Alloy solidification: Assessment and improvement of an easy-to-apply model

It has been a central task of solidification research to predict solute microsegregation. Apart from the Lever rule and the Scheil-Gulliver equation, which concern two extreme cases, a long list of microsegregation models has been proposed. However, the use of these models often requires essential experimental input information, e.g., the secondary dendrite arm spacing (λ), cooling rate (T˙) or actual solidification range (ΔT). This requirement disables these models for alloy solidification with no measured values for λ, T˙ and ΔT. Furthermore, not all of these required experimental data are easily obtainable. It is therefore highly desirable to have an easy-to-apply predictive model that is independent of experimental input, akin to the Lever rule or Scheil-Gulliver model. Gong, Chen, and co-workers have recently proposed such a model, referred to as the Gong-Chen model, by averaging the solid fractions (fs) of the Lever rule and Scheil-Gulliver model as the actual solid fraction. We provide a systematic assessment of this model versus established solidification microsegregation models and address a latent deficiency of the model, i.e., it allows the Lever rule solid fraction fs to be greater than one (fs > 1). It is shown that the Gong-Chen model can serve as a generic model for alloy solidification until fs reaches about 0.9, beyond which (fs > 0.9) its applicability is dictated by both the equilibrium solute partition coefficient (k) and the solute diffusion coefficient in the solid (Ds), which has been tabulated in detail.