COMPARISON OF 2 CLUSTER-EXPANSION METHODS FOR THE ENERGETICS OF PD-V ALLOYS

The formation energies of substitutional transition-metal alloys are e xamined by several means. First, two types of direct total-energy calc ulations are considered, namely, (i) the local-density approximation ( LDA), and (ii) a tight-binding (TB) approximation thereof. Second, the se directly calculated total energies are used to construct two Ising- like cluster expansions that, if sufficiently accurate, could be used to construct the full statistical mechanics of transition-metal alloys . These are (a) the Connolly-Williams (CW) method, and (b) direct conf igurational averaging (DCA). Finally, the ability of these two cluster expansions [(a) and (b)] to fit and predict a large number of the und erlying directly calculated [(i) and (ii)] total energies is tested, b y the average prediction error chi. These tests are performed for a la rge number of Pd-V alloys, and also to a more limited extent, for the Pd-Rh, Pd-Ti, and Pt-V systems. We find for Pd-V that (i) direct TB ca lculations show significant overbinding (too-negative formation energi es) relative to the LDA, with average error of chi=112 meV/atom (a typ ical formation energy of Pd0.50V0.50 is similar to -250 meV/atom); (ii ) the CW cluster expansion mimics quite well the results of the respec tive direct calculations, whether LDA (chi=19 meV/atom) or TB (chi=19 meV/atom); (iii) the DCA cluster expansions provides a less accurate d epiction of the TB energies on which it is based (chi=65 meV/atom); (i v) the prediction errors for the equimolar random alloys are significa ntly larger using the DCA than using the CW method. In Light of (i) ab ove, it appears that the tight-binding model needs to be refined befor e it can be used systematically for (either DCA or CW) cluster expansi ons.