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Due to its excellent optical properties, such as low absorption and scattering, amorphous ${\text{Ta}}_2{\mathrm{O}}_5$is commonly used as an optical coating material, often in combination with ${\mathrm{SiO}}_2$layers to produce a highly reflective stack. However, the high mechanical loss of ${\text{Ta}}_2{\mathrm{O}}_5$limits the thermal-noise performance of such coatings when used in precision measurement applications. Doping with ${\mathrm{TiO}}_2$has previously been shown to slightly reduce the mechanical loss, but it is still very high compared to many other materials, particularly at low temperatures. In this paper, we present a detailed study of different heat treatment temperatures and of Ti concentrations of up to nominally 75%. We show a significant mechanical-loss reduction for the mixture with the highest Ti cation content, which crystallized after heat treatment at 500°C. The resulting loss is much lower than that of pure ${\mathrm{TiO}}_2$or that of ${\text{Ta}}_2{\mathrm{O}}_5$after crystallization, making further studies highly interesting, in particular investigations of scattering which may pose a major drawback for optical applications. 

Abstract The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape consisting of three nested detectors with 10 km arms, where each detector has a 'xylophone' configuration made of an interferometer tuned toward high frequencies, and an interferometer tuned toward low frequencies and working at cryogenic temperature. Here, we examine the scientific perspectives under possible variations of this reference design. We perform a detailed evaluation of the science case for a single triangular geometry observatory, and we compare it with the results obtained for a network of two L-shaped detectors (either parallel or misaligned) located in Europe, considering different choices of arm-length for both the triangle and the 2L geometries. We also study how the science output changes in the absence of the low-frequency instrument, both for the triangle and the 2L configurations. We examine a broad class of simple 'metrics' that quantify the science output, related to compact binary coalescences, multi-messenger astronomy and stochastic backgrounds, and we then examine the impact of different detector designs on a more specific set of scientific objectives.