Solid solubilities in divalent alloys

Solubility trends for a variety of solutes in seven prototypical simple divalent metal hosts are examined. In this paper, we present a macroscopic model for predicting solubility trends. This model should prove more successful than the classical approaches of Hume-Rothery or Darken and Gurry. The method is an extension of a cellular scheme developed by Miedema, and involves two chemical coordinates. These coordinates, which characterize charge transfer between neighboring cells and the charge-density mismatch at cellular boundaries, appear to be superior coordinates for determining solubilities trends, as contrasted with classical coordinates such as atomic size or electronegativity. Moreover, we note the Miedema's coordinates are shown to accurately describe recent experiments that involve site energy preferences of metastable implants in Be. This dramatic result suggests that Miedema's coordinates may describe metastable systems and as a consequence are more widely applicable than might be expected. Finally, we note that our results have consequences for a pseudopotential description of intermetallic alloys and compounds.