First-Principles Study of Phase Stability of \textit{bcc} XZn (X $=$ Cu, Ag, and Au) Alloys*

First-principles density functional theory is used here to study phase stability/instability and anomalies in formation of the \textit{bcc} phases of the aforementioned XZn (X $=$ Cu, Ag, and Au) alloys. The CuZn and AgZn alloys have a disordered \textit{bcc} structure at high temperature; however, this is not the case for the AuZn alloy. The AgZn alloy also has a lower \textit{bcc} order-disorder (critical) temperature compared to CuZn and AuZn alloys. It is shown that these anomalies in \textit{bcc} structure of XZn systems can be explained in terms of the bond strength between the X and Zn atoms. Charge density studies and pair potential modeling of XZn alloys show that the Ag-Zn bond is significantly weaker than the Cu-Zn and Au-Zn bonds. The lattice parameters, bulk modules, elastic constants, Debye temperatures, and heats of formation for the \textit{bcc} phases of the three XZn alloys are calculated and compared with available experimental values.