Cluster-plus-glue-atom model and universal composition formulas [cluster](glue atom)_x for BCC solid solution alloys

The structures of solid solution alloys are characterized by chemical short-range orders that determine largely the alloy performance. In the present work, the cluster-plus-glue-atom model, which suits for the description of chemical short-range orders in solid solutions, is introduced in the structural description of BCC solid solutions. In this model, solute atoms form 1st-neighbor clusters in the solvent matrix, so that a stable solid solution is represented by a specific local unit containing the characteristic cluster plus certain number of outer-shell 2nd neighbor glue atoms, or expressed in cluster formula [cluster](glue atom)_x. The cluster packing geometry is then analyzed and their structural stability is discussed in terms of cluster packing density. The cluster packing density reaches the maximum when x = 1, signifying that these alloys might possess special stabilities and henceforth good properties. Commonly-used BCC alloys in Zr-, Ti-, V-, Nb-, Ta-, Mo-, W-, and U-based systems are found to conform to the as-mentioned composition formulas, and in particular to that with x = 1, thus unveiling universal composition rules for BCC metals.