molecule or a whole molecule itself. In this work, the density distributions of the components perpendicular to the interface are described as Gaussian or tanh functions. These forms are chosen because they have analytical Fourier transforms. Fitting reflectivity profiles rather than partial structure factors reduces the sensitivity of the analysis to imperfections in one or more data sets. With existing kinematic methods, it is difficult to combine X-ray and neutron measurements. The new method readily allows such a combination, which is of importance if the capacity for isotopic substitution is limited or information about the counter-ion distribution is desired. It is also demonstrated that constraints posed by the stoichiometry of the interfacial species, by volume filling and molecular geometry, or from the results of the application of other experimental techniques, may readily be incorporated into the new fitting procedure.