Meaning
Analytical solidification models calculate solute redistribution during alloy freezing under assumptions of zero solid diffusion and complete liquid mixing. Calculations applying the scheil gulliver equation predict the liquid fraction and solute concentration as a function of temperature throughout the freezing range. The mathematical formulation uses equilibrium partition coefficients to model non-equilibrium casting conditions without requiring dynamic mass transport computations.
Metallurgists use this equation to estimate microsegregation severity and microstructural phase fractions in cast aluminum structural pack housings.
Model Assumption
Derivation of the differential relation assumes local thermodynamic equilibrium at the moving solid-liquid interface while neglecting back-diffusion in the solid state. In calculations using the scheil gulliver equation, solute rejected by the advancing solid interface instantly homogenizes within the liquid phase. These idealized assumptions establish a theoretical maximum for microsegregation during rapid cooling.
Phase Prediction
Solute enrichment in the liquid phase steadily increases as the solid fraction grows toward completion. Output from the scheil gulliver equation reveals the temperature at which secondary intermetallic phases or terminal eutectic structures begin to freeze. This information guides alloy composition adjustments to avoid low-melting-point liquid films that cause hot tearing.
Industry Limit
Solid-state diffusion occurring in real casting processes causes actual solidification paths to deviate from theoretical predictions. Finite element thermodynamic software incorporates modified versions to account for partial solid diffusion.
