INTRODUCTION 2 Due to the difficulties inherent in validating theoretical models for grain-boundary pre- melting directly from experimental measurements, the authors recently proposed an in- dependent methodology for calculating grain-boundary disjoining forces from equilibrium molecular-dynamics (MD) simulations [20]. The technique represents an extension of the Despite its practical importance in the context of solidification defects, the magnitude and spatial extent of grain-boundary disjoining forces in metals and alloys remain incompletely understood. As in the case of surface premelting [5], these forces can in principle be probed experimentally through measurements of the extent of equilibrium premelting as a function of temperature near the bulk melting point. In comparison to surface premelting, however, the challenges inherent in characterizing the structure of “buried” internal interfaces at high homologous temperatures have significantly limited the number of direct experimental studies of grain-boundary premelting [6–13]. This situation has provided motivation for several recent theoretical studies based on conventional phase-field [14–17] and phase-field- crystal (PFC) [18, 19] methods, which have led to new insights into the rich variety of possible premelting behavior that may be exhibited by grain boundaries as a function of their bi-crystallography. At high homologous temperatures the atomic structure of a grain boundary often dis- plays pronounced disorder. In some cases this structural disorder can involve the formation of nanometer-scale intergranular films with liquid-like properties below the bulk melting point, a phenomenon commonly referred to as grain-boundary premelting. The interfacial thermodynamic driving forces underlying grain-boundary premelting are understood to be an important factor influencing grain coalescence behavior during the late stages of solidifi- cation (e.g., [1]). Specifically, when premelting is thermodynamically favored there exists an associated repulsive “disjoining pressure” which hinders the coalescence of two misoriented grains at nanometer-scale distances. In such cases a significant undercooling may be required for dendrite arms to merge to form solid “bridges” that are capable of sustaining thermal- contraction stresses without grain sliding or rupture. The quantitative characterization of grain-boundary disjoining forces is thus an important issue in the context of modeling the formation of solidification defects, known as “hot tears,” which occur deep within the mushy zone during casting or welding [1–4].