Stability of Zr-Al alloys

The Zr-Al alloy system has one of the more complicated binary transition-metal aluminide phase diagrams: ten reported intermediate phases belonging to four different crystal systems. In order to understand the competition among different structures and concentrations, the heats of formation of a number of different possible structures were calculated using both all-electron and pseudopotential methods. The ${\mathrm{Zr}}_5{\mathrm{Al}}_3$ $\mathrm{}\left(\mathrm{tI}32\mathrm{}\right)\mathrm{}$ and ${\mathrm{Zr}}_5{\mathrm{Al}}_4$ $\mathrm{}\left(\mathrm{hP}18\mathrm{}\right)\mathrm{}$ phases are predicted to be high-temperature phases. The existence of the large number of observed phases is attributed to the fact that the heats of formation for ${\mathrm{Zr}}_x{\mathrm{Al}}_{1-x}$ for $x=0.25\mathrm{}–0.75$ fall on a nearly straight line, suggesting that these phases should have narrow composition ranges. In addition, a simple procedure to modify and test the pseudopotentials is presented and shown to yield calculated metallic alloy properties in good agreement with the all-electron results.