Assessment of Hardness Based on Phase Diagrams

This chapter summarizes the methodology and development of a general equation, in order to obtain a series of equations to assess the hardness of different Al-Cu-Zn alloys, based on their chemical composition. This methodology produces an assessment of hardness with a maximal deviation of 5%, in as-cast, homogenized and quenching alloys, for both alloys created in laboratories like commercials. This method entails the generation of linear equations by a linear regression method, obtained from a zone of the phase diagram, when the composition is changed from linear to planar form. Therefore, if the chemical composition of samples varies, the percentage of each phase will also vary, causing a change in mechanical properties in a linear manner. If the heat treatments are the same for all samples, then the changes in mechanical properties are proportional for each of them, maintaining the linear relationship in mechanical properties in accordance with chemical composition. This methodology is applicable for any ternary alloy along with its equilibrium diagram

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M>70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0<e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level