METHODOLOGY modeled by Eqs. 2 and 3, respectively. To compute quantitative values for the disjoining potentials from these simulations, we make use of the following relation between G ( w ) and the equilibrium distribution P ( w ) of grain-boundary widths sampled by the MD systems at a temperature T : P ( w ) ∝ exp [ − AG ( w ) /k$_{B}$T ], where A is the interfacial area. Calculations of P ( w ) by MD, combined with an accurate knowledge of the bulk melting properties un- derlying Δ G$_{f}$ allows one to extract Ψ( w ), as described below. Since the MD simulations are based on a short-ranged classical interatomic-potential model, they do not include the long-ranged dispersion-force contributions to Ψ( w ), and thus sample Ψ$_{sr}$( w ) directly. In this study the simulations were based on an embedded-atom method (EAM) inter- atomic potential model for Ni developed by Foiles, Baskes and Daw (FBD) [39]. This po- tential was chosen as we have in previous work characterized both the bulk melting properties and solid-liquid interfacial free energies for FBD Ni; both sets of properties are prerequisites for a quantitative study of grain-boundary premelting. As reviewed in Ref. [20] the melting temperature for the FBD Ni potential has been bracketed to lie in the range T$_{M}$=1709-1710 K, and the value of the solid-liquid interfacial free energy has been calculated to be γ$_{SL}$ =285 mJ/m 2 [40]. The latent heat for the potential was also calculated to be 0.015 eV/ ˚ A $^{3}$. In the present study we considered the following three different grain boundary struc- tures: a Σ9 symmetric 〈 011 〉{ 411 } 38.9 o tilt boundary (hereafter referred to as the Σ9 tilt boundary), a Σ11 symmetric 〈 011 〉{ 311 } 50.5 o tilt boundary (hereafter referred to as the Σ11 tilt boundary), and a Σ9 〈 115 〉 120 o twist boundary (hereafter referred to for convenience as the Σ9 twist boundary, even though we recognize that this boundary can also be described as a symmetric tilt boundary). These were selected from a large library of grain boundary structures that fit into moderately-sized periodic simulation cells, developed in the work of Olmsted et al.[41]. As shown in Table I, the selected boundaries have zero-temperature en- ergies ( γ 0 $_{GB}$) that span a range of values relative to 2 γ$_{SL}$ , and were thus expected to feature a range of premelting behavior. 6