The visibility distance of interferometric gravitational wave detectors is limited by mirror thermal
noise at mid-range frequency, where the first coalescence GW signals have been detected and
where many others are expected in the next future. In particular, for enhanced second generation
and third generation we need to increase the performance of the test mass multilayer reflective
coatings. The Virgo collaboration is setting up a coating R&D group on many issues, including
especially metrology (loss angle measurements, thermoelastic effect modeling), new materials
(new oxides, nitrates, fluoride, new cosputtered mixing and nanolayered composites) completely
characterized (optically, mechanically and morphologically), optimization of deposition parameters,
with the aim of developing new coating materials and technologies for the AdVirgo upgrades
and for future detectors. Another objective is to understand the losses in amorphous materials,
framing coating research in the more general context of the physics of glasses and amorphous
materials. One of the developed research lines is the study of thermoelastic damping in crystalline
materials, that are promising candidates for cryogenic test masses and particularly suitable
substrates for coating research. A detailed discussion on models, based on a semi-analytical calculation
starting from the heat diffusion equation, for crystalline substrates will be reported. A
new study on the changes in thermoelastic loss after coating deposition, with some preliminary
results, will be also reported.