FIG. 5: Snapshots from a MD simulation at an undercooling 2 K illustrating the dynamic nature of the grain-boundary width. The snapshots corresponding to the Σ9 tilt grain boundary are on the right of the panel. The snapshots to the left are from the Σ9 twist boundary discussed elsewhere [20]. The atoms are colored by the difference between the two order parameters as described above. FIG. 4: The distribution function P ( w ) vs w from the MD simulations for the three different boundaries at 1708 K. The green diamonds and the red circles correspond to the Σ9 tilt and twist grain boundaries respectively. TheΣ11 tilt boundary is represented by the black triangles. The lines represent a least square fit of the premelting models of Eqs. 1 and 2 for the Σ9 twist grain boundary, Eqs. 1 and 3 for the Σ9 tilt boundary and a gaussian fit for the Σ11 tilt boundary. The snapshots next to each figure correspond to the widest grain boundary for each boundary and are color coded according to the φ$_{i}$ values. Lighter color (red in the on-line figure) indicates an atom with an environment corresponding to one of the two grains, darker color (blue in the on-line figure) represents atoms in some other environment. illustrated in the snapshot of this boundary in Fig. 4, thick and extended regions of disorder up to a nanometer or more in thickness are often observed in part of the boundary, with much narrower, more ordered regions in between. For the remainder of this section we will focus on the behavior of the two Σ9 boundaries, showing that the temperature dependence of the width histograms can be accurately described by the disjoining-potential formalism described above. 17