Theory of solid solubility for rare earth metal based alloys

Both parabola and ellipse separating schemes are used to study the solid solubilities for the binary alloy systems based on the 13 rare earth metals. It has been found that the soluble elements can be separated from the insoluble ones by a parabolyy ₁=a?bx ₁ ² or an ellipse(x ₂?m)²/c²+(y₂?n)²/d²=1. The results show that the overall reliabilities of the solid solubilities for the 897 binary alloys based on the rare earth metals are 89.2% and 92.8% for the parabola and ellipse regularities respectively. The constants a and b in the parabola equation, andm, n, c andd in the ellipse equation are discussed, which can be related to some appropriate parameters for each host metal respectively.