Immiscibility in Liquid Metal Systems

A review is given of the various expressions that have been derived to predict the miscibility behaviour of alloy systems, with particular reference to the suggested modifications to the Hildebrand rule for non-polar liquids. The original Hildebrand formula was based on a solubility parameter, delta, and the atomic volume, V, and immiscibility was predicted between two liquids if 1/2 (V(A) + V(B)) (delta(A) - delta(B))(2) > 2RT Mott introduced a correction term in this expression to allow for the difference in electronegativity (chi(A) - chi(B)) between the two component elements and defined a Mott number, 1/2 (V(A) + V(B)) (delta(A) - delta(B))(2) - 2RT/23060 (chi(A) - chi(B))(2), where T is the melting point, in degrees absolute, of the more refractory metal. It was postulated that if the calculated Mott number for a given binary alloy system was greater than the number of bonds that could be formed, the two metals would be immiscible in the liquid state. In an earlier paper, the Mott number was compared with the lower Pauling valency of the two elements and when this is applied to 1401 known alloy systems, the overall agreement is 85% compared with 59.9% conforming to the simple Hildebrand rule. In this paper, an alternative suggestion is made that the Mott number can be compared with the mean group valency of the two alloying elements. On this basis, of the 1401 systems analysed, 1181 conform, compared with 1191 on the earlier criterion.