NIOBIUM HYDRIDE PHASE-BEHAVIOR STUDIED USING THE CLUSTER-VARIATION METHOD

We present several models for NbH phase behavior based on the cluster-variation method. The most important of these are the single-tetragonal-cell (STC) model and the twelve-cluster (TWC) model, which have as their basic clusters the single tetragonal cell and a twelve-sited cluster, respectively. The following conclusions can be drawn from our study of these models. From the STC ground-state analysis we find that, for interactions confined to the single tetragonal cell (a subset of the first 14 shells for the tetrahedral lattice), (1) it is possible to predict the and phases but not the phase, and (2) many-body interactions are needed to eliminate an extraneous pure phase (i.e., a phase that is not observed experimentally) at concentration [H]/[Nb]=0.25, assuming the, and phases are ground states. These observations suggest that longer-range interactions than those in the STC are important for NbH phase formation and many-body interactions may be necessary to eliminate unwanted phases at lower concentrations. We have also generated phase diagrams that are qualitatively similar (in the ordered regions) to experimental NbH phase diagrams. Our study of the TWC model shows that it is more accurate in comparison with a Monte Carlo model than the existing entropy approximations of Boureau, Richards, and MacGillivray, Soteros, and Hall. Furthermore, using the TWC model it is possible to predict an - phase envelope that compares well with the Futran and Hall Monte Carlo calculation. This is the first analytic free-energy calculation to predict the - transition. Using the TWC model we also show that, as Shirley and Hall have conjectured, many-body interactions work to lower the - critical temperature when compared with calculations including only pair interactions. Since pair-interaction calculations overestimate the critical temperature, this is further evidence of the importance of many-body interactions. © 1990 The American Physical Society.