A new correction factor to calculate the relative intensity of X-ray diffraction by LB films

Abstract

This paper presents a new correction factor for the calculation of the relative X-ray diffraction intensities which plays an important role in the case of very thin samples (whose thickness is very small compared with the X-ray penetration depth, i.e. less than ≈ 100 nm). This factor, called the volume ( V) factor, arises from the variation of the effective volume irradiated by the incident beam which occurs as the incidence angle θ is varied. For a uniform flat specimen, the value of the effective irradiated volume is proportional to the portion of the specimen area which is irradiated by the incident beam. In the θ−2 θ geometry, this is proportional to 1 sin θ . By also taking Lorentz and polarization factors into account, the corrected expression of the relative intensity I c of the thin specimen can be written as follows: I c = I m sin 2 θ sin θ(1 + cos 2 2 θ) where I m is the measured intensity; 2θ is the scattering angle. In addition, especially for a specimen thickness larger than 100 nm, a more accurate evaluation of the intensities requires the consideration of the absorption effects. Accordingly, the relative intensity of a Langmuir-Blodgett (LB) film can be expressed as: I c = I m sin 2 θ(1 − e −2 μS/ sin θ ) (1 + cos 2 2 θ) where μ is the linear absorption coefficient and S is the thickness of the film. The electron density distribution of a lead stearate LB film was calculated by Fourier inversion of the X-ray diffraction spectra. The result clearly shows that the application of the volume correction leads to a more reasonable electron density distribution.