Thick-target correction in PIXE for randomly inhomogeneous samples

Inhomogeneous structure in a thick sample presents a multitude of difficult problems in e.g. particle-induced X-ray emission (PIXE) analysis. The yield for the elements analysed will deviate from the homogeneous case because of unpredictable cross-sections, attenuation coefficients and stopping powers throughout the range of the impinging particle. In this paper, an attempt is made to correct for these inhomogeneity effects for a particular type of inhomogeneities, namely for randomly distributed ones. A model based on a randomly distributed structure of inhomogeneities is employed to calculate the deviation from the normal homogenous thick-target correction. In the model an average is calculated over a finite set of positions of the inclusion. A critical parameter is the size of the beam spot, which must be sufficiently large to allow the inclusions in the measured volume to be considered randomly distributed. The size and density of the inclusions are varied according to known properties of the specimens. The model can be further refined according to the need of the actual application, and the principle of the approach is equally valid for other ion beam analysis (IBA) techniques as well as for e.g. XRF