Argon bubble formation in tantalum oxide-based films for gravitational wave interferometer mirrors

The argon content of titanium dioxide doped tantalum pentoxide thin films was quantified in a spatially resolved way using HAADF images and DualEELS. Films annealed at 300$^{\circ}$C, 400$^{\circ}$C and 600$^{\circ}$C were investigated to see if there was a relationship between annealing temperature and bubble formation. It was shown using HAADF imaging that argon is present in most of these films and that bubbles of argon start to form after annealing at 400$^{\circ}$C and coarsen after annealing at 600$^{\circ}$C. A semi-empirical standard was created for the quantification using argon data from the EELS atlas and experimental data scaled using a Hartree Slater cross section. The density and pressure of argon within the bubbles was calculated for 35 bubbles in the 600$^{\circ}$C sample. The bubbles had a mean diameter, density and pressure of 22\r{A}, 870kg/m$^3$ and 400MPa, respectively. The pressure was calculated using the Van der Waals equation. The bubbles may affect the properties of the films, which are used as optical coatings for mirrors in gravitational wave detectors. This spatially resolved quantification technique can be readily applied to other small noble gas bubbles in a range of materials.