  Amorphous tantala (a-Ta2O5) is an important technological material that has
wide ranging applications in electronics, optics and the biomedical industry.
It is used as the high refractive index layers in the multi-layer dielectric
mirror coatings in the latest generation of gravitational wave interferometers,
as well as other precision interferometers. One of the current limitations in
sensitivity of gravitational wave detectors is Brownian thermal noise that
arises from the tantala mirror coatings. Measurements have shown differences in
mechanical loss of the mirror coatings, which is directly related to Brownian
thermal noise, in response to thermal annealing. We utilise scanning electron
diffraction to perform Fluctuation Electron Microscopy (FEM) on Ion Beam
Sputtered (IBS) amorphous tantala coatings, definitively showing an increase in
the medium range order (MRO), as determined from the variance between the
diffraction patterns in the scan, due to thermal annealing at increasing
temperatures. Moreover, we employ Virtual Dark-Field Imaging (VDFi) to
spatially resolve the FEM signal, enabling investigation of the persistence of
the fragments responsible for the medium range order, as well as the extent of
the ordering over nm length scales, and show ordered patches larger than 5 nm
in the highest temperature annealed sample. These structural changes directly
correlate with the observed changes in mechanical loss.
