The solid lines in Fig. 6 represent the least square fits of the MD data for P ( w ) to the disjoining-potential formulas given by Eqs. 7, 1 and 2 for the Σ9 twist boundary, and Eqs. 7, 1 and 3 for the Σ9 tilt boundary. For the Σ9 twist boundary the potential parameters obtained from the separate fits to the data for the individual temperatures span the range δ =0.25 to 0.29 nm, and Δ γ =101 to 150 mJ/m $^{2}$. For the Σ9 tilt boundary the fitted values for δ$_{1}$ and δ$_{2}$ ranged between 0.142 to 0.144 and 0.143 to 0.144 nm, respectively, Δ$_{1}$ − Δ$_{2}$ spanned the values 103 to 163 mJ/m $^{2}$, and Δ$_{2}$ / Δ$_{1}$ took values between 1.003 and 1.006. With these fitted potential parameters, the disjoining potential for the Σ9 tilt boundary exhibits a weak minimum at a width w$_{m}$ with values ranging between 0.32 and 0.36 nm, and a depth relative to 2 γ$_{SL}$ varying between -7 and -11 mJ/m $^{2}$. The fact that the MD calculated width histograms can be accurately described by disjoining potentials with a relatively narrow range of fitted potential parameter values indicates that the formalism described in the previous section represents a valid model for describing the temperature dependence of the structural disorder observed in these boundaries. In order to refine the calculation of the disjoining potential for the Σ9 twist and tilt boundaries, we employ the histogram analysis described in the previous section, involving a refinement of both the shift parameters a$_{i}$ and the potential parameters in Eqs. 2 and 3 for the twist and tilt boundaries, respectively. The resulting fits are shown in Fig. 7 and correspond to the following values for the potential parameters: δ = 0 . 25 nm and Δ γ = 156 mJ/m 2 for the Σ9 twist boundary, and Δ$_{1}$ − Δ$_{2}$ = 103 mJ/m $^{2}$, Δ$_{2}$ / Δ$_{1}$ = 1 . 003, δ$_{1}$ = 0 . 1471 nm, δ$_{2}$ = 0 . 1474 nm for the Σ9 tilt boundary. These parameter values are consistent with the values given above from the independent fits. The excellent agreement of the fits with the MD data in Fig. 7 again indicates that the disjoining-potential formalism represents an accurate framework for modeling the premelting behavior of these Σ9 boundaries. The analysis used to obtain the results in fits in Fig. 6 assumed a melting point of T$_{M}$ = 1710 K. If the melting temperature is changed even by one degree,i.e., T$_{M}$ = 1709 K then poor fits to P ( w ) are obtained for the data at the lowest undercoolings. The calculated disjoining potentials in Fig. 7 are characterized by the following features. For the Σ9 tilt boundary the disjoining potential has a minimum at a finite width, w$_{m}$ ,which corresponds to the average equilibrium grain boundary width at the melting temperature. The potential is repulsive for w < w$_{m}$ and attractive for w > w$_{m}$ . In contrast, the Σ9 twist boundary features a purely repulsive disjoining potential that is well modeled by exponential 19