Physical analysis of the inverse problem of X-ray reflectometry

Soft x-ray reflectometry, hard x-ray photoelectron spectroscopy and transmission electron microscopy investigations of the internal structure of TiO2(Ti)/SiO2/Si stacks

“…Therefore, we did not add the calculated reflectivity curves to figure 1 for these cases. According to [20], we can conclude that the minimal feature size in the concentration profiles, which can still be reconstructed correctly, is about λ/(4 sin θ max ) ∼ 1 nm for our experiments, where θ max is the maximum measured angle.…”

“…However, even for hard x-rays or neutrons, where radiation absorption can often be neglected, such reconstruction is ambiguous in the absence of additional a priori information about the sample [17][18][19][20].…”

“…The approach is based on the genetic algorithm used together with phase inversion to impose a set of general constraints that will limit the number of possible solutions. Similarly, the approach developed in [20] allows us to select, among a great number of possible solutions, those providing the desired (modeled) reflectivity amplitude behavior at large q ≡ k sin θ (where k = 2π/λ) including unphysical values q > k.…”

“…In this study, we apply the well-known philosophical principle of Ockham's razor: when several models describe some physical phenomenon, use the simplest one consistent with the experimental data (see also [20]). In other words, we consider a sequence of models of progressively increasing complexity until the necessary accuracy is achieved in fitting experimental data.…”

Kinetics of the formation of a phospholipid multilayer on a silica sol surface

“…1). In this work, the ordering of the multilayer is studied within the model-independent approach to the reconstruction of profiles of the electron density from X-ray reflectometry data without any a priori assumptions on the structure of the multilayer [8][9][10][11][12]. According to our data, the characteristic time of formation of the structure of the surface is (1 − 7) × 10 5 s; after that, the lipid film can be considered as a two-dimensional organic crystal with a quite high degree of perfection We study multilayers of 1,2-distearoyl-sn-glycero-3-phosphoholine (DSPC) or C 44 H 88 NO 8 P [2].…”