A facile method for the density determination of ceramic thin films using X-ray reflectivity

A fast and non-destructive method based on X-ray reflectivity was developed to determine the density of sol–gel derived ceramic thin films, without prior assumptions on the microstructure of the system. The thin film density is calculated from the critical angle θc, i.e. the maximum angle at which total external reflection is still observed, which becomes increasingly difficult for imperfect films. We propose a simple numerical approach, instead of laborious fitting procedures, to determine the thin film density. A pseudo-critical angle, θpc, was defined by the first minimum in the 3rd derivative of the reflectivity curves. The measured samples were compared with calibration curves obtained from simulations with changing film densities. Although the absolute positions of θc and θpc are different, similar shifts are observed with changing density. The accuracy of the described method was validated by determining the density of single crystal substrates (ρrel = 100 %) and by Rutherford backscattering spectroscopy in combination with scanning electron microscopy. Varying sample size, film thickness, and film/interface roughness of yttria-stabilized zirconia films were found to have no influence on the final calculated density.