Generalized skew-symmetric interfacial probability distribution in reflectivity and small-angle scattering analysis

Abstract

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivitiesviaParratt's recursive formula, or small-angle scatteringviathe concentric onion model that is also developed in this work.