Thin Solid Films, Vol.284-285, 377-380, 1996
A New Correction Factor to Calculate the Relative Intensity of X-Ray-Diffraction by lb Films
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 approximate to 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 theta 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 theta-2 theta geometry, this is proportional to 1/sin theta. 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 theta sin theta(1 + cos(2) 2 theta) where I-m is the measured intensity; 2 theta 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 theta(1-e(-2 mu S/sin theta))(1 + cos(2) 2 theta) where mu 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.