Energetics of transition-metal alloy formation: Ti, Zr, and Hf alloyed with the heavier 4dand 5delements

Total-energy calculations yielding heats of formation for ordered compounds of Ti, Zr, and Hf alloyed with Tc, Re, Ru, Os, Rh, Ir, Pd, and Pt are presented. There exist both experimentally based phase diagrams and a substantial number of experimental heats of formation for these systems, and the present results are in accord with these; e.g., the co-occurrence of compounds at differing compositions is correctly predicted. The heats, as a function of the fractional alloy composition x, generally differ markedly from the x(1-x) dependence so often envoked. An explanation of the heat behavior for the Ti-, Zr-, and Hf-depleted alloys is found in their densities of states and is associated with the d bands of the other alloy constituent being decoupled from the Fermi level.