The valence of transition metal atoms in metallic alloys

Abstract

THE ‘valence’ of transition metal atoms in metallic alloys has long been and still is a source of controversy. On the one hand, there are measurements such as those of Haworth and Hume-Rothery¹ which indicate quite small valences, there are electron concentration rules in numerous Hume-Rothery β and γ phases which indicate ‘zero’ valences, and there are measurements (for example, Coppens²) which even indicate ‘negative’ valences, whereas on the other hand, melting points, hardness and heats of atomisation indicate much higher valences. In this paper we point out that the valence of a transition metal atom in a metallic alloy cannot usefully be described by a single number. Three parameters are required: the number of outer electrons contributed to partly filled energy bands, the number entering filled bands lying below the Fermi level, and a parameter (0<α<1) describing the effectiveness for cohesion of the hybridisation of the filled bands originally derived from d states with those originally derived from s and/or p states.