Scheil

The Scheil model, also known as the Scheil-Gobbs equation, is a computational tool used in materials science and metallurgy to describe the solidification process of alloys. It provides a simplified approximation of how multi-component alloys solidify from the liquid phase, emphasizing the effects of solute redistribution during cooling.

Developed by Emil Scheil in the early 20th century and later refined with contributions from T. F. Gobbs, the model assumes that no diffusion occurs within the solid phase during solidification. Instead, all solutes are redistributed exclusively within the remaining liquid, leading to concentration gradients. This assumption makes the Scheil model particularly suited for alloys where solid-state diffusion is slow compared to liquid-phase diffusion.

The model employs a mathematical relationship linking the composition of the solidified alloy to the fraction of liquid remaining, allowing engineers to predict microstructural development, segregation patterns, and compositional variations as a function of cooling. It is widely used in the design and analysis of casting, welding, and additive manufacturing processes.

While the Scheil model offers valuable insights, it has limitations. Its assumptions neglect solid-state diffusion and the effects of initial temperature gradients, which can result in deviations from real-world behavior. As such, it is often complemented with other models that account for diffusion and phase transformations.

Overall, the Scheil model remains a fundamental tool in metallurgical research and process optimization, helping to understand and control microstructural evolution during alloy solidification.