Bond-parametric function and size factor model for formation in binary rare earth metal-based amorphous alloys

Herein, the formation of binary rare earth metal-based amorphous alloys is systematically studied by the bond-parametric function and size factor model. The theoretical results have been obtained for the 1230 binary alloys based on the 15 rare earth metals (La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu). The results revealed that the formed amorphous constituent elements region and the unformed amorphous constituent elements region can be separated precisely from each other by an ellipse curve, and the elliptic equation of $$ \frac{{\left( {x - m} \right)^{2} }}{{c^{2} }} + \frac{{\left( {y - n} \right)^{2} }}{{d^{2} }} = 1 $$ . The constants m, n, c, and d in the elliptic equation are positively correlated to the parameters R, y, (µR3)−1/2, and E for each host metal, respectively. The overall reliability of the calculation upon comparison with the experimental data for 92 binary rare earth metal-based amorphous alloys was found to be 92.4%. This indicates that the theoretical results are in very good agreement with the experimental data.