A Comprehensive Model for Spinodal Decomposition in Ag–Cu Alloys Based on Phase-Field Theory and In Situ TEM

Ag-Cu alloy, composed of thermodynamically immiscible elements, belongs to far-from-equilibrium alloy systems that will undergo spinodal decomposition over an extensive range of compositions. Although numerous researchers have qualitatively explained the spinodal decomposition phenomenon, such as uphill diffusion in solid solution alloys, there remains a lack of discussion on mobility and interface thickness. Particularly, the quantitative spatiotemporal resolution of nanostructures is crucial for applications in Ag-Cu alloy packaging. Therefore, we proposed a comprehensive model to predict the evolution of spinodal decomposition in Ag-Cu alloy, which was based on the Cahn-Hilliard equation and combined in situ transmission electron microscopy observations. In the initial stage, the microstructure of Ag-Cu alloy is primarily determined by the competitive relationship between the initial compositions and the immiscibility gap asymmetry. As the spinodal progresses, the elastic strain energy gradually dominates the total free energy, determining the final microstructure. Furthermore, step aging can form fine hierarchical morphologies of spinodal decomposition. This work bridged the gap between phase-field simulations and experimental results of the Ag-Cu spinodal decomposition, which is underexplored in the existing literature. It realizes the spatiotemporal quantification of spinodal decomposition nanostructures and provides theoretical guidance for related research in the future.