Analysis of errors of beta thickness gages when testing two-layer coatings on multi-layer products

Formulae for calculating errors arising when testing two-layer coatings on multilayer articles have been deduced and analysed. The formulae take into consideration the instability of two measurement results with different boundary energy of β-radiation sources under conditions when the thickness of the coating and article layers can be less than the saturation thickness. The dependences of absolute errors of two-layer coating β-thickness gages on the thickness, density and atomic number of the layer material and on the boundary energies of used beta sources have been studied. As an example, estimate of errors occurred when testing with the help of 86Kr and 90Sr β-sources the thickness of nickel and molybdenum two-layer coatings is given. The given analysis of beta thickness gages errors makes it possible to determine by calculations an optimum set of two β-sources with different boundary energies and estimate the limiting capabilities of the method with regard for the effect of the background radiation