In Eq. 1, G ( w ) represents the total excess free energy of a premelted grain boundary of width w , which is composed of two contributions: Δ G$_{f}$ represents the bulk free energy difference between liquid and solid phases (positive below the melting point), per unit volume, while Ψ( w ) represents the width-dependent interfacial free energy, which we refer to as the dis- joining potential. The function Ψ( w ) takes the limits of γ$_{GB}$ (the interfacial free energy of a hypothetical “dry” grain boundary) and 2 γ$_{SL}$ (twice the solid-liquid interfacial free energy) for small and infinite values of w , respectively. For intermediate values of the width Ψ( w ) can display a complex dependence on w . The dependence of Ψ( w ) on w is generally governed by distinct short and long-ranged contributions. An attractive interaction between solid-liquid interfaces [35, 36] arises due to dispersion forces which are dominant at large w , and are predicted to give rise to finite interfacial widths at T$_{M}$ [35]. For systems where the wetting condition, γ$_{GB}$ > 2 γ$_{SL}$ holds, a repulsive contribution to Ψ( w ) arises from short-ranged structural interactions (Ψ$_{sr}$) associ- ated with the overlap of the density waves in the diffuse regions of the solid-liquid interfaces. Mean-field arguments [37], as well as lattice-gas models (e.g., [28]), yield an exponentially decaying form for this short-ranged contribution: where Δ γ = γ$_{GB}$ − 2 γ$_{SL}$ and δ is an interaction length on the order of the atomic spacing. In the absence of long-ranged dispersion forces, insertion of Eq. 2 into Eq. 1 leads to the pre- diction of an equilibrium grain boundary width that diverges logarithmically as the melting temperature ( T$_{M}$ ) is approached from below. In previous work [20] we have argued, based on previous estimates of the dispersion forces for surface premelting, that the structural con- tributions to the disjoining potential for grain-boundary premelting in metals are expected to dominate the long-ranged dispersion contributions for nanometer-scale grain-boundary widths. Recent theoretical results demonstrate that Ψ$_{sr}$( w ) can generally display more complex dependencies on w than suggested by Eq. 2. Diffuse-interface phase field models [14–16], which neglect dispersion forces and thus model Ψ$_{sr}$ directly, have shown that depending on grain-boundary misorientation and the detailed choice of interfacial thermodynamic param- eters, the premelting transition can exhibit either the continuous behavior associated with 4 Ψ$_{sr}$( w ) = 2 γ$_{SL}$ + Δ γ exp[ − w/δ ] (2)