Non-equilibrium segregation during alloy solidification

The solute redistribution law that predicts non-equilibrium phase constitution in compositionally cored binary alloys is usually attributed as Scheil's equation. Earlier studies on this subject by G. H. Gulliver are occasionally cited but are thought by some to be either approximate or incomplete. It is shown that Gulliver fully recognized and developed the limit laws for non-equilibrium segregation in solidifying binary alloys no later than 1913 - almost 30 years prior to the publication of Scheil's paper. For reasons that remain obscure, however, he chose not to provide, or perhaps to burden, the reader of his paper with the mathematical details connecting his unusual, geometrically based derivation to the now well known segregation power law for solidification. By contrast, Scheil's familiar integral form for this power law was derived from a differential mass balance, which provides the standard mathematical setting used for this important equation. It is concluded that attribution of this significant accomplishment in solidification theory should properly be shared by both researchers and called the Gulliver-Scheil equation.