GLYPH<s49>GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s53> GLYPH<s48> GLYPH<s45>GLYPH<s53> GLYPH<s89> GLYPH<s40>GLYPH<s119>GLYPH<s41>GLYPH<s32>GLYPH<s45>GLYPH<s32>GLYPH<s50> GLYPH<s103> GLYPH<s115>GLYPH<s108> GLYPH<s32>GLYPH<s32>GLYPH<s40>GLYPH<s109>GLYPH<s74>GLYPH<s47>GLYPH<s109> GLYPH<s50> GLYPH<s41> GLYPH<s50>GLYPH<s46>GLYPH<s48> GLYPH<s49>GLYPH<s46>GLYPH<s53> GLYPH<s49>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s53> GLYPH<s71>GLYPH<s114>GLYPH<s97>GLYPH<s105>GLYPH<s110>GLYPH<s32>GLYPH<s66>GLYPH<s111>GLYPH<s117>GLYPH<s110>GLYPH<s100>GLYPH<s97>GLYPH<s114>GLYPH<s121>GLYPH<s32>GLYPH<s87>GLYPH<s105>GLYPH<s100>GLYPH<s116>GLYPH<s104>GLYPH<s44>GLYPH<s32>GLYPH<s119>GLYPH<s32>GLYPH<s40>GLYPH<s110>GLYPH<s109>GLYPH<s41> GLYPH<s183>GLYPH<s57>GLYPH<s32>GLYPH<s220>GLYPH<s49>GLYPH<s49>GLYPH<s53>GLYPH<s221>GLYPH<s32>GLYPH<s116>GLYPH<s119>GLYPH<s105>GLYPH<s115>GLYPH<s116>GLYPH<s32>GLYPH<s98>GLYPH<s111>GLYPH<s117>GLYPH<s110>GLYPH<s100>GLYPH<s97>GLYPH<s114>GLYPH<s121> GLYPH<s183>GLYPH<s57>GLYPH<s32>GLYPH<s220>GLYPH<s49>GLYPH<s49>GLYPH<s48>GLYPH<s221>GLYPH<s32>GLYPH<s123>GLYPH<s52>GLYPH<s49>GLYPH<s49>GLYPH<s125>GLYPH<s32> GLYPH<s115>GLYPH<s121>GLYPH<s109>GLYPH<s109>GLYPH<s101>GLYPH<s116>GLYPH<s114>GLYPH<s105>GLYPH<s99>GLYPH<s32>GLYPH<s116>GLYPH<s105>GLYPH<s108>GLYPH<s116>GLYPH<s32>GLYPH<s98>GLYPH<s111>GLYPH<s117>GLYPH<s110>GLYPH<s100>GLYPH<s97>GLYPH<s114>GLYPH<s121> FIG. 7: An illustration of the histogram method used to extract the disjoining potential. It shows the merged data from individual histogram data used to reproduce the complete disjoining potential Ψ( w ) for the Σ9 twist and the Σ9 tilt boundaries. The solid line is the best fit to the exponential decay given in Eq. 2 for the Σ9 twist boundary, and a double exponential function in Eq. 3 for the Σ9 tilt grain boundary. form given in Eq. 2, as expected based on the logarithmic divergence of the excess volume calculated for this boundary (see Fig. 3). In this paper we have presented a detailed description of a method for computing the disjoining potential for grain-boundary premelting and grain coalescence from an analysis of width fluctuations measured in equilibrium MD simulations. The approach has been applied to two grain boundaries in an EAM model of elemental Ni. For the Σ9 twist boundary, which features an excess volume that increases logarithmically as T$_{M}$ is approached from below, the measured width histograms are consistent with a disjoining potential that decays exponentially, with a decay length of approximately 0 . 25 nm and a maximum value at zero width of approximately 160 mJ/m 2 relative to 2 γ$_{SL}$ . For the Σ9 tilt boundary, which features an excess volume that remains finite at T$_{M}$ , the measured width histograms are shown to be consistent with a disjoining potential that features a weak attractive minimum at w$_{m}$ ≈ 0 . 34 nm, with a depth relative to 2 γ$_{SL}$ of approximately -8 mJ/m $^{2}$. It is interesting to compare the results of the present work with previous studies of grain- SUMMARY AND DISCUSSION 20