Morphological Instability at the Solidification Interface of Alloys: A Generalized Curvature-Driven Paradigm Beyond Constitutional Supercooling

Since 1953, "constitutional supercooling" has been the standard paradigm for alloy interface instability. However, this model relies on heuristic assumptions and fails to account for dynamic, local interactions. This paper presents a rigorous reinterpretation using the qualitative theory of nonlinear interface equations. We demonstrate that instability originates from the generalized effect of curvature on the driving force, which extends beyond conventional interfacial energy. By applying the maximum principle, we provide a definitive mathematical resolution to the long-standing mystery of morphological evolution, establishing a new paradigm that transcends the traditional framework.