In our study, a complete review of the literature, critical evaluation and thermodynamic assessment of the Cu-Zn, Cu-Se and Zn-Se binary systems were carried out. The modified quasi-chemical model (MQM) was applied to describe the Gibbs energy of the liquid phase. The Gibbs energies of all intermetallic compounds and terminal solid solutions were described using the compound energy formalism (CEF) model. The re-optimization of the Cu-Zn binary system was carried out by considering the ordered bcc_B2 crystal structure of the β’ phase. Moreover, the β and δ phases in the Cu-Zn binary system with the same bcc_A2 crystal structure were modeled as one single phase in the present work. A self-consistent thermodynamic database was constructed for the Cu-Zn, Cu-Se and Zn-Se binary systems, work that formed part of a comprehensive thermodynamic database development project researching zinc-based biodegradable materials.

The departure of nitrogen bubbles from duplex stainless steel (DSS) is essential for studying the precipitation behavior of bubbles during solidification. In the current work, the numerical and theoretical derivation of analytical formula were used to study the bubble departure at the solid–liquid interface. In the paper, the departure radius of bubbles was deduced by numerical analysis. Based on the works of subcooled boiling flow, the forces of bubbles were analyzed at the solid–liquid interface. The critical condition of bubble departure was theoretically obtained. The effects of various factors on bubble departure and slip were also analyzed. The results showed that the critical radius of the bubble departure increased at the solid–liquid interface when reducing the interface inclination angle, the depth of liquid steel, the contact angle, the flow velocity of liquid steel, and the gas pressure on the surface of liquid steel. Moreover, when the interface inclination angle equaled zero, there was no slip in the interface direction before bubble departure, letting the bubbles float directly. However, when the interface inclination angle equaled π/4 or π/2, the bubbles slid along the interface before bubble departure in the x negative direction, which was more likely to cause the bubbles to be trapped.